Differential is a mechanism that distributes the torque supplied to it between the output shafts and ensures their rotation with unequal angular velocities.

Differential classification and requirements are detailed in.

On modern cars, symmetrical bevel differentials are most common (Figure 1.1). Such differentials, often called simple ones, are used on both cars and trucks, both as inter-wheel and center-to-center.

Figure 1.1 - Design diagram of a symmetric conical differential

Satellites and half-axle gears are made with spur teeth. The number of teeth of satellites and gears can be either even or odd, but according to the assembly conditions, the condition must be obeyed:

where is the number of teeth of the half-axle gear; - the number of satellites; K is an integer.

The spike of the cross under the satellite experiences crushing and shearing stresses.

Collapse stress s, Pa, is calculated by the formula

, (1.2)

where is the moment on the differential housing, N × m; - radius of application of the axial force acting on the satellite axis, m; - diameter of the satellite axis (diameter of the spike of the cross), m; l is the length of the axis on which the satellite rotates, m.

The moment on the body, N × m, of the cross-axle differential of a car with a wheel arrangement 4 2 is determined by the formula

, (1.3)

where is the maximum engine torque, N × m; - gear ratio of the first stage of the gearbox; - gear ratio of the main transfer.

The radius of application of the axial force, m, acting on the axis of the satellite, is determined by the formula

, (1.4)

where is the outer circumferential module, m.

The diameter of the spike of the cross, m, is calculated by the formula

, (1.5)

where is the permissible pressure between the spikes and the satellites, Pa.

Permissible pressure between cleats and differential pinions:

· Passenger cars - = 80 MPa;

· Trucks - = 100 MPa.

The length of the l-axis, m, on which the satellite rotates, can be approximately determined by the formula

, (1.6)

where b is the width of the satellite gear ring, m; - half of the angle of the initial cone of the satellite, deg.

Half of the angle of the initial cone of the satellite, degrees, is calculated by the formula

, (1.7)

where is the number of satellite teeth.

Permissible shear stress - [s] = 50 ¸ 60 MPa.

Shear stress, Pa, the satellite axis is determined by the formula

. (1.8)

Allowable shear stresses - = 100 ¸ 120 MPa.

The radial forces in the symmetrical differential are balanced, the axial forces are absorbed by the differential housing.

The ends of the satellites are designed for crushing under the action of axial force. Axial force, N, is determined by the formula

, (1.9)

where is the radius of application of the circumferential force in the engagement, m.

The angle of engagement is a = 20 °.

The radius of application of the circumferential force in the engagement in the calculations can be taken equal to the radius of application of the axial force acting on the satellite axis.

The crushing stress, Pa, the end of the satellite is calculated by the formula

, (1.10)

where is the diameter of the end surface of the satellite, which perceives the axial load, m.

The diameter of the end surface of the satellite, m, taking the axial load, is determined by the formula

. (1.11)

Permissible shear stress - = 10 ¸ 20 MPa.

The ends of the side gears are designed for crushing under the action of an axial force acting on the side gear.

The axial force, N, acting on the half-axle gear, is determined by the formula

. (1.12)

The crushing stress of the end of the half-axle gear, Pa, is calculated by the formula

, (1.13)

where, - the largest and smallest radii of the end surface of the gear, taking the axial load, respectively, m.

The largest radius of the gear end surface can be taken equal to the radius of application of the axial force acting on the satellite axis.

The smallest radius of the end surface of the gear can be approximately determined by the formula

, (1.14)

where is the radius of the semiaxis, m.

The minimum diameters of the semiaxes are shown in table 1.2.

Table 1.2 - Minimum diameters of semiaxes

Continuation of table. 1.2

Permissible shear stress - = 40 ¸ 70 MPa.

When turning, the number of revolutions of the satellite on the axle does not exceed = 20 ¸ 30 rpm. Therefore, a depreciation calculation is not required. The number of revolutions rises sharply during slipping, but this case is not typical for normal operating conditions.

