A. A. Enaev
Cars.
Design and calculation
steering controls
Educational and methodological manual
Bratsk 2004
|
2. PURPOSE, REQUIREMENTS AND CLASSIFICATION… 3. CHOOSING A METHOD FOR TURNING VEHICLES……… 4. SELECTION OF STEERING SCHEME……………. 5. STEERING MECHANISMS…………………………….. 5.1. Purpose, requirements, classification……………... 5.2. Estimated parameters of the steering mechanism………….. 5.3. Selecting the type of steering mechanism………………………. 5.4. Materials used for the manufacture of steering mechanisms……………………………………………………………………... 6. STEERING DRIVES………………………………………………………. 6.1. Purpose, requirements, classification……………... 6.2. Estimated parameters of the steering drive…………….. 6.3. Selecting the type of steering drive…………………………. 6.4. Materials used for the manufacture of steering gears……………………………………………………… 7. POWER STEERING……………….. 7.1. Purpose, requirements, classification……………... 7.2. Estimated power steering parameters………………………………………………………………. 7.3. Selecting an amplifier layout………………... 7.4. Amplifier pumps………………………………………………………... 7.5. Materials used for the manufacture of pump amplifiers……………………………………………………………………... 8. CALCULATION OF STEERING…………………………... 8.1. Kinematic calculation of the steering drive……………. 8.2. Steering ratio……………. 9. POWER CALCULATION OF STEERING………... 9.1. Steering wheel force……………………………… 9.2. The force developed by the amplifier cylinder………….. 9.3. Force on wheels when braking…………………... 9.4. Forces on transverse and longitudinal rods…………… 10. HYDRAULIC CALCULATION OF THE AMPLIFIER…………… 11. STRENGTH CALCULATION OF STEERING CONTROL.. 11.1. Calculation of steering mechanisms……………………………... 11.2. Calculations of steering drives…………………………… |
Design and calculation of steering controls is one of the components of the course project in the discipline "Cars".
At the first stage of the course design, it is necessary to perform a traction calculation and study the operational properties of the car, using the guidelines “Cars. General provisions. Traction calculation" and then proceed, in accordance with the assignment, to the design and calculation of the unit or vehicle chassis system.
When designing and calculating steering controls, it is necessary to select the recommended literature and carefully read this manual. The sequence of work on designing and calculating steering controls is as follows:
1. Select the method of turning the car, the steering scheme, the type of steering mechanism, and the amplifier layout (if necessary).
2. Perform kinematic calculations, force calculations, hydraulic calculations of the amplifier (if the steering system is equipped with an amplifier).
3. Select the dimensions of the parts and perform a strength calculation.
This training manual describes in detail how to perform all these types of work.
2. PURPOSE, REQUIREMENTS AND CLASSIFICATION
Steering– this is a set of devices that serve to turn the steered wheels of a car when the driver acts on the steering wheel and consists of a steering mechanism and a drive (Fig. 1).
The steering gear is the part of the steering from the steering wheel to the steering arm, and the steering gear includes parts from the steering arm to the steering axle.
Rice. 1. Steering diagram:
1 – steering wheel; 2 – steering shaft; 3 – steering column; 4 – gearbox; 5 – steering bipod; 6 – longitudinal steering rod; 7 – rotary axle; 8 – steering axle lever; 9 – side lever; 10 – transverse thrust
The following requirements apply to the steering:
1) ensuring high maneuverability of vehicles, which makes sharp and fast turns possible in relatively limited areas;
2) ease of control, assessed by the amount of force applied to the steering wheel.
For passenger cars without power assistance when driving, this force is 50...100 N, and with power assistance - 10...20 N. For trucks, the force on the steering wheel is regulated: 250...500 N - for steering without power assistance; 120 N – for power steering;
3) rolling of the steered wheels with minimal lateral slip and slip when turning the car;
4) accuracy of the tracking action, primarily kinematic, in which any given position of the steering wheel will correspond to a well-defined pre-calculated curvature of rotation;
As noted above, power steering is a rudimentary automatic control system with tight feedback. With an unfavorable combination of parameters, a system of this type may turn out to be unstable. In this case, the instability of the system is expressed in self-oscillations of the driven wheels. Such fluctuations were observed on some experimental samples of domestic cars.
The task of dynamic calculation is to find conditions under which self-oscillations could not occur if all the necessary parameters for the calculation are known, or to identify which parameters should be changed in order to stop self-oscillations on the experimental sample, if they are observed.
