1 Overview of drive axle

The automobile drive axle is an important part of the transmission system, which is generally located at the end of the transmission system. It is mainly composed of main reducer, differential, half shaft, axle housing and so on.

There are many types of drive axle arrangements, which can be divided into front drive, rear drive and four-wheel drive (that is, two drive axles) according to the different distribution positions. At present, the two widely used are front-engine front-wheel drive and front-engine rear-wheel drive. The front-engine front-wheel drive connects the drive axle and the gearbox as a whole, and the torque is directly input from the gearbox to the final reducer during transmission, eliminating the need for transmission. This makes the vehicle structure more compact, good ride comfort, and high fuel economy. The front-engine rear-wheel drive is a more traditional arrangement. Compared with the front-wheel drive, the driving wheels have greater adhesion to the ground. Therefore, this form is very suitable for climbing or accelerating start, and the driving stability of the car And good maneuverability. In addition, there are mid-engine rear-wheel drive, rear-engine rear-wheel drive, etc., but the scope of application is relatively small.

The function of the drive axle mainly has the following four points[1]:

① Decelerate and increase torque, change the direction of torque transmission. When the car is running, the transmission ratio is changed through the transmission, and the appropriate torque and speed are output. But when the transmission is in the highest gear, the output speed is higher, so the power needs to be processed by the final drive to reduce the speed and increase the torque. Secondly, the power output by the engine can only be transmitted to the wheels after 90° steering, so the final drive has the function of changing the direction of torque transmission.

②Meet the differential speed requirements of the left and right wheels, and distribute the torque reasonably. When a car is driving or turning on uneven roads, the outer wheels rotate fast and the inner wheels rotate slowly. In order to meet this requirement, the differential drives the side gears through the rotation of the planetary gears to achieve the differential effect. At the same time, the differential can also distribute the torque reasonably to improve the car's passability.

③Transmit torque. The drive axle is a power transmission mechanism, in which the role of the half shaft is to transmit the torque output by the differential to the driving wheels [2].

④ Carry the weight and transmission force of the whole vehicle. The axle housing in the drive axle has strong rigidity and strength. It bears the vertical force between the road surface and the frame, as well as the longitudinal force such as driving force and braking force, and the lateral force generated when the vehicle turns.

2 Analysis of the structure and principle of the differential

There are two main functions of the differential. One is to transfer the power from the main reducer to the left and right half shafts, and the other is to act as a differential to ensure that the wheels and the ground do pure rolling.

2.1 Structural analysis of bevel gear differential

The ordinary bevel gear differential is composed of 2 half-shaft gears, planetary gear shaft (cross shaft), 2-4 planetary gears and a housing. The power is transmitted in the order of main reduction driven gear-differential case-planetary gear shaft-planetary gear-side gear-side shaft-drive wheel. When the car turns right, the additional resistance acts on the planetary gears, and the resulting moment acts as a differential. Its rotation makes the peripheral speed of the left side of the planetary gear equal to the sum of the speed of rotation and turnover, and the right side is equal to the difference between the speed of rotation and turnover, which causes the speed of the left half shaft to increase and the speed of the right half shaft to slow down, ensuring that the car makes smooth cornering. [3].

The differential is a planetary gear mechanism. Due to the existence of axial force, there will always be serious wear of the differential in the actual use process, and mainly adhesive wear and fatigue wear, which seriously affects the differential. The work performance even affects the safety of the entire vehicle. Therefore, a flat gasket is installed between the side gear and the differential case, and a spherical gasket is installed between the planetary gear and the differential case. At the same time, a gasket with low roughness and high hardness should be selected to reduce The wear and tear of the differential can prolong the service life.

2.2 Principle analysis of bevel gear differential

2.2.1 Analysis of differential speed principle

The working principle of the bevel planetary gear differential is shown in Figure 1. ω0 is the speed of the driven gear of the main reducer. Since the differential case and the driven gear of the main reducer are fixedly connected together to form a planetary gear carrier, ω0 is both The speed of the differential case. ω1 and ω2 are the rotation speeds of the left and right side gears, respectively.

pagenumber_ebook=44,pagenumber_book=38

Figure 1 Working principle diagram of bevel gear differential

① The car drives in a straight line on a straight road.

The planetary gear drives the half-shaft gears together and revolves around the center line of the half-shaft without rotating motion. At this time, ω1=ω2=ω3, and the differential does not have a differential effect.

