A. A. Yenaev
Cars.
Design and calculation
steering controls
Teaching manual
Bratsk 2004.
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2. Appointment, requirements and classification ... 3. Selecting the method of rotation of cars ......... 4. Select the steering scheme .................. 5. Steering mechanisms ....................................... .. 5.1. Appointment, requirements, classification ............... ... 5.2. Estimated parameters of the steering mechanism ............ .. 5.3. Select the type of steering mechanism ............................ 5.4. Materials used for the manufacture of steering mechanisms ......................................................... ... 6. Steering drives .................................................. 6.1. Appointment, requirements, classification ............... ... 6.2. Estimated steering parameters ............... .. 6.3. Choosing a steering wheel type ............................... 6.4. Materials used for the manufacture of steering drives ................................................................. 7. Steering amplifiers .................. .. 7.1. Appointment, requirements, classification ............... ... 7.2. Estimated parameters of the steering amplifier ........................................................................ 7.3. Choosing a layout layout scheme .................. ... 7.4. Pumps amplifiers .......................................... ... 7.5. Materials used for the manufacture of pump amplifiers ......................................................... ... 8. Calculation of the steering ........................ ... 8.1. Kinematic calculation of the steering wheel ................ 8.2. Transmission number of steering ................ 9. Silence Calculation of the steering ......... ... 9.1. Effort on the steering wheel .................................... 9.2. Effort developed by a cylinder amplifier ............ .. 9.3. Effort on wheels when braking ..................... ... 9.4. Efforts on the transverse and longitudinal traction ............... 10. Hydraulic calculation of the amplifier ............... 11. The strength calculation of the steering. 11.1. Calculation of the steering mechanisms .............................. ... 11.2. Calculations of steering drives ................................. |
Design and calculation of steering controls is one of the components of the course project on the "Cars" discipline.
At the first stage of the course design, it is necessary to perform a traction calculation and explore the operating properties of the car using the guidelines "Cars. General provisions. Traction calculation "and then proceed, in accordance with the task, to design and calculate the unit or the car chassis system.
When designing and calculating steering controls, it is necessary to choose the recommended literature, carefully read this benefit. The sequence of work on the design and calculation of steering controls is as follows:
1. Select a vehicle turning method, a steering scheme, the type of steering mechanism, the amplifier layout circuit (if necessary).
2. Perform a kinematic calculation, power calculation, hydraulic calculation of the amplifier (if the steering of the amplifier is provided in the steering).
3. Select the dimensions of the parts and perform the strength calculation.
In this teaching and methodological manual, it is described in detail how to fulfill all these types of work.
2. Purpose, Requirements and Classification
Steering - This is a set of devices that serve to rotate the driven wheels of the car when the driver is exposed to the steering wheel and consisting of steering mechanism and drive (Fig. 1).
The steering mechanism is part of the steering wheel from the steering wheel to the steering tower, and the steering wheel turns on the parts from the steering tower to the rotary pin.
Fig. 1. Scheme of the steering:
1 - steering wheel; 2 - steering shaft; 3 - steering column; 4 - gearbox; 5 - steering bump; 6 - longitudinal tie Rod; 7 - swivel pin; 8 - arm of the swivel pin; 9 - side lever; 10 - transverse thrust
The following requirements are presented to the steering control:
1) Ensuring high maneuverability motor vehiclesat which steep and rapid turns are possible on relatively limited areas;
2) the ease of control, the validation of the force applied to the steering wheel.
For passenger cars Without an amplifier, this force is 50 ... 100 N, and with an amplifier - 10 ... 20 N. For trucks, force on the steering wheel is regulated: 250 ... 500 H - for steering without an amplifier; 120 H - for steering with an amplifier;
3) the combustion of controlled wheels with minimal side expansion and sliding when the car is rotated;
4) the accuracy of the tracking action, primarily kinematic, in which any given steering wheel will correspond to a fully defined pre-calculated curvature of rotation;
Car control mechanisms - These are mechanisms that are designed to provide the movement of the car in the right direction, and its slowdown or stop if necessary. Control mechanisms include steering and car brake system.
Steering car - this isa combination of mechanisms serving, for rotation of controlled wheels, providescar trafficin the specified direction. Transferring the power of the steering wheel to controlled wheels provides a steering wheel drive. To facilitate the control of the car, power steering amplifiers , machine steering wheel light and comfortable.
1 - transverse thrust; 2 - Lower lever; 3 - swivel pin; 4 - top lever; 5 - longitudinal traction; 6 - power steering; 7 - steering; 8 - steering shaft; 9 - steering wheel.
The principle of operation of the steering
Each controlled wheel is installed on a swivel fist, connected to the front axle by a hundred, which is fixedly attached to the front axle. When rotating the driver of the steering wheel, the force is transmitted by means of thrust and levers on the swivel fists, which turn to a certain angle (sets the driver), changing the direction of the vehicle movement.