Let us first consider the physical essence of the process of vibration of the steered wheels. Let us turn again to the amplifier circuit shown in Fig. 1. The amplifier can be turned on both by the driver when applying force to the steering wheel, and by the driven wheels from shocks from the road.
As experiments show, such vibrations can occur during straight-line movement of a car at high speed, when turning when moving at low speed, and also when turning wheels in place.
Let's consider the first case. When turning the steered wheel due to shocks from the road or for any other reason, the distributor body will begin to move relative to the spool, and as soon as the gap Δ 1 is eliminated, the liquid will begin to flow into cavity A of the power cylinder. The steering wheel and steering bipod are considered stationary. The pressure in cavity A will increase and prevent further turning. Due to the elasticity of the rubber hoses of the hydraulic system and the elasticity of the mechanical connections, filling cavity A with liquid (to create working pressure) requires a certain time, during which the steered wheels have time to turn at a certain angle. Under the influence of pressure in cavity A, the wheels will begin to turn in the other direction until the spool reaches the neutral position. Then the pressure decreases. The inertial force, as well as the residual pressure in cavity A, will turn the steered wheels from the neutral position to the right, and the cycle will repeat from the right cavity.
This process is depicted in Fig. 33, a and b.
The angle θ 0 corresponds to the rotation of the steered wheels at which the force transmitted to the steering drive reaches the value necessary to move the spool.
In Fig. Figure 33c shows the dependence p = f(θ), constructed from the curves in Fig. 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 of the amplifier. The area of the indicator diagram determines the work expended by the amplifier to swing the steered wheels.
It should be noted that the described process can only be observed if the steering wheel remains stationary when the steering wheels oscillate. If the steering wheel is turned, the power does not turn on. For example, amplifiers with distributor drives from the angular displacement of the upper part of the steering shaft relative to the lower part usually have this property and do not cause self-oscillations
When the steered wheels are turned in place or when the car is moving at low speed, the oscillations caused by the amplifier differ in nature from those considered. The pressure during such oscillations increases only in one cavity. The indicator diagram for this case is shown in Fig. 33, g.
Such fluctuations can be explained as follows. If at the moment corresponding to the rotation of the wheels through a certain angle θ r, the steering wheel is held back, then the steered wheels (under the influence of inertia forces and residual pressure in the power cylinder) will continue to move and turn through an angle θ r + θ max. The pressure in the power cylinder will drop to 0, since the spool will be in a position corresponding to the rotation of the wheels through an angle θ r. After this, the elastic force of the tire will begin to turn the steered wheel in the opposite direction. When the wheel turns again through an angle θ r, the amplifier turns on. The pressure in the system will not begin to increase immediately, but after some time, during which the steered wheel can rotate through an angle θ r -θ max. The turn to the left will stop at this moment, as the power cylinder will come into operation, and the cycle will repeat from the beginning.
Typically, the work of the amplifier, determined by the area of the indicator diagrams, is insignificant compared to the work of friction in the pins, steering rod joints and rubber, and self-oscillations are not possible. When the areas of indicator diagrams are large and the work determined by them is comparable to the work of friction, undamped oscillations are possible. Such a case is examined below.
To find the conditions for the stability of the system, we will impose restrictions on it:
- The steered wheels have one degree of freedom and can only rotate around the king pins within the clearance in the power distributor.
- The steering wheel is firmly fixed in the neutral position.
- The connection between the wheels is absolutely rigid.
- The mass of the spool and the parts connecting it to the control wheels is negligible.
- The friction forces in the system are proportional to the first powers of angular velocities.
- The rigidities of the system elements are constant and do not depend on the magnitude of the corresponding displacements or deformations.
The remaining assumptions made during the analysis are specified during the presentation.
Below we examine the stability of steering controls with hydraulic boosters mounted in two possible options: with long feedback and short.
The structural and design diagrams of the first option are shown in Fig. 34 and 35 are solid lines, the second is dashed. In the first option, feedback acts on the distributor after the power cylinder has rotated the steered wheels. In the second option, the distributor body moves, turning off the amplifier, simultaneously with the power cylinder rod.
First, let's look at each element of the long-loop circuit.
Steering gear(not shown on the block diagram). Turning the steering wheel at a certain small angle a causes a force T c in the longitudinal thrust
T c = c 1 (αi r.m l c - x 1), (26)
where c 1 is the stiffness of the steering shaft and longitudinal thrust reduced to the longitudinal thrust; l c - bipod length; x 1 - spool movement.
