VEHICLE CLUTCH DESIGN
1
INTRODUCTION
The clutch is designed for short-term separation of the engine crankshaft from the
transmission and their subsequent connection, which is necessary for smooth starting of the
car and shifting gears while driving. The clutch also serves to protect the transmission and
the car engine from overload by inertial moments.
The first cars were equipped with band clutches in which a metal band wrapped around the
outside of a metal drum. Them the peculiarity was that in the normal position they were
constantly turned off and turned on by moving the lever to a certain position. Their main
disadvantage was the need to use complex adjusting units that compensate for the wear of
the working surfaces.
The cone clutches that appeared later were constantly engaged (Figure 1). The engine
flywheel 2, which was the leading element of the clutch, was attached to the crankshaft
flange and had a conical surface on the inside. Corresponding outer conical the surface had
a cone 9, which was, together with the clutch cover 7, a driven element, which moved in
the axial direction along the splines of the input shaft of the gearbox. In the urned on
(working) position, the cone 9 with the friction lining 10 were held by the force of the spring
8. The clutch was disengaged when the driver pressed the clutch pedal 4 and through the
lever 5 and the clutch release clutch 3 squeezed the spring 8.
In conical clutches, the angle between the friction surface and the axis of the cone was 15°.
In the latest designs, friction linings were usedmade of friction materials with an asbestos
base.
The main disadvantage of cone clutches was the large moment of inertia of the driven
element, as a result of which it rotated for a long time after the clutch was disengaged,
making gear shifting difficult.
2
Tapered clutches have been replaced by multi-disc clutches operating in an oil bath. They
consisted of alternating steel and bronze discs fixed on splines with driven and driving
drums, 7 i.e. had a large number of friction surfaces and ensured high smoothness of
inclusion. However, the driven drum with multiple driven discs had a large moment of
inertia, which made gear shifting difficult. In addition, at negative ambient temperatures,
the oil thickened, the drive and driven discs stuck together, and the clutch did not disengage.
Later, such clutches were found wide application as disc friction control elements in
planetary gearboxes, as well as multi-disc clutches. Further development of multi-plate
clutches was dry multi-plate clutches. Their drive discs are fitted with friction material pads
3
riveted to the discs on both sides. These clutches are capable of transmitting particularly
high torque in a relatively small size. However, they have the same disadvantage:
Large moment of inertia of driven parts .In addition, the driven metal discs located between
the friction linings have a small thickness (no more than 4 mm), have low thermal
conductivity, strongly heats up when the clutch slips, which accelerates the wear of the
linings, and sometimes leads to warping of the discs and impaired cleanliness of the clutch
release.
1- CLASSIFICATION OF CLUTCHES
1.1. According to the method of torque transmission - frictional, hydraulic (fluid
couplings) and electromagnetic powder.
The most widespread are friction clutches, in which torque from driving parts connected to
the crankshaft the engine is transmitted to driven parts connected to the transmission car,
by means of frictional forces. For hydraulic clutches (fluid couplings) the connection of the
leading and driven parts is carried out by a moving stream liquid, and for electromagnetic
powder - an electromagnetic field
1.2. According to the shape of the friction surfaces, they are disc, conical and drum. In
modern car designs, only disc clutches are used.
1.3. By the number of driven disks - single, double and multi-disk.
Double-disc clutches (see Appendix 1) are used on trucks. Their use is caused by the need
to transmit a large torque, which is achieved by increasing the area of friction surfaces
without increasing the diameter of the clutch. They have relatively large indicators of mass,
axial overall length and displacement of the release clutch. In addition, in their designs, in
order to ensure clean shutdown, it is required to provide for the forced movement of the
middle drive disk.
1.4. According to the state of the friction surfaces - dry and wet (they work, respectively,
without lubrication of the friction surfaces and in an oil bath). Single and double-disc
clutches are used only dry, and multi-disc clutches are mainly wet.
1.5. If possible, the transmission of torque in the absence of external control action normally closed and normally open, and the latter are rarely used.
4
1.6. According to the method of creating pressure on the working surfaces of the clutch
- spring, centrifugal and semi-centrifugal. Spring clutches use central diaphragm springs,
peripherally located cylindrical springs or, very rarely, central conical springs.
In centrifugal and semi-centrifugal clutches, the compressive force of friction pairs is fully
or partially provided by the kinetic energy of the weights attached to the clutch release
levers. Centrifugal clutches are rarely used due to their large cost, less reliability and design
complexity when implementing the clutch safety function. Semi-centrifugal clutch
currently not used due to their inherent disadvantages (see subsection 5.3).
1.7. According to the number of power flows transmitted through the clutch elements
- single-flow, when the entire power flow from the engine is transmitted to the transmission,
and double-flow, when one power flow from the engine is transmitted to the transmission,
and the other to power selection drive unit or when power from the engine is transmitted to
the transmission by two parallel streams.
