The following radii are distinguished for car wheels (Fig. 3.4): static r s, dynamic r D and rolling radius r quality.
Static radius is the distance from the axis of the stationary wheel to the road surface. It depends on the load on the wheel and the air pressure in the tire. The static radius decreases with increasing load and decreasing tire pressure, and vice versa.
Dynamic radius is the distance from the axis of the rolling wheel to the road surface. It depends on the load, the air pressure in the tire, the driving speed and the moment transmitted through the wheel. The dynamic radius increases with an increase in travel speed and a decrease in the transmitted torque, and vice versa.
Rolling radius the ratio of the linear speed of the wheel axis to its angular speed is called:
The rolling radius, which depends on the load, the air pressure in the tire, the transmitted torque, wheel slip and slip, is determined experimentally or calculated by the formula
(3.13.)
where n to - the number of full revolutions of the wheel; S K - the distance traveled by the wheel for the full number of revolutions.
From expression (3.13) it follows that with complete slipping of the wheel (S k = 0), the rolling radius r quality= 0, and with full slip (n to = 0) g quality → lake.
Studies have shown that on roads with a hard surface and good adhesion, the rolling radius, static and dynamic radii differ insignificantly from each other. Therefore it is possible
When performing calculations, we will use this approximate value in the future. The corresponding value will be called the radius of the wheel and will be denoted by r k.
For various types of tires, the wheel radius can be determined according to GOST, which regulates static radii for a number of load values.
ki and tire pressure. In addition, the wheel radius, m, can be calculated from the nominal tire dimensions using the expression
(3.14)
Rice. 3.4. Wheel radii
To select tires and determine the wheel rolling radius by their dimensions, it is necessary to know the load distribution over the axles.
In passenger cars, the distribution of the gross weight across the axles depends mainly on the layout. With the classic layout, the rear axle accounts for 52 ... 55% of the total weight, for front-wheel drive vehicles 48%.
The rolling radius of the wheel rк is selected depending on the load on one wheel. The greatest load on the wheel is determined by the position of the center of mass of the car, which is established according to the preliminary sketch or prototype of the car.
G2 = Ga * 48% = 14000 * 48% = 6720N
G1 = Ga * 52% = 14000 * 52% = 7280N
Therefore, the load on each wheel of the front and rear axle of the car, respectively, can be determined by the formulas:
P1 = 7280/2 = 3360 N
P2 = 6720/2 = 3640 N
The distance from the front axle to the center of mass is found by the formula:
L-base of the car, mm.
a = (6720 * 2.46) / 14000 = 1.18m.
Distance from center of mass to rear axle:
h = 2.46-1.18 = 1.27m
Tire type (according to the GOST table) - 165-13 / 6.45-13. From these dimensions, you can determine the radius of the wheel in a free state:
Where b is the width of the tire section (165 mm)
d - tire rim diameter (13 inches)
1inch = 25.4mm
rc = 13 * 25.4 / 2 + 165 = 330 mm
The rolling radius of the wheel rk is determined taking into account the deformation, depending on the load:
rk = 0.5 * d + (1-k) * b (9)
where k is the coefficient of radial deformation. For standard and wide-profile tires, k is taken as 0.3
rk = 0.5 * 330 + (1-0.3) * 165 = 280mm = 0.28m
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When an elastic (deformed) wheel rolls under the influence of force factors, tangential deformation of the tire occurs, in which the actual distance from the axis of rotation of the wheel to the supporting surface decreases. This distance is called dynamic radius r d wheels. Its value depends on a number of design and operational factors, such as the stiffness of the tire and the internal pressure in it, the weight of the car per wheel, the speed of movement, acceleration, rolling resistance, etc.
The dynamic radius decreases with increasing torque and decreasing tire pressure. The quantity r d slightly increases with an increase in vehicle speed due to an increase in centrifugal forces. The dynamic radius of the wheel is the shoulder of the pushing force. Therefore, it is also called power radius.
Rolling of an elastic wheel on a hard supporting surface (for example, on an asphalt or concrete highway) is accompanied by some slippage of the tread elements of the wheel in the zone of its contact with the road. This is due to the difference in the lengths of the sections of the wheel and the road that come into contact. This phenomenon is called elastic slip tires, unlike slip(slipping) when all tread elements are displaced relative to the bearing surface. There would be no elastic slippage if these sections were absolutely equal. But this is only possible when the wheel and the road are in arc contact. In reality, the support contour of the deformed wheel comes into contact with the flat surface of the undeformed road and slippage becomes inevitable.