Distributor drive. For the distributor control drive, the input quantity is the force T c, the output quantity is the spool displacement x 1. The drive equation, taking into account feedback on the angle of rotation of the steered wheels θ and pressure in the system p, has the following form for T c >T n:
(27)
where K о.с is the feedback force coefficient for the angle of rotation of the steered wheels; c n - stiffness of the centering springs.
Distributor. The oscillations caused by the amplifier of a moving car are associated with the alternate activation of one or the other cavities of the power cylinder. The distributor equation in this case has the form
where Q is the amount of liquid entering the pipelines of the power cylinder; x 1 -θl з K о.с = Δx - displacement of the spool in the housing.
The function f(Δx) is nonlinear and depends on the design of the distributor spool and the pump performance. In the general case, given the characteristics of the pump and the design of the distributor, the amount of liquid Q entering the power cylinder depends both on the stroke Δx of the spool in the housing and on the pressure difference Δp at the inlet and outlet of the distributor.
Amplifier distributors are designed so that, on the one hand, with relatively large technological tolerances on linear dimensions, they have a minimum pressure in the system when the spool is in the neutral position, and on the other hand, a minimum displacement of the spool to drive the amplifier. As a result, the spool valve of the amplifier according to the characteristic Q = f(Δx, Δp) is close to the valve one, i.e., the value of Q does not depend on the pressure Δp and is only a function of the spool displacement. Taking into account the direction of action of the power cylinder, it will look as shown in Fig. 36, a. This characteristic is characteristic of relay links of automatic control systems. The linearization of these functions was carried out using the harmonic linearization method. As a result, we obtain for the first scheme (Fig. 36, a)
where Δx 0 is the displacement of the spool in the housing, at which a sharp increase in pressure begins; Q 0 - the amount of liquid entering the pressure line when the working slots are blocked; a is the maximum stroke of the spool in the housing, determined by the amplitude of vibration of the driven wheels.
Pipelines. The pressure in the system is determined by the amount of liquid entering the pressure line and the elasticity of the line:
where x 2 is the piston stroke of the power cylinder, positive direction towards the action of pressure; c 2 - volumetric rigidity of the hydraulic system; c g = dp / dV g (V g = volume of the hydraulic system pressure line).
Power cylinder. In turn, the stroke of the power cylinder rod is determined by the angle of rotation of the steered wheels and the deformation of the parts connecting the power cylinder with the steered wheels and with the fulcrum
(31)
where l 2 is the arm of application of the force of the power cylinder relative to the axes of the wheel pins; c 2 - rigidity of the power cylinder fastening, reduced to the stroke of the power cylinder rod.
Steered wheels. The equation for the rotation of the steered wheels relative to the pivots is of the second order and, generally speaking, is nonlinear. Considering that the vibrations of the steered wheels occur with relatively small amplitudes (up to 3-4°), it can be assumed that the stabilizing moments caused by the elasticity of the rubber and the inclination of the pivots are proportional to the first degree of the angle of rotation of the steered wheels, and the friction in the system depends on the first degree of the angular wheel turning speed. The linearized equation looks like this:
where J is the moment of inertia of the steered wheels and parts rigidly connected to them relative to the axes of the pins; G - coefficient characterizing friction losses in the steering gear, hydraulic system and wheel tires; N is a coefficient characterizing the effect of the stabilizing moment resulting from the inclination of the king pins and the elasticity of the tire rubber.
The stiffness of the steering drive is not taken into account in the equation, since it is assumed that the vibrations are small and occur in the range of angles at which the spool body moves a distance less than or equal to the full stroke. The product Fl 2 p determines the magnitude of the moment created by the power cylinder relative to the kingpin, and the product f re l e K o.s p is the force of reaction from the feedback to the magnitude of the stabilizing moment. The influence of the moment created by the centering springs can be neglected due to its smallness compared to the stabilizing one.
Thus, in addition to the above assumptions, the following restrictions are imposed on the system:
- the forces in the longitudinal thrust linearly depend on the rotation of the bipod shaft; there is no friction in the longitudinal thrust joints and in the drive to the spool;
- the distributor is a link with a relay characteristic, i.e., until a certain displacement Δx 0 of the spool in the housing, 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 fluid entering the line, i.e., the volumetric stiffness of the hydraulic system c g is constant.
