Differential - a mechanism for distributing the torque of the input shaft between the two output axle shafts of the drive wheels or, on off-road vehicles, for distributing torque between the front and rear drive axles.
This is a part of the transmission, which on classic and front-wheel drive cars is usually made as a single unit with the final drive, and on SUVs it is built into the transfer case. A free differential always divides the torque supplied to it equally - regardless of whether the drive wheels (or drive axles) rotate at equal or different speeds.
Purpose of the differential
When the car moves along curved sections of the road - for example, in turns - the wheels of the drive axle roll along circles of different lengths. The outer (with respect to the vehicle's turning center) wheel travels a longer distance than the inner wheel. This difference is greater the steeper the turn. A similar problem arises in driving in a straight line, if driving wheels of different dimensions are used, etc. If in these situations the wheels are connected with a rigid axle, it turns out that one wheel rotates faster than necessary to pass a given trajectory, and the other slower. This means that both wheels will slip, experience increased loads, heat up and wear out more strongly. Fuel consumption will also increase. Finally, it breaks the vehicle's directional stability and leads to its skidding or drifting - especially on slippery roads.
To compensate for the difference in the path traveled by the driving wheels, a special mechanism is used - a differential. The simplest, free differential equalizes the torques (or traction forces) of both drive wheels, and if the speeds of their rotation (or linear movement) are different, then the power on them is proportional to this difference. A wheel that spins faster uses slightly more power than one that spins slower.
Thus, the differential is designed to ensure the rotation of the drive wheels with different angular speeds while constantly transmitting torque to both wheels of the drive axle. The same logic is present in the operation of the center differential.
Device and principle of operation
The differential of the classic design is simple. For example, on a rear-wheel drive vehicle, rotation from the driven shaft of the gearbox is transmitted through the propeller shaft to the drive bevel gear of the final drive, which is in constant engagement with the driven gear of the final drive. The driven gear is at the same time a differential case, in which the axis of satellites - small bevel gears - is fixed perpendicular to the axis of the driven gear. The latter rotate together with the differential housing relative to the axis of the final drive driven gear. The satellites are in constant engagement with the bevel gears of the left and right axle shafts of the drive wheels.
With a rectilinear movement of the car, the satellites do not rotate about their own axis. But each, like an equal-arm lever, divides the torque of the driven gear of the main gear equally between the gears of the axle shafts.
When the car moves along a curved path, the inner wheel with respect to the center of the circle described by the car rotates more slowly, the outer wheel rotates faster - while the satellites rotate around their axis, running around the gears of the axle shafts. But the principle of dividing the moment equally between the wheels is preserved. The power supplied to the wheels is redistributed, because it is equal to the product of the torque and the angular velocity of the wheel. If the turning radius is so small that the inner wheel stops, then the outer wheel rotates at twice the speed of a car moving in a straight line. So, the differential does not change the torque, but redistributes power between the wheels. The latter is always greater on the wheel that spins faster.
Application of differentials
In cars with one leading axle, one differential is installed, combined with the final drive. In vehicles with two or more drive axles, differentials are installed in each drive axle (for example, in a three-axle truck or bus with two rear drive axles, differentials are installed in the middle and rear axles). In cars with a connected all-wheel drive, differentials are installed in each drive axle (a two-axle all-wheel drive jeep with a connected front drive axle has two differentials - one in each drive axle), but the operation of these machines with a permanently connected front axle is not recommended due to increased wear of the main gears and wheels due to unevenly distributed power between the axles. In turn, in cross-country vehicles with permanently connected drive axles, three differentials are used - one in each drive axle and one center differential installed in transfer box. The center differential distributes power between the drive axles depending on the length of the path traveled by the wheels of the axle. For example, the front wheels can climb a hill, the rear wheels can still move in a straight line - the front wheels describe a longer path than the rear ones, respectively, the center differential ensures that more engine power is transferred to the front axle than to the rear. On multi-axle vehicles with several driving axles, an inter-bogie differential is used.
The differential does not apply to vehicles with one drive wheel - in particular, motorcycles and tricycles with two front steerable wheels. If the tricycle is built according to the scheme with one front steered wheel and two rear driving wheels, then an automobile drive axle with a differential is used on it. Typically, such tricycles are built on individual orders based on popular heavy models (for example, custom tricycles based on Harley-Davidson).
On race cars based on production models (for example, rally or circuit racing), the differential is blocked before races, since such cars take corners at high speed and with a skid. In this case, the tendency of the car to skid due to the lack of a differential is considered an advantage.
Lack of Differential
The main disadvantage of the classic differential design is the problem of wheel slip, which has lost contact with the road surface. When one of the drive wheels rotates in the suspended state, its speed is twice as high as it would be at the same speed of the driven gear of the differential during normal movement in a straight line. But the second wheel does not rotate at all. The reason is simple. The moment of resistance to the rotation of the suspended wheel is negligible, and the torque supplied to it is correspondingly small. This means that the torque on the opposite wheel is just as small - it stands. If one of the wheels is slipping - with increased speed, but with significant resistance (for example, in mud, sand, etc.), then the same torque is applied to the other, not slipping, wheel. As a result, the car can move at low speed. In this case, a higher power is supplied to the slipping wheel - it is spent on heating the tire, road, etc. The slip effect reduces the patency of a car with a free differential. To solve this problem, cars are equipped with differential lock mechanisms - manual or automatic - of various designs.
Differential locks
- Manual differential lock
The easiest way to lock the differential is to use a manual mechanism. This type of blocking is used on off-road vehicles. Blocking is carried out by blocking clutches that fix the satellites. The differential is disabled. The advantages of this type of lock include the simplicity and reliability of the design, the disadvantages are the need to accurately assess the traffic situation and turn off the differential lock when driving on high-quality roads in order to avoid breakdowns of the main gear and the drive axle as a whole. - Electronic differential lock
On modern all-wheel drive off-road passenger cars with advanced computer control of the operation of units and mechanisms, an anti-slip system with electronic control is installed. As soon as on-board computer of the vehicle (or the electronic unit of the traction control system) receives a signal from the rotation sensor that one wheel of the axle rotates much faster than the second, free wheel braked by a service brake - thanks to the free differential, power is transferred to the wheel, which has not lost contact with the road surface. This system requires a separate brake drive system for all four wheels and precise debugging of the sensors. Anti-slip systems allow you to finely adjust the distribution of power depending on the condition of the road surface and avoid loss of engine power when the differential is activated. On the other hand, the control system of sensors and brake actuators (on solenoids) has inertia, so it works with some delay, which the driver has to take into account.
Racing cars sometimes use friction differentials with electronically controlled brake bands.
- Automatic locking with friction clutch
Sports cars produced in small series or by order are sometimes equipped with friction self-locking differentials. On production machines, these differentials are rare, as they require special maintenance and are subject to intense wear. Friction clutches are installed between the side gears and the differential housing. With a rectilinear movement of the car, the axle shafts rotate with the same angular velocity - the friction force in the friction clutches is zero, the differential distributes power between the wheels of the drive axle equally. As soon as one of the semi-axes begins to rotate faster, the friction clutch discs approach each other, due to the friction forces that arise, the clutch slows down the rotation of the free semi-axis. This type of differential is characterized by low efficiency with a large difference in the angular speeds of the driving wheels (for example, on turns with a small radius of curvature).
When the car is moving, the torque is transmitted from and then, through the main gear and differential, to the drive wheels. allows you to increase or decrease the torque transmitted and at the same time reduce and accordingly increase the speed of rotation of the wheels. The gear ratio in the main gear is selected in such a way that the maximum torque and speed of the drive wheels are in the most optimal values for specific vehicle. In addition, the final drive is very often the subject of car tuning.
Final drive device
In fact, the main gear is nothing more than a gear reduction gear, in which the drive gear is connected to the output shaft of the gearbox, and the driven gear is connected to the wheels of the car. Type gear connection main gears are divided into the following varieties:
- cylindrical - in most cases it is used on vehicles with a transverse arrangement and gearboxes and front-wheel drive;
- conical - is used very rarely, as it has large dimensions and high level noise;
- hypoid - the most popular type of final drive, which is used on most cars with classic rear-wheel drive. The hypoid gear is small in size and low in noise;
- worm - practically not used on cars due to the complexity of manufacturing and high cost.
It is also worth noting that front-wheel drive and rear-wheel drive cars have a different final drive arrangement. In front-wheel drive vehicles with a transverse gearbox and power unit, the cylindrical main gear is located directly in the gearbox housing.
In vehicles with classic rear-wheel drive, final drive installed in the drive axle housing and connected to the gearbox through. In functionality hypoid gear rear-wheel drive car also includes a 90-degree rotation due to bevel gears. Despite the different types and arrangements, the purpose of the final drive remains the same.
Vehicle differential
Vehicle differential most often combined with the main gear and is located respectively in the gearbox housing or in the rear axle housing. However, the differential can also be installed between the leading axles of an all-wheel drive vehicle. The differential is and is divided into the following varieties:
- conical - in most cases, it is installed together with the main gear between the wheels of one drive axle;
- cylindrical - most often used for decoupling the leading axles of all-wheel drive vehicles;
- worm - is universal and is installed both between the wheels and between the drive axles.
The main purpose of the differential is to distribute torque between the wheels of the car and change their rotational speed relative to each other. For example turning a car without a differential would be simply impossible, since when turning, the outer wheel must necessarily rotate at a higher frequency than the inner one.
Differentials exist symmetrical and asymmetrical. The symmetrical differential transmits equal torque to both wheels and is most often installed in conjunction with the final drive. An asymmetric differential allows you to transmit torque in various proportions and is set between.
The differential consists of a housing, satellite gears and side gears. The housing is usually combined with the driven gear of the final drive. Satellite gears play the role of a planetary gearbox and connect the side gears to the differential housing. Semi-axial (sun) gears are connected to the drive wheels by means of semi-axes on splined joints.
With all the pluses of the simplest differential there is also a disadvantage. The fact is that the rotational speed can be distributed to the wheels not only in a ratio, for example, 50/50, 40/60 or 35/65, but also 0/100. That is, absolutely all the torque can be transferred to one wheel of the car, while the second wheel will be absolutely static. This happens if the car is stuck in mud or ice.
However, modern differentials are more perfect and practically devoid of this drawback. Many differentials have hard automatic or manual locking. In addition, modern passenger all-wheel drive vehicles are equipped with a system exchange rate stability, which is based on the optimal distribution of torque between the axles and individual wheels, depending on the trajectory.
Differential mathematical
An informal description of the mathematical differential
Definitions
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Properties
differential automotive
Wheel slip problem
Ways to solve the problem of a slipping wheel.
Manual differential lock
Electronic differential control
self-locking differential
Friction self-locking differential
Viscous coupling
Cam/gear self-locking differential
Hydrorotor self-locking differential
Hypoid self-locking differentials
Dual Pump System
Torsen differential
Forced differential lock
Disc differential lock
Cam differential lock
Viscous differential lock
Screw lock differential
Connecting brains
self-locking differential
Limited slip differentials
Blocking ratio
Fully locking differentials
Multi-plate differentials
Differential "Kwaif"
Differential "Thorsen"
Gerotor differential (Gerodisk or Hydra-lock)
Torque Sensitive Lsd. Differentials with friction preload blocks
Self-locking differentials with hypoid (worm or screw) and helical gearing
Controlling the operation of differentials using electronic brake force control systems (Traction Control, etc.)
Differentials, self-locking from the difference in speeds.
Mechanical, mixed type
Differentials, self-locking from the difference in torque
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Electric differential
Differential mathematical
Differential- this is (from lat. differentia - difference - difference)
Differential- this (from lat. differetia difference, difference) in mathematics, the main linear part of the increment of a function.
Differential is a small change in magnitude in mathematical terms due to the same little change variable.
The theory of differential equations is one of the largest branches of modern mathematics. In order to characterize its place in modern mathematical science, it is first of all necessary to emphasize the main features of the theory of differential equations, which consists of two vast areas of mathematics: the theory of ordinary differential equations and the theory of partial differential equations.
The first feature is the direct connection between the theory of differential equations and applications. Describing mathematics as a method of penetrating the secrets of nature, we can say that the main way to apply this method is the formation and study of mathematical models of the real world. When studying any physical phenomena, the researcher first of all creates its mathematical idealization or, in other words, a mathematical model, that is, neglecting the secondary characteristics of the phenomenon, he writes down the basic laws governing this phenomenon in mathematical form. Very often these laws can be expressed as differential equations. These are models of various phenomena in continuum mechanics, chemical reactions, electrical and magnetic phenomena, etc.
By investigating the resulting differential equations, together with additional conditions, which, as a rule, are given in the form of initial and boundary conditions, a mathematician receives information about an ongoing phenomenon, sometimes he can find out its past and future. The study of a mathematical model by mathematical methods allows not only to obtain qualitative characteristics of physical phenomena and calculate the course of a real process with a given degree of accuracy, but also makes it possible to penetrate into the essence of physical phenomena, and sometimes to predict new physical effects. It happens that the very nature of a physical phenomenon suggests both approaches and methods of mathematical research. The criterion for the correct choice of a mathematical model is practice, comparison data mathematical research with experimental data.