The load on the teeth of the satellites and half-axle gears is determined from the condition that the circumferential force is equally distributed between all the satellites and each satellite transmits the force by two teeth.

The design moment on the satellite and on the half-axle gear is calculated by the formula

. (1.15)

The calculation of the teeth of the differential gears for bending stresses is carried out according to the formulas for bevel main gears. Permissible bending stresses of the teeth - = 500 ¸ 800 MPa.

When choosing the main parameters of the gear wheels of symmetric bevel differentials, the data in Table 1.1 can be used.


Table 1.1 - Geometric parameters of symmetric conical differentials

Automobile Number of teeth External circumferential module, mm Taper distance, mm Profile angle Rim width, mm Number of satellites
satellites gears
ZAZ-968 3,50 39,13 20 ° 30 ¢ 11,0
Moskvich-2140 4,13 35,53 22 ° 30 ¢ 12,6
VAZ-2101 4,0 37,77 22 ° 30 ¢ 12,0
GAZ-24 5,0 47,20 23 ° 30 ¢ –––
UAZ-469 4,75 44,90 22 ° 30 ¢ 35,0
GAZ-53A 5,75 62,62 22 ° 30 ¢ 21,0
ZIL-130 6,35 78,09 22 ° 30 ¢ 27,0
Ural-375 N 6,35 78,09 20 ° 27,0
KamAZ-5320 6,35 78,09 22 ° 30 ¢ 27,0
MAZ-5335 5,50 62,77 20 ° 22,5
KrAZ-257B1 8,0 98,39 20 ° 30,2
BelAZ-540A 8,0 98,39 20 ° 30,2
BelAZ-548A 9,0 110,68 20 ° 37,0

1. Bocharov NF Design and calculation of high cross-country vehicles: textbook for technical colleges / NF Bocharov, IS Tsitovich, AA Polungyan. - M .: Mechanical Engineering, 1983 .-- 299 p.

2. Bukharin N. A. Cars. Design, load modes, work processes, strength of vehicle units: textbook. manual for universities / N. A. Bukharin, V. S. Prozorov, M. M. Shchukin. - M .: Mashinostroenie, 1973 .-- 504 p.

3. Lukin P. P. Design and calculation of the car: a textbook for students of technical colleges / P. P. Lukin, G. A. Gasparyants, V. F. Rodionov. - M .: Mashinostroenie, 1984 .-- 376 p.

4. Osepchugov V. V. Automobile: Analysis of the structure, elements of calculation: a textbook for university students / V. V. Osepchugov, A. K. Frumkin. - M .: Mashinostroenie, 1989 .-- 304 p.

5. Design of vehicle transmissions: Reference book / AI Grishkevich [and others]. - M .: Mechanical Engineering, 1984 .-- 272 p.

Compilers

Alexey Vladimirovich Buyankin

Vladimir Georgievich Romashko

It is recommended to choose the outer circumferential module of the bevel gears of the differentials by analogy with the design of the differentials of modern transport vehicles. For these purposes, the following formulas are used

;

; (1)

;

where is the empirical coefficient,

Number of satellite teeth,

Estimated moment,

Number of satellites

where is the number of teeth of the semi-axle gear.

The relation to bevel differentials is, etc.

In all cases, the condition of collection must be met

,

where is an integer.

All differential gears are spur gear. Ring gear width

where the outer cone distance

The parameters of the original contour are taken in accordance with GOST 13754-88. The following parameters are allowed:. The displacement coefficients and are assumed to be equal in modulus, but positive for the satellite, and negative for the gear.

With the original contour in accordance with GOST, take:

, then ,

at, then .

In differentials, blocking takes place with the help of hydraulic friction clutches. If the friction clutch blocks the differential axle shaft, then the frictional moment of the clutch

where the calculated radius of the driving wheel,

Bevel gear efficiency.

