When an elastic (deformed) wheel rolls under the influence of force factors, tangential deformation of the tire occurs, during 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 vehicle per wheel, speed, acceleration, rolling resistance, etc.

The dynamic radius decreases with increasing torque and decreasing tire pressure. Magnitude r d increases slightly with increasing vehicle speed due to increased centrifugal forces. The dynamic radius of the wheel is the shoulder for applying the pushing force. That's why it is also called force radius.

The rolling of an elastic wheel on a hard supporting surface (for example, on an asphalt or concrete highway) is accompanied by some slipping of the wheel tread elements in the area of ​​its contact with the road. This is explained by the difference in the lengths of the sections of the wheel and road that come into contact. This phenomenon is called elastic slippage tires, unlike slip(slip), when all tread elements move relative to the supporting surface. There would be no elastic slippage if these sections were absolutely equal. But this is only possible if the wheel and road have contact along an arc. 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 calculations, use the concept kinematic radius wheels ( rolling radius) r to. Thus, the calculated rolling radius r k represents such a radius of the fictitious undeformed wheel, which, in the absence of slipping, 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, which serves to express the calculated kinematic relationship between the speed of movement v vehicle and wheel angular speed ω to:

The peculiarity of the rolling radius of a wheel is that it cannot be measured directly, but is determined only theoretically. If we rewrite the above formula as:

, (τ - time)

then from the resulting expression it is clear that to determine the value r by calculation. To do this you need to measure the path S traversed by the wheel behind 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 hardness of the road or, conversely, with an increase in the hardness of the tire and the softness of the road. On a soft dirt road high blood pressure in the tire increases losses due to ground deformation. 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 increased cross-country ability.

However, on a hard supporting surface at low pressure, excessive tire deflection occurs with an increase in the rolling friction arm A. A compromise solution to this problem is to use tires with adjustable internal pressure.

In practical calculations, the rolling radius of a wheel is estimated using the approximate formula:

r k = (0.85…0.9) r 0 (here r 0 - free radius of the wheel).

For paved roads (wheel movement with minimal slippage) the following is accepted: r k = r d.

P E T R O Z A V O D S K I Y

STATE UNIVERSITY

FACULTY OF FORESTRY ENGINEERING

Department of Traction Machines

FORESTRY MACHINES

(Lecture notes. Part 2)

This lecture notes does not pretend to be complete, therefore, for a complete study of individual issues, it is necessary to use the recommended literature (each issue is discussed in detail during classroom lessons).

The summary outlines the purpose and place of forestry (mobile) machines in logging production, the general and traction dynamics of wheeled and tracked vehicles(traction balance of cars and tractors, traction and speed characteristics and power balance, cross-country ability, stability and general dynamics of forestry machines.). The types of transmissions, their structure and principle of operation (advantages and disadvantages), requirements for them are considered; elements of mechanical and hydraulic transmission schemes are considered (clutches, gearboxes, transfer cases, cardan and final drives, differential and its kinematics and statics, turning mechanisms of tracked vehicles, the basics of the theory of turning of tracked (skidding) vehicles, determination of the main parameters of turning and braking systems, steering elements, installation of steered wheels, etc., fluid coupling and torque converter circuits, their characteristics).

In conclusion, brief information is provided about the chassis systems of wheeled vehicles, suspensions of wheeled and tracked vehicles.

The notes can be used to study the following disciplines:

“Theory and design of wheeled and tracked vehicles”,

"Mobile vehicle transmissions"

"Transmissions and control mechanisms of forestry machines",

"Forest transport vehicles"

"Forest harvesting machines"

and can be useful to students and graduate students involved in traction calculations of wheeled and tracked vehicles during coursework and diploma design, research on traction and adhesion qualities, the fundamentals of the theory of rotation, etc. of forestry and general-purpose machines.

The abstract was developed by a professor at the Department of Traction Machines

M. I. Kulikov

INTRODUCTION

The leading place in the mechanization of forestry work is increasingly occupied by forestry machines. Forestry machines are machines used in the forestry industry for transportation of timber, which includes transportation (skidding) and removal of timber (wheeled and tracked tractors, timber trucks, etc.). The basis for most forestry machines are general purpose vehicles and tractors (ZIL, MAZ, Ural, KamAZ, KRAZ, T-130, MTZ-82, etc.). There are a number of requirements for forestry machines, the main ones being:

1. Compliance of the machine design with operating conditions and ensuring high-performance operation.

2. High traction and dynamic qualities, high cross-country ability, good adhesion of the propeller to the ground, high maneuverability, good adaptability for operation in various climatic conditions, etc.