②Turning and other driving conditions of the car.

When the differential acts as a differential, the planetary gear not only revolves around the centerline of the semi-shaft, but also revolves around the planetary gear shaft. At this time, the peripheral speed of one side of the planetary gear is equal to the sum of the speed of rotation and the revolution, and the other side is equal to the difference between the speed of rotation and the revolution. Assuming that the rotation of the planetary gear is ω3, the rotation speed of the outer wheel and its semi-shaft will increase, and its rotation speed is:

pagenumber_ebook=45,pagenumber_book=39

The speed of the inner wheel and its half shaft will decrease, and its speed is:

pagenumber_ebook=45,pagenumber_book=39

z1 and z3 are the number of teeth of the outer side gear and planetary gear, respectively.

Add the above two formulas to get:

pagenumber_ebook=45,pagenumber_book=39

This is the motion characteristic equation of the bevel planetary gear differential [4].

2.2.2 Analysis of torque distribution characteristics

The torque is transmitted to the differential through the main reducer, and is proportionally distributed to the left and right driving wheels by the differential. In Figure 1, F indicates that the planetary gear receives the force of the cross shaft, and its direction points upward; the two sides of the planetary gear will receive the reaction force of F/2, and its direction points downward. ΔF represents the additional resistance due to the movement of the friction element.

① The car drives in a straight line on a straight road.

When the car is driving in a straight line on a flat road, the friction elements of the differential do not move relative to each other. The differential only receives the forces of F and F/2, and its forces are balanced, and the radii of the side gears are equal. Is r, so the torque transmitted to the left and right half shafts is equal. Input torque M0, output torque M1, M2 satisfy the following relationship.

pagenumber_ebook=45,pagenumber_book=39

②Turning and other driving conditions of the car.

When the car turns and other driving conditions, the planetary gear receives additional resistance ΔF and starts to rotate. Its rotation torque is 2ΔFr' (r' is the radius of the planetary gear). This torque makes the planetary gear apply the same magnitude to the left and right side gears. The force in the opposite direction is shown in Figure 1.

For the outer side axle gear, the rotation speed is faster and the torque is smaller.

pagenumber_ebook=45,pagenumber_book=39

For the inner side axle gear, the rotation speed is slower and the torque is larger.

pagenumber_ebook=45,pagenumber_book=39

M0, M1, and M2 satisfy the following relationship.

pagenumber_ebook=45,pagenumber_book=39

Since the internal friction of the ordinary conical planetary gear differential is not large, the torque transmitted to the left and right side gears can be regarded as approximately equal. This is the torque distribution characteristic of the ordinary conical planetary gear differential.

2.2.3 Analysis of mechanical characteristics

The internal friction torque in the differential exists in the following parts: one is between the planetary gear and the housing and the gear shaft, the internal friction torque is uniformly denoted by Msp; the second is between the planetary gear and the sliding bearing, denoted by Mbp; the third is Between the half shaft gear and the housing, it is represented by Msd

① Force analysis of planetary gears.

Carry on the force analysis to the planetary gear, as shown in Figure 2.

pagenumber_ebook=45,pagenumber_book=39

Figure 2 The force analysis diagram of the planetary gear

Fn represents the positive pressure of the side gears on the planetary gears, and decomposes Fn into Fn1, Fn2, and Fn3. Fn1 is the equivalent circular force, which makes the planetary gear have a tendency to rotate; Fn2 is the radial component of the positive pressure, which makes the planetary gear and the side gear have a tendency to compress; Fn3 is the axial component of the positive pressure, which makes Planetary gears have a tendency to move along the gear shaft. Then there is the following relationship:

pagenumber_ebook=45,pagenumber_book=39

Among them, α is the pressure angle of the planetary gear, and θ is the cone apex angle.

From equation (8), we can get:

pagenumber_ebook=45,pagenumber_book=39

Suppose the pitch radius of the half-shaft gear is rd, the pitch radius of the planetary gear is rp, the radius of the hole matching the gear shaft is rk, the radius of the large end of the spherical surface is r, the radius of the back spherical surface is Rs, the input torque of the differential Is M0, the positive pressure between the planetary gear and the housing is [5]:

pagenumber_ebook=45,pagenumber_book=39

μsp is the sliding friction coefficient between the planetary gear and the housing, and the friction between the two is:

pagenumber_ebook=45,pagenumber_book=39

The friction torque can be expressed as:

pagenumber_ebook=45,pagenumber_book=39

After finishing:

pagenumber_ebook=45,pagenumber_book=39

In the same way, the friction between the planetary gear and the sliding bearing is:

pagenumber_ebook=45,pagenumber_book=39

After finishing, the friction torque can be obtained as:

pagenumber_ebook=46,pagenumber_book=40

② Force analysis of the half shaft gear.