The considered hydraulic power steering scheme is described by a system of seven equations (26) - (32).
The study of system stability was carried out using an algebraic criterion Rous-Hurwitz.
To achieve this, several transformations have been made. The characteristic equation of the system and the condition for its stability are found, which is determined by the following inequality:
(33)
From inequality (33) it follows that when a≤Δx 0 oscillations are impossible, since the negative term of the inequality is equal to 0.
The amplitude of movement of the spool in the housing at a given constant amplitude of oscillation of the driven wheels θ max is found from the following relationship:
(34)
If at angle θ max the pressure p = p max, then the displacement a depends on the ratio of the stiffnesses of the centering springs and longitudinal thrust c n / c 1, the area of the reaction plungers f r.e., the precompression force of the centering springs T n and the feedback coefficient K os. The larger the ratio c n / c 1 and the area of the reactive 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 way of eliminating self-oscillations is not always possible, since an increase in the stiffness of the centering springs and the size of the reaction elements, increasing the forces on the steering wheel, affect the vehicle's controllability, and a decrease in the rigidity of the longitudinal thrust can contribute to the occurrence of shimmy-type oscillations.
Four of the five positive terms of inequality (33) include as a factor the parameter Г, which characterizes friction in the steering, tire rubber and damping due to fluid flows in the amplifier. It is usually difficult for a designer to vary this parameter. The negative term includes the liquid flow rate Q0 and the feedback coefficient K o.s. as factors. As their values decrease, the tendency to self-oscillation decreases. The value of Q 0 is close to the pump performance. So, to eliminate self-oscillations caused by the amplifier while the car is moving, you need:
- Increasing the stiffness of the centering springs or increasing the area of the reaction plungers, if this is possible due to ease of steering.
- Reducing pump performance without reducing the steering speed of the steering wheels below the minimum permissible.
- Reducing the feedback gain K o.s., i.e. reducing the stroke of the spool body (or spool) caused by the rotation of the steered wheels.
If these methods cannot eliminate self-oscillations, then it is necessary to change the steering layout or introduce a special vibration damper (liquid or dry friction damper) into the power steering system. Let's consider another possible arrangement of an amplifier on a car, which has a lesser tendency to excite self-oscillations. It differs from the previous one in shorter feedback (see the dashed line in Fig. 34 and 35).
The equations of the distributor and the drive to it differ from the corresponding equations of the previous diagram.
The drive equation to the distributor has the form for T c >T n:
(35)
2 distributor equation
(36)
where i e is the kinematic transmission ratio between the movement of the distributor spool and the corresponding movement of the power cylinder rod.
A similar study of the new system of equations leads to the following condition for the absence of self-oscillations in a system with short feedback
(37)
The resulting inequality differs from inequality (33) in the increased value of the positive terms. As a result, all positive terms are larger than negative ones for the real values of the parameters included in them, so a system with short feedback is almost always stable. Friction in the system, characterized by the parameter Г, can be reduced to zero, since the fourth positive term of the inequality does not contain this parameter.
In Fig. Figure 37 shows the dependence curves of the amount of friction required to dampen oscillations in the system (parameter G) on the pump performance, calculated using formulas (33) and (37).
The stability zone for each amplifier is located between the ordinate axis and the corresponding curve. In the calculations, the amplitude of oscillation of the spool in the housing was taken to be the minimum possible from the condition of turning on the amplifier: a≥Δx 0 = 0.05 cm.
The remaining parameters included in equations (33) and (37) had the following values (which approximately corresponds to the steering control of a truck with a carrying capacity 8-12 t): J = 600 kg*cm*sec 2 / rad; N = 40,000 kg*cm / rad; Q = 200 cm 3 / sec; F = 40 cm 2; l 2 = 20 cm; l 3 = 20 cm; c g = 2 kg/cm 5; c 1 = 500 kg/cm; c 2 = 500 kg/cm; c n = 100 kg/cm; f r.e = 3 cm 2.
For an amplifier with long feedback, the instability zone lies in the range of real values of the parameter Г, for an amplifier with short feedback - in the range of non-occurring parameter values.
Let us consider the vibrations of the steered wheels that occur when turning in place. The indicator diagram of the power cylinder during such oscillations is shown in Fig. 33, g. The dependence of the amount of liquid entering the power cylinder on the movement of the spool in the distributor body has the form shown in Fig. 36, b. During such oscillations, the gap Δx 0 in the spool has already been eliminated by turning the steering wheel and, at the slightest displacement of the spool, causes a flow of fluid into the power cylinder and an increase in pressure in it.