3. Promising design, making it possible to modernize the original basic model for a long time.

4.High reliability and wear resistance of parts, assemblies and assemblies, their unification.

5.High efficiency - minimal costs for fuels and lubricants, spare parts, maintenance, etc.

In addition, additional requirements are imposed on timber trucks: increasing the trip load, increasing the speed of movement and improving cross-country ability.

Meeting these requirements is usually achieved by increasing the engine power per ton of road train weight and increasing its total load capacity. From year to year, the power of automobile engines and the carrying capacity of road trains are increasing (ZIL-131-110 kW-12.0 t; MAZ-509-132 kW-17.0 t; KRAZ-255 - 176 kW-23.0 t; KRAZ-260-220 kW-29 ,0 t).

Improving the transmission and chassis systems play a leading role in increasing the average speed of a vehicle and increasing its cross-country ability. Logging is carried out by special tractors - skidders, which transport the wood in a semi-submerged position. IN last years Intensive development of new designs of special machines is underway.

Skidders were first created in the USSR in 1946. Mainly in logging operations, tracked vehicles are used, which have better maneuverability than wheeled ones (most logging is carried out in areas with low bearing capacity of soils). However, the advantages of a wheeled propulsion system - high speeds, smooth running, etc. forced designers to take the path of developing new wheeled vehicles with cross-country ability(TLK-4, TLK-6, ShLK, etc.).

Increasing the productivity and traction qualities of tracked tractors is achieved by increasing the load capacity and engine power.

TRANSMISSION OF ENGINE TORQUE TO DRIVERS

FORESTRY MACHINE WHEELS. TRANSMISSION EFFICIENCY

On modern cars and tractors, both foreign and domestic, use piston internal combustion engines, the development of which has established a tendency to increase their speed. This leads to their compactness and low weight. However, on the other hand, this leads to the fact that the torque on the shaft of these engines is significantly less than the torque that must be supplied to the drive wheels of the machine, despite the relatively large power of these engines. Consequently, in order to obtain the torque necessary for movement on the drive wheels, it is necessary to introduce an additional device into the system - “engine - drive wheels”, which ensures not only the transmission of engine torque, but also its increase. The role of this device in modern cars and tractors is performed by the transmission. The transmission includes a number of mechanisms: clutch, gearbox, cardan, main, final (final) gears, turning mechanisms, and additional gearboxes (transfer boxes) that establish constant gear ratio. The torque from the engine is transmitted to the gearbox through clutches. On modern machines, the main distribution is friction clutches clutch. The ratio of the friction torque of the clutch M m to the rated engine torque Me is called the clutch safety factor β:

β=M m / M e (1)

The value of this coefficient varies in a wide range (1.5 - 3.8) for trucks and tractors and is selected from the conditions of the magnitude of the friction work during slipping during acceleration of the tractor unit, as well as protection against damage to engine and transmission parts under possible overloads.

When choosing coefficient β, the possible change in the coefficient of friction of the clutch discs, a decrease in the pressure force of the springs due to wear of the friction surfaces, etc. are also taken into account. From the clutch, torque is transmitted through the gearbox and other transmission elements to the drive wheels. In the absence of slipping between the driving and driven disks of the clutch (δ clutch = 0), the transmission gear ratio in general form will be determined: i tr =ω e /ω k = n e /n k, (2)

where ω e and n e are the angular velocity and rotational speed of the engine crankshaft, respectively;

ω k and n k are the angular velocity and rotational speed of the drive wheels, respectively.

Equality (2) can be represented as:

i tr =i k ∙i rk ∙i gl ∙ii kp = i k ∙i rk ∙i o, (2΄)

where i к – gear ratio of the gearbox;

i рк – transfer ratio of the transfer case;

i gl – gear ratio of the main (central) gear;

i - gear ratio of the turning mechanism;

i gearbox – final drive gear ratio;

i o – constant gear ratio implemented in the main, turning mechanism, and final gears, as well as in other transmission gearboxes.