Control mechanisms, device
Steering consists of the following mechanisms:
1. Steering mechanism -
slowing transmission, transforming the rotation of the steering wheel shaft into rotation of the shaft shaft. This mechanism increases the force applied to the steering wheel The driver makes it easier for his work.
2. Steering wheel drive -the system of thrust and levers in combination with the steering mechanism turn the car.
3. A amplifier of the steering wheel (not on all cars) -it is used to reduce the effort required for the rotation of the steering wheel.
1 - steering wheel; 2 - shaft bearings housing; 3 - Bearing; 4 - steering wheel shaft; 5 - Cardan shaft of the steering; 6 - craving steering trapezium; 7 - tip; 8 - washer; 9 - finger hinge; 10 - Cross cardanian Vala; 11 - sliding plug; 12 - the tip of the cylinder; 13 - Sealing Ring; 14 - tip nut; 15 - cylinder; 16-stroke with stock; 17 - Sealing Ring; 18 - Ring supporting; 19 - cuff; 20 - Pressing Ring; 21 - nut; 22 - protective coupling; 23 - craving steering trapezium; 24 - Maslenka; 25 - rod tip; 26 - Ring lock; 27 - plug; 28 - Spring; 29 - coaching springs; 30 - Sealing ring; 31 - upper liner; 32 - finger ball; 33 - Lower liner; 34 - lining; 35 - protective coupling; 36 - lever swivel fist; 37 - Turning fist housing.
Steering device:
1 - the spool body; 2 - Sealing ring; 3 - Rolling Plunger Ring; 4 - cuff; 5 - steering mechanism; 6 - sector; 7 - the plug of the filling hole; 8 - worm; 9 - side cover of crankcase; 10 - cover; 11 - Cork drain hole; 12 - the sleeve is spacer; 13 - needle bearing; 14 - power steering; 15 - craving for steering steering; 16 - shaft of the steering mechanism; 17 - spool; 18 - Spring; 19 - plunger; 20 - cover of the spool housing.
Oil tank. 1 - Tank Corps; 2 - filter; 3 - filter housing; 4 - valve bypass; 5 - cover; 6 - Sapun; 7 - plug of the filler neck; 8 - Ring; 9 - Suction hose.
Pump of an amplifying mechanism. 1 - pump cover; 2 - stator; 3 - rotor; 4 - body; 5 - needle bearing; 6 - spacer; 7 - pulley; 8 - roller; 9 - collector; 10 - distribution disc.
Schematic diagram. 1 - pipelines of temple pressure; 2 - the mechanism of the steering; 3 - pump of an amplifying mechanism; 4 - drain hose; 5 - Oil tank; 6 - Suction hose; 7 - injection hose; 8 - reinforcement mechanism; 9 - hoses.
Car steering KAMAZ
1 is the housing of the control valve of the hydraulic agent; 2 - radiator; 3 - Cardan shaft; 4 - steering column; 5 - pipeline low pressure; 6 - High Pressure Pipeline; 7- tank hydraulic system; 8-pump hydraulic switch; 9 - Cup; 10 - longitudinal traction; 11 - steering mechanism with a hydraulic agent; 12 - corner gearbox.
Car steering mechanism KAMAZ:
1 - jet plunger; 2- control valve housing; 3 - lead gear wheel; 4 - slave gear wheel; 5, 22 and 29-stop rings; 6 - sleeve; 7 and 31 - stubborn colas k ", 8 - sealing ring; 9 and 15 - bandages; 10 - bypass valve; 11 and 28 - covers; 12 - Carter; 13 - Rake piston; 14 - plug; 16 and 20 - nuts; 17 - chute; 18 - ball; 19 - sector; 21 - lock washer; 23 - body; 24 - stubborn bearing; 25 - plunger; 26 - spool; 27- adjusting screw; 30- adjusting washer; 32-toggled shaft sector.
Car steering ZIL;
1 - hydraulic power pump; 2 - pump tank; 3 - low pressure hose; 4 - high pressure hose; 5 column; 6 - contact device signal; 7 - rotation pointer switch; eight cardan hinge; 9 - Cardan shaft; 10 - steering mechanism; 11 - Cup.
Car steering MAZ-5335:
1 - longitudinal steering traction; 2- power steering; 3 - Cup; 4 - steering mechanism; 5- cardan steering drive hinge; 6 - steering shaft; 7 - steering wheel; 8 - transverse steering; 9- left lever transverse steering traction; 10 - swivel lever.
As noted above, the steering with the amplifier is an elementary automatic control system with rigid feedback. With an unfavorable combination of parameters, the system of this type may be unstable in this case The instability of the system is expressed in auto-oscillations of controlled wheels. Such oscillations were observed on some experimental samples of domestic cars.
The task of the dynamic calculation is to find the conditions under which self-oscillations could not occur if all the necessary parameters are known to calculate, or reveal what parameters should be changed to stop self-oscillations on the experimental sample if they are observed.