According to the formula (1)

The number of teeth of a flat wheel, and for holes. gears at 90º. Corresponds to the contour of the rack teeth.

Coefficient taking into account the influence of two-sided load application,

Bending endurance limit of teeth corresponding to the base number of stress cycles,

Factor taking into account the influence of tooth shape and concentration on bending,

The coefficient taking into account the dynamic load,

The ratio of the width of the ring gear.

To calculate the half-axle gears and satellites, the greatest moment of adhesion of the driving wheels to the road surface is selected.

where is the adhesion coefficient,

Ratio,

Efficiency of onboard bevel gear.

The moment acting on the satellite

The cross of the satellite is calculated for shear from the circumferential force

where is the average radius of action of the circumferential force on the crosspiece.

where is the average radius of the contact surface of the satellite and the spike of the crosspiece relative to the axis of the semi-axial gears,

Cross spike diameter,

Length of the cylindrical surface of the satellite for the spike spike.

The crushing stress in the contact of the spike of the crosspiece with the differential case is also calculated.

where is the length of the cylindrical surface of the differential housing under the cross spike.

The gears of the crosspiece and differential rusks are made of high-alloy steels used for the manufacture of transmission units, with carburizing to a depth of 1.5 ... 1.9 mm and hardening to HRC e from 58 to 63 with a core hardness of 30 to 40. Differential housings are cast from ductile iron 35 ... 10 or steel.

Determine the number of satellite teeth according to the following formula

,

where is the gear ratio from the satellite to the half-axle gear.

It is usually taken in calculations based on the condition for placing the half-axle gears of the splined end of the half-shaft of the desired diameter and limiting the size of the differential.

In the differential of the satellites from 2 to 4.

Half-shafts

The half-shafts are used to transfer torque from the center differential to the drive wheels of the machine and, in fact, are the drive shafts. With dependent wheel suspension, the axle shafts are located inside the crankcase and, as a rule, are connected to the axle gears of the differential by splines, and to the hubs of the driving wheels using splines or flanges that are integral with the axle shafts. All types of axle shafts are designed for fatigue resistance and static strength, assuming that the beams will not deform. In the calculation, the following force factors acting on the semi-axis are taken:

- in the case of intensive acceleration or deceleration, the maximum torque and bending moments act along the axes;

- when the car is skidding on a turn, the bending moment relative to the horizontal axis of the platform is taken into account;

- in the case of crossing an obstacle, the bending moment relative to the horizontal axis to the site of the dangerous section of the semi-axis is taken into account.

Take into account the dynamic factor used for heavily loaded vehicles in the range from 2 to 2.5, and for vehicles with high cross-country ability from 2.5 to 3.

When calculating the estimates of the static strength of the semiaxes, additional stresses are applied:

s w: ascii = "Cambria Math" w: h-ansi = "Cambria Math" /> PI"> .

In this case, the equivalent stress, which is compared with the allowable one, is calculated by the following formulas

,

where is the diameter of the semiaxis in the dangerous section.

For semi-unloaded and ¾ unloaded semi-axles with intensive acceleration or deceleration

,

where bending moments about the axes and.

When the car skids on a bend

When crossing obstacles

In existing designs, the diameter of the axle shafts for load vehicles is taken as mm.

Planetary gears

Basic relationships of planetary mechanisms.

A planetary mechanism is a mechanism consisting of gear wheels in which the geometric axis of at least one wheel is movable. A gear wheel with a movable geometric axis is called a satellite. The satellite can have one or more toothed rims, or consist of several meshing wheels.

Classification of three-link planetary gears

The link in which the axes of the satellites are installed is the carrier (h). A gear wheel, the geometric axis of which coincides with the main axis of the mechanism - central (a, b, k). The main link of the planetary mechanism is called the link that perceives the external moment in the loaded transmission, and is central.

a - sun gear,

h - carrier,

g - satellite,

b - ring gear (epicyclic).