To compile a mathematical model in the form of differential equations, it is necessary, as a rule, to know only local connections and it is not necessary information about the physical phenomenon as a whole. The mathematical model makes it possible to study the phenomenon as a whole, predict its development, and make quantitative estimates of the changes that occur in it over time. Recall that on the basis of the analysis of differential equations, electromagnetic waves were discovered in this way, and only after Hertz's experimental confirmation of the actual existence of electromagnetic oscillations, it became possible to consider Maxwell's equations as a mathematical model of a real physical phenomenon.
As is known, the theory of ordinary differential equations began to develop in the 17th century simultaneously with the emergence of differential and integral calculus. It can be said that the need to solve differential equations for the needs of mechanics, that is, to find the trajectories of motion, in turn, was the impetus for the creation of a new calculus by Newton. The organic connection between the physical and the mathematical was clearly manifested in Newton's method of fluxes. Laws Newton are a mathematical model mechanical movement. Applications of the new calculus to problems of geometry and mechanics went through ordinary differential equations; at the same time, it was possible to solve problems that for a long time could not be solved. In celestial mechanics, it turned out to be possible not only to obtain and explain already known facts, but also to make new discoveries (for example, the discovery of the planet Neptune by Le Verrier in 1846 based on the analysis of differential equations).
Ordinary differential equations arise when the unknown function depends on only one independent variable. The relationship between an independent variable, an unknown function, and its derivatives up to a certain order constitutes a differential equation. At present, the theory of ordinary differential equations is a rich, widely branched theory. One of the main problems of this theory is the existence of solutions for differential equations that satisfy additional conditions (initial Cauchy data, when it is required to determine a solution that takes given values at some point and given values of derivatives up to a certain finite order, boundary conditions, etc.), uniqueness solutions, its sustainability. The stability of the solution is understood as small changes in the solution with small changes in the additional data of the problem and the functions that determine the equation itself. Important for applications are the study of the nature of the solution, or, as they say, the qualitative behavior of the solution, finding methods for the numerical solution of equations. The theory should put in the hands of the engineer and the physicist the methods of an economical and rapid solution for the physicist.
Partial differential equations began to be studied much later. It should be emphasized that the theory of partial differential equations arose on the basis of specific physical problems leading to the study of individual partial differential equations, which were called the basic equations of mathematical physics. The study of mathematical models of specific physical problems led to the creation in the middle of the 18th century of a new branch of analysis - the equations of mathematical physics, which can be considered as the science of mathematical models of physical phenomena.
The foundations of this science were laid by the works of D "Alembert (1717 - 1783), Euler (1707 - 1783), Bernoulli (1700 - 1782), Lagrange (1736 - 1813), Laplace (1749 - 1827), Poisson (1781 - 1840), Fourier (1768 - 1830) and other scientists. It is interesting that many of them were not only mathematicians, but also astronomers, mechanics, physicists. The ideas and methods developed by them in the study of specific problems of mathematical physics turned out to be applicable to physics wide classes of differential equations, which at the end of the 19th century served as the basis for the development of the general theory of differential equations.
The most important equations of mathematical physics are: the Laplace equation, the equations physics conductivity, wave equation.
Here we assume that the function u depends on t and three variables x1, x2, x3. A partial differential equation is a relationship between independent variables, an unknown function, and its partial derivatives up to some order. The system of equations is defined similarly when there are several unknown functions.
Isn't it surprising that an equation as simple as the Laplace equation contains a huge wealth of remarkable properties, has a wide variety of applications, many books have been written about it, many hundreds of articles have been devoted to it published over the past centuries, and Despite this, there are still many difficult unresolved problems associated with it.
A wide variety of physical problems of a completely different nature lead to the study of the Laplace equation. This equation is found in problems of electrostatics, potential theory, hydrodynamics, heat transfer theory and many other branches of physics, as well as in the theory of functions of a complex variable and in various areas of mathematical analysis. Laplace's equation is the simplest representative of a wide class of so-called elliptic equations.
Here, perhaps, it is appropriate to recall the words of A. Poincaré: "Mathematics is the art of giving one name to different things." These words are an expression of the fact that mathematics studies, by one method, with the help of a mathematical model, various phenomena of the real world.
Just like the Laplace equation, an important place in the theory of partial differential equations and its applications is occupied by the heat equation. This equation is found in the theory of heat transfer, in the theory of diffusion and many other branches of physics, and also plays an important role in probability theory. It is the simplest representative of the class of so-called parabolic equations. Some properties of the solutions of the heat equation resemble the properties of the solutions of the Laplace equation, which is in agreement with their physical meaning, since the Laplace equation describes, in particular, a stationary temperature distribution. The heat equation was derived and first studied in 1822 in the famous work J. Fourier "Analytical theory of heat", which played an important role in the development of methods of mathematical physics and the theory of trigonometric series.
Physics The wave equation describes various wave processes, in particular the propagation of sound waves. It plays an important role in acoustics. This is a representative of the class of so-called hyperbolic equations.
The study of the basic equations of mathematical physics made it possible to classify equations and systems by physical derivatives. I.G. In the 1930s, Petrovsky singled out and first studied the classes of elliptic, parabolic, and hyperbolic systems that now bear his name. At present, these are the most well-studied classes of equations.
It is important to note that in order to check the correctness of a mathematical model, existence theorems for solutions to the corresponding differential equations are very important, since a mathematical model is not always adequate to a specific phenomenon, and the existence of a solution to the corresponding mathematical problem does not follow from the existence of a solution to a real problem (physical, chemical, biological).
At present, the use of modern electronic computers plays an important role in the development of the theory of differential equations. The study of differential equations often makes it easier to conduct a computational experiment to identify certain properties of their solutions, which can then be theoretically substantiated and serve as a foundation for further theoretical research.
The computational experiment has also become a powerful tool for theoretical research in physics. It is carried out on a mathematical model of a physical phenomenon, but at the same time, other parameters are calculated from one model parameters and conclusions are drawn about the properties of the physical phenomenon under study. The purpose of the computational experiment is to build with the necessary accuracy with the help of a computer for the least possible computer time an adequate quantitative description of the physical phenomenon under study. Such an experiment is very often based on the numerical solution of a system of partial differential equations. From here comes the connection between the theory of differential equations and computational mathematics and, in particular, with such important sections of it as the method of finite differences, the method of finite elements, and others.
So, the first feature of the theory of differential equations is its close connection with applications. In other words, we can say that the theory of differential equations was born from applications. In this section - the theory of differential equations - mathematics primarily acts as an integral part of natural science, on which the conclusion and understanding of the quantitative and qualitative laws that make up the content of the sciences of nature is based.
It is natural science that is a remarkable source of new problems for the theory of differential equations, it largely determines the direction of their research, gives the correct orientation to these studies. Moreover, differential equations cannot fruitfully develop in isolation from physical problems. And not only because nature is richer than human imagination. The theory developed in recent years on the unsolvability of certain classes of partial differential equations shows that even very simple linear partial differential equations with infinitely differentiable coefficients may not have a single solution, not only in the usual sense, but also in classes of generalized functions, and in classes of hyperfunctions, and, therefore, a meaningful theory cannot be constructed for them (the theory of generalized functions, which generalizes the basic concept of mathematical analysis - the concept of a function, was created in the middle of our century by the works of S.L. Sobolev and L. Schwartz).
The study of partial differential equations in the general case is such a difficult task that if someone randomly writes even a linear partial differential equation, then with a high probability not a single mathematician will be able to say anything about it and, in particular, , find out if this equation has at least one solution.
The problems of physics and other natural sciences supply the theory of differential physics with problems from which rich theories grow. However, it also happens that a mathematical research born within the framework of mathematics itself, after a considerable time after its implementation, finds application in specific physical problems as a result of their deeper study. One such example is the Tricomi problem for equations of mixed type, which, more than a quarter of a century after its solution, has found important applications in problems of modern gas dynamics in the study of supersonic gas flows.
F. Klein in his book "Lectures on the Development of Mathematics in the 19th Century" wrote that "mathematics followed on the heels of physical thinking and, on the contrary, received the most powerful impulses from the problems put forward by physics."
The second feature of the theory of differential equations is its connection with other branches of mathematics, such as functional analysis, algebra, and probability theory. The theory of differential equations and especially the theory of partial differential equations widely use the basic concepts, ideas and methods of these areas of mathematics and, moreover, influence their problems and the nature of research. Some large and important sections of mathematics have been brought to life by problems in the theory of differential equations. A classic example of such an interaction with other areas of mathematics is the study of string vibrations carried out in the middle of the 18th century.
The string vibration equation was derived by D "Alembert in 1747. He also obtained a formula that gives the solution to this equation: u (t, x) \u003d F1 (x + t) + F2 (x - t), where F1 and F2 are arbitrary functions. Euler obtained a formula for it that gives a solution for it with given initial conditions (the Cauchy problem). (This formula is now called the d'Alembert formula.) The question arose of which functions to consider as a solution. Euler believed that this could be an arbitrarily drawn curve. D "Alembert believed that the solution should be written in an analytical expression. D. Bernoulli argued that all solutions are represented in the form of trigonometric series. D" Alamber and Euler did not agree with him. In connection with this dispute, problems arose to clarify the concept of a function, the most important concept of mathematical analysis, as well as the question of the conditions for the representability of a function in the form of a trigonometric series, which was later considered by Fourier, Dirichlet and other major mathematicians and the study of which led to the creation of the theory of trigonometric series. As is known, the needs of the development of the theory of trigonometric series led to the creation of modern measure theory, set theory, and function theory.
In the study of specific differential equations arising in the process of solving physical problems, methods were often created that had great generality and were applied without a rigorous mathematical justification to a wide range of mathematical problems. Such methods are, for example, the Fourier method, the Ritz method, the Galerkin method, perturbation theory methods, and others. The effectiveness of the application of these methods was one of the reasons for the attempts of their rigorous mathematical justification. This led to the creation of new mathematical theories, new areas of research. This is how the theory of the Fourier integral, the theory of expansion in terms of eigenfunctions, and, further, the spectral theory of operators and other theories arose.
In the first development of the theory of ordinary differential equations, one of the main tasks was to find a general solution in quadratures, that is, through integrals of known functions (this was done by Euler, Riccati, Lagrange, D "Alembert, etc.). The problems of integrating differential equations with constant coefficients were great influence on the development of linear algebra. In 1841, Liouville showed that the Riccati equation y" + a(x)y + b(x)y2 = c(x) cannot be solved in general by quadratures. The study of continuous transformation groups in connection with the problems of integrating differential equations led to the creation of the theory of Lie groups.
The beginning of the qualitative theory of differential equations was laid in works famous French mathematician Poincaré. These studies of Poincare on ordinary differential equations led him to create the foundations of modern topology.
Thus, differential equations are, as it were, at the crossroads of mathematical roads. On the one hand, new important achievements in topology, algebra, functional analysis, function theory and other areas of mathematics immediately lead to progress in the theory of differential equations and thus find their way to applications. On the other hand, the problems of physics, formulated in the language of differential equations, give rise to new directions in mathematics, lead to the need to improve the mathematical apparatus, give rise to new mathematical theories that have internal laws of development, their own problems.
In his Lectures on the Development of Mathematics in the 19th Century, F. Klein wrote: "Mathematics today resembles weapons production in peacetime. Samples delight the connoisseur. The purpose of these things fades into the background."
Despite these words, one can say that one cannot stand for the "disarmament" of mathematics. Recall, for example, that the ancient Greeks studied conic sections long before it was discovered that planets move along them. Indeed, the theory of conic sections created by the ancient Greeks did not find its application for almost two thousand years, until Kepler used it to create a theory of the motion of celestial bodies. Based on Kepler's theory, Newton created mechanics, which is the basis of all physics and technology.
Another such example is group theory, which originated at the end of the 18th century (Lagphysics, 1771) in the depths of mathematics itself and found fruitful application only at the end of the 19th century, first in crystallography, and later in theoretical physics and other natural sciences. Returning to the present, we note that the most important scientific and technical tasks, such as mastering atophysics energy, space flights, were successfully solved in the Union of Soviet Socialist Republics () also due to the high theoretical level of development of mathematics in our country.
Thus, in the theory of differential equations, the main line of development of mathematics is clearly traced: from the concrete and particular through abstraction to the concrete and particular.
As already mentioned, in the 18th and 19th centuries, it was mainly the specific equations of mathematical physics that were studied. From the general results of the theory of partial differential equations in this period we should note the construction of the theory of equations with partial derivatives of the first order (Monge, Cauchy, Charpy) and the Kovalevskaya theorem.
Theorems on the existence of an analytic (that is, representable as a power series) solution for ordinary differential equations, as well as for linear systems of partial differential equations, were proved earlier by Cauchy (Cauchy, 1789 - 1857). These issues have been discussed in several articles. But Cauchy's work was not known to Weierstrass, who suggested S.V. Kovalevskaya to study the question of the existence of analytic solutions of partial differential equations as a doctoral dissertation. (I note that Cauchy published 789 articles and a large number of monographs; his legacy is huge, so it is not surprising that some of his results could go unnoticed for some time.) S.V. Kovalevskaya in her work relied on lectures by Weierstrass, where a problem with initial conditions for ordinary differential equations was considered. The study of Kovalevskaya gave the question of the solvability of the Cauchy problem for equations and systems with partial derivatives, in a certain sense, a final character. Poincaré highly valued this work by Kovalevskaya. He wrote: "Kovalevskaya greatly simplified the proof and gave the theorem its final form."