The torque on the driving wheels of the machine is determined by:

M k =M e ∙i tr ∙η tr, (3)

η tr – transmission efficiency, which is determined from the relation:

η tr =N to /N e =(N e - N tr)/N e =1-(N tr / N e) , (4)

where Nk is the power supplied to the drive wheels;

Ntr – power lost in the transmission.

Transmission efficiency η tr takes into account mechanical losses that occur in bearings, gear couplings of the gearbox, central and final gears, and losses during oil churning. Transmission efficiency is usually determined experimentally. It depends on the type of transmission design, the quality of manufacturing and assembly, the degree of loading, oil viscosity, etc. The efficiency of modern automobile and tractor transmissions at nominal operating mode is in the range of 0.8..0.93 and depends on the number of pairs of gears connected in series η kp = 0.97..0.98; η c.p. =0.975..0.990.

In accordance with this, the value of η tr can be approximately calculated:

η tr = η c.p. ∙η kp (4΄)

Without taking into account losses when idling:

η cold =1-M cold / M e, (5)

where M idle is the moment of resistance reduced to the transmission input shaft that occurs when the transmission is idling.

m ts, m To - number of pairs of cylindrical and bevel gears, respectively.

Wheel rolling radii

A car (tractor) moves as a result of the action of various forces on it, which are divided into driving forces and forces of resistance to movement. The main driving force is the traction force applied to the drive wheels. Traction force arises as a result of engine operation and is caused by the interaction of the drive wheels with the road. Traction force Pk is defined as the ratio of the torque on the axle shafts to the radius of the drive wheels during uniform vehicle movement. Therefore, to determine the traction force, it is necessary to know the radius of the drive wheel. Since elastic pneumatic tires are installed on the wheels of the car, the radius of the wheel changes while driving. In this regard, the following wheel radii are distinguished:

1. Nominal – radius of the wheel in a free state: r n =d/2+H, (6)

where d is the rim diameter (tire seat diameter), m;

H – total height of the tire profile, m.

2. Static r c – the distance from the road surface to the axis of the loaded stationary wheel.

r with =(d/2+H)∙λ , (7)

where λ is the radial deformation coefficient of the tire.

3. Dynamic r d – distance from the road surface to the axis of a rolling loaded wheel. This radius increases with a decrease in the perceived load of the wheel G k and an increase in the internal air pressure in the tire p w.

As the speed of the vehicle increases, under the influence of centrifugal forces, the tire stretches in the radial direction, as a result of which the radius r d increases. When a wheel rolls, the deformation of the rolling surface also changes compared to a stationary wheel. Therefore, the shoulder of application of the resultant tangential reactions of the road r d differs from r c. However, as experiments have shown, for practical traction calculations it is possible to take r c ~ ​​r d.

The kinematic (rolling) radius of the wheel r k is the radius of such a conditional non-deformable ring that has the same angular and linear speeds with a given elastic wheel.

For a wheel rolling under the influence of torque, the tread elements that come into contact with the road are compressed, and the wheel passes less way than during free rolling; on a wheel loaded with braking torque, the tread elements that come into contact with the road are stretched. Therefore, the brake wheel travels a slightly longer distance at equal speeds than a freely rolling wheel. Thus, under the influence of torque, the radius rк decreases, and under the influence of braking torque, it increases. To determine the value of r k using the “chalk prints” method, a transverse line is drawn on the road with chalk or paint, onto which a car wheel rolls, and then leaves prints on the road.

Measuring the distance l between the extreme prints, determine the rolling radius using the formula: r k = l / 2π∙n, (8)

where n is the wheel rotation speed corresponding to the distance l .

In case of complete wheel slip, the distance l = 0 and radius r к = 0. During sliding of non-rotating wheels (“SW”) rotation speed n=0 and r к
.

Due to the wide variety of types of deformation of a pneumatic tire, its radius does not have one specific value, like that of a wheel with a rigid rim.

The following rolling radii of wheels with pneumatic tires are distinguished: free g 0, static r cv dynamic g a and kinematic g k.

Free radius g 0- this is the largest radius of the treadmill of a wheel free from external load. It is equal to the distance from the surface of the treadmill to the wheel axis.