To take this phenomenon into account in the calculations, the concept is used kinematic radius wheels ( rolling radius) r to... Thus, the calculated rolling radius r k is such a radius of the fictitious undeformed a wheel that, in the absence of slippage, has the same linear (translational) rolling speeds with the real (deformed) wheel v and angular rotation ω to... That is, the value r to characterizes conditional radius that serves to express the calculated kinematic relationship between the speed of movement v vehicle and the angular speed of rotation of the wheel ω to:
The peculiarity of the rolling radius of a wheel is that it cannot be measured directly, but is determined only theoretically. If you rewrite the above formula as:
, (τ
- time)
then it can be seen from the obtained expression that to determine the value r to can be calculated. To do this, you need to measure the path S traversed by the wheel for n revolutions, and divide it by the angle of rotation of the wheel ( φ to = 2πn).
The amount of elastic slippage increases with a simultaneous increase in the elasticity (compliance) of the tire and the stiffness of the road, or, conversely, with an increase in the stiffness of the tire and the softness of the road. On soft dirt roads, increased tire pressure increases soil deformation losses. Reducing the internal pressure in the tire allows on soft soils to reduce the movement of soil particles and deformation of its layers, which leads to a decrease in rolling resistance and an increase in cross-country ability.
However, on a hard bearing surface at low pressure, excessive tire deflection occurs with an increase in the rolling friction arm. but... A compromise solution to this problem is the use of tires with an adjustable inflation pressure.
In practical calculations, the rolling radius of a wheel is estimated using an approximate formula:
r k = (0.85 ... 0.9) r 0 (here r 0 - wheel free radius).
For paved roads (wheel movement with minimal slippage), take: r k = r d.
To select tires and determine the wheel rolling radii by their dimensions, it is necessary to know the load distribution over the axles.
In passenger cars, the distribution of the gross weight across the axles depends mainly on the layout. With the classic layout, the rear axle accounts for 52 ... 55% of the total weight, for front-wheel drive vehicles 48%.
The rolling radius of the wheel r k is selected depending on the load on one wheel. The greatest load on the wheel is determined by the position of the center of mass of the car, which is established according to a preliminary sketch or a prototype of the car.
Therefore, the load on each wheel of the front and rear axle of the car, respectively, can be determined by the formulas:
P 1 = G 1/2, (6)
P 2 = G 2 / 2. (7)
where G 1, G 2 are the total mass loads on the front and rear axles of the vehicle, respectively.
The distance from the front axle to the center of mass is found by the formula:
a = G 2 * L / G a, (8)
where G a - the module of the gravity of the vehicle (N);
L is the base of the car.
Distance from center of mass to rear axle
We select tires based on the load on each wheel according to Table 1.
Table 1 - Car tires
| Bus designation | Bus designation | ||
| 155-13/6,45-13 | 240-508 (8,15-20) | ||
| 165-13/6,45-13 | 260-508P (9.00P-20) | ||
| 5,90-13 | 280-508 (10,00-20) | ||
| 155/80 R13 | 300-508 (11.00R-20) | ||
| 155/82 R13 | 320-508 (12,00-20) | ||
| 175/70 R13 | 370-508 (14,00-20) | ||
| 175-13/6,95-13 | 430-610 (16,00-24) | ||
| 165/80 R13 | 500-610 (18,00-25) | ||
| 6,40-13 | 500-635 (18,00-25) | ||
| 185-14/7,35-14 | 570-711 (21,00-78) | ||
| 175-16/6,95-16 | 570-838 (21,00-33) | ||
| 205/70 R14 | 760-838 (27,00-33) | ||
| 6,50-16 | |||
| 8,40-15 | |||
| 185/80 R15 | |||
| 220-508P (7,50R-20) | |||
| 240-508 (8,25-20) | |||
| 240-381 (8,25-20) |
For example: 165-13 / 6.45-13 with a maximum load of 4250 N, 165 and 6.45 - the width of the profile is mm and inches, respectively, the rim rim diameter is 13 inches. From these dimensions, you can determine the radius of the wheel in a free state
r c = + b, (10)
where b is the width of the tire profile (mm);
d - tire rim diameter (mm), (1 inch = 25.4 mm)
The rolling radius of the wheel r k is determined taking into account the deformation, depending on the load
r k = 0.5 * d + (1 - k) * b, (11)
where k is the coefficient of radial deformation. For standard and wide-profile tires, k is taken as 0.1 ... 0.16.