The planetary mechanism, in which all 3 main links rotate, is called a differential. Planetary gears are designated according to the correspondence of the available satellites, gearing and parameter values. Planetary mechanisms, in which the main links are 2 central wheels and a carrier, are designated 2k-h. A planetary gearbox can consist of one planetary gear unit or several connected to each other. The classification of three-link planetary gears of type 2k-h is given in the classification of three-bar planetary gears. Three-link planetary mechanisms of type A and D are more widespread in planetary gearboxes, much less often of type B. Kinematic and power characteristics of three-link planetary mechanisms are determined by its kinematic parameter r wsp: rsidR = "00000000"> "> equal to the gear ratio from link a to link b when carrier h is stopped.

where are both the angular velocity and the rotation frequency of the link, respectively.

Expressions for determining the parameter, taking into account the sign, are indicated in the classification table for three-link planetary mechanisms. The reduced equation of the parameter r wsp: rsidR = "00000000"> "> is known as the Willis formula and can be directly used for calculations in the analysis and synthesis of planetary gearboxes, but it is more convenient to use it in a transformed form:

This equation is often called the basic equation of the kinematics of the three-link mechanism. In some cases, the parameter is used k... In this case, the basic equation of kinematics takes the following form

Purpose of work:

Determine the load on the teeth of the satellites, half-axle gears,

crosspiece and loads from the satellites on the differential housing.

Prototype:

Take the Kia Spectra differential as a prototype.

Conical differential, two-satellite

Determination of the load on the tooth of the satellite and half-axle gears

The load on the tooth of the satellite and half-axle gears is determined from the condition that the circumferential force is equally distributed between all the satellites, and each satellite transmits the force by two teeth. The circumferential force acting on one satellite,

where r1 is the radius of application of the force,

nc is the number of satellites, nc = 2;

Mmax - maximum moment,

developed by the engine,

Mmax = 130 N.m;

iТР - transmission ratio,

iТР = iКП1 * iГП = ;

Kd - dynamic factor,

2.5> Kd> 1.5, in the calculation we take Kd = 2.

Figure 12 Calculation diagram of the differential

The spike under the satellite is experiencing shear stress

Transforming the formulas, we get:

where we take τav = 120 MPa, and from this we can find d:

The spike of the crosspiece under the satellite also experiences crushing stress:

where we take σcm = 60 MPa, based on this we find l1;

The spike of the cross under the satellite experiences crushing stress at the attachment point in the differential housing under the action of a circumferential force:

where the radius of application of force m;

where we take σcm = 60 MPa, and from this we find l2;

In the course of the calculation, the load on the teeth of the satellites, half-axle gears, the crosspiece and the loads from the side of the satellites on the differential housing was determined. Loads, calculated taking into account all the assumptions, satisfy the accepted conditions.

Ministry of Education of the Russian Federation

South Ural State University

Department "Cars"

Explanatory note to the course project

For the course: "Design and calculation of the car"

On the topic: "Calculation of the car VAZ 2104"

AT - 434.00.00.00.00 PZ

Completed: student of group AT-434

Ivanov I.I.

Checked by: A.G. Ulanov

Chelyabinsk 2010


1. Calculation of adhesion

1.1 Assessment of wear resistance of friction linings

1.2 Assessment of adhesion thermal stress

2. Calculation of cardan transmission

3. Calculation of the differential

4. Calculation of the synchronizer


1. Calculation of adhesion

The purpose of the clutch. Clutch requirements

The clutch is designed for smooth starting of the car from a place, short-term separation of the engine and transmission when changing gears and preventing the impact on the transmission of high dynamic loads arising during transient modes and when driving on roads with poor coverage. When designing friction clutches, in addition to the basic requirements (minimum dead weight, simple design, high reliability, etc.)