Preview physical essence The process of oscillation of control wheels. Re-turn to the amplifier scheme shown in Fig. 1. The amplifier can be included as a driver when an effort is applied to the steering wheel and controlled wheels from the shocks from the road.
As experiments show, such oscillations can occur during the straight-line movement of the car at high speed, on turns when driving at low speed, as well as when turning the wheels in place.
Consider the first case. When the controlled wheel is rotated from the journey from the road or for another any reason, the dispenser body will begin to shift relative to the spool, and, as soon as the gap δ 1 is eliminated, the liquid will begin to flow into the power cylinder cavity. The steering wheel and the power steering is considered to be fixed pressure in the cavity A will increase and prevent the continuation of the rotation. Due to the elasticity of rubber hoses of the hydraulic system and the elasticity of mechanical connections to fill the cavity A liquid (to create a working pressure), a certain time is required during which controlled wheels will have time to turn to some angle. Under the action of pressure in the cavity of the wheels will begin to rotate to the other side until the spool takes the neutral position. Then the pressure decreases. The power of inertia, as well as the residual pressure in the cavity, and rotate controlled wheels from the neutral position to the right, and the cycle is repeated from the right cavity.
This process is depicted in Fig. 33, a and b.
The angle θ 0 corresponds to this rotation of controlled wheels, in which the force transmitted by the steering drive reaches the value necessary to move the spool.
In fig. 33, the dependence P \u003d f (θ) is shown, built by curve. 33, a and b. Since the stroke of the rod can be considered a linear function of the angle of rotation (due to the smallness of the angle θ max), the graph (Fig. 33, c) can be considered as an indicator diagram of the power cylinder amplifier. The area of \u200b\u200bthe indicator diagram determines the work spent by the amplifier to rock the controlled wheels.
It should be noted that the process described can only be observed if the steering wheel remains stationary when the steering wheels are oscillations. If the steering wheel rotates, the amplifier does not turn on. For example, the amplifiers with the drivers of distributors from the angular displacement of the upper part of the steering shaft relative to the bottom usually have this property and do not cause auto-oscilps
When turning controlled wheels in place or when the car moves at a low speed, the oscillations caused by the amplifier differ in nature from the pressure considered during such oscillations increases only in one cavity. The indicator diagram for this case is shown in Fig. 33, G.
Such oscillations can be explained as follows. If at the time corresponding to the rotation of the wheels to some angle θ r, delay the steering wheel, then controlled wheels (under the action of inertia and residual pressure for power in the power cylinder) will continue to move and turn to the angle θ r + θ max. The pressure in the power cylinder will fall to 0, since the spool will be in a position corresponding to the rotation of the wheels at the angle θ r. After that, the power of elasticity of the tire will start rotating the wheel-controlled wheel in the opposite direction. When the wheel turns back to the angle θ R, the amplifier will turn on. The pressure in the system will begin to rise not immediately, but after a while, for which the controlled wheel can turn to the angle θ R -θ max. Rotate to the left at this point will stop, since the power cylinder will enter into work, and the cycle will be repeated first.
Typically, the work of the amplifier, determined by the area of \u200b\u200bindicator charts, is insignificant compared to the work of friction in pile, steering and rubber compounds, and self-oscillations are not possible. When the area of \u200b\u200bindicator diagrams is large, and the work, they are determined, comparable to the work of friction, the unlucky oscillations are likely. Such a case is investigated below.
To find the stability conditions of the system, we have limitations for it:
- Controlled wheels have one degree of freedom and can be rotated only around a squash within the gap in the amplifier distributor.
- The steering wheel is rigidly fixed in a neutral position.
- The connection between the wheels is absolutely tough.
- The mass of the spool and parts connecting it with the control wheels is negligible.
- Friction forces in the system are proportional to the first degrees of angular velocities.
- The stiffness of the system elements is constant and does not depend on the value of the corresponding displacements or deformations.
The remaining admitted assumptions are negotiated during the presentation.
Below are the stability of steering with hydraulic motors mounted for two possible options: with long feedback and short.
The structural and calculated scheme of the first option is shown in Fig. 34 and 35 solid lines, second - bar. At the first embodiment, feedback acts on the distributor after the power cylinder has rotated the controlled wheels. With a second embodiment, the dispenser housing moves, turning off the amplifier, simultaneously with the stream of the power cylinder.
First, consider each element of a diagram with long feedback.
Steering gear (on the structural scheme is not shown). Rotate the steering wheel on some small angle A causes a force t c in a longitudinal pull
T C \u003d C 1 (αi R.M L C - x 1), (26)
where C 1 is the rigidity of the steering shaft and longitudinal thrust below; L C - fat length; x 1 - moving the spool.
Distributor drive. To drive the control of the switchgear, the input value is T C, the output is the offset of the spool X 1. The drive equation, taking into account feedback at the angle of rotation of the controlled wheels θ and by pressure in the system P, has the following form at T C\u003e T N:
(27)
where k o.s - the coefficient of feedback force at the corner of the rotation of the controlled wheels; C n - rigidity of centering springs.