Linearization of the function (see Fig. 36, c) gives the equation
(38)
The coefficient N in equation (32) will be determined in this case not by the effect of the stabilizing moment, but by the severity of the tires on torsion in contact. For the system considered as an example, it can be taken equal to N = 400,000 kg*cm/rad.
The stability condition for a system with long feedback can be obtained from equation (33) by substituting into it instead of the expression expressions (2Q 0 / πa).
As a result we get
(39)
The terms of inequality (39), containing the parameter a in the numerator, decrease with decreasing oscillation amplitude and, starting from some sufficiently small values of a, they can be neglected. Then the stability condition is expressed in a simpler form:
(40)
With real parameter ratios, the inequality is not observed and amplifiers arranged according to a circuit with long feedback almost always cause self-oscillations of the driven wheels when turning in place with one amplitude or another.
It is possible to eliminate these oscillations without changing the type of feedback (and, consequently, the layout of the amplifier) to some extent only by changing the shape of the characteristic Q = f(Δx), giving it a slope (see Fig. 36, d), or by significantly increasing the damping in the system (parameter G). Technically, to change the shape of the characteristics, special bevels are made on the working edges of the spools. Calculating the stability of a system 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 displacement of the spool Δx can no longer be accepted, because the working area of overlapping the working slots is stretched and the amount of incoming fluid Q in this section also depends on the pressure difference in the system before and after the spool. The method of increasing damping is discussed below.
Let's consider what happens when turning in place if short feedback is provided. In equation (37), the expression [(4π) (Q 0 / a)]√ should be replaced by the expression (2 / π)*(Q 0 / a). As a result, we obtain the inequality
(41)
Having excluded, as in the previous case, the terms containing the value a in the numerator, we obtain
(42)
In inequality (42), the negative term is approximately an order of magnitude smaller than in the previous one, and therefore, in a system with short feedback, self-oscillations do not occur under realistically possible combinations of parameters.
Thus, in order to obtain a knowingly stable power steering system, the feedback should cover only the practically inertia-free parts of the system (usually the power cylinder and the connecting parts directly associated with it). In the most difficult cases, when it is not possible to arrange the power cylinder and the distributor in close proximity to one another, to dampen self-oscillations, hydraulic dampers (shock absorbers) or hydraulic locks are introduced into the system - devices that allow fluid to pass into the power cylinder or back only when pressure is applied from the distributor.
The loads and stresses acting in the steering parts can be calculated by setting the maximum force on the steering wheel or determining this force by the maximum resistance to turning the steering wheels of the car in place (which is more appropriate). These loads are static.
IN steering gear The steering wheel, steering shaft and steering gear are calculated.
Maximum force per steering wheel for steering systems without power amplifiers –
= 400 N; for cars with amplifiers – 
= 800 N.
When calculating the maximum force on the steering wheel based on the maximum resistance to turning of the steered wheels in place, the moment of resistance to turning can be determined from the empirical relationship:
,
(13.12)
Where 
– coefficient of adhesion when turning the steered wheel in place; 
– wheel load; 
– air pressure in the tire.
The force on the steering wheel for turning in place is calculated by the formula:
,
(13.13)
Where 
– angular steering ratio; 
– steering wheel radius; 
– Steering efficiency.
Based on the given or found force on the steering wheel, the loads and stresses in the steering parts are calculated.
Spokes The bending of the steering wheel is calculated, assuming that the force on the steering wheel is distributed equally between the spokes. The bending stresses of the spokes are determined by the formula:
,
(13.14)
Where 
– knitting needle length; 
– spoke diameter; 
– number of spokes.
Steering shaft usually made tubular. The shaft works in torsion, loaded with torque:
.
(13.15)
The torsional stresses of the tubular shaft are calculated using the formula:
,
(13.16)
Where 
,
– outer and inner diameters of the shaft, respectively.
Permissible torsional stresses of the steering shaft – [ 
] = 100 MPa.
The steering shaft is also checked for rigidity based on the angle of twist:
,
(13.17)
Where 
– shaft length; 
–modulus of elasticity of the 2nd kind.
Allowable twist angle – [ 
] = 5 ÷ 8° per meter of shaft length.
IN worm-roller steering gear The globoid worm and roller are calculated for compression, the contact stresses in the mesh at which are determined by the formula:
,
(13.18)
Where 
– axial force acting on the worm; 
– contact area of one roller flange with the worm; 
– number of roller ridges.