The Kovalevskaya theorem occupies an important place in the modern theory of partial differential equations. She, perhaps, belongs to one of the first places in terms of the number of applications in various areas of the theory of partial differential equations: Holmgren's theorem on the uniqueness of the solution of the Cauchy problem, existence theorems for the solution of the Cauchy problem for hyperbolic equations (Schauder, Petrovsky), the modern theory of solvability of linear equations, and many other results use Kovalevskaya's theorem.
An important achievement in the theory of partial differential equations was the creation at the turn of the 19th century of the theory of Fredholm integral equations and the solution of basic boundary value problems for the Laplace equation. It can be considered that the main results of the development of the theory of equations with partial derivatives of the 19th century were summed up in the textbook by E. Gours "Course of Mathematical Analysis", published in the 20s of our century. It should be noted the great contribution made to the theory of differential equations and mathematical physics by the works of M.V. Ostrogradsky on variational methods, the works of A.M. Lyapunov on the theory of potential and on the theory of stability of motion, the works of V.A. Steklov on the physics of the Fourier method and others.
The thirties and later years of our century were period rapid development of the general theory of partial differential equations. In the works of I.G. Petrovsky, the foundations of the general theory of systems of equations with partial derivatives were laid, classes of systems of equations were distinguished, which are currently called elliptic, hyperbolic and parabolic in the sense of Petrovsky systems, their properties were studied, and their characteristic problems were studied.
The ideas of functional analysis began to penetrate deeper and deeper into the theory of partial differential equations. The concept of a generalized solution was introduced as an element of some functional space. The idea of a generalized solution was systematically carried out in the works of S.L. Sobolev. In connection with the study of differential equations, in the 1930s Sobolev created the theory of generalized functions, which plays an exceptionally important role in modern mathematics and physics. S.L. Sobolev developed a theory attachments functional spaces, which are currently called Sobolev spaces. A.N. Tikhonov developed the theory of ill-posed problems.
Outstanding contribution Russian mathematicians N.N. Bogolyubov, A.N. Kolmogorov, I.G. Petrovsky, L.S. Pontryagin, S.L. Sobolev, A.N. Tikhonov and others.
Influence on the development of the theory of partial differential equations in our country provided a seminar, which in the 40s and 50s was led by I.G. Petrovsky, S.L. Sobolev, A.N. Tikhonov. A problem review article by I.G. Petrovsky "On some problems in the theory of partial differential equations", published in 1946 in the journal "Advances in Mathematical Sciences". It outlines the state of the theory of partial differential equations of that time and outlines the ways of its further development. Now, almost 50 years later, we can say that the development of the theory of partial differential equations followed exactly the path outlined in this remarkable article.
At present, the theory of partial differential equations is a rich, highly branched theory. A theory of boundary value problems for elliptic operators is constructed on the basis of a recently created new apparatus - the theory of pseudodifferential operators, the index problem is solved, and mixed problems for hyperbolic equations are studied. An important role in modern studies of hyperbolic equations is played by Fourier integral operators, which generalize the Fourier transform operator to the case when the phase function in the exponent, generally speaking, depends nonlinearly on independent variables and frequencies. With the help of Fourier integral operators, the question of the propagation of singularities of solutions of differential equations, which originates from the classical works of Huygens, is studied. In recent decades, conditions for the correct formulation of boundary value problems have been found, and questions of the smoothness of solutions for elliptic and parabolic systems have been studied. Nonlinear second-order elliptic and parabolic equations and broad classes of first-order nonlinear equations are studied, the Cauchy problem is investigated for them, and a theory of discontinuous solutions is constructed. The Navier-Stokes system, the system of boundary layer equations, equations of elasticity theory, filtration equations and many other important equations of mathematical physics were subjected to deep study.
An interesting example of attracting ideas and tools from other areas of mathematics is the solution in recent years of the Cauchy problem for the Korteweg-de Vries equation using the inverse problem of scattering theory. On the basis of the method that arose in this case, new classes of integrable nonlinear equations and systems are found. In this case, the application of the methods of algebraic geometry played a significant role, which made it possible, in particular, to integrate the Yang-Mills equations, which play an important role in quantum field theory.
In recent decades, a new branch of the theory of partial differential equations has arisen and is being intensively developed - the theory of averaging of differential operators. This theory arose under the influence of problems in physics, continuum mechanics and technology, in particular, related to the study of composites (highly inhomogeneous materials currently widely used in engineering), porous media, and perforated materials. Such problems lead to partial differential equations with rapidly oscillating coefficients or in domains with complex boundaries. The numerical solution of such problems is extremely difficult. An asymptotic analysis of the problem is required, which leads to averaging problems.
Many works in recent years have been devoted to the study of the behavior of solutions of evolutionary equations (that is, equations describing processes that develop in time) with an unlimited increase in time and the so-called attractors that arise in this case. The question of the nature of the smoothness of solutions to boundary value problems in domains with a nonsmooth boundary continues to attract the attention of researchers; a large number of papers in recent years have been devoted to the study of specific nonlinear problems of mathematical physics.
Over the past one and a half to two decades, the face of the qualitative theory of ordinary differential equations has changed dramatically. One of the important achievements is the discovery of limiting regimes, which are called attractors.
It turned out that, along with stationary and periodic limiting regimes, limiting regimes of a completely different nature are possible, namely, those in which each individual trajectory is unstable, and the very phenomenon of reaching a given limiting regime is structurally stable. The discovery and detailed study of such limiting modes, called attractors, for systems of ordinary differential equations required the use of tools of differential geometry and topology, functional analysis and probability theory. At present, these mathematical concepts are being intensively introduced into applications. So, for example, the phenomena occurring during the transition of a laminar flow to a turbulent one with an increase in Reynolds numbers are described by an attractor. The study of attractors has also been undertaken for partial differential equations.
Another important achievement in the theory of ordinary differential equations was the study of the structural stability of systems. When using any mathematical model, the question arises of the correctness of applying mathematical results to reality. If the result is highly sensitive to the slightest change in the model, then arbitrarily small changes in the model will lead to a model with completely different properties. Such results cannot be extended to the real one under study, since when building a model, some idealization is always carried out and the parameters are determined only approximately.
This led A.A. Andronov and L.S. Pontryagin to the concept of roughness of a system of ordinary differential equations or the concept of structural stability. This concept turned out to be very fruitful in the case of a small dimension of the phase space (1 or 2), and in this case the issues of structural stability were studied in detail.
In 1965, Smale showed that with a large dimension of the phase space, there are systems in some neighborhood of which there is not a single structurally stable system, that is, such that, with a small change in the vector field, it remains in a certain sense equivalent to the original one. This result is of fundamental importance for the qualitative theory of ordinary differential equations, since it shows the unsolvability of the problem of topological classification of systems of ordinary differential equations, and can be compared in its meaning with Liouville's theorem on the unsolvability of differential equations in quadratures.
Important achievements include the construction of A.N. Kolmogorov of perturbation theory of Hamiltonian systems, justification of the averaging method for many-particle systems, development of the theory of bifurcations, perturbation theory, theory of relaxation oscillations, further in-depth study of Lyapunov exponents, creation of a theory of optimal control of processes described by differential equations.
Thus, the theory of differential equations is currently an exceptionally content-rich, rapidly developing branch of mathematics, closely related to other areas of mathematics and its applications.
Bourbaki, speaking about the architecture of mathematics, characterizes its current state as follows:
“To give a general idea of mathematical science at the present time means to engage in such a business, which, as it seems, from the very beginning encounters almost insurmountable difficulties due to the vastness and variety of the material under consideration. Articles on pure mathematics published throughout the world on average within one years, amount to many thousands of pages.Not all of them, of course, have the same value, nevertheless, after cleaning from the inevitable garbage, it turns out that every year the mathematical science is enriched with a mass of new results, acquires an ever more diverse content and constantly gives offshoots in the form of theories. which are constantly modified, rearranged, compared and combined with each other. No mathematician is able to trace this development in all details, even if he devotes all his activity to this. Many of the mathematicians settle down in some nook and cranny of mathematical science, where they come from do not seek to go out and not only almost completely ignore everything that does not concern the subject of their research, but are unable even to understand the language and terminology of their brethren, whose specialty is far from them. (N. Bourbaki, "Essays on the History of Mathematics", Moscow: IL, 1963)
However, it seems to me that one cannot deny the importance for mathematical research even of those who are "in the back street" of mathematical science. The main channel of mathematics, like a large river, is fed primarily by small streams. Major discoveries, breakthroughs in the front of research are very often provided and prepared by the painstaking work of many researchers. All of the above applies not only to the whole of mathematics, but also to one of its most extensive sections - the theory of differential equations, which at present is a difficult-to-observe set of facts, ideas and methods that are very useful for applications and stimulate theoretical research in all other sections. mathematics.
Many branches of the theory of differential equations have grown so much that they have become independent sciences. It can be said that most of the paths connecting abstract mathematical theories and applications in the natural sciences pass through differential equations. All this provides the theory of differential equations with an honorable place in modern science.
Usually the differential of f is denoted df, and its value at x is denoted dxf, and sometimes dfx and df[x]. Some authors prefer to use the roman font for df to emphasize that the differential is an operator.
An informal description of the mathematical differential
Consider a smooth function f(x). Let's draw a tangent to it at the point x, and set aside on this tangent a segment of such length that its projection onto the x-axis is equal to Δx. The projection of this segment onto the y-axis is called the differential of the function f(x) at the point x from Δx.
Thus, the differential can be understood as a function of two variables x and Δx,
df/(x, ∆x)→dxf(∆x)
determined by the relation
dxf(Δx) = f "(x)Δx.
Definitions.
For functions
The differential of a smooth real-valued function f defined on M (M is a smooth manifold) is a 1-form, usually denoted df and defined by the relation
where Xf denotes the derivative of f with respect to the vector X in the tangent bundle M.
For displays
The differential of a smooth mapping from a smooth manifold to F/M→N is a mapping between their tangent bundles, dF/TM→TN, such that for any smooth function g/N→R we have
dF(X) g = X(Fog)
where Xf denotes the derivative of f with respect to the X direction. (On the left side of the equality, the derivative in N of the function g with respect to dF(X) is taken; on the right side, in M of the function F o g with respect to X).
This notion naturally generalizes the differential of a function.
Related definitions
A smooth mapping F/M →N is called a submersion if, for any point x Є M, the differential d x F / T x M → T F(x) N is surjective.
A smooth map F / M → N is called a smooth immersion if for any point x Є M the differential d x F / T x M → T F(x) N is injective.
Properties
The composition differential is equal to the composition of differentials:
d (F o G) = d F o d G or d x (F o G) = d G(x) F o d x G
Automobile differential
Differential- This is a mechanical device that transmits rotation from one source to two independent acquirers in such a way that the angular velocities of rotation of the source and both consumers may be different relative to each other and their ratio may not be constant.
Differential- this (from the Latin differentia - difference, difference), one of the basic concepts of differential calculus. ... (Modern Encyclopedia)
Differential- this is the name of the differential mechanism in the drive of the driving wheels of a car, tractor or other wheeled vehicles. The most common differential with bevel gears. ... (Big Encyclopedic Dictionary)
The purpose of the automotive differential
In car models and maps, the drive wheels are on the same common axle. It's okay when automobile rides in a straight line. However, in a corner, the inner wheel travels a shorter distance than the outer wheel, so this design causes the inner wheel to slip, which negatively affects the vehicle's handling, especially when driving at high speeds. In order for the drive wheels to rotate out of sync, a differential is used.
Purpose of the differential:
Transfers torque from the engine to the drive wheels.
Serves as an additional downshift.
Allows the wheels to rotate at different angular speeds (because of this, the differential got its name).
Automotive Differential Location
On vehicles with a single drive axle, the differential is located on the drive axle. Tandem axle vehicles have two differentials, one for each axle. On all-terrain vehicles with switchable all-wheel drive, one differential on each axle. On such machines it is not recommended to drive on roads with all-wheel drive turned on. On all-wheel drive vehicles there are three differentials: one on each axle (inter-wheel), plus one distributes torque between the axles (inter-axle). With three or four driving axles (wheel formula 6Ch6 or 8Ch8), an inter-bogie differential is also added.
Automobile differential device
Classic automotive differentials are based on a planetary gear. cardan shaft through a bevel gear it rotates the gearbox, the gearbox through gears independent of each other rotates the axle shafts. Such an engagement has not one, but two degrees of freedom, and each of the semi-axes rotates as fast as it can. Only the total speed of rotation of the semiaxes is constant.
Wheel slip problem
In a conventional differential, if one of the wheels is on ice or in the air, it is this wheel that will spin (while the second wheel, standing on solid ground, is motionless; it would be more logical to transfer torque to it).
Similarly, in a race car in a corner, the inner wheel is loaded less than the outer wheel, so there is not enough torque being transmitted to the outer wheel while the inner wheel is on the verge of slipping.
Thus, the problem of a slipping wheel worsens the handling and patency of the car.
Ways to solve the problem of a slipping wheel. Manual differential lock
On command from the cab, the differential gears are locked and the wheels rotate synchronously. Thus, the differential can be locked on viscous ground, and disengaged on asphalt. It is used in all-terrain vehicles and off-road vehicles.
When driving on such vehicles, you must not engage the lock when automobile is moving. You also need to know that the torque generated by the motor is so great that it can break the locking mechanism or axle shaft. The locked differential can only be driven at low speeds and only on difficult terrain. The included lock, especially in the front axle, adversely affects handling.