The static radius r st is the distance from the axis of a stationary wheel loaded with a normal load to the plane of its support. The static radius values ​​at maximum load are regulated by the standard for each tire.

Dynamic radius g i- this is the distance from the axis of the moving wheel to the point of application of the resulting elementary soil reactions acting on the wheel.

Static and dynamic radii decrease as normal load increases and tire pressure decreases. Dependence of dynamic radius on torque load, obtained experimentally by E.A. Chudakov, shown in Fig. 9, A, schedule 1. It can be seen from the figure that with increasing torque M vea, transmitted by the wheel, its dynamic radius decreases. This is explained by the fact that the vertical distance between the wheel axis and its supporting surface decreases due to the torsional deformation of the tire sidewall. In addition, under the influence of torque, not only a tangential force arises, but also a normal component, which tends to press the wheel to the road surface.

Rice. 9. Dependencies obtained by E.A. Chudakov: a - change in dynamic (I and kinematic ( 2) wheel radii depending on the driving torque: b - change in the kinematic radius of the wheel under the influence of driving and braking torques

The magnitude of the dynamic radius also depends on the depth of the rut when moving on deformable ground or soil. The greater the rut depth, the smaller the dynamic radius. The dynamic radius of the wheel is the shoulder of application of the tangential reaction of the soil pushing the drive wheel. Therefore, the dynamic radius is also called the force radius.

Kinematic radius or rolling radius of a wheel is divided by 2k the actual distance traveled by the wheel in one revolution. The kinematic radius is also defined as the radius of such a fictitious wheel with a rigid rim, which, in the absence of slipping and slipping, has the same angular velocity of rotation and translational speed as the real wheel:

where v K is the forward rolling speed of the wheel; с к - angular speed of rotation of the wheel; S K- wheel path per revolution, taking into account slipping or sliding.

From expression (5) it follows that with full wheel slip (v K = 0) the radius g to= 0, and with full sliding (with k = 0) the kinematic radius is equal to ©о.

In Fig. 9, A(schedule 2) presented by E.A. Chudakov, the dependence of the change in the kinematic radius of the wheel on the action of the torque M led on it. It follows from the figure that the magnitude of the change in the dynamic and kinematic radii depending on the action of the moment is different. The steeper dependence of the kinematic radius of the wheel compared to the dependence of the dynamic radius can be explained by the action of two factors on it. Firstly, the kinematic radius decreases by the same amount by which the dynamic radius decreases from the action of the driving moment, as shown in Fig. 9, i, schedule /. Secondly, the driving or braking torque applied to the tire causes compressive or tensile deformation of the running part of the tire. The processes accompanying these deformations are easy to trace if you imagine the wheel in the form of a cylindrical elastic spiral with uniform winding of turns. As shown in Fig. 10, a, under the influence of the driving moment, the running part of the tire (front) is compressed, as a result of which the total perimeter of the tire tread circumference decreases, the wheel path S K becomes smaller per revolution. The greater the compression deformation of the tire in the running part, the greater the reduction in distance SK, which, in accordance with (5), is proportional to the decrease in the kinematic radius g k.

When the braking torque is applied, the opposite phenomenon occurs. The stretched elements of the tire fit the supporting surface

(Fig. 10, b). Tire perimeter and wheel path SK, traveled per revolution increase as the braking torque increases. Therefore, the kinematic radius increases.

Rice. 10. Scheme of tire deformation from the action of moments M led (a) and M t(b)

In Fig. 9, b shows the dependence of the change in the radius of the wheel on the action of the active torque and brake on it M 1 moments with stable adhesion of the wheel to the supporting surface. E.A. Chudakov proposed the following formula for determining the radius of the wheel:

where g to 0 is the rolling radius of the wheel in free rolling mode, when the driving moment and the moment of rolling resistance are equal to each other; A, t is the coefficient of tangential elasticity of the tire, depending on its type and design, which is found from the results of experiments.

In engineering calculations, the static radius of a given tire given in the standard at a set air pressure and maximum load on it is usually used as the dynamic and kinematic radii. It is assumed that the wheel moves on an indestructible surface.

