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 soft dirt roads, increased tire pressure 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.

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 The ratio of the linear speed of the wheel axis to its angular speed is called:

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.

As studies have shown, on roads with hard surfaces 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

To select tires and determine wheel rolling radii based on their sizes, it is necessary to know the load distribution across the axles.

For passenger cars, the distribution of the load from the total weight across axles depends mainly on the layout. With a classic layout, the rear axle accounts for 52...55% of the load of the total weight, for front-wheel drive vehicles 48%.

The rolling radius of the wheel rk 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 prototype of the car.

Consequently, the load on each wheel of the front and rear axles 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 loads from the total mass on the front and rear axles of the car, respectively.

We find the distance from the front axle to the center of mass using the formula:

a=G 2 *L/G a , (8)

where G a is the vehicle’s gravity module (N);

L – car base.

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

Tire designation	Tire 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 - profile width mm and inches, respectively, rim seat diameter 13 inches. From these dimensions you can determine the radius of the wheel in a free state.

r c = + b, (10)

where b – tire profile width (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 radial deformation coefficient. For standard and wide-profile tires, k is taken as 0.1…0.16.

Calculation of external characteristics of the engine

The calculation begins with determining the power Nev required to ensure movement at a given maximum speed Vmax.

When the vehicle is in steady motion, 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 - 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 car, m2;

Transmission efficiency;

K p – correction coefficient.

Total road resistance coefficient for trucks and road trains

=(0.015+0.02)+6*10 -6 * V . (14)

We find the frontal area for passenger cars 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 coefficient.

For existing passenger cars, the engine speed ratio is in the range of 30...35, for trucks with a carburetor engine - 35...45; for trucks with a diesel engine – 30…35.

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 .

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 recent years, intensive development of new designs of special machines has been carried out.

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 increased 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

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 a constant gear ratio. The torque from the engine is transmitted to the gearbox through clutches. On modern cars, friction clutches are the most common type. 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 during 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.

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.

/ 2π∙n, (8) l .

where n is the wheel rotation speed corresponding to the distance l In case of complete wheel slip, the distance
.

Wheel rolling radii

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