Calculation of the external characteristics of the engine
The calculation begins with determining the power N ev required to drive at a given maximum speed V max.
With a steady motion of the car, the engine power, depending on road conditions, can be expressed by the following formula (kW):
N ev = V max * (G a * + K in * F * V) / (1000 * * K p), (12)
where is the coefficient of total road resistance for passenger cars is determined by the formula:
0.01 + 5 * 10 -6 * V. (13)
K in - streamlining coefficient, K in = 0.3 N * s 2 * m -4;
F - frontal area of the vehicle, m 2;
Transmission efficiency;
K p - correction factor.
Total road resistance coefficient for trucks and road trains
= (0.015 + 0.02) + 6 * 10 -6 * V. (fourteen)
The frontal area for passenger cars is found from the formula:
F A = 0.8 * B g * H g, (15)
where B g - overall width;
H g - overall height.
Frontal area for trucks
F A = B * H g, (16)
Engine speed
The engine crankshaft speed n v, corresponding to the maximum vehicle speed, is determined from the equation (min -1):
n v = Vmax *, (17)
where is the engine speed factor.
For existing passenger cars, the engine rpm is within the range of 30 ... 35, for trucks with a carburetor engine - 35 ... 45; for trucks with a diesel engine - 30 ... 35.
All forces acting on the vehicle from the side of the road are transmitted through the wheels. The radius of a wheel equipped with a pneumatic tire, depending on the weight of the load, the mode of movement, internal air pressure, tread wear, can vary.
The following radii are distinguished for wheels:
1) free; 3) dynamic;
2) static; 4) kinematic.
Free radius(r sv) is the distance from the axis of a stationary and unloaded wheel to the outermost part of the treadmill. For one and the same wheel, the Rw value depends only on the value of the internal air pressure in the tire.
The free wheel radius is indicated in the tire specification. If the specified characteristic is absent in the reference data, then its value can be determined by the tire marking.
Static radius(r st) - it is the distance from the center of a stationary wheel, loaded with normal force only, to the reference plane. The value of the static radius is less than the free one by the amount of radial deformation:
r st = r sv - h z = r sv - R z / S w, (5.1)
where h z = R z / С w - radial (normal) deformation of the tire, m;
R z - normal road reaction, N;
S w - radial (normal) stiffness of the tire, N / m.
The normal reaction of the road acting on one wheel can be determined by the formula:
R z = G О / 2, (5.2)
where G About - the weight of the car per axle.
From formula (1) we find the value of the radial stiffness of the tire:
C w = R z / r sv - r st, (5.3)
The radial stiffness of a tire depends on its design and the internal air pressure pw. If the dependence of C w on r w is known, then the deformation value of the tire can be determined at any internal air pressure. At nominal air pressure and load, the static wheel radius can be found using the formula:
r st = 0.5d o + (1 - l w) H w, (5.4)
where d o is the diameter of the wheel rim, m;
H w - the height of the tire profile in a free state, m;
l w - coefficient of radial deformation of the tire.
For tires of a regular profile, as well as wide-profile tires, l w = 0.10 - 0.15; for arched and pneumatic rollers l w = 0.20 - 0.25.
The nominal value r of the wheel in relation to the nominal load and internal air pressure is indicated in the technical specification of the tire.
Dynamic radius(r d) is the distance from the center of the rolling wheel to the reference plane. The value of r d depends mainly on the internal air pressure in the tire, the vertical load on the wheel and the speed of its movement. As the vehicle speed increases, the dynamic radius increases slightly, which is explained by the elongation of the tire by centrifugal inertia forces.
Kinematic radius(r к) is the radius of a conditional non-deformed wheel rolling without sliding, which has the same angular and linear velocities with this elastic wheel:
r к = V x / w к. (5.5)
The value of r k is determined empirically, for this, the path S traversed by the car for n to full revolutions is measured:
r k = V x / w k = V x * t / w k * t = S / 2p n k, (5.6)
where V x is the linear speed of the wheel;
w к - angular speed of the wheel;
t is the time of movement.
The difference between the radii r d and r k is due to the presence of slippage in the contact area of the tire with the road.
In the case of complete slipping of the wheel, the path traveled by the wheel is equal to zero S = 0, and therefore r to = 0. During the sliding of the braked non-rotating (locked) wheels, i.e. when sliding, n to = 0 and r to ® ¥.
When a car moves on roads with a hard surface and good adhesion, approximately r to = r d = r c = r is taken.