Distributor. The oscillations caused by the amplifier of the moving car are associated with the alternate inclusion of the one, then another cavities of the power cylinder. The distributor equation in this case has the form
where q is the amount of fluid entering the pipelines of the power cylinder; x 1 -θl s k o.s \u003d Δx - shift of the spool in the case.
The function f (δx) is nonlinear and depends on the design of the spool of the distributor and pump performance. In the general case, with a given characteristic of the pump and the design of the distributor, the amount of liquid q entering the power cylinder depends on both the Δx of the spool in the case and on the pressure difference ΔP at the inlet to the distributor and output from it.
The amplifier distributors are designed so that, on the one hand, with relatively large technological tolerances on linear dimensions, have a minimum pressure in the system with a neutral position of the spool, and on the other, the minimum shift of the spool to bring the amplifier into action. As a result, the spool distributor of the amplifier according to the characteristic Q \u003d F (Δx, Δp) is close to the valve, i.e. the value q does not depend on the pressure Δp and is only a spool displacement function. Taking into account the direction of the power cylinder, it will look like, as shown in Fig. 36, a. This characteristic is characteristic of relay links of automatic control systems. Linearization of these functions was carried out according to the method of harmonic linearization. As a result, we get for the first scheme (Fig. 36, a)
where Δx 0 is the shift of the spool in the housing at which the sharp increase in pressure begins; Q 0 - the amount of fluid entering the pressure line at the overlapped working clips; A - the maximum stroke of the spool in the housing, determined by the amplitude of the oscillations of the controlled wheels.
Pipelines. The pressure in the system is determined by the amount entered into the pressure line of the liquid and the elasticity of the highway:
where x 2 is the stroke of the piston of the power cylinder, the positive direction towards the pressure of the pressure; C 2 - bulk rigidity of the hydraulic system; c r \u003d dp / dv g (v r \u003d volume of pressure highway hydraulic system).
Power cylinder. In turn, the stroke of the strength cylinder is determined by the angle of rotation of the driven wheels and the deformation of the communication part of the power cylinder with controlled wheels and the point of the support
(31)
where L 2 is the shoulder of the effort of the power cylinder relative to the axes of the pivot wheels; C 2 - stiffness of the fastening of the power cylinder, shown to the rod of the power cylinder.
Controlled wheels. The equation of rotation of the controlled wheels relative to the pussher has the second order and, generally speaking, is non-linear. Considering that the oscillations of the controlled wheels occur with relatively small amplitudes (up to 3-4 °), it can be assumed that the stabilizing moments caused by the elasticity of rubber and the slope of the kingle, are proportional to the first degree of the angle of rotation of the controlled wheels, and the friction in the system depends on the first degree of the corner The rotation speeds of the wheels. The equation in a linearized form looks like this:
where J is the moment of inertia of controlled wheels and parts, rigidly related relative to the axes of a king. G is a coefficient characterizing friction losses in a steering wheel drive, a hydraulic system and in the tires of the wheels; N is a coefficient characterizing the effect of a stabilizing moment resulting from tilting tires and elasticity of tire rubber.
The rigidity of the steering drive in the equation is not taken into account, as it is believed that the oscillations are small and occur in the interval of the angles in which the casing of the spool moves to a distance less than the full turn or equal to it. The piece of FL 2 P determines the value of the moment created by the power cylinder relative to the pivota, and the product F radi L E K O.С P is the reaction force from the feedback side by the value of the stabilizing moment. The influence of the moment created by the centering springs can be neglected due to its smallness compared to stabilizing.
Thus, in addition to the above assumptions, the following restrictions are superimposed on the system:
- efforts in the longitudinal thrust are linearly dependent on the turn of the shaft of the tower, friction in the hinge of the longitudinal traction and in the drive to the spool is missing;
- the distributor is a link with a relay characteristic, that is, to a certain displacement Δx 0 of the spool in the housing, the liquid from the pump does not enter the power cylinder;
- the pressure in the pressure line and the power cylinder is directly proportional to the excess volume of the fluid entered into the highway, i.e., the bulk rigidity of the hydraulic system C is constant.
The considered steering control circuit with a hydraulic amplifier is described by the system of seven equations (26) - (32).
The study of the stability of the system was carried out using an algebraic criterion Raus Gurvitsa.
For this, several transformations are produced. The characteristic equation of the system and its stability is found, which is determined by the following inequality:
(33)
From inequality (33) it follows that at a≤Δx 0 oscillations are not possible, since the negative member of the inequality is 0.