The following must be ensured:

· Reliable transmission of torque from the engine to the transmission under any operating conditions;

· Smooth starting of the car from a place and full engagement of the clutch;

· Complete disconnection of the engine from the transmission with a guaranteed gap between the friction surfaces;

· The minimum moment of inertia of the driven elements of the clutch for easier gear shifting and reduction of wear of the friction surface in the synchronizer;

· The necessary removal of heat from the friction surface;

· Protection of transmission from dynamic overloads.

Selectable parameters

We select the outer diameter of the driven disk from the condition that M d max = 116NChm and the maximum engine crankshaft speed umax = 5600 rpm = 586.1 rad / s:

D n = 204 mm - outer diameter of the lining,

D n = 146 mm - inner diameter of the lining,

d = 3.3 mm - thickness of the friction lining,

i = 2 is the number of pairs of friction surfaces.


1.1 Assessment of clutch wear resistance

The degree of loading and wear resistance of clutch linings are usually evaluated by two main parameters:

· Specific pressure on friction surfaces;

· Specific work of clutch slipping.

Calculation of specific pressure on friction surfaces:

p 0 = ≤, N / m 2,

where p pr is the force of normal compression of the disks, N;

F is the area of ​​the working surface of one friction lining,

F = = 0.785 H (0.204 2 + 0.146 2) = 0.049 m 2;

[р 0] = 0.25 MPa - allowable pressure, providing the required service life of the linings.

Determination of the force of normal compression:

where M d max is the maximum engine torque, LFm; = 1.5 - coefficient of adhesion safety; = 0.4 - coefficient of friction; R cf - the average radius of the friction lining,

R cf = 0.0875 m, p pr = 2,485 kN, a

p 0 = , 0,05 < 0,25 МПа –


the required resource of the linings is provided.

Calculation of the specific work of clutch slipping:

where L beats - specific slip work; L d - the work of slipping when starting the car from a standstill, J; F sum - the total area of ​​the working surfaces of the pads, m 2;

J,

where J a is the moment of inertia of the car, reduced to the input shaft of the gearbox,

O f = dH (b f) H NCHmb

where, m a = 1445 kg is the total mass of the car; m n = 0 kg is the total mass of the trailer; i k and i 0 - gear ratios, respectively, of the gearbox and main transmission (i k = 3.67, i 0 = 3.9); d = 1.46 - coefficient of accounting for rotating masses.

J a = 1.46Ch1400Ch = 0.67 LFm 2;

Estimated angular frequency of rotation of the engine crankshaft, rad / s; for a car with a carburetor engine; = = 586.1 3 = 195.35 rad / s, where M r is the moment of resistance to movement when starting off,


M m = g LFm,

where, w = 0.02 is the rolling resistance coefficient (on a horizontal road with an asphalt surface); s tr = 0.82 - efficiency transmissions.

M m = = 4.14 LFm.

L d = = 50652 J.

L beats = = 0.52 MJ / m 2

L beats = 0.52 MJ / m 2 = 4 MJ / m 2,

hence the required resource of the linings is provided.

1.2 Assessment of adhesion thermal stress

The heating of the clutch parts in one operation is determined by the formula:

where = 0.5 is the fraction of heat spent on heating the part; c = 0.48 kJ / (kgChK) - heat capacity of the part; m d - part weight, kg; [Dt] = 1015.

m d = CHN (R n - R int)

where = 7200m 3 / kg is the density of cast iron, R n = 102 mm is the outer radius of the pressure plate,

R vn = 73mm - inner radius of the pressure plate, m d = 4.92 kg.

Dt = = 10.7 [Dt]

1.3 Calculation of the diaphragm spring

The design scheme for determining the parameters of the diaphragm spring is shown in Fig. 1. The diaphragm spring is a Belvia spring modified for use in automotive clutches. The pressure of the spring is created by its section between the support rings mounted on rivets fixed to the clutch cover and the outer edge of the spring abutting against the clutch pressure plate. The petals are simultaneously the release levers, their elasticity contributes to the smooth engagement of the clutch.