The axial force acting on the worm is calculated using the formula:
,
(13.19)
Where 
– initial radius of the worm in the smallest section; 
– angle of elevation of the helix of the worm.
The contact area of one roller flange with the worm can be determined by the formula:
Where 
And 
– engagement radii of the roller and worm, respectively; 
And 
– angles of engagement of the roller and worm.
Allowable compression stresses – [
] = 2500 ÷ 3500 MPa.
IN rack and pinion gear the “screw – ball nut” pair is checked for compression, taking into account the radial load on one ball:
,
(13.21)
Where 
–
number of working turns; 
–
the number of balls on one turn (with the groove completely filled); 
–
the contact angle of the balls with the grooves.
The strength of the ball is determined by contact stresses, calculated using the formula:
,
(13.22)
Where 
–
coefficient of curvature of contacting surfaces; 
–
modulus of elasticity of the 1st kind; 
And 
–
diameters of the ball and groove, respectively.
Permissible contact stresses [ 
] = 2500 ÷3500 MPa.
In the “rack-sector” pair, teeth are calculated for bending and contact stresses similarly to cylindrical gearing. In this case, the circumferential force on the sector teeth (in the absence or inoperative amplifier) is determined by the formula:
,
(13.23)
Where 
– radius of the initial circle of the sector.
Permissible stresses – [ 
] = 300 ÷400 MPa; [ 
] = 1500 MPa.
Rack and pinion steering are calculated similarly.
IN steering gear calculate the steering bipod shaft, steering bipod, steering bipod pin, longitudinal and transverse steering rods, steering arm and steering knuckle levers (steering axles).
Bipod steering shaft count on torsion.
In the absence of a voltage amplifier for the bipod shaft, the bipod is determined by the formula:
,
(13.24)
Where 
– bipod shaft diameter.
Permissible stresses – [ 
] = 300 ÷350 MPa.
Bipod calculation carried out for bending and torsion in a dangerous section A-A.
In the absence of an amplifier, the maximum force acting on the ball pin from the longitudinal steering rod is calculated using the formula:
,
(13.25)
Where 
– the distance between the centers of the heads of the steering bipod.
Bipod bending stresses are determined by the formula:
,
(13.26)
Where 
– bipod bend arm; a And b– dimensions of the bipod section.
Bipod torsional stresses are determined by the formula:
,
(13.27)
Where 
– Torsion shoulder.
Permissible stress [ 
] = 150 ÷200 MPa; [ 
] = 60 ÷80 MPa.
Bipod ball pin are designed for bending and shearing in a dangerous section B-B and for crushing between the tie rods.
The bending stresses of the bipod pin are calculated using the formula:
,
(13.28)
Where e– finger bend shoulder; 
– diameter of the finger in the dangerous section.
The finger shear stress is determined by the formula:
.
(13.29)
The pin crushing stress is calculated using the formula:
,
(13.30)
Where 
– diameter of the ball head of the finger.
Permissible stresses – [ 
] = 300 ÷400 MPa; [ 
] = 25 ÷35 MPa; [ 
] = 25 ÷35 MPa.
Calculation of ball pins of longitudinal and transverse steering rods is carried out similarly to the calculation of the ball pin of the steering bipod, taking into account the current loads on each pin.
Longitudinal steering rod They are calculated for compression and longitudinal bending.
N 
Compression stress is determined by the formula:
,
(13.31)
Where 
– cross-sectional area of the rod.
During longitudinal bending, critical stresses arise in the rod, which are calculated using the formula:
,
(13.32)
Where 
–modulus of elasticity of the 1st kind; J– moment of inertia of the tubular section; 
– length of thrust at the centers of the ball pins.
The traction stability margin can be determined by the formula:
.
(13.33)
The traction stability margin should be – 
=1.5 ÷2.5.
Tie rod loaded by force:
,
(13.34)
Where 
And 
– active lengths of the steering arm and steering knuckle arm, respectively.
The transverse tie rod is designed for compression and longitudinal bending in the same way as the longitudinal tie rod.
Swivel lever count on bending and torsion.
.
(13.35)
.
(13.36)
Permissible stresses – [ 
] = 150 ÷ 200 MPa; [ 
] = 60 ÷ 80 MPa.
Steering knuckle arms also count on bending and torsion.
Bending stresses are determined by the formula:
.