1.8. By control method:
 clutches with forced steering، fully controlled by the driver
 clutches with automated control، which are equipped with automatic devices that
provide at least control the process of starting the car from a place
 automatic clutches (hydraulic and centrifugal) with internal automaticity, i.e. increasing
the transmitted torque with increasing engine speed.
The vast majority of cars are equipped with permanently closed clutches with forced
control
2- REQUIREMENTS FOR CLUTCHES
The clutch is an independent mechanism, to the design of which, in addition to general
technical requirements (simplicity of design, long service life, low weight, low
maintenance) the following special requirements are imposed:
 reliable transmission of torque from the driving parts of the clutch to its driven parts in
any operating conditions of the car
5
 the ability to transfer torque in the opposite direction (from the driving wheels of the
car to the engine) when the engine is running or not, which is necessary for braking the
car with the engine, and starting the engine by towing a car
 cleanliness of shutdown, i.e. fast (less than 0.25 s) and complete separation of friction
surfaces
 smoothness of inclusion (achieved by ensuring axial and tangential compliance of the
driven disk)
 the possibility of long-term work with sliding (slipping), i.e. kinematic mismatch
between the speeds of rotation of the leading and driven elements of the clutch, which
is necessary for the smooth start of the vehicle, as well as fine regulation of its speed
when maneuvering
 the minimum moment of inertia of the driven elements (necessary to quickly reduce the
speed of rotation of the input shaft of the gearbox when gear shifting);
 normal thermal operation
 the balance of the rotating masses (necessary to reduce the dynamic loads in the clutch
parts at high speeds of the engine crankshaft)
 protection of transmission and car engine from overload by inertial torque
 reliability in work
 Ease and convenience of control (assessed by the effort on the control pedal and the
amount of its travel when the clutch is disengaged).
3- FRICTION CLUTCH DESIGNS
3.1. Diaphragm pressure spring clutch
Figure 3.1 shows a frictional single disc clutch with a diaphragm pressure spring. Clutch
with engine flywheel located in a cast crankcase 1, fixed at the rear end of the engine block.
The clutch consists of driving parts: a casing 12, bolted to the engine flywheel, and a
pressure plate 4, connected to the casing by three elastic plates 2 using rivet 3, and driven
parts: driven disk with friction linings and driven shaft.
6
The engine flywheel, shroud and pressure plate rotate at the engine crankshaft speed. In
addition, the pressure plate due to its elasticity the connecting plates have the ability to
move axially
The drive plate is located between the pressure plate and the engine flywheel. It is connected
to the hub 19 through a spring-friction damper (damper) of torsional vibrations.
In the overwhelming majority of cars, the gearbox housing is connected directly to the
clutch housing 1, and the hub of the driven disc is connected to the input shaft of the gearbox
by 8 splines, and there is no clutch driven shaft. The front end of the input shaft of the
gearbox is mounted on the roller bearing in the engine flywheel groove, and the rear end in
the ball bearing in the gearbox housing. In addition to the driving and driven parts, groups
of parts is distinguished in the clutch that carries out its engaged and disengaged: a
7
diaphragm spring 6, a clutch 10 for disengaging the clutch with a release bearing 7 and a
fork 13 for disengaging the clutch, and a clutch drive.
The clutch is engaged under the action of the force generated by the pressure spring (s), and
disengaged as a result of overcoming this force when acting on the clutch pedal and, through
the drive, on the clutch release clutch and the spring (s).
The clutch discs are compressed by a diaphragm pressure spring 6, cut into petals (see
Figure 3.2, pos. 1), which act as clutch release levers. It is installed between the casing 12
and the pressure plate 4 and is clamped in an almost completely straightened state between
two support rings 5, fixed by pins (or rivets) riveted on the casing. The outer edge of the
spring rests on the ledge pressure plate and due to its elasticity moves it axially towards the
flywheel, clamping the driven disc with the required force.
Figure 3.2 - Clutch basket 1-diaphragm spring 2 - elastic plate fastening
the pressure plate to the clutch cover 3 and 4 - rivets for fastening the
spring to the pressure disc and casing
8
Coupling 10 release the clutch with the release bearing 7 is installed on a bushing, along
which the fork 13 of the release of the clutch can be moved, pivotally mounted on a ball
bearing 11, fixed in the clutch housing. The fork fits into the recesses of the clutch release
clutch and connected to it by a retaining spring. The outer end of the fork, extending
outward through the crankcase hatch, is connected to the rod 14 of the working cylinder 16
of the clutch release hydraulic actuator. The initial position, the clutch engaging /
disengaging mechanism is set using release spring of the fork (see figure 3.3).