The amplitude of the movement of the spool in the housing at a given permanent amplitude of the oscillations of the controlled wheels θ max is from the following relationship:
(34)
If, with an angle θ max, the pressure P \u003d P max, then the move A depends on the ratio of the tightness of the centering springs and the longitudinal thrust C N / C 1, the area of \u200b\u200bthe reactive plungers F R.E, the preliminary compression force of the centering springs T n and the coefficient of the K OS. The greater the ratio C N / C 1 and the area of \u200b\u200bthe jet elements, the more likely it is that the value of A will be less than the value Δx 0, and self-oscillations are impossible.
However, this path of elimination of self-oscillations is not always possible, as an increase in the rigidity of the centering springs and the size of the jet elements, increasing the force on the steering wheel, affect the controllability of the car, and the reduction of the hardness of the longitudinal thrust can contribute to the occurrence of vibrations type Shimmi.
In four of the five positive members of inequality (33), it includes a factor in the parameter of rod, characterizing friction in the steering, rubber tires and damping due to fluid flows in the amplifier. Typically, the constructor is difficult to vary this parameter. As a factory in a negative term, the fluid flow rate Q 0 and the feedback coefficient K O.S. With a decrease in their values, the tendency to self-oscillation decreases. The value of Q 0 is close to pump performance. So, to eliminate the self-oscillating caused by the amplifier during the movement of the car, it is required:
- Increasing the rigidity of centering springs or an increase in the area of \u200b\u200bjet plungers, if possible, by the conditions of ease of steering.
- Reducing the pump performance without lowering the rotation speed of the controlled wheels below the minimum permissible.
- Reducing the coefficient of amplification of feedback K O.S., i.e., reducing the stroke of the spool hull (or spool) caused by the rotation of the controlled wheels.
If these methods cannot be eliminated by self-oscillations, then it is necessary to change the layout layout or enter a special oscillation damper (liquid or dry friction damper) into the steering system with an amplifier. Consider another possible option for laying an amplifier by car with a smaller propensity to excitation of self-oscillations. It differs from the previous shorter feedback (see the bar line in Fig. 34 and 35).
The distributor equations and drive to it differ from the corresponding equations of the previous scheme.
The drive equation to the distributor is viewed at t C\u003e T N:
(35)
2 Equation of the distributor
(36)
where I E is a kinematic transfer ratio between the movement of the distributor's spool and the corresponding movement of the stem cylinder.
A similar study of the new system of equations leads to the following condition for the absence of self-oscillations in a short-feedback system.
(37)
The resulting inequality differs from inequality (33) an increased value of positive members. As a result, all positive terms are more negative with the real values \u200b\u200bof the parameters included in them, so the system with a short feedback is almost always stable. Friction in the system characterized by parameter r can be reduced to zero, since the fourth positive member of the inequality does not contain this parameter.
In fig. 37 The curves of the dependence of the friction values \u200b\u200brequired to waste oscillations in the system (parameter d) on the performance of the pump calculated by formulas (33) and (37) are presented.
The stability zone for each of the amplifiers is between the axis of the ordinate and the corresponding curve. When calculating the amplitude of the oscillations of the spool in the case, it was made minimally possible from the condition of turning on the amplifier: a≥Δx 0 \u003d 0.05 cm.
The remaining parameters included in equations (33) and (37) had the following values \u200b\u200b(which approximately corresponds to the steering control truck Load capacity 8-12 T.): J \u003d 600 kg * cm * sec 2 / glad; N \u003d 40 000 kg * cm / happy; Q \u003d 200 cm 3 / s; F \u003d 40 cm 2; L 2 \u003d 20 cm; L 3 \u003d 20 cm; c r \u003d 2 kg / cm 5; C 1 \u003d 500 kg / cm; C 2 \u003d 500 kg / cm; C n \u003d 100 kg / cm; F R.E \u003d 3 cm 2.
The amplifier with a long feedback is a zone of instability lies in the range of real values \u200b\u200bof the G parameter, the amplifier with a short feedback - in the range of non-encountered parameter values.
Consider the oscillations of the controlled wheels arising from the turns on the spot. The indicator diagram of the power cylinder during such oscillations is shown in Fig. 33, the dependence of the amount of fluid incoming in the power cylinder on the movement of the spool in the dispenser's housing is viewed in Fig. 36, b. During such oscillations, the gap Δx 0 in the spool is already eliminated by the rotation of the steering wheel and at the slightest shift of the spool causes the flow of fluid into the power cylinder and the pressure growth in it.
Linearization of the function (see Fig. 36, c) gives the equation
(38)
The N in equation (32) will be determined in this case not by the action of the stabilizing moment, but the brutality of tires to twisting in contact. It can be adopted for the system considered as an example N \u003d 400 000 kg * cm / pleased.
The stability condition for a long-feedback system can be obtained from equation (33) by substituting into it instead of expression Expressions (2Q 0 / πa).