(13.37)
Torsional stresses are calculated using the formula:
.
(13.38)
Thus, in the absence of an amplifier, the strength calculation of steering parts is based on the maximum force on the steering wheel. In the presence of an amplifier, the steering drive parts located between the amplifier and the steered wheels are also loaded with the force developed by the amplifier, which must be taken into account when making calculations.
Amplifier calculation usually includes the following steps:
choosing the type and layout of the amplifier;
static calculation - determination of forces and displacements, dimensions of the hydraulic cylinder and distribution device, centering springs and areas of the reaction chambers;
dynamic calculation - determination of the amplifier turn-on time, analysis of oscillations and stability of the amplifier;
hydraulic calculation - determination of pump performance, pipeline diameters, etc.
As control loads acting on the steering parts, we can take the loads that arise when the steered wheels hit road irregularities, as well as the loads that arise in the steering drive, for example, when braking due to unequal braking forces on the steered wheels or when breaking tires of one of the steered wheels.
These additional calculations allow us to more fully evaluate the strength characteristics of steering parts.
Steering gear, which is a system of rods and levers, serves to transmit force from the bipod to the steering axles and implement a given relationship between the angles of rotation of the steered wheels. When designing steering controls, kinetic and force calculations of the steering drive and strength calculations of steering components and parts are performed.
The main task of the kinematic calculation of the steering drive is to determine the angles of rotation of the steered wheels, find the gear ratios of the steering mechanism, drive and control as a whole, select the parameters of the steering linkage and coordinate the kinematics of the steering and suspension. Based on the turning geometry of the trolleybus (Fig. 50), provided that the steered front wheels roll without slipping and their instantaneous center of rotation lies at the intersection of the rotation axes of all wheels (outer and inner) rotation angles wheels are connected by dependence:
, (4)
where is the distance between the points of intersection of the axes of the pivots with the supporting surface.
Figure 50. Scheme of turning a trolleybus without taking into account the lateral elasticity of the tires.
From the obtained expression (4) it follows that the difference between the cotangents of the rotation angles of the external and internal steered wheels must always be a constant value, and the instantaneous center of rotation of the trolleybus (point 0) must lie on the extension of the unsteered axis.
Only if these theoretical conditions are met will the weight of the trolleybus wheel move without slipping when turning, i.e. have a clean rolling. The steering linkage is required to provide the relationships between the steering angles of the steering wheels that result from the steering geometry.
The parameters of the steering linkage are the pivot width (Fig. 51), distance P between the centers of the ball joints of the trapezoid arms; length T and angle θ
tilt of the steering axle arms. The selection of trapezoid parameters with lateral rigid steering wheels begins with determining the angle θ
tilting the trapezoid arms. They are positioned in such a way that A -(0.7...0.8,)L with a rear transverse link. Corner θ
can be found for maximum theoretical angles and 
according to the formula:
or according to the graphs shown in (Fig. 7b). Angle value θ = 66...74°, and the ratio of the length of the levers to the length of the transverse rod t/n = 0.12....0.16. Length m accept as much as possible according to the layout conditions. Then
.
Figure 51. Steering linkage diagram and dependence a/L from l 0 /L 1-3: when m/n equal to 0.12, respectively; 0.14; 0.16
The overall kinematic steering ratio, determined by the gear ratios of the mechanism U m and drive U pc equal to the ratio of the total angle of rotation of the steering wheel to the angle of rotation of the wheel from lock to lock
.
For normal operation of the steering drive, the maximum value of angles a, and a, is within the limits 
. For trolleybuses, the total number of steering wheel revolutions when turning the steered wheels by 40° (± 20°) from the neutral position should not exceed 3.5 ( =
1260 o) without taking into account the angle of free rotation of the steering wheel, which corresponds to 
.
A schematic layout of the steering drive is performed to determine the dimensions and spatial location of the bipod, rods and levers, as well as the drive gear ratio. At the same time, they strive to ensure simultaneous symmetry of the extreme positions of the bipod relative to its neutral position, as well as equality of kinematic gear ratios of the drive when turning the wheels both to the right and to the left. If the angles between the bipod and the longitudinal rod, as well as between the rod and the swing arm in its extreme position, are approximately the same, then these conditions are met.
In the power calculation, the forces are determined: those necessary to turn the steered wheels in place, developed by the amplifier cylinder; on the steering wheel with the power amplifier working and not working; on the steering wheel on the side of the distributor reactive elements; on wheels when braking; on individual steering components.