When driving along a rut, the static radius is the distance from the wheel axis to the bottom of the rut. However, when the wheel moves along a track, the point of application of the resultant of the elementary reactions of the soil, which forms the torque (driving or resistance), will be located above the bottom of the track and below the soil surface (see Fig. 17). The dynamic radius in this case depends on the depth of the track: the deeper it is, the greater the difference between the static and dynamic radii of the wheels, the greater the calculation error from the assumption g l = g st

A car (tractor) moves as a result of the action of various forces on it, which are divided into driving forces and forces of resistance to movement. The main driving force is the traction force applied to the drive wheels. Traction force arises as a result of engine operation and is caused by the interaction of the drive wheels with the road. Traction force Pk is defined as the ratio of the moment on the axle shafts to the radius of the drive wheels during uniform motion of the vehicle. Therefore, to determine the traction force, it is necessary to know the radius of the drive wheel. Since elastic pneumatic tires are installed on the wheels of the car, the radius of the wheel changes while driving. In this regard, the following wheel radii are distinguished:

1. Nominal – radius of the wheel in a free state: r n =d/2+H, (6)

where d – rim diameter, m;

H – total height of the tire profile, m.

2. Static r c – the distance from the road surface to the axis of the loaded stationary wheel.

r with =(d/2+H)∙λ , (7)

where λ is the radial deformation coefficient of the tire.

3. Dynamic r d – distance from the road surface to the axis of a rolling loaded wheel. This radius increases with a decrease in the perceived load of the wheel G k and an increase in the internal air pressure in the tire p w.

As the speed of the vehicle increases, under the influence of centrifugal forces, the tire stretches in the radial direction, as a result of which the radius r d increases. When a wheel rolls, the deformation of the rolling surface also changes compared to a stationary wheel. Therefore, the shoulder of application of the resultant tangential reactions of the road r d differs from r c. However, as experiments have shown, for practical traction calculations it is possible to take r c ~ ​​r d.

4 Kinematic radius (rolling) of the wheel r k - the radius of such a conditional non-deformable ring that has the same angular and linear speeds with a given elastic wheel.

For a wheel rolling under the influence of torque, the tread elements that come into contact with the road are compressed, and the wheel at equal rotation speeds travels a shorter distance than during free rolling; on a wheel loaded with braking torque, the tread elements that come into contact with the road are stretched. Therefore, the brake wheel travels a slightly longer distance at equal speeds than a freely rolling wheel. Thus, under the influence of torque, the radius rк decreases, and under the influence of braking torque, it increases. To determine the value of r k using the “chalk prints” method, a transverse line is drawn on the road with chalk or paint, onto which a car wheel rolls, and then leaves prints on the road.

Measuring the distance l between the extreme prints, determine the rolling radius using the formula: r k = l / 2π∙n, (8)

where n is the wheel rotation speed corresponding to the distance l .

In case of complete wheel slip, the distance l = 0 and radius r to = 0. During sliding of non-rotating wheels (“SW”), rotation frequency n=0 and r to .

The wheels of a car (Fig. 3.4) have the following radii: 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 as the load increases and the air pressure in the tire decreases, and vice versa.

Dynamic radius is the distance from the axis of a rolling wheel to the road surface. It depends on the load, air pressure in the tire, speed and torque transmitted through the wheel. The dynamic radius increases with increasing speed and decreasing transmitted torque, and vice versa.

Rolling radius is called the ratio of the linear speed of the wheel axle to its angular velocity:

The rolling radius, depending on the load, air pressure in the tire, transmitted torque, slipping and slipping of the wheel, is determined experimentally or calculated using the formula

(3.13.)

Where n to - number of full wheel revolutions; S K - the distance traveled by the wheel for the full number of revolutions.

From expression (3.13) it follows that when the wheel is completely slipping (S k = 0), the rolling radius r quality= 0, and with full sliding (n k = 0) g quality → oz.

Studies have shown that on paved roads and good grip the rolling radius, static and dynamic radii differ slightly from each other. Therefore it is possible

When performing calculations in the future, we will use this approximate value. We will call the corresponding value the radius of the wheel and denote it 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 air pressure in tires. In addition, the wheel radius, m, can be calculated from the nominal tire dimensions using the expression

(3.14)

Rice. 3.4. Wheel radii