E is the modulus of elasticity of the first kind;

0.25 - Poisson's ratio;

H is the height of the spring;

h is the thickness of the spring;

f pr - deflection of the spring;

We accept that: h = 2mm, a = 60mm, c = 70mm, d = 80mm, b = 90mm, H = 5mm.


Table 1

R press, kN f, mm
4,29 1
5,0 2
3,66 3
1,82 4
1 5
2,73 6
5,03 6,5

Fig. 1 Diaphragm spring

Fig. 2 Diagram of displacement versus spring force

car clutch differential synchronizer


2. Calculation of cardan transmission

Initial data:

Prototype: VAZ-2103 car

Max. frequent rotation: 5600 rpm = 586.1 rad / s

Engine torque: 116 Nm

Gear ratio 1 gear: 3.67

Gear ratio 4: 1.00

Shaft inner diameter: 66mm

Wall thickness: 2mm

Propeller shaft length:

"Gearbox - Intermediate support": 606mm

"Intermediate support - Rear axle": 785 mm

Density of shaft material: 7800 kg / m 2

2.1 Determination of the critical speed

,

Determination of the maximum rotational speed of the propeller shaft:

,

where = 1.1 ... 1.2

Reduced moment of inertia:

Propeller shaft weight

Then the critical angular velocity for the propeller shaft is:

Conditional check:

In this case, the condition is met, since

2.2 Determination of the torsional stress

Shaft torsion stress:

M cr = M dv. max H i 1 Chz kp = 116Ch3.67Ch0.99 = 421

Nm - torque on the output shaft of the gearbox in the lowest gear,

Torsional moment of resistance.

Hence,

The condition for the torsional stress of the propeller shaft is fulfilled.

2.3 Calculation of the universal joint shaft

Determination of the crushing stress of the spikes of the cross:

where r = 47.2 mm is the distance between the centers of the needle rollers,

Installation angle of the propeller shaft,

3 0 - for cars.

Therefore, the normal force

Fig. 3 Propeller shaft cross collar stress:


Determination of the bending stress of the spikes of the cross:

Determination of shear stress:

where d w is the diameter of the spike, d w = 14.7 mm.

Therefore, the shear stress:

Conclusion: In the calculation, the main parameters of the propeller shaft drive the rear wheels of the VAZ - 2104 were determined. The results obtained satisfy all the norms and assumptions.


3. Calculation of the differential

It is necessary to determine the load on the teeth of the satellites, half-axle gears, the cross and the loads from the satellites on the differential housing.

Requirements for the unit: When analyzing and evaluating the design of the differential, like other mechanisms, one should be guided by the requirements imposed on them:

Distribution of torque between the wheels and axles in a proportion that provides the best performance (maximum tractive force, good stability and controllability)

In addition, the following general requirements are imposed on the differential, as well as to all mechanisms of the car: ensuring the minimum size and weight, simplicity of device and maintenance, manufacturability, maintainability.

Prototype: As a prototype, we take the differential of a VAZ-2104 car. The differential is conical, two-satellite.

3.1 Determination of the load on the tooth of the satellite and half-axle gears

The load on the tooth of the satellite and half-axle gears is determined from the condition that the circumferential force is equally distributed between all the satellites, and each satellite transmits the force by two teeth. Circumferential force acting on one satellite:

where, r 1 - radius of application, r 1 = 0.025 m;

r 2 = 0.036 m;

n s - the number of satellites, n s = 2;

M to max - the maximum torque developed by the engine, M to max = 116 LFm;

u KP1 - first gear ratio, u KP1 = 3.67;

u GP - gear ratio of the main gear, u GP = 3.9;

К З = 1.7 - safety factor for the automotive industry;

The spike under the satellite is experiencing shear stress

Fig. 4 Satellite tooth

where [= 100 MPa, based on this, you can find d;