As a result, we get
(39)
Members of inequality (39) containing the parameter A in a numerator decrease with a decrease in the amplitude of oscillations and, starting with some sufficiently small values \u200b\u200bof A, they can be neglected. Then the stability condition is expressed in a simpler form:
(40)
With the actual ratios of parameters, the inequality is not observed and amplifiers composed according to a diagram with a long feedback, almost always cause auto-oscillations of controlled wheels when turning on a place with a particular amplitude.
To eliminate these oscillations without changing the type of feedback (and, consequently, the layout of the amplifier) \u200b\u200bcan be reduced to some extent a change in the shape of the characteristics Q \u003d F (Δx), giving it a tilt (see Fig. 36, d), or a significant increase in damping in the system (parameter d). Technically, there are special squeaks on the working edges of the spools to change the form of the characteristics. The calculation of the system for stability with such a distributor is much more complicated, since the assumption that the amount of liquid q entering the power cylinder depends only on the offset of the Δx spool, it can no longer be accepted, because the working segment of the working slots is stretched and the number of incoming Fluid q on this section also depends on the pressure drop in the system to the spool and after it. The method of increasing damping is discussed below.
Consider what happens when turning on the spot if a short feedback is carried out. In equation (37) expression [(4π) (Q 0 / A)] √ should be replaced by an expression (2 / π) * (Q 0 / a). As a result, we get inequality
(41)
Excluding, as in the previous case, members containing the amount and in the numerator, we get
(42)
In inequality (42), a negative term is about an order of magnitude less than in the previous one, and therefore in the system with a short feedback in real combinations of auto-oscillation parameters do not occur.
Thus, to obtain a well-stable steering system with a hydraulicer, feedback should be covered only by almost non-indication links of the system (usually a power cylinder and associated connecting parts directly). In the most difficult cases, when it is not possible to comply with the power cylinder and the distributor in close proximity to one of the other for cleaning the auto-oscillation into the system, the hydrodempefhers (shock absorbers) or hydraulic cylinders - devices transmitting liquid in the power cylinder or back only under the action of pressure from the distributor.
Loads and voltages acting in steering parts can be calculated by setting the maximum force on the steering wheel or determining this force to the maximum resistance to the rotation of the car's controlled wheels on the spot (which is more appropriate). These loads are static.
IN steering mechanism Calculate steering wheel, steering shaft and steering.
Maximum effort on steering wheel For steering controls without amplifiers -
\u003d 400 N; For cars with amplifiers - 
\u003d 800 N.
When calculating the maximum effort on the steering wheel to the maximum resistance to the rotation of the controlled wheels at the site of the resistance, the turn can be determined by empirical dependence:
,
(13.12)
where 
-Caffefing when rotating the controlled wheel in place; 
- load on the wheel; 
- Air pressure in the tire.
Effort on the steering wheel for turning on site is calculated by the formula:
,
(13.13)
where 
- angular gear ratio of steering; 
- steering wheelradius; 
- CPD steering.
According to a predetermined or found force on the steering wheel, the loads and voltages in the steering parts are calculated.
Spokes the steering wheel is calculated on the bend, assuming that the force on the steering wheel is distributed between the spokes of equally. The bending stresses of the spokes are determined by the formula:
,
(13.14)
where 
-Tlin needles; 
- the diameter of the needles; 
- Specz.
Steering Val. Typically perform tubular. The shaft works for a twist, loading the moment:
.
(13.15)
The tension voltage of the tubular shaft is calculated by the formula:
,
(13.16)
where 
,
-Ador and inner shaft diameters, respectively.
Permissible steering voltages of the steering shaft - [ 
] \u003d 100 MPa.
The steering shaft is also tested for rigidity around the corner of twisting:
,
(13.17)
where 
-Tlin shaft; 
- Module elasticity of the 2nd kind.
Valid twisting angle - [ 
] \u003d 5 ÷ 8 ° per meter of the shaft length.
IN worm-roller steering The global worm and roller are calculated on compression, contact voltages in engagement at which is determined by the formula:
,
(13.18)
where 
- Surgery, acting on the worm; 
- the area of \u200b\u200bcontact of one roller crest with a worm; 
-In the ridges of the roller.
The axial force acting on the worm is calculated by the formula:
,
(13.19)
where 
- the initial radius of the worm in the smallest section; 
- An angle of lifting the helm of the worm.
The area of \u200b\u200bcontact of one roller crest with a worm can be determined by the formula:
where 
and 
- Roller and worm engagement frames, respectively; 
and 
- Roller and worm engagement angles.
Permissible compression stresses - [
] \u003d 2500 ÷ 3500 MPa.
IN vinograde transmission The pair "Screw - Ball Nut" is checked for compression, taking into account the radial load on one ball:
,
(13.21)
where 
–
number of work turns; 
–
the number of balls on one turn (with full filling of the groove); 
–
contact angle balls with grooves.
The strength of the ball is determined by contact stresses calculated by the formula:
,
(13.22)
where 
–
the coefficient of curvature of contacting surfaces; 
–
module of elasticity of the 1st kind; 
and 
–
ball diameters and grooves, respectively.