Electronic differential control
On SUVs equipped with an anti-slip system (TRC and others), if one of the wheels is slipping, it is braked by a service brake.
A similar solution was applied in Formula 1 in 1998 by the McLaren team: in a turn, the inner wheel was braked by a service brake. This system was quickly banned, but the design took root in Formula 1 friction differential, in which the clutch is additionally controlled by a computer. In 2002, the technical regulations were tightened; from this year to this day, only differentials of the simplest type are allowed in Formula 1.
The advantage of electronic control is that there is increased traction in the corner and the amount of lock can be adjusted depending on the rider's preference. On a straight line, there is no loss of engine power at all. The disadvantage is that the sensors and actuators have some inertia, and such a differential is insensitive to rapidly changing road conditions.
The Self-Locking Differential, as its name suggests, decides when it should engage. This is determined by the difference in the speed of rotation of the drive wheels. If this Difference is small (moves in a turn), then the Differential behaves like a normal “open”, but as soon as one of the wheels slips, the difference in the angular speeds of the wheels increases sharply, and the lock is activated. Technically, this can be implemented in many ways, but the most common are disk (friction, increased friction, LSD), viscous (viscous couplings) and screw (worm).
Friction self-locking differential
This type of Differential (as, indeed, a viscous coupling) is based on the fact that on a straight semi-axis they rotate synchronously with the rotor, but in a turn it appears Difference in angular speeds.
A friction clutch is made between the rotor 2 and axle shaft 4 (depending on the design, the clutch can be on one axle shaft or on two; this does not affect driving performance). When the Car is moving in a straight line, the rotor and axle shaft rotate at the same speed, and there is no friction. The greater the difference in the speed of the axle shafts, the higher the friction force.
The most efficient form of the Differential, it requires periodic maintenance and therefore never set to production cars(only for sports and tuned).
Viscous coupling Got its name from lat. viscosus - viscous. Its main elements are:
Housing and shaft sealed with seals.
Disks, one half of which is splined to the body, the other to the shaft. The discs have channels and holes to increase the friction viscosity of the fluid.
Silicone (organosilicon) fluid that has high viscosity and fills the body by 80-90%.
A simplified version of the friction differential. On one of the axle shafts there is a reservoir filled with a viscous liquid. Two packs of disks are immersed in this liquid; one is connected to the rotor, the second to the axle shaft. The greater the Difference in the speeds of the wheels, the greater the Difference in the speeds of rotation of the disks, and the greater the viscous resistance.
The advantage of this design is simplicity and low cost. The disadvantage is that the viscous coupling is rather inertial and refuses to work on complete off-road conditions. good driving performance the viscous coupling does not provide, and is used only in "SUVs" (SUVs that sacrifice patency for comfort) between the axles. For installation as an axial differential, this design is too cumbersome.
Sometimes, instead of the Differential, they put a bevel gear with a viscous coupling on one of the axle shafts.
It is well suited for operation in conditions of unstable road surfaces (snow, ice, shallow dirt), however, in real off-road conditions, its abilities are far from outstanding: the viscous coupling cannot cope with constant changes in the state of adhesion of bridges to the ground, it is late when turned on, overheats and goes out of building. Therefore, such a solution is most often used on purely “civilian”, road cars, where blocking is required incomplete and for a short time. But, unlike the disk one, it is standard equipment for many all-wheel drive vehicles. Such a scheme was, for example, in the Mitsubishi Eclipse GSX transmission, all-wheel drive Subaru with a manual gearbox, as well as in the BMW325ix and all-wheel drive Toyota Celica turbo.
The viscous coupling transmits the torque supplied to it due to internal friction in the fluid located between the disks. When their speeds are the same, the clutch transmits a small part of the force (5-7%). When the driven disks lag behind the leading ones, the liquid mixes, its temperature and viscosity increase, it expands and compresses the air. When it is almost fully compressed, the pressure in the clutch rises sharply, which causes the discs to move axially along the splines until they make mechanical contact. This leads to a sharp increase in the transmitted torque ("hump effect"), which can adversely affect the vehicle's handling. As a result of rotation is transmitted due to mechanical friction, the temperature and, accordingly, the pressure of the fluid gradually decrease, the disks come out of mechanical contact. The viscous coupling can be installed as an independent unit between the driving axles or "embedded" in a conical differential.
Cam/gear self-locking differential
The principle of operation is similar, but the axle shafts are connected by a gear or cam pair. Thus, when one of the wheels slips, the differential is abruptly blocked. Therefore, such a system is used only in military and special equipment (for example, in armored personnel carriers), where a large traction force and high durability are needed to the detriment of controllability.
Instead of the classic planetary gear mechanism, cam or gear pairs are used, which, with a small difference in the angular speeds of the semi-axes, have the ability to mutually rotate (jump), and when slipping, they jam and block the semi-axes with each other. It is not difficult to imagine what happens to the car when such a lock is activated in a turn. Some instances simply turn off one of the axle shafts at the moment a small speed difference occurs (due to the use of overrunning clutches). That is why, only the Differentials of military and special equipment (armored personnel carriers, etc.) are equipped with such locks on a regular basis.
Hydrorotor self-locking differential
An attempt to improve the efficiency and durability of the friction differential. When a Difference occurs in the angular velocities, the pump pumps fluid into the cylinder, and the piston compresses the friction pack, blocking the differential.
Hypoid self-locking differentials
There are three types of such Differentials. All of them are based on the property of a hypoid gear or worm gear to "jam" at a certain ratio of torques. Such differentials transfer most of the torque (up to 80%) to the non-spinning wheel.
There are two more types of Differentials based on the same property: the Quaife Type Differential and the Planetary Differential.
Used in SUVs and racing cars. Disadvantages: complexity; big loss power than a conventional differential.
Dual Pump System
Dual Pump System - a system with two pumps, automatically connecting the second axle when one is missing. Used in systems all-wheel drive Honda. Advantages: works automatically, saves on a good road. Disadvantages: limited cross-country ability, complexity, towing restrictions.
Torsen differential
The Torsen type differential was invented in 1958 by the American Vernon Gleeseman. It has the advantages of a viscous coupling and does not have its disadvantages. Name Torsen came from English. Torque sensitive ("torque sensitive"). Torsen - JTEKT Torsen North America Inc.
The design of the Thorsen Differential is based on worm gears rotating on different axes. Each side gear is a worm gear splined to the output cups. Inside are 2 or 3 sets of planetary worm gears (called element gears) perpendicular to the axis of the side gears. Each set consists of 2 worm gears connected to each other by driven gears and meshed with side gears. Thus, the two side gears are interconnected by means of elemental worm gears.
When the clutch on the wheel changes, the pressure between the element gears and the side gears changes, causing the element pair to counter-rotate, shifting the torque to the other side. Unlike other designs, torque sensors operate in virtually any environment. Even if the wheels are spinning at different speeds (turning, going over bumps), they still always get torque based on traction.
Off-road differential calculus
In a car with a drive on one axle, only one Differential is used, interwheel, in an all-wheel drive car there are as many as three - two interwheel and one interaxle. The device is necessary and useful. The fact is that the Car is designed not only to move in a straight line, but can also move along a curved path - that is, turn. Anyone who has taken the trouble to think about this question will easily notice that when turning, two wheels of the same axle travel a different distance, which means that their speed of rotation must also be different. This Difference is provided by the Differential. This is an important feature that improves the controllability of the car in the corner, increases the "mileage" of tires, reduces Probability drift and so on.
Nevertheless, there are moments in automotive life when the Differential begins to interfere with movement. If one of the two drive wheels hits a slippery surface, its resistance to rotation drops sharply, traction decreases, and the wheel is unable to provide the necessary traction. Such a wheel will begin to slip and rotate faster than it should. The second wheel may stop altogether. That's it - get out and push! And then it would be nice to somehow “turn off” this very Differential in order to allow the car to push off with all the drive wheels. And actually for this, there is such a technical phenomenon as “Differential lock”. Locks are used on off-road vehicles, as well as on sports cars - that is, where different reasons great Probability slip. There are a lot of technical principles of blocking, but first, let's brush up on the device of a conventional, that is, “open” Differential.
The differential is installed in the main gear housing and receives torque from its driven gear. In the box of the Differential are bevel gears-satellites. They engage with gears mounted on the axle shafts, and those, in turn, rotate the drive wheels. When driving on a flat and straight road, the angular speeds of the wheels are the same, and the satellites do not rotate around their axis. When turning or driving over bumps, when the wheels of the right and left sides pass a different path, the satellites begin to rotate and redistribute the torque. In general, the device is not very complicated. The principle of blocking it also looks obvious - to stop the rotation of the satellites and that's it. However, this can be done in a variety of ways.
Forced differential lock
The easiest way to block the Differential is forced. The driver with a special drive (mechanical, pneumatic or even electric) stops the rotation of the satellites for a while, and the wheels of the car begin to rotate at the same speed. This method is most often used on SUVs. The system is simple, reliable and very efficient. The only drawback is a bunch of levers in the cabin, with which the driver must turn the lock on and off in a timely manner, depending on road conditions. However, in modern cars, levers are more often replaced by buttons. However, the main feature remains - the decision to turn on the lock is made and implemented by the driver.
Forced blocking is good for real SUVs storming the deep abyss of Russian open spaces. Efficient and reliable in the mud, it is completely unsuitable for driving on roads, so turning off the lock in time is just as important as turning it on, because with a locked Differential, the Car consumes more fuel, it has intense tire wear, and in a sharp turn, the locked axle will certainly skid . Therefore, in the era of universal automation, a self-locking differential naturally appeared.
With this type of blocking, the Differential actually ceases to perform its functions and turns into a simple clutch that rigidly connects the axle shafts (or cardans) to each other and constantly transmits rotation to them at an equal angular velocity. In order to completely block the classic Differential, it is enough either to block the possibility of axial rotation of the satellites, or to rigidly connect the Differential cup to one of the axle shafts. Wherein, planetary gear is blocked and does not distribute torque along the axes. The torques transmitted on the axle shaft depend directly on the adhesion of each of the wheels to the road. The picture shows the blocking scheme of the ARB Organization for a bridged Differential, in which the satellites are blocked. The blocking is connected using a drive controlled by the driver from the car. The following types of actuators are mainly used: pneumatic, electric, hydraulic or mechanical. This type of blocking is used for both bridge and center Differentials. Since a fully locked Differential does NOT distribute the received torque equally between the axles, in the event of a sharp loss of traction of one of the wheels, the transmitted torque to the half-axle of the wheel with good grip will increase dramatically. Therefore, it is necessary to use such locks very carefully, since the force of the motor is quite enough to “break” the locking mechanism or break the axle shaft. It is advisable to use such locks only at low speeds for moving over difficult terrain, since when they are used in bridges (especially in steering ones), the Car loses a lot of controllability. You can only enable this kind of blocking when the car is stopped. As a rule, full-fledged frame SUVs such as Toyota Land cruiser, 4Runner (Hilux Surf), Mercedes G-Class, etc.
Disc lock differential
The main part in such a device is a friction clutch. It is inserted between one of the axle shafts and the differential box. Bronze discs are installed in the splines of the sleeve connected to the Differential box, steel discs sit on the splines of the axle shaft. The disks are pressed against each other by springs. When both wheels experience the same resistance, the entire Differential rotates as one and there is no friction in the clutch, but if the torque on the wheels is different, the clutch begins to slow down the rotation of the faster wheel.
A more complex design with double friction clutches has become widespread in american cars. In it, the crosspiece is replaced by two separate axes of satellites intersecting at right angles. The axes can move relative to each other, for which their ends have bevels. With non-rotating satellites, the force to the axle shafts is transmitted in the same way as in a simple Differential. When the satellites rotate, the latter will shift the end bevels of the axles so that the force on the friction clutch will increase for the lagging axle shaft and decrease for the faster rotating axle. In this case, the magnitude of the braking torque will not be constant, as in the Differential with one disc clutch, but proportional to the moment transmitted to the wheels.
This differential requires the use of a special gear oil to function properly. In addition, disks wear out rather quickly, and the device requires frequent adjustment. Disc lock is a favorite solution of cross-country racing drivers. First of all, because of the ability to customize the operation for specific conditions on the track. However, for the average user, the not weak jerks that this lock gives to the steering wheel during acceleration (on the front-wheel drive) matter. Racers are ready for this, but the average driver may not be able to cope.
Cam Lock Differential
On civilian vehicles, this type of lock is rarely used. In cam locks, instead of the classic planetary gear mechanism, cam pairs are used, which, with a small difference in the angular speeds of the semi-axes, have the ability to mutually rotate (jump), and when slipping, they jam and block the semi-axes with each other. Some types of devices, when such a lock is triggered in a turn, simply turn off one of the semi-axes at the moment a small speed difference occurs. The lock is released when the slipping wheel stops slipping. This type of differential is quite durable and does not require special oils. That is why such locks are regularly equipped with Differentials of military and special equipment (armored personnel carriers and the like).
Cam locking is reliable and effective, but it works abruptly, very hard and locks tightly. For a passenger car, such a solution is unacceptable - at a high speed, the operation of the lock will almost inevitably cause an instant skid. Therefore, cam systems are used mainly by extreme jeepers and the military.