Force F, required to turn the steered wheels on the horizontal surface of the trolleybus, is found based on the total moment M Σ on the axles of the steered wheels:
Where M f– moment of resistance to rolling of the steered wheels when turning around the king pins; M φ– the moment of resistance to tire deformation and friction in contact with the supporting surface due to tire slipping; M β, M φ– moments caused by the transverse and longitudinal inclination of the kingpins (Fig. 8).
Figure 52. To calculate the moment of resistance to wheel rotation.
The moment of resistance to rolling of the steered wheels when turning around the kingpins is determined by the relationship:
,
Where f– rolling resistance coefficient; G 1– axial load transmitted by steered wheels; – radius of wheel rolling around the kingpin axis: =0.06...0.08 m; l– trunnion length; r 0– design radius of the wheel; λ – wheel camber angle; β – angle of inclination of the king pin.
The moment of resistance to tire deformation and friction in contact with the supporting surface as a result of tire slipping is determined by the relationship:
,
where is the arm of the sliding friction force relative to the center of the tire imprint.
If we assume that the pressure is distributed evenly over the print area,
,
where is the free radius of the wheel. In the case when .
When calculating the coefficient of adhesion with the supporting surface is selected as maximum φ= 0.8.
The moments caused by the transverse and longitudinal inclination of the kingpins are equal to:
where is the average angle of rotation of the wheel; 
; γ
– angle of inclination of the kingpin back.
Steering wheel rim force
,
where is the radius of the steering wheel; η – Steering efficiency: η= 0.7…0.85.
Calculation of steering elements
The loads in the steering and steering gear elements are determined based on the following two design cases˸
According to a given calculated force on the steering wheel;
According to the maximum resistance to turning of the steered wheels in place.
When driving a car on roads with uneven surfaces or when braking with different coefficients of adhesion under the steered wheels, a number of steering parts perceive dynamic loads that limit the strength and reliability of the steering. The dynamic impact is taken into account by introducing a dynamic coefficient to d = 1.5...3.0.
Design steering wheel force for passenger cars P PK = 700 N. To determine the force on the steering wheel based on the maximum resistance to turning of the steered wheels in place 166 Steering, it is necessary to calculate the moment of resistance to turning using the following empirical formula
M c = (2р о/3)V О ък/рш ,
where p o is the coefficient of adhesion when turning the wheel in place ((p o = 0.9...1.0), G k is the load on the steered wheel, p w is the air pressure in the tire.
Steering wheel force to turn in place
P w = Mc /(u a R PK nPp y),
where u a is the angular gear ratio.
If the calculated value of the force on the steering wheel exceeds the above conditional calculated force, then the vehicle requires the installation of power steering. Steering shaft. In most designs, the ᴇᴦο is made hollow. The steering shaft is loaded with torque
M RK = P PK R PK .
Torsional stress of hollow shaft
t = M PK D/. (8.4)
Allowable stress [t] = 100 MPa.
The twist angle of the steering shaft is also checked, which is allowed within 5...8° per meter of shaft length.
Steering gear. For a mechanism including a globoid worm and a roller, the contact stress in the mesh is determined
o= Px /(Fn) , (8.5)
P x - axial force perceived by the worm; F is the contact area of one roller ridge with the worm (the sum of the areas of two segments, Fig. 8.4), and is the number of roller ridges.
Axial force
Px = Mrk /(r wo tgP),
Worm material: cyanidated steel ZOKH, 35KH, 40KH, ZOKHN; roller material: case-hardened steel 12ХНЗА, 15ХН.
Allowable stress [a] = 7...8MPa.
For a screw-rack mechanism in the “screw-ball nut” link, the conditional radial load P 0 per ball is determined
P w = 5P x /(mz COs -$con) ,
where m is the number of working turns, z is the number of balls on one turn, 8 con is the angle of contact of the balls with the grooves (d con = 45 o).
Contact stress, which determines the strength of the ball
where E is the elastic modulus, d m is the diameter of the ball, d k is the diameter of the groove, k kr is a coefficient depending on
curvature of contacting surfaces (kkr = 0.6...0.8).
Allowable stress [a (Zh] = 2500..3500 MPa based on the diameter of the ball. According to GOST 3722-81, the breaking load acting on one ball must be determined.
Calculation of steering elements - concept and types. Classification and features of the category "Calculation of steering elements" 2015, 2017-2018.