Permissible contact stresses [ 
] \u003d 2500 ÷ 3500 MPa.
In a pair of "Reik - Sector", the bending teeth and contact voltages are calculated similarly to cylindrical engagement. In this case, the circumferential force on the teeth of the sector (in the absence or non-working amplifier) \u200b\u200bis determined by the formula:
,
(13.23)
where 
- Radius of the initial circumference of the sector.
Valid voltages - [ 
] \u003d 300 ÷ 400 MPa; [ 
] \u003d 1500 MPa.
Rush steering Calculate in the same way.
IN steering drive Calculate the shaft of the steering bump, the steering bush, the finger of the steering bump, the longitudinal and transverse steering rods, the rotary lever and the levers of the swivel fists (swivel tracks).
Tree steering bump Calculate for twist.
In the absence of a voltage amplifier, the tower shaft is determined by the formula:
,
(13.24)
where 
- Cup shaft diameter.
Valid voltages - [ 
] \u003d 300 ÷ 350 MPa.
Calculation of Cushka spend on bending and twist in a dangerous section BUT-BUT.
In the absence of an amplifier, the maximum force acting on the ball finger from the longitudinal steering traction is calculated by the formula:
,
(13.25)
where 
- Training between the centers of the steering tower heads.
Cushion bending voltage is determined by the formula:
,
(13.26)
where 
- Top bending shoulder; a. and b. - sizes of the cross section.
The tension voltage of the bore is determined by the formula:
,
(13.27)
where 
- Breaking.
Valid stresses [ 
] \u003d 150 ÷ \u200b\u200b200 MPa; [ 
] \u003d 60 ÷ 80 MPa.
Ball Finger Cushkin Calculate on bending and slice in a dangerous section B.-B. And on the crumpled between the crown of the longitudinal steering thrust.
Thick thread bending voltage calculated by the formula:
,
(13.28)
where e. - Finger bending shoulder; 
Diameter finger in a dangerous section.
Finger cut voltages are determined by the formula:
.
(13.29)
The stress of the finger crumpled is calculated by the formula:
,
(13.30)
where 
- diameter of the ball head of the finger.
Valid voltages - [ 
] \u003d 300 ÷ 400 MPa; [ 
] \u003d 25 ÷ 35 MPa; [ 
] \u003d 25 ÷ 35 MPa.
Calculation of ball fingers of longitudinal and transverse steering It is carried out similar to the calculation of the ball finger of the steering tower, taking into account the current loads on each finger.
Longitudinal steering Calculate on compression and longitudinal bending.
N. 
adjustments of compression are determined by the formula:
,
(13.31)
where 
- area cross section traction.
With longitudinal bending, critical stresses occur in the rod, which are calculated by the formula:
,
(13.32)
where 
- module elasticity of the 1st; J. - moment of inertia of tubular section; 
- Length of thrust on the centers of the ball fingers.
The stability supply of thrust can be determined by the formula:
.
(13.33)
The stability supply of traction must be - 
\u003d 1.5 ÷ 2.5.
Cross steering traction loaded by force:
,
(13.34)
where 
and 
- The active lengths of the swivel lever and the lever of the swivel fist, respectively.
The transverse steering crave is calculated on compression and a longitudinal bend just like the longitudinal steering.
Rotary lever Calculate on bending and twist.
.
(13.35)
.
(13.36)
Valid voltages - [ 
] \u003d 150 ÷ \u200b\u200b200 MPa; [ 
] \u003d 60 ÷ 80 MPa.
Rotary Kulakov levers Also calculated on bending and twist.
Bend voltage is determined by the formula:
.
(13.37)
Tension voltages are calculated by the formula:
.
(13.38)
Thus, in the absence of an amplifier, the strength calculation of the steering parts is the maximum force on the steering wheel. With an amplifier, the parts of the steering drive located between the amplifier and controlled wheels are loaded, in addition, an effort developed by the amplifier, which must be considered when calculating.
Calculation of amplifier Usually includes the following steps:
select the type and layout of the amplifier;
static calculation - determination of forces and movements, sizes of the hydraulic cylinder and distribution device, centering springs and areas of jet chambers;
dynamic calculation - determination of the inclusion of the amplifier, the analysis of oscillations and stability of the amplifier;
hydraulic calculation - determination of pump performance, pipeline diameters, etc.
The loads that act on the steering parts can be taken by loads arising when driving driven wheels on road irregularities, as well as loads arising in a steering wheel drive, for example, when braking due to unequal brake forces on controlled wheels or when breaking Tires of one of the controlled wheels.
These additional calculations allow you to fully estimate the strength characteristics of the steering parts.
Steering drivepresenting a system of thrust and levers, serves to transmit effort from bustling on the rotary pin and the implementation of the specified dependence between the angles of rotation of the controlled wheels. When designing steering controls, kinetic and power calculation of the steering actuator and the strength calculation of the nodes and parts of the steering is performed.