Viscous differential lock
The principle of its operation is very similar to the disk one, even the disks themselves are present here. However, their adhesion occurs not due to friction of the surfaces, but due to the properties of a special viscous liquid based on silicone, which “knows how” to harden when heated. The hydraulic clutch consists of a large number of discs with sticky working surfaces that transmit torque depending on the difference in the speeds of the input and output shafts. Heating occurs when one half shaft begins to rotate faster than the other. In the hardened silicone, the discs are firmly engaged and the axle shafts are blocked. Viscous couplings do not require maintenance and are considered quite reliable, however, for their long-term operation, it is necessary to maintain the complete tightness of the device.
Screw lock differential
The principle of its operation is as follows: in normal mode, the screws (or worms, as they are called because of their characteristic shape) freely roll around the central gear. In this case, each axle shaft has its own satellites, which are connected in pairs with the satellites of the opposite axle shaft by the usual spur gearing. The axis of the satellite is perpendicular to the semiaxis.
During normal movement and equality of the moments transmitted on the semi-axle, the hypoid pairs, consisting of the satellite and the drive gear, are either stopped or rotated, providing the difference in angular velocities in the turn. As soon as the Differential tries to give a moment to one of the semi-axes, then the hypoid pair of this semi-axis begins to wedged and in the extreme position block with the Differential cup. This leads to partial blocking of the Differential. When the moment equalizes, the screws return to their original position.
This design operates in the widest range of torque ratios (from 2.5:1 to 5.0:1). The actuation range is regulated by the angle of inclination of the screw teeth. Such differentials are little affected Wear and tear(the service life of the device is comparable to the resource of a box or a classic Differential), and ordinary transmission oil is used.
Screw blocking (Torsen and Quaife types) is well suited for ordinary cars in winter, as well as summer residents and tourists. It is not as efficient as other types, and is not suitable for serious off-road, but it works smoothly and does not require special driving skills from the driver. For a long time, Torsen has been the traditional solution for Audi Quattro, but then it was replaced by electronic systems.
Connecting brains
The tendency to translate as much as possible more systems in the car for control by wire, the differential lock did not pass. Roughly operating mechanical systems are now successfully replacing "smart" devices that include blocking at the command of a computer. The VTD (Variable Torque Distribution) scheme, for example, is used on the world rally star, the Subaru Impreza. Blocking there is carried out by hydromechanical clutches with electronic control. The principle of their operation is somewhat reminiscent of disk ones, but at the command of the computer, the degree of pressing the disks changes with the help of hydraulics, changing from “free” to complete blocking. This provides the machine with amazing freedom of control on any surface. The famous xDrive from is implemented in a similar way - there is also a package of disks, the compression ratio of which is determined by electronics. Moreover, technically, this system is implemented surprisingly elegantly - a low-power electric motor, followed by two reduction gears, a worm gear and a planetary one, then an eccentric, which, turning, displaces a long lever. And he, in turn, clamps the clutch pack.
But the most surprising and non-obvious way to implement blocking is... not to block Differential at all! How is this possible? Yes, easily! Modern ABS systems allow you to control the brake mechanisms of each wheel separately, and this can be quite used. After all, it is enough to slow down the slipping wheel, and the usual “free” Differential will itself transfer the torque to another, without any interference in its Work! So, for example, the 4ETS electronic transmission control system, which is included in the 4Matic smart all-wheel drive kit on Mercedes cars, works.
If the car did not bother to equip the locks at the factory - do not despair. For most common brands, there are tuning kits that replace the standard Differential with a self-locking one - as a rule, Torsen and Quaife screw systems are used for this. However, it must be understood that any technical change, introduced into the design of the car, has its downside. So, limited-slip differentials have a shorter service life, increase the load on the transmission and change the behavior of the car in critical modes. So it makes sense to think - is it worth it?
Self-locking Differential
A lot of people have probably heard of such a thing as LSD. For medical students, I explain: this is not a drug, this is Limited Slip Differential, but in our opinion - Limited Slip Differential. A device that allows you to partially compensate for the main drawback of a free Differential, namely its complete helplessness when one wheel hits a slippery surface.
Limited slip differentials
When the vehicle is moving around a curve, on uneven roads, etc. wheels travel a path of different lengths. This is due to the difference in radii when turning and because of the difference in the distance traveled when crossing an obstacle. Therefore, the wheels must rotate at different speeds, otherwise this will lead to increased Wear and tear tires.
In the transmission of Cars with one drive axle, the Differential is installed between the wheel drives (half shafts, CV joints, etc.), therefore it is called interwheel. In all-wheel drive vehicles (with all-wheel drive) it can also be located between the drive axles (center differential).
In the ideal case, the Car is standing on a concrete surface and the grip of both wheels is the same. Another thing is when one wheel is on ice and the other on dry pavement. This is where the differential fails. One wheel shamelessly slips, and the second quietly smokes "aside" and chuckles, watching the first one try to pull the car off. The situation is familiar to almost all motorists who have ever left a snowy yard.
On passenger cars intended for driving on paved roads, most widespread received a differential with bevel gears.
It is a gear with movable axes of gears (such gears are called planetary). Its main elements are:
A housing with which the driven gear of the final drive (transmitting torque from the cardan shaft to the differential housing) is rigidly connected. On passenger cars, as a rule, the body has a one-piece design and windows for mounting gears
Satellites are bevel gears that can rotate around an axis. Passenger Car Differentials usually have two satellites;
The axis of the satellites, rigidly fixed in the housing and rotating with it. It has spiral grooves to improve the lubrication of the satellites;
Two bevel gears engaged with satellites and rigidly connected to the output shafts of the Differential (half shafts, CV joints, etc.). These gears are called semi-axial.
This type of Differential is also called symmetrical, as they equally distribute the torque between the wheels. This is because the planetary gear works like an equal arm and transmits only equal forces to the gears and wheels. As mentioned above, if one of the wheels has little grip, the torque on it is small, so a symmetrical Differential applies the same force to the other wheel. That is, if one of the wheels is slipping, it means that the traction force on the second wheel is insignificant, which negatively affects the patency. To improve it on cars, full or partial blocking of differentials is used, the degree of which is estimated by the blocking coefficient.
Blocking ratio
The blocking coefficient (Kb) is the ratio of the torque on the trailing wheel to the torque on the leading one. Its value for a symmetrical Differential is 1 (the torques on both wheels are equal), for Limited Slip Differentials Kb - 3-5.
The more Kb, the better the car's cross-country ability, but the worse the handling.
With a large blocking coefficient, the controllability and stability of the vehicle when driving on asphalt deteriorate. This is due to the fact that the moment on the lagging wheel is several times greater and it tries, as it were, to "push" the Car out of the turn. Or, in a more understandable language, there is understeer. In addition, tire wear increases due to partial slip, the load on the drive elements, efficiency decreases, which leads to an increase in fuel costs.
Fully locking differentials
They have a clutch rigidly connecting (blocking) the differential housing and the output shaft gear. The clutch drive can be mechanical, hydraulic or pneumatic, and the lock is controlled by the driver (locking the center differential on the VAZ-21213). After overcoming a difficult area, the driver must immediately turn off the lock, which requires additional attention from him. Otherwise, excessive loads will act on the tires and transmission. They can lead to breakage of the axle shafts or the Differential.
For mechanisms of increased friction - multi-disk Differentials, viscous couplings, Differentials "Kvayf" and "Torsen" blocking (partial) is carried out automatically, without the participation of the driver.
Multi-Disc Differentials
Its main difference from the symmetrical Differential is the presence of a spring-loaded package of friction discs, one of which is rigidly connected to the housing, and the other to the side gears.
At different wheel speeds, the side gears of the Differential rotate faster or slower than the housing. Due to this, friction forces arise between the friction discs, which prevent the free rotation of the gears, that is, they partially lock. Accordingly, on the lagging wheel, the torque and traction force increase.
A similar effect can be achieved by slightly tightening the handbrake on rear-wheel drive vehicles.
Friction discs in some designs are not spring-loaded, but compressed by fluid pressure generated by the pump. For example, one of these designs is called the "gerotor differential" (from the English. Gear - gear). It has a gear pump that creates fluid pressure at different speeds of rotation of the side gears of the housing.
Differential "Kwaif"
The design of the mechanism, registered under Trademark (trademark)"Quaife" (Quaife). His satellites are arranged in two rows parallel to the axis of rotation of the body. Moreover, they are not mounted on axes, but are located in the openings of the body closed at both ends. The right row of satellites engages with the right side gear, the left row with the left one. In addition, satellites from different rows are engaged with each other in pairs. All gears have helical teeth.
When one of the wheels begins to lag behind, the semi-axial gear associated with it begins to rotate more slowly than the body and turn the satellite that engages with it. It transmits the movement to the satellite associated with it from another row, and that, in turn, to the semi-axial gear. This ensures different wheel speeds when cornering. Due to the difference in torques on the wheels in the screw engagement, axial and radial forces arise, pressing the side gears and satellites with their ends to the housing. The latter are also pressed by the tops of the teeth to the surface of the holes in which they are located. Due to this, forces arise that perform partial blocking, which increases the traction force on the lagging wheel and, accordingly, the total traction force of the vehicle, increasing its cross-country ability.
The value of the blocking coefficient depends on the angle of inclination of the teeth of the satellites and side gears. By installing sets of satellites and gears with different tooth inclination into the housing, the blocking coefficient is changed depending on the characteristics of the vehicle and the conditions of its use.
Differential "Thorsen"
They got their name from English. Torque - torque and sensitive - sensitive, that is, sensitive to torque. Movements manufactured under this Trademark (trademark) have two types of structures.
The first one is shown in Fig.8. The satellites are located in the housing perpendicular to its axis and are connected to each other in pairs by means of a spur gear, and are connected to the side gears by a worm gear.
At the turn, the side gear associated with the lagging wheel turns the satellite that engages with it, which, in turn, rotates the second satellite and the other side gear. Such a "chain" of the wheels of the car provides the ability to rotate at different speeds. The friction forces arising in the worm gear from the difference in the moments on the wheels carry out a partial blocking of the Differential.
The use of sets of satellites and gears with different worm gear profiles makes it possible to change the blocking coefficient. The disadvantage of this option is the complexity of the design and assembly.
The second type of "Torsen" is shown in Figure 9. The satellites are located parallel to the axis of the Differential body in its holes and are connected in pairs to each other and to the side gears by screw engagement. The operation of the mechanism on corners and partial blocking are carried out in the same way as in the Quaif. This version of the design is less complicated, in addition, it allows to reduce the diameter of the Differential housing.
Here is what those for whom they were created write about the use of such structures (Excerpts from an article by Ivan Evdokimov, 4x4 club, June No. 6, 2003):
"There are different ways to block Differentials, but basically blockages are divided into two large groups: Differentials that are hard to block, 100% (the so-called lockers, from the English locker - "lock"), and Limited Slip Differentials (in the English version - " Limited Slip, or LSD - Limited Slip Differential). Each of these options has its own advantages and disadvantages. The main disadvantage of "hard" locks is their amazing ability to destroy the transmission.
As for Limited Slip Differentials, their main drawback is the lack of 100% blocking of the Differential and, accordingly, the lack of torque transferred to the loaded wheel. Plus increased Depreciation of such mechanisms."
"... Two high-slip locking mechanisms for UAZ gear axles were handed over to us for testing: one of the Torsen type, the second of the Quief type. The mechanisms were developed and adapted for gear axles Ulyanovsk SUV engineer I. A. Plakhotin of the UAZ Automobile Preparation Section of Automobile Plant No. 40 together with organization SVR Convertions. By the way, even before the editorial test, these devices have passed development tests on UAZ vehicles that took part in heavy trophy raids. Well, let's see how this economy works? For comparison, two "UAZ" were taken: one with the usual "open" Differentials, and the second - with a Quief-type Differential in the front axle and a Torsen-type Differential in the rear.
My first thought was that the self-locking mechanisms in the axles should have a noticeable effect on the car's handling (especially on the turning radius). I sit behind the wheel of a car without blocking, perform several "eights" on the paved area, and immediately - behind the wheel of a "blocked" car. I repeat the exercise - and, surprisingly, no difference. And now the same thing, but smarter. Again, no effect ... I do the "rearrangement" alternately on one machine, then on the other - I don't feel the difference. And only when turning in the "extreme" mode, the effort on the steering wheel slightly increased, but at the same time, the maneuver itself on the "blocked" car turned out to be faster.
“On a dry dirt road on the road to our traditional training ground, the blocking action did not manifest itself in any way. However, when crossing the first ditch diagonally, the “blocked” car immediately showed its advantage (A car with conventional differentials overcame the ditch, desperately slipping). with self-locking Differentials, I overcame it without straining, on the first try, and the usual one - only with acceleration ... We leave for a clay track. Of course, the UAZ with gear axles on such obstacles and without blocking goes very well. Until it starts to cling to bridges for the ground or until you try to get out of this very rut ... So, the UAZ with the locking mechanisms in the interwheel Differentials not only rides better - it moves calmly where the car without locks is already starting to stop and skid.