The spike of the cross under the satellite also experiences crushing stress


where [= 55 MPa, based on this, you can find l 1;

The spike of the cross under the satellite experiences crushing stress at the attachment point in the differential housing under the action of a circumferential force

where [= 55 MPa, based on this, you can find l 2;

3.2 Determination of the pressure of the end of the satellite on the differential housing

The pressure of the end of the satellite on the differential housing is determined by the crushing voltage.

where [= 15 MPa;


4. Calculation of the synchronizer

Requirements for the unit: When analyzing and assessing the design of the gearbox, like other mechanisms, one should be guided by the requirements imposed on them:

· Provision of optimal traction - speed and fuel - economic properties of the vehicle at a given external characteristics of the engine;

· Noiselessness during operation and gear shifting;

· Ease of management;

· High efficiency;

In addition, the following general requirements are imposed on the gearbox, as well as to all mechanisms of the car:

· Ensuring the minimum size and weight;

· Simplicity of the device and maintenance;

· Manufacturability;

· Maintainability;

The gearbox is four-speed with synchronizers in all forward gears. The main gear is cylindrical, helical.

Gear ratios:

first gear - 3.75;

second gear - 2.30;

third gear - 1.349;

fourth gear - 1;

reverse gear - 3.53;

main gear - 3.9;

n is the maximum engine speed,

n - 5600 rpm;


4.1 Determination of the frictional moment in the synchronizer

To equalize the angular velocities of the connected elements, it is necessary to create a friction moment M tr on the surfaces of the cones

where t is the synchronization time, t = 1 s;

J is the moment of inertia corresponding to the parts rotating together with the gear of the included transfer;

w e - the angular velocity of the crankshaft,

- the gear ratio of the included transfer, = 2.30,

- the gear ratio of the switched off transmission, = 3.75.

;

;

The moment of inertia of the drive shaft is determined from the ratio

The frictional moment created on the body surfaces can be expressed in terms of the normal force P n on the synchronization cones:

(3)

where P n is the normal force on the friction surface;

µ - coefficient of friction, µ = 0.06;

r cf is the average radius of the cone.

In turn, the normal force can be expressed in terms of the force Q generated by the driver when the gear is engaged.

Substituting equation (4) into equation (3) and expressing the average radius of the cone, we get the following

Q - the effort created by the driver when the gear is engaged are determined by the formula

where P roar is the force applied to the gear shift knob; P roar = 60 N;

5 drive gear ratio,

Q = 60h5 = 12 N,

The width of the synchronizer ring along the generatrix of the cone is determined by the formula

where = 1MPa - conditional allowable pressure.

Fig 1. Synchronizer circuit

The surfaces of the blocking elements are performed at an angle that satisfies the condition

where μ is the coefficient of friction of the blocking surfaces,

29 mm - average radius on which the blocking elements are located

In order that the transmission cannot be switched on until the angular velocities are completely equalized, the force Q applied to the synchronizer coupling must be less


Fig 2. Diagram of the dynamic system of the synchronizer

When performing a course project, you must determine:

differential gear module;

pressure on the axis of the satellites in the satellite;

pressure on the pinion axle in the differential box;

pressure at the end of the satellites;

side pressure of half-axle gears.

The average modulus of the differential gears is determined by the maximum torque, taking into account the fact that each satellite transmits the load through two teeth

where q is the number of satellites; - the number of satellite teeth;
;
- is determined as when calculating gears of a gearbox.

The pressure on the axis of the satellite in the satellite itself

.

Pressure on the pinion axle in the differential box

.

Side pressure of satellites

.

Side pressure of half-axle gears

,

where r is the radius of the midpoint of the satellite tooth; d is the diameter of the satellite axis; - the radius of the center point of the satellite axis in the differential box; - diameter of the end bearing surface of the satellite; and - smaller and larger diameters of the contact surfaces of the half-axle gear with the differential housing.