Carry on the force analysis to the half shaft gear, as shown in Figure 3.

pagenumber_ebook=46,pagenumber_book=40

Figure 3 Force analysis diagram of side gear

pagenumber_ebook=46, pagenumber_book=40 represents the positive pressure of the planetary gear on the side gear, which can be decomposed into radial force pagenumber_ebook=46, pagenumber_book=40, axial force pagenumber_ebook=46, pagenumber_book=40, and the resultant force pagenumber_ebook=46, pagenumber_book =40, pagenumber_ebook=46, pagenumber_book=40 in addition to the equivalent circular force, it also includes the additional force generated by Msp and Mbp on the side gear. The relationship is as follows:

pagenumber_ebook=46,pagenumber_book=40

In the formula, α is the pressure angle of the planetary gear and β is the cone apex angle of the side gear.

From equation (16)

pagenumber_ebook=46,pagenumber_book=40

Let μsd be the coefficient of dynamic friction between the side gear and the housing, then the friction force is

pagenumber_ebook=46,pagenumber_book=40

Pagenumber_ebook=46, pagenumber_book=40 has different expressions for inner and outer half shaft gears, the equivalent circular force is pagenumber_ebook=46, pagenumber_book=40 outer gear expressions:

pagenumber_ebook=46,pagenumber_book=40

Inner gear expression:

pagenumber_ebook=46,pagenumber_book=40

Then the friction torque on the outside and inside is:

pagenumber_ebook=46,pagenumber_book=40

3 Analysis of the performance parameters of the differential

The performance parameters of the evaluation differential mainly include the locking coefficient and the torque distribution coefficient.

The locking coefficient is a physical quantity that characterizes the "locking" degree of the differential. At present, the locking coefficient K can be expressed in two ways. The first is

pagenumber_ebook=46,pagenumber_book=40

M1——The torque on the fast turning half shaft;

M2——The torque on the slow turning half shaft.

That is, the maximum value of the ratio of the torque on the side of the slow turning half shaft to the side of the fast turning half shaft. This expression shows the torque conditions for the differential to work. The ratio of the torque difference between the left and right sides of the axle must be greater than or equal to the locking coefficient before the differential can work. The value is a number greater than 1.

The second way of expression:

pagenumber_ebook=46,pagenumber_book=40

Where

ΔM——The internal friction torque of the differential;

M0——The input torque of the differential.

That is, the ratio of the internal friction torque of the differential to the input torque. K<1 under this expression.

The torque distribution coefficient is the total ratio of the torque of the slow-rotating half shaft to the total input torque, expressed by the formula:

pagenumber_ebook=46,pagenumber_book=40

It characterizes the distribution of left and right torque. Obviously, ξ<1. Generally speaking, a differential with a larger ξ value has a larger locking coefficient.

The locking coefficient K and the torque distribution coefficient ξ are the main performance parameters for evaluating the differential. When producing cars, the company will choose the appropriate differential according to the model, the applicable road surface and customer needs. Generally speaking, it seems that the larger the locking coefficient, the better, but too large locking coefficient will cause a series of problems such as difficult steering, unstable driving, etc. Therefore, the locking coefficient should be limited to an appropriate range. For ordinary bevel gear differentials, the values ​​of K=1.1～1.5 and ξ=0.55～0.6 are appropriate, but for vehicles that need to drive on complex roads, such as off-road vehicles, the locking coefficient should continue to be increased. .

4 Conclusion

This article introduces the structural characteristics of the drive axle and the differential in detail; focuses on the working principle of the differential, and analyzes the three aspects of the differential principle, torque distribution characteristics, and mechanical characteristics; when the internal friction factor is fully considered On the basis, the calculation model of internal friction torque is constructed; finally, the influence of the locking coefficient and torque distribution coefficient on the performance of the differential is analyzed, which has certain guiding significance for the selection of the appropriate differential for the car.