“The work of both the Quif and the Torsen is very interesting when hanging diagonally. If you fix the car in the “classic diagonal” position, then at first nothing happens (the hung wheels rotate slowly and helplessly), but it’s worth gradually increasing the engine speed, how the car begins to twitch noticeably at first, and then, with an increase in speed, smoothly moves away. From the differentials, sounds of a characteristic low tone are heard from the differentials. Obstacles of the "trial" type showed the complete superiority of "blocked" bridges over ordinary ones. I still wanted to find a position in which the degree of blocking of the Differentials was not enough.To do this, I had to rest the right front wheel against a large earthen mound (left front wheel was in the pit, and the right rear on a bump). The car is up! Wheels rowed helplessly diagonally, Differentials howled like wounded animals, and the SUV did not move ... "I'll try a little sharper," I thought. I release the accelerator pedal, then abruptly push it down, and - lo and behold! - a jerk, the machine flies over a seemingly impregnable hillock ... "
The most interesting thing is that such mechanisms have long been used for road cars. Firstly, such a device greatly increases the vehicle's cross-country ability in difficult conditions. Especially rear-wheel drive when driving on slippery surfaces.
Secondly, the use of a partial lock can come in handy when racing in winter conditions or on gravel roads, where it is very important to use even a small grip during acceleration.
So we got to the main topic of this article, namely, the use of such a Differential in Moskvich.
I have long met information on the Internet that some of the tuning companies offer own developments these Differentials for advantage V. One of my favorite and respected magazines "Behind the wheel" at one time even arranged a test of two nines, one of which was loaded with LSD.
The conclusion was something like this: for virgin snow and front-wheel drive, the cross-country ability practically did not change. But on ice, the nine with LSD went through slippery sections much faster and the control was more pleasant.
The benefit of such a modification is also evidenced by the fact that such mechanisms were also used in rally cars at allied competitions.
I learned about their existence in Muscovites by chance - from the mechanic of our Minsk ambulance;).
Ten years ago they were given the Political Party of bridges equipped with such Differentials. They were put on sanitary IZH heels. The cross-country ability of such cars was then comparable only with the kings of dirt - UAZs.
The wheel, hidden by 2/3 in deep snow, icy track, mud and deep puddles - all this was just a minor nuisance on the way of IZhakov.
I was very interested in who made such diffs. The answer was found on the Internet - the famous Omsk plant of gearboxes and reducers. I don’t know how they are doing now, the plant does not have a website, but some Sellers have such a position in their price lists.
Therefore, I began to intensively search for ends where you can at least find out something about where you can get LSD for Moskvich.
Having bypassed most of the familiar zhelezyachnikov and Muscovite disassemblers, I found what I was looking for. One of them just had the diff I needed lying around. Gearbox is in near perfect condition.
In the automotive industry, the differential is one of the key parts of the transmission. First of all, it serves to transfer rotation from the gearbox to the wheels of the drive axle. Why is a differential needed for this? In any turn, the path of a wheel of an axle moving along the short (inner) radius is less than the path of another wheel of the same axle that is traveling along the long (outer) radius. As a result of this, the angular velocity of rotation of the inner wheel must be less than the angular velocity of rotation of the outer wheel. In the case of a non-driving axle, this condition is quite simple to fulfill, since both wheels are not connected to each other and rotate independently. But if the axle is leading, then it is necessary to transmit rotation simultaneously to both wheels (if rotation is transmitted to only one wheel, then traction properties vehicle and its handling will be unacceptable). If the wheels of the drive axle are rigidly connected and the rotation is transferred to a single axis of both wheels, the Car will not be able to turn normally, since the wheels, having equal angular velocity, will tend to go the same way in the turn. The differential allows you to solve this problem: it transmits rotation to the separate axles of both wheels (half shafts) through its planetary mechanism with any ratio of the angular speeds of rotation of the semi-axes. As a result, the Vehicle can move normally and handle well both on a straight path and in a turn. Scheme of the Differential and planetary mechanism in the picture on the right. However, the design of the planetary gear has a very unpleasant property: the planetary gear tends to transfer the rotation received from the Differential cup to where it is easier. For example, if both wheels of an axle have the same traction and the force required to spin each wheel is the same, the differential will distribute the rotation evenly between the wheels. But as soon as there is a noticeable Difference in the grip of the wheels with the road (for example, one wheel hit the ice, and the other remained on the asphalt), the Differential will immediately begin to redistribute the rotation to the wheel, the force for which is the least (that is, to the one that is on ice). As a result, the wheel on the asphalt will stop receiving rotation and stop, and the wheel on the ice will receive all the rotation from the Differential. Why and how does this happen?
The fact is that the planetary mechanism transmits rotation to the gears of the axle shafts through satellites. The satellite transmits equal torque simultaneously to two axle shafts, as it is a lever with equal arms relative to its own axis of rotation, through which the satellite receives traction. When driving in a straight line with good road grip on both wheels, the satellites do not rotate around their axis and transmit maximum torque from the Differential cup to the axle shaft. The differential cup, planetary gear and axle shafts rotate with equal angular speed as a whole. When the car turns, the satellites begin to turn around their axis, actuating the planetary mechanism and providing the difference in the angular speeds of the axle shafts, however, they continue to transmit the optimal torque to both axle shafts, since the road grip of both wheels remains high. As soon as one of the wheels begins to lose traction, the force required to rotate it immediately decreases and the torque on its axle shaft drops. Since the satellites transmit equal torque to the axle shafts of both wheels, the torque drops on the axle shaft of the wheel with good road grip, as well as on the Differential cup, and on the entire transmission as a whole. In this situation, the reduced torque is no longer enough to rotate a wheel with good road grip, but it is quite enough to rotate a wheel with poor road grip, which continues to rotate (slip) due to the axial rotation of the satellites. At the same time, the planetary mechanism acts as a gearbox that increases the angular speed of rotation of the slipping wheel. As a result, the wheel with good road grip stops (as does the Car), and the spinning wheel rotates at twice the angular speed relative to the angular speed of the Differential cup. The engine is running almost without load, as the total force (torque) on the entire transmission has fallen.
In all-wheel drive vehicles, the Differential is usually equipped with two axles, and often the Differential can also be found between the axles (center Differential). Thus, we get a transmission scheme in which there are as many as three Differentials: two bridge and one center. The latter is necessary for constant movement with all-wheel drive and transmission of rotation to all four wheels, since in a turn, the wheels of the steering front axle have completely different angular speeds than the wheels of the rear axle. The center differential is designed to transmit rotation from the gearbox to both drive axles with a different ratio of angular speeds. This scheme with three Differentials is one of the most common schemes for permanent all-wheel drive (Full time 4WD). However, this is a topic for another section. In this section, we are interested in the Differential and its properties. Returning to the problematic property of the planetary mechanism described above, it is interesting to consider the situation when an all-wheel drive Car with an inter-axle differential on one of the four wheels hit the same ice (or slippery pit). What will happen then? The differential of the bridge, the wheel of which is on the ice, will give all the received rotation to this wheel. The Center Differential, in turn, also seeks to transfer rotation to where it is easier. Naturally, it is easier for the Center Differential to rotate an axle with a wheel spinning on ice than an axle whose wheels have good grip and can move the Car. As a result, the torque in the entire transmission will drop, and the rotation will be transmitted to the only wheel on the ice, since this torque will not be enough to rotate the three wheels with good grip. As a result: of the four driving wheels, only one remains, which is slipping on ice - the all-wheel drive Car is “stuck”.
It is quite clear that the property of the Differential to always distribute the resulting torque equally between the axles (50/50), greatly impairs the car's patency and controllability. Since in order to continue driving the car in the situations discussed above, it is necessary to transfer more torque to the wheels with the best road grip. How to force the Differentials to redistribute torque in favor of such wheels? For this, they have developed various ways partial and full, manual and automatic blocking of Differentials, which will be discussed below.
Speed Sensitive Lsd. Automatic locking using Viscous coupling as "Slip Limiter".
In this case, one of the axle shafts with a Differential cup is locked. The viscous coupling is mounted tolerably half-axle in such a way that one of its drives is rigidly attached to the Differential cup, and the other to the half-axle. During normal movement, the angular speeds of rotation of the cup and axle shaft are the same, or slightly different (in turn). Accordingly, the working planes of the viscous coupling have the same small discrepancy in angular velocities and the coupling remains open. As soon as one of the axes begins to receive a higher angular velocity of rotation relative to the other, friction appears in the viscous coupling and it begins to block. Moreover, the greater the Difference in speeds, the stronger the friction inside the viscous coupling and the degree of its blocking, and hence the degree of blocking of the Differential. Due to the obtained frictional moment between the Differential cup and the axle shaft, the Differential redistributes the torque in favor of the axle with the best road grip (lagging axle shaft). As the degree of blocking of the viscous coupling increases and the angular velocities of the cup and half shaft equalize, the friction inside the viscous coupling begins to fall, which leads to a smooth opening of the viscous coupling and to the disengagement of the blocking. This scheme is used for center differentials, since its design is too massive for installation on a bridge gearbox. Such a locking mechanism is well suited for use in poor road conditions, however, in real off-road conditions, its abilities are far from outstanding: the viscous coupling cannot cope with constant changes in the state of adhesion of bridges to the ground, it is late when turned on, overheats and fails. This type of center differential lock can be found both as the main and only means of locking on “parquet” SUVs: Toyota Rav4, Lexus RX300, etc., and as an additional lock (in addition to 100% forced lock) on full-size Toyota Land Cruiser SUVs
Gerotor Differential (Gerodisk or Hydra-lock)
American Organization ASHA Corp. equipped the classic Differential with a locking device consisting of an oil pump with a piston and a set of friction plates (friction block) installed between the Differential cup and the gear of one of the axle shafts. The principle of operation of this blocking is practically no different from the blocking discussed above using a viscous coupling. The oil pump is mounted coaxially to the axle shaft in such a way that its body is attached to the differential cup, and the injection rotor is attached to the axle shaft. If there is a difference in the angular velocities of the axle shaft and the Differential cup, the pump starts to pump oil onto the piston and squeeze the friction block, thereby blocking the gear of the axle shaft with the Differential cup. Due to the received friction moment, the Differential redistributes the torque to the lagging axle shaft (the axle shaft with the best grip). This design is called Gerodisk (Hydra-Lock) and is standardly installed on Chrysler SUVs. A detailed layout of the device can be seen by clicking on the picture. For almost all friction based differentials, it is necessary to apply special oil, which contains additives that ensure the normal operation of the friction blocks.
Torque Sensitive Lsd. Differentials with friction preload blocks.
The device of such Differentials is quite simple and fundamentally does not differ in any way from the device of a conventional open Differential. To create additional friction, sets of friction plate blocks (which are marked in the picture on the right with red dots) are added between the axle shafts and the Differential cup. That is why such Differentials are often referred to as "friction based LSD". Quite often, friction blocks are spring-loaded. When one of the axle shafts begins to run (wheel slip), the Differential redistributes the torque in favor of the lagging axle shaft due to the friction moment on the friction plates. This type of blocking has a very big drawback - under the influence of plate friction, the Differential prevents even a small difference in the angular speeds of the axle shafts (which is necessary in corners), which negatively affects the vehicle's handling, as well as cost tires and fuel. In this regard, the locking ratio of these Differentials is usually chosen small (otherwise, the Vehicle will have inadequate handling on the road). Nevertheless, for motorsport, models of such Differentials are produced with a rather high structural friction of the plates and, accordingly, a high blocking factor. In addition to the above drawbacks, one more can be distinguished - the service life of the friction blocks in such Differentials is short and over time, the friction blocks wear out, thereby reducing the differential blocking coefficient. For all friction based differentials, it is necessary to use a special oil that contains additives that ensure the normal operation of the friction blocks. These Differentials are standardly installed in the rear axle of many SUVs - Toyota 4Runner (Hilux Surf), Toyota Land Cruiser, Nissan Terrano, Kia Sportage and so on.
Self-locking differentials with hypoid (worm or helical) and helical gearing.
This is one of the most interesting, effective, technological and practical forms of differential locking. The principle of operation is based on the property of a hypoid or helical pair to "wedged". In this regard, the main (or all) gears in such Differentials are helical or hypoid. There are not so many varieties of designs - three main types can be distinguished.
First type produces Organization Zexel Torsen. (T-1) Hypoid pairs are the drive axle gears and pinion gears. Moreover, each axle shaft has its own satellites, which are paired with the satellites of the opposite axle shaft by the usual spur gearing. It should be noted that the axis of the satellite is perpendicular to the semiaxis. During normal movement and equality of the torques transmitted to the axle shafts, the hypoid pairs "satellite / drive gear" are either stopped or rotated, providing the difference in the angular velocities of the axle shafts in the turn. As soon as one of the axle shafts begins to slip and the torque on it drops, the hypoid axle/satellite pairs begin to rotate and wedged, creating friction with the Differential cup and with each other, which leads to partial blocking of the Differential. Due to the moment of friction, the differential redistributes the torque in favor of the lagging axle shaft. This design works in the largest torque distribution range - from 2.5/1 to 5.0/1. The operating range is regulated by the angle of inclination of the teeth of the worm.
Author second Type is an Englishman Rod Quaife. In this Differential, helical gears of semiaxes and helical gears of satellites are used. The axes of the satellites are parallel to the semiaxes. The satellites are located in the original pockets of the Differential cup. At the same time, paired satellites do not have spur gearing, but form between themselves another hypoid pair, which, when wedged, also participates in process blocking. A similar device has the Differential True Trac Organization Tractech. Even in our Russian Federation, the production of similar Differentials under domestic cars UAZ, etc. And here is the Organization Zexel Torsen in its Differential, the T-2 offered a slightly different layout for essentially the same device (pictured right). Due to their unusual design, the paired satellites are connected to each other from the outside by sun gears. Compared to the first type, these Differentials have a smaller blocking ratio, but they are more sensitive to the Torque Difference and operate earlier (starting from 1.4/1). Organization Tractech recently released axle torque sensitive differential electrac, equipped with a forced electric lock.