Allowable pressures
- are 70 MPa.

In the process of graduate design, it is also necessary to analyze the effect of a particular differential on fuel efficiency, traction properties, cross-country ability and vehicle handling.

6.6. Semiaxis calculation

Design schemes for loading semi-unloaded and fully unloaded semi-axles, as the most common, are shown in Fig. 6.2.

Figure 6.2 shows the following force factors affecting the drive wheel: torque from traction
or from brake
strength; the traction caused by this moment or brake braking force with the central brake; lateral force when cornering or skidding: normal reaction ... The combined action of the maximum longitudinal or lateral forces is eliminated due to the limited value of the adhesion of the wheel to the road.

In the general case, when calculating the semiaxes, three characteristic loading modes are considered:

a) maximum traction or braking;

b) skidding of the car

c) crossing an obstacle.

Fully loaded axle shafts should be calculated only for the first load mode, since only this mode is characterized by the effect of torque.

Analytical expressions for calculating the forces and reactions acting on the drive wheel under the specified loading conditions are given in Table 6.2.

Table 6.2

Analytical expressions for calculating the forces and reactions acting on the drive wheel

Strength, reaction

Maximum thrust

or braking

car

let

(by engine)

(by clutch)

* The calculation uses one of the coefficients or characterizing the redistribution of normal reactions, respectively, from traction force or from braking.

** The “+” sign refers to the inner wheel axle in relation to the skid direction, the “-” sign refers to the outer wheel axle.

Dynamic load redistribution coefficient for all vehicles and for all-wheel drive vehicles is determined by the formula

,

where - ordinate of the center of mass of the vehicle;
on the front axle.

The upper sign of the formula refers to the front axle during braking and to the rear axle during acceleration, the lower one - to the front axle during acceleration and to the rear axle during braking.

When accelerating in a rear-wheel drive vehicle, the coefficient of dynamic redistribution of the load on the rear axle
, in a front-wheel drive vehicle, the coefficient of dynamic redistribution of the load on the front axle
, where L is the base of the car m,
.

The values ​​of forces and reactions in table 6.2 are calculated at
,
, dynamic factor
taken equal to: 1.75 - for cars and 2.5 - for trucks.

The dimensions of the axle shafts are determined based on the most dangerous loading case. The calculation is carried out according to the most loaded section (for a semi-unloaded semi-axle - the bearing installation zone).

In the first loading mode, bending and torsion stresses arise in the dangerous section of the semi-unloaded semi-axle. Equivalent stresses, based on the third theory of strength, are determined by the formula

, (6.1)

where d is the diameter of the semiaxis in the dangerous section.

The smaller of the two values ​​of the traction force is substituted into formula (6.1) determined by the analytical dependences of Table 6.2 - by the engine and by the adhesion of the wheels to the road.

When drifting, bending stresses acting on the semi-axis:

,

where the upper signs refer to the inner semiaxis, and the lower ones to the outer one in relation to the direction of the skid.

When driving wheels over an obstacle, bending stresses

.

Fully unloaded axle shaft is calculated only for torsion at maximum tractive force
.

The axle shaft is also calculated torsional stiffness, estimated by the relative angle of twist, which should not exceed
for 1 m length

,

where is the polar moment of inertia of the semiaxis section.

The half-shafts are made of alloy steels of the 30KhGS, 40KhMA, 40Kh brands and are hardened by HFC. Safety factor for yield strength
... In completed structures
MPa,
MPa.

Semi-axle splines count on crushing and shearing: [ ] = 70MPa,
MPa.

When using cardan shafts to drive wheels, they are calculated according to the method described in Section 4.

Axle and wheel bearings are selected according to the static load on the wheel,
... Other loads acting on the wheel are neglected due to their relative smallness.
or short duration of action
... The design number of revolutions of the bearings is based on the average vehicle speed.