B
Bearing 7 acts on the petals of the
diaphragm spring directly (Figure 3.3, A) or
through the stop flange of the shutdown
clutch (Figure 3.3, B). As a rule, the stop
flange is connected to the clutch housing by
elastic connecting plates, allowing flange to
move in the axial direction (Figure 3.4). A
friction ring is glued to the flange, which
rotates the outer release bearing races when
disengaging the clutch.
9
The release bearing of the clutch is closed and sealed. Lubricant is laid in it during
assembly. Reliable transmission of torque by the clutch when the state without slipping of
the driven discs is provided by a sufficient friction force between the rubbing surfaces,
which depends on the force generated by the pressure springs.
Figure 3.5 - Mechanisms providing a guaranteed clearance between friction surfaces:
a - lever; b - with a rod and a release spring; c - with an adjusting bolt and a release
spring; S - working clearance
During the operation of the car as a result of wear of friction linings the pressure plate
moves to the side flywheel by changing the stiffness of the clutch springs. In clutches with
peripheral coil springs that have linear characteristic of elasticity, this leads to a decrease in
the pressing force and the transmitted frictional moment up to the onset of clutch slipping.
In diaphragm spring clutches, which has a non-linear characteristic elasticity, pushing force
during wear overlays are kept approximately constant. To disengage the clutch with a
10
diaphragm spring, significantly less force is required than for clutching with peripheral
springs.
Fast and complete disconnection of the engine from the transmission (cleanliness of the
clutch release) is necessary for shock less gear shifting. This is achieved by obtaining a
guaranteed the gap between the friction surfaces with the clutch pedal fully depressed,
which is ensured by forced retraction of the pressure plate (from the driven one) at a certain
distance using the release levers or special springs. In clutches with peripheral springs, to
achieve cleanliness of release, the number of pressure springs should be a multiple of the
number of release levers, which prevents the pressure plate from skewing. For double-disc
clutches, there are special lever or spring devices for forced movement of the middle drive
disk to a position in which both driven disks will be in a free state (Figure 3.5).
In the lever device (Figure 3.5, a), installed on the middle drive disc, the helical coil spring
torsion when turning off the clutch turns the equal-arm lever. The lever, resting its ends
against the pressure plate and the flywheel, sets the middle drive plate to the same distance
from the flywheel and pressure plate.
In spring devices, release springs are located between the flywheel and the middle drive
disc. The amount of required movements (S) of the middle disc when disengaging the clutch
under the action of these springs, set:
 By means of rods located between the middle disc and the casing (Figure 3.5, b). The
rods, made in one piece with the studs, are secured with nuts on the middle clutch disc.
On the opposite ends of the rods, split rings are put on, with which the rods, when the
clutch is disengaged, abut against stop strips bolted to the clutch cover
 With the help of adjusting bolts screwed into the clutch cover and locked with locknuts
When the clutch is completely disengaged, (the pressure plate is fully retracted), the gap Δn
between the rubbing surfaces in single-disc clutches is 0.75 ... 1.0 mm, in double-disc
clutches - 0.5 ... 0.6 mm, and in multi-disc clutches - 0.25 ... 0.30 mm, the travel of the
pressure plate does not exceed 1.5 ... 2.0 mm for single-disc clutches and 2.0 ... 2.5 mm for
double-disc clutches.
The smooth engagement of the clutch is dictated by the need to reduce the dynamic loads
in the transmission when starting off and gear shifting, which is achieved by gradually
11
releasing the clutch pedal when engaging, and is also provided by the pliability of the driven
disc.
4- CLUTCH CALCULATION
Clutch calculation includes:
1) determination of the calculated moment Мс of clutch friction
2) determination of the work Ab of the clutch slipping, the specific work Aaud of slipping
and the temperature t0 of the clutch parts during slipping
3) calculation of clutch parts for strength
4) calculation of the clutch control drive (determination of the effort on the control pedal
and full pedal travel when the clutch is completely disengaged).
4.1. Determination of the design clutch friction torque
Estimated coupling frictional moment
𝑀𝑐 = 𝛽 ∗ 𝑀𝑒𝑚𝑎𝑥 = 𝐹𝑠𝑡 ∗ 𝑍𝑓 ∗ 𝜇 ∗ 𝑅𝑐
(1)
𝑀𝑐 = 𝛽 ∗ 𝑀𝑒𝑚𝑎𝑥 = 𝐹𝑠 ∗ 𝑛𝑠 ∗ 𝑍𝑓 ∗ 𝜇 ∗ 𝑅𝑐
(2 )
Where β is the coefficient of clutch safety. When choosing it, proceed from the fact that too
low a value leads to an increase in the time slipping of the clutch when starting the car, its
increased heating and wear, and unnecessarily high - to an increase in size, weight and
effort, necessary to control the clutch, as well as the deterioration of protection transmission
and engine overload. In this regard, the calculations usually accept:
12
 for