Third type produced by the Organization Zexel Torsen(T-3) and is used mainly for center differentials. As in the second type, this Differential uses helical gears of semiaxes and helical gears of satellites. The axes of the satellites are parallel to the semiaxes. The planetary structure of the design allows you to shift the nominal torque distribution in favor of one of the axles. For example, the T-3 differential used on the 4th generation 4Runner has a nominal torque distribution of 40/60 in favor of the rear axle. Accordingly, the entire range of Partial Blocking Operation is shifted: from (front/rear) 53/47 to 29/71. In general, the offset of the nominal torque distribution between the axles is possible in the range from 65/35 to 35/65. The operation of partial blocking provides 20-30% redistribution of the moments transmitted on the axle shaft. Also, the similar structure of the Differential makes it compact, which in turn simplifies the design and improves the layout of the transfer case.
The above differentials are very popular in motorsport. Moreover, many manufacturers install such Differentials on their models regularly, both as inter-axle and inter-wheel Differentials. For example, Toyota installs such Differentials on both passenger cars (Supra, Celica, Rav4, Lexus IS300, RX300, etc.) and SUVs (4Runner (Hilux Surf), Land-Cruiser, Mega-Cruiser, Lexus GX470) and buses (Coaster Mini-Bus). These differentials do not require the use of special oil additives (unlike friction-based differentials), but it is better to use a quality oil for loaded hypoid gears.
Management of the Differentials with the help of electronic brake force control systems (Traction Control, etc.)
IN modern automotive industry more and more electronic vehicle control systems are being used. It is already rare to find Cars that are not equipped with an ABS system (which prevents the wheels from locking when braking). Moreover, since the end of the 80s of the last century, leading manufacturers began to equip their flagship models with traction control and wheel adhesion control systems - Traction Control. For example, Toyota installed Traction Control on the Lexus LS400 in 1989 (90). The principle of operation of such a system is simple: universal (they also serve ABS) rotation sensors installed on the controlled wheels detect the start of slipping of one wheel of the axle relative to the other, and the system automatically brakes the wheel that has slipped, thereby increasing the load on it and forcing the differential to equivalently increase the torque by wheel with good road grip. With a strong slip, the system can also limit the supply of fuel to the cylinders. The operation of such a system is very effective, especially on rear-wheel drive vehicles. As a rule, such a system can be forcibly deactivated with a button on the dashboard. Over time, the electronic brake force control system has been improved and more and more new features have been added to it, working along with ABS and TRAC. (e.g. steering wheel release differential control for more successful completion turns). All manufacturers named these functions differently, but the meaning remained the same. And so, these systems began to be installed on all-wheel drive Cars and SUVs, and in some cases they are the only means of controlling traction and redistributing torque between axles and wheels (Mercedes ML, bmw X5). If the SUV is equipped with more serious means of torque distribution (slip differentials and hard locks), then the electronic brake force control system very successfully complements these tools. A good example of this is excellent handling and cross-country ability of the latest generation of Toyota SUVs 4Runner (Hilux Surf), Prado, Lexus GX470. Being representatives of the same platform, they have a Torsen T-3 center differential with the ability to hard lock, as well as an electronic brake force and traction control system with many functions to help the driver drive the car.
Differentials, self-locking from the difference in speeds. Work Based Friction Forces:
English name: Friction Based Traction Adding Devices (FBTAD) or limited Slip Differential (LSD).
Limited slip differential. Commonly used friction discs, cones or gears to reduce mutual wheel slip. Do not block Differential by 100%.
Produced Differentials:
Eaton Limited Slip Differential
Auburn (cone principle)
Vari-Lok Organizations Dana
Traction Equalizer Meritor Organization (formerly Rockwell International)
LSD Organizations KAAZ
As well as various car companies only for their Cars.
Mechanical, mixed type and others:
English name: Speed Sensing Traction Adding Devices (SSTAD) or Automatic Locking.
Operating principle:
a) mechanical.
Differential with automatic blocking (English: Locker). Cam clutches are used as the locking mechanism. When mutual slippage of the wheels occurs, the Differential is automatically blocked at 100%.
Produced Differentials:
Lock-Right Organizations PowerTrax, Detroit Locker, Detroit soft locker, Detroit EZ-Locker TracTech Organizations, Gov-Lock Eaton Organizations (all GM Vehicles) - both friction discs and gears are used in the design
b) silicone fluid (viscous coupling);
V) wheel speed sensors and brakes. Usage example: ML-320 Mercedes Organization.
Differentials, self-locking from the difference in torque
English name: Torque Sensing Traction Adding Devices (TSTAD).
Operating principle: worm gears. Invented by the Gleason Organization in the 50s. Do not block Differential by 100%.
Produced Differentials: TorSen, TrueTrac, Quaife, Powr-Trak
Manually lockable differentials
English name: Manual Operated Traction Adding Devices (MOTAD)
Operating principle: compressed air, solenoid, electric motor.
Differential with manual, that is, forced , locking (English: Manual Locking). Cam clutches are used as the locking mechanism. When the button is turned on, the differential is blocked by 100%.
Produced Differentials:
ARB Air Locker (for almost all brands),
KAM Axle Differential Locker (for Land Rover and Suzuki). Activated by compressed air or cable
Vacuum Differential Locking Unit Jack McNamara Differential Specialist Pty. Ltd. (for Land Rover and Toyota). Turned on by vacuum
Ox Locker OX TRAX, INC. Turns on with a cable
Lockable Differential with electric drive TracTech Companies
K&S Vacuum Locker
Tochigi Fuji Sangyo Locking Differential. Installed on Jeep Rubicon
And also automobile Companies only for their Cars (Mercedes, Toyota, Mitsubishi)
What locks are there for Jeep Cherokee and Grand Cherokee axles?
|
front axle |
rear axle |
||
|
power Locker (LSD) |
|||
Note:
On Cherokee (some models) they installed the rear axle of the DANA-44 model (equipment - tow package).
On the Cherokee since 1995 (but occasionally found on earlier models), they began to install the Chrysler 8.25 bridge. Two varieties: with 27 and 29 splines at the ends of the axle shafts. For a model with 27 splines, everything that goes for DANA-30 and 35 bridges is suitable. With a model with 29 splines, everything is more complicated: the AMC-20 bridge (CJ of the 80s) also has 29 splines and you can use this using ingenuity.
The Grand Cherokee optionally comes with DANA-44 (with an aluminum case), which does not perform very well under heavy loads (weak and "likes" to burst, bends under heavy loads).
Many who were going to buy an SUV, when choosing a certain model, of course, could come across the term “differential lock”. But what is it? Like this? And what is the principle of operation and the need for this very differential? As practice shows, not all future potential "jeep drivers" know.
In this article, we will talk about what is a differential And why is he in the car. What varieties does it come in and on which cars is it intended to be installed?
History of the differential
The appearance of the differential in the automotive world was not long in coming. Only a few years later, after the first cars with an internal combustion engine (ICE) began to roll off the assembly line. For a long time, things were not as sweet as they are now, and the first automobile samples that worked with the help of an engine were very poorly controlled.
Wheels located on the same axis rotated at the same angular speed during the turn, and this already led to the fact that the wheel running along the outer diameter was slipping heavily. We solved this problem quite simply: by borrowing the differential from steam carts.
This mechanism was invented in France in 1828 engineer Oliver Pekke-Rom. It was a device that consisted of shafts and gears. Through it, the torque from the internal combustion engine was transmitted to the drive wheels. But another bad luck happened - the wheels began to slip, which lost traction with the road surface. Often this manifested itself while driving on a road with icy areas.
The wheel, which was on the ice, rotated at a higher speed than the wheel, which remained on a surface more suitable for movement. This led to a skid. After the designers began to think about how to adjust the differential so that the wheels rotate at the same speed in order to prevent the appearance of drifts.
The first person to experiment on a differential with minimal slip was none other than Ferdinand Porsche. It took at least three years. They were equipped with the first models of cars of the brand. In the following decades, engineers developed various types of differentials, which we will tell you about next.
Principle of operation and device
Let's perhaps start with the type of differential that is the easiest to consider, the open differential. We'll start with the simplest type of differential, called an open differential. So, The design of the differential includes the following parts:
- Drive shaft. Its task is to transmit torque. The shaft leads it from the transmission to the very beginning of the differential.
- Drive shaft drive gear. Gear in the form of a helical cone, necessary for coupling differential mechanisms.
- Ring gear. An element that is driven. It also has the shape of a cone and is rotated by a drive gear. The system of the driving and driven gears together is called the final drive. It serves as the final step in reducing the speed of rotation that eventually reaches the wheels. The drive gear is much smaller in size than the crown gear., therefore, to carry out one revolution of the slave, the first one needs to make more than one revolution around its axis.
- Half shaft gears. Are last frontier transmission of rotation of the drive shaft to the wheels.
- Satellites is a planetary mechanism that key role in providing different angular speeds of the wheels when making a turn.
When you move in a straight line on your car, the entire differential mechanism rotates at the same speed: the input shaft rotates at the same speed as the axle shafts, respectively, the wheels themselves rotate at the same speed. But as soon as you turn the steering wheel, the situation instantly changes radically. The main players now satellites protrude, which are unlocked under the influence of the difference in loads on the wheels when, for example, one wheel starts to slip and therefore moves faster.
All the power of the motor passes directly through them. And as a result of the fact that the satellites are two gears that are independent, then there is a transfer of different speeds of rotation to two semi-axes. But the power is not divided equally, and is transmitted to the wheel that is moving at the outer edge of the car's turn. Consequently, it begins to spin much faster due to the quantitative addition of revolutions. And the difference in the distribution of power between the wheels is the greater, the smaller the turning radius of the car, that is, the more you turn the steering wheel.
What is a differential lock and how does it work?
Differential lock is one of the most effective ways to improve off-road performance car. Any car that is intended directly or indirectly for off-road is equipped with a mechanism at the factory that locks the center differential. Also, cars are equipped with mechanisms that block the front and rear axles.
blocking this mechanism Like any technological solution, it has its advantages and disadvantages. To understand when it is necessary to use differential locks, and which cases simply prohibit its use, you need to understand the principles on which its operation is based.
Try to make a long jump from a place in the winter snowy time. Yeah. But it doesn’t work, and all because one of your feet was on a slippery icy surface, and the other on dry pavement. Because of this, it was not possible to make a championship jump. One leg slipped out from under you, and the brain did not orient itself in time and did not give the command to put all the force to push into the other leg. The result of this experiment is quite funny and comical: your legs parted and you almost collapsed on the fifth point.
So what to do in this case, so that both legs have the opportunity to perfectly push off the ground? And everything is very, very simple. You just need to turn two pushing legs into one, tying them firmly together with a strong belt or harness. Now they will work as one unit and will use the maximum push force from one stable ground with good grip. A similar process occurs in the car at the moment of interaction of its driving wheels with the road.
Let's imagine a situation in which a rear wheel drive car stops randomly so that its left wheel is on a slippery surface and its right wheel is on asphalt. As you know, standard low friction center differential, which is located on rear axle vehicle, always provides the wheels with equal circumferential force. The left wheel, which is on ice, is not able to move from a slippery surface with great effort due to lack of traction.
And because of this, the differential is not able to provide him with a huge effort, since this is simply impossible physically. And in this case a similar force will be applied to the wheel which is located on the asphalt surface. It will even out the forces that are distributed between the wheels, focusing on the left wheel.
As a result, the car will move with slipping, but slowly. His wheels will not be able to use enough force to push, which would be necessary for the adhesion of the right wheel, which under the given conditions will be neither more nor less, but as much as seven times greater than that of the left. Due to this property of distributing tractive force equally, the right wheel will only use a seventh of its traction capacity. To put it simply, the push could have happened seven times more powerful, but the differential was not brought to it. enough strength to carry out this maneuver.
Therefore, it is necessary to implement such a connection between the wheels to ensure joint rotation or slipping, as if it were a single wheel. To solve this problem, a special mechanism is used that blocks the rotation of the differential gears and connects the two wheels to each other by a conditional rigid connection with constant rotation and the same speed. Such a mechanism is called a "differential locking (disconnecting) mechanism", or in the common people - a lock.
A differential that is locked is not able to equalize the inter-wheel force, thereby making them connected by a single axle. As a result, each wheel receives the maximum possible force, which is necessary for the best grip of the wheels. Therefore, where the grip of the wheels with the road surface is better, more force will be applied there.
What are the differentials
The basis of the differential is planetary reductor. The type of gear that is used can conditionally divide the differential into three type:
- Worm;
Cylindrical;
Conical.
The worm differential is the most versatile and is installed both between the axles and between the wheels. The cylindrical type is often located in SUVs between the axles. The conical type is mainly used as a cross-axle differential.
Allocate the same symmetric And asymmetrical differentials. The asymmetric differential design is installed in all-wheel drive vehicles between the axles, distributing torque in various proportions. The symmetrical type transmits equal torque to the axle between the two wheels. Differentials are also divided according to the type of blocking:manual lock and electronic lock.