The main task of the kinematic calculation of the steering drive is to determine the angles of rotation of the controlled wheels, finding gear ratios The steering mechanism, drive and control in general, the choice of the parameters of the steering trapezoid and coordination of the kinematics of the steering and suspension. Based on the geometry of trolleybus rotation (Fig. 50), provided that the controlled front wheels roll without slipping and their instantaneous turning center lies at the intersection of the axes of the rotation of all wheels outdoor, and internal corners turnwheels are associated with addiction:
, (4)
where - the distance between the intersection points of the axes of the kingnery with the support surface.
Figure 50. Turning circuit Trolleybus excluding the side elasticity of tires.
From the resulting expression (4) it follows that the difference in the corners of the turning of external and internal controlled wheels should always be a permanent value, and the instantaneous center of rotation of the trolleybus (point 0) must lie on the continuation of an unmanaged axis.
Only subject to these theoretical conditions the weight of the wheel of the trolleybus on the rotation will move without slip, i.e. Have pure combination. From the steering trapezium it is required that it ensures that the ratio between the angles of rotation of the controlled wheels can be protected from geometry.
The parameters of the steering trapezium are a pivot width (Fig. 51), distance pbetween the centers of the ball hinges of the trapezium levers; length t.and corner θ
tilt levers of rotary pin. Selection of trapezium parameters when tight in the lateral direction of controlled wheels begins with an angle definition θ
tilt levers of trapezium. They are located so that but -(0.7...0.8,)L. for rear location transverse thrust. Angle θ
can be found for maximum theoretical angles and 
according to the formula:
or by the graphs given on (Fig. 7b). Angle value θ \u003d 66 ... 74 °, and the ratio of the length of the levers to the length of the transverse thrust t / n \u003d0.12 .... 0.16. Length m. They are taken possible greater under the layout conditions. Then
.
Figure 51. Scheme of the steering trapezium and addiction a / L. from l 0 / L 1-3: Ply m / N. equal, respectively, 0.12; 0.14; 0.16.
Common kinematic transfer number of steering, determined by gear ratios of the mechanism U M.and drive U PCequally, the ratio of the full angle of rotation of the steering wheel to the corner of the wheel turning from the stop until it stops
.
For normal work steering drive maximum angles A, and A, is within 
. For trolleybuses, the total number of revolutions of the steering wheel when rotating the controlled wheels on 40 o (± 20 °) from the neutral position should not exceed 3.5 ( =
1260 o) without taking into account the angle of free turning of the steering wheel, which corresponds to 
.
The schematic layout of the steering drive is performed to determine the size and location in the scene space, thrust and levers, as well as the transfer number of the drive. At the same time, they strive to ensure the simultaneous symmetry of the extreme positions of the oxca relative to its neutral position, as well as the equality of the kinematic gear ratios of the drive when the wheels are rotated both to the right and left. If the angles between the compound and the longitudinal burden, as well as between the thrust and the rotary lever in its extreme position are approximately the same, then these conditions are performed.
Efforts are determined in the force calculation: necessary for the rotation of the controlled wheels on the spot developing the amplifier cylinder; on the steering wheel with a working and non-working amplifier; on the steering wheel on the side of the reactive elements of the distributor; on the wheels when braking; On separate parts of the steering.
Force F.necessary for the rotation of the controlled wheels on the horizontal surface of the trolleybus, is based on the total moment M Σ.on the chapels of controlled wheels:
where M F.-Moment resistance to rolling controlled wheels when turning around a pivot; M φ.-Moment resistance of deformation of tires and friction in contact with the support surface in the consequence of the tire slipping; M β, M φ.-Moments caused by the transverse and longitudinal slope of the kingle (Fig. 8).
Figure 52. To calculate the moment of resistance to the rotation of the wheel.
The moment of resistance to rolling the controlled wheels when it turns around the squastine is determined by the dependence:
,
where f.- the coefficient of resistance to rolling; G 1.– axial load transmitted by controlled wheels; - Radius of running the wheel around the axis of the pivot: \u003d 0.06 ... 0.08 m; l.-Tlin pin; r 0-Creative radius of the wheel; λ - the corner of the collapse of the wheels; β - The angle of inclination of the kkvorn.
The moment of resistance of the deformation of tires and friction in contact with the support surface in the consequence of tire slippage is determined by the dependence:
,
where - Shoulder of the friction force of slipping relative to the tire print center.
If we take that the pressure on the area of \u200b\u200bthe imprint is distributed evenly,
,
where is the free radius of the wheel. In the case when.
When calculating the clutch coefficient with a support surface is selected maximum φ= 0.8.
The moments caused by the transverse and longitudinal slope of the kingnery are equal:
where - the average angle of rotation of the wheel; 
; γ
- The angle of inclination of the pivot back.
Effort on the rim of the steering wheel
,
where is the radius of the steering wheel; η - RED steering: η= 0.7…0.85.