Manual differential lock
Based on the name, the axle differential lock is activated at the initiative of the driver by pressing a button or switching a certain toggle switch. In this case, the satellite gears are blocked, as a result of which the drive wheels begin to rotate at the same speed. Often, SUVs are equipped with a manual differential lock. It is recommended to turn it on to overcome difficult off-road conditions, and turn it off when entering a regular asphalt road.
Electronic or automatic differential lock
Automatic differential locking is carried out by commands of the electronic control unit, which analyzes the state in which the road surface is located, using ABS and ESP. The ECU then blocks the satellite gears on its own. According to the degree of blocking, this device can be conditionally divided into a differential with full and partial blocking.
Full differential lock
The inclusion of such a lock implies the fact that the satellite gears stop completely, and the mechanism takes on the functions of a conventional clutch, thereby transmitting an equal torque to the two axle shafts. As a result, both wheels rotate at the same angular speed. If it happens that at least one wheel loses grip, then the torque from it is fully transferred to the other wheel, which remains to force off-road. Such a differential device has been successfully implemented on Toyota Land Cruiser, Mercedes-Benz G-Class and others.
Partial differential lock
Engaging this lock does not completely stop the satellite gears, but allows them to slip. This effect is available thanks to self-locking differentials. Depending on the type of operation of this mechanism, it is divided into two kinds: Speed sensitive(activated when a difference in the angular speeds of rotation of the semiaxes is noticed) and Torque sensitive(activated in case of a decrease in the torque of one axle shaft). This type of operation of the differential device can be found on SUVs Mitsubishi Pajero, Audi Q-series and BMW X-series.
Differential group Speed sensitive differs in structure. One of these mechanisms is the one in which the viscous coupling performs the differential function. The viscous coupling differs from the friction differential in its lower reliability. It is because of this that it has a place to be installed on cars that are not designed to overcome impassable wilds and deep fords or on cars with a sporty character.
Another mechanism representing the Speed sensitive group is called the gerotor differential. The role of blocking elements is played here oil pump and friction plates mounted between the differential housing and the satellite gears of the axle shafts. Although according to the principle of operation, it is similar to a viscous coupling.
Differentials that belong to the group Torque sensitive are also different in their design. For example, there is a mechanism using a friction differential. Its peculiarity lies in the difference in the angular velocities of the wheels in turns and when moving in a straight line. When the car is moving in a straight line, the angular speed of rotation of both wheels is the same, and during cornering, the torque for the wheels is different.
Another type of differentials - with hypoid and helical gearing. They are subdivided into three groups.
First – with hypoid gear
Here, each axle shaft has its own satellite gears. They are attached to each other by spur gearing, located perpendicular to each other. In the event of a difference in the angular velocities of the driving wheels, the gears of the semi-axes are wedged. As a result, the gears rub against the differential housing. The differential is partially blocked and the torque is redistributed to the axle, with a lower speed of angular rotation. After equalizing the semi-axial speeds, the blocking is deactivated.
Second – with helical gearing
Similar to the first, but the location of the satellite gears is parallel to the axle shafts. These units are attached to each other by helical gearing. The satellites of this mechanism are mounted in special niches on the differential housing. When there is a difference in the angular speed of the wheel rotation, the gears wedged and mate with the gears that are in the niches of the differential housing. There is a partial blockage. The direction of the torque is determined on the axis with a lower rotational speed.
Third – with helical gears of semiaxes and helical gears of satellites
Used in center differentials. The principle is the same - shifting torque to an axle with less rotation. The displacement range of this species is quite large - from 65/35 to 35/65. When the angular speed of the wheel rotation of both axles is stabilized and equalized, the differential is unlocked. These differential groups are widely used in the automotive industry on both conventional and sports models.
Advantages and disadvantages of differential locks
+ the possibility of wheel blocking up to 70%;
Minimum maintenance;
No jerks on the steering wheel;
The gearbox does not require pouring special oil;
Installation does not entail any difficulties;
Ensuring the best off-road vehicle performance;
Longer life of the structure;
Better car handling;
Ability to corner at higher speeds;
The car is easier to get out of a skid.
Over time, the preload drops;
It is required to replace the adjusting elements every 40 thousand kilometers for better design performance;
Not timely or late adjustment work cause the system to not work correctly.
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The differential in a car works to accomplish the following three tasks:
- The differential transfers the power of the engine to the wheels of the car.
- Takes the last step in reducing the number of revolutions to the wheels (we remember that the gearbox takes the first such step) and, therefore, increasing the torque transmitted to the same drive wheels.
- By transferring power to the drive wheels (always an even number of wheels on the same axle: either two or all four), the differential allows each of them to spin at different speeds (which is exactly what the differential gets its name from).
In this article, you will learn why your car needs different wheel speeds, how it is provided, what a differential is, how a differential works and what are its main disadvantages. We will also look at several of its types.
What is a differential for?
Car wheels rotate at different speeds, especially when turning. You can see in the animation below that each wheel travels a very different distance when the car turns, and that the inside wheels travel a much shorter distance than the outside wheels. Since the speed is equal to the distance divided by the time required to travel that distance, it turns out that the wheels that travel the shorter distance turn at a lower speed: thus, when turning left, the left wheels will turn more slowly than the right ones, and vice versa. It should also be noted that the front wheels travel a different distance than the rear wheels travel.
Click to view animation
For cars with a drive on only one axle of the wheels - whether it be on the rear wheels or on the front - the difference in the rotation of the front wheels to the rear is not a problem. There is no connection between them, so they rotate independently. But the drive wheels are interconnected so that one engine and transmission must drive both wheels, while at different speeds of their rotation. But what if we have only one engine ?! If your vehicle is not equipped with a differential, the wheels must be locked together, being forced to spin at the same speed. This would make cornering maneuvers - even at small angles - difficult: in such cars, in order to be able to turn, one of the tires would necessarily have to slide, or the other would have to spin. And with modern tires and asphalt roads, this will require a lot of effort. This force will have to be transmitted through the axle from one wheel to the other, thus placing a very heavy burden on the axle components.
It is with this problem that the differential copes flawlessly.
What is a differential?
Differential is a device that splits the motor torque into two paths with outputs, allowing each output to rotate at a different speed.
The differential is available on all modern cars and trucks, as well as on many all-wheel drive vehicles. Moreover, all four-wheel drive cars must have a differential between each set of driving wheels on the same axle, and, in addition, they need a differential between pairs of front and rear wheels (remember the beginning of the article - because the front wheels travel a different distance, unlike the rear wheels when the vehicle is moving in a direction other than a straight line?).
However, some 4WD vehicles do not have a differential between the front and rear wheels, and instead, these pairs of wheels are tightly coupled so that the front and rear wheels must turn at the same speed. That is why manufacturers do not recommend driving on hard surfaces in all-wheel drive mode on such cars, but turning it on only off-road.
Now let's find out where the differential is usually located in the car, depending on the type of car drive:
How does a differential work?
We will start with the simplest type of differential, called open differential. But first we need to learn some terms - look at the figure below, you will find the main components of the differential operation there:
Thus, the differential consists of the following main parts:
- Drive shaft - transmits torque, leading it from the gearbox to the beginning of the differential
- The drive shaft drive gear is a small cone-shaped helical gear that is used to couple with the differential mechanism
- The ring gear is the driven gear, also in the shape of a cone, which is driven (rotated) by the drive gear. The driving and driven gears, taken together, are called final drive and it is they that serve as the last stage of the reduction in the speed of rotation, which will eventually reach the wheels (the ring gear is always smaller than the drive gear, which means that the drive gear will have to make many more revolutions while the driven gear makes only one revolution around itself).
- Axle gears are the last gears on the way to transfer rotation from the drive shaft to the wheels.
- Satellites are a planetary mechanism, which just plays a key role in ensuring the difference in wheel rotation when turning.
- Half shafts - shafts going from the differential directly to the wheels.
And now let's move on to the key and most important understanding of how the differential works, and look at the animations below, how the above components of an open differential work in two cases:
- When the car is driving straight.
- When the car is turning.
See for yourself - everything is quite simple:
Click on the "Turn" button to see how the differential works during a turn, and "Going straight" to see how its components move during a straight line
As we can see, when we drive straight in our car, in fact, the entire differential mechanism rotates at the same speed: the rotational speed of the input shaft is equal to the rotational speed of the axle shafts and, accordingly, the rotational speed of the wheels. But as soon as we turn the steering wheel a little, the situation changes, and the satellites now take on their main role, which are unlocked due to the difference in the load on the wheels (when one wheel tries to spin, spinning faster), and all the power from the engine now passes through them. And due to the fact that two satellites are two independent gears, it turns out that they transmit different speeds of rotation to the semi-axes, as if bifurcating it, but not dividing all the power equally, but transferring the most power to the wheel that moves along the outer edge in turning time of the car and, accordingly, spinning it more (increasing its number of revolutions). And the difference in the transmitted power is the stronger, the steeper the car turns (more precisely, the smaller the turning radius of this car).
What is the main disadvantage of the differential?
An open differential transfers rotation to one or another wheel in almost any ratio, including the ratio of 100% / 0% - when one of the drive wheels takes on all the torque. At the same time, the distribution of such rotation between the wheels occurs when the load on these wheels (and along with them on the axle shaft) changes - that is, a wheel with a lower load in a turn receives more rotation. But here lies one significant disadvantage, which takes place under certain conditions, namely, when both drive wheels are in mud, snow or ice, and the car starts to slip - in this case, the wheel that has less grip will receive the lion's share of rotation. Simply put, if you, for example, are stuck in the snow, sitting "on your belly" - when one wheel is engaged with the snow surface, and the second one hangs in the air at all, then just that wheel will receive power due to the appropriate distribution along the axle shafts of the differential, which is on weight, and it is it that will spin helplessly in the air. This problem is especially acute for SUVs and all-terrain vehicles.
What types of differentials are there?
The solution to these problems is limited slip differential(LSD, also called limited slip differential). Limited slip differentials use different mechanisms to ensure proper differential action under different riding conditions. When the wheel slips, this differential allows more torque to be transferred to the non-skid wheel.
On SUVs and all-terrain vehicles, differentials with manual disengagement are also used, which, however, are very often not protected from accidental disabling or disabling at the wrong time due to ignorance - the fact is that the ability to disengage the differential on the go entails its possible breakdown, and this common problem.
What is a viscous coupling (viscous coupling)?
Viscous coupling is most often found in all four-wheel drive vehicles. And, if you read an article about the principle of operation of a torque converter, then you should know that a viscous coupling has a similar scheme of operation. It is widely used to connect the rear wheels to the front wheels so that when one set of wheels begins to slip, the torque will be transferred to the other set, thus solving the problem of the slipping wheel described above.
A viscous clutch has two sets of plates inside a sealed housing that is filled with a viscous fluid (slightly more viscous than gear oil, for example). One set of plates is connected to each output shaft. Under normal conditions, both sets of plates and their portion of the viscous fluid move at the same speed. But when one axle tries to spin faster, perhaps because it is slipping, the many plates corresponding to that axle's wheels spin faster than the others. The viscous fluid between the plates tries to catch up with the faster disks, thereby leading the slow disks to the same. This transfers more torque to the slower spinning wheels, which are just not slipping.
Viscous coupling device
When the car turns, the difference in speed between the wheels on the same axle is not as great as when one of the wheels simply slips. The faster the plates rotate relative to each other, the more torque is applied to the clutch. The clutch does not prevent the coils from turning because the amount of torque transmitted during the turn is small.
A simple egg experiment will help explain the behavior of the viscous coupling. If you put an egg on the kitchen table, the shell, white and yolk will not move. But when you start spinning the egg, the eggshell will move at a higher speed than the white, and the white is a little faster, eating the yolk, but the yolk will then quickly catch up. By the way, to verify these words, conduct an experiment as soon as you have an egg: spin it fast enough, and then stop it, then just release the egg, and it will start to rotate again (well, or at least twitch in the direction of the previous rotation) . In this experiment, we used friction between the shell, white and yolk, applying force only to the shell. First, we actually untwisted the shell, and with some delay behind the shell, due to friction, the protein began to unwind, and then the yolk. And when we stopped the shell, that same friction - between the still moving yolk, white and shell - applied force to the shell, causing it to speed up. So in the case of a viscous coupling, the force is transferred between the liquid and the sets of plates in the same way as between the yolk, protein and shell.
What is a Torsen differential?
The Torsen differential is a purely mechanical device: it is not tied to any, as well as clutches or viscous fluids, and at its core is a fairly simple mechanism, very similar to an open differential.
Torsen works the same as open differential when the amount of torque between the two drive wheels is equal. But as soon as one of the wheels starts to lose traction, the difference in torque causes the gears in the Torsen differential to lock together.
Such a differential is often used in powerful and very powerful all-wheel drive vehicles. Like a viscous coupling, it is often used to transfer power between the front and rear wheels. And in this application, the Torsen differential outperforms viscous because it delivers torque to the wheels in a stable manner before slip actually begins. However, if one set of wheels loses traction completely, then the Torsen differential will not be able to transfer torque to the other set of wheels due to its design and how such a differential works.
This is what a modern Torsen differential looks like
By the way, almost all Hummer cars use a Torsen differential between the front and rear axles. That being said, the Hummer user manual offers a new solution to the problem of one wheel completely losing traction: press the brake pedal. By applying the brake, torque is applied to the wheels that are in the air, and then transferred to the wheels, which can pull the car out of the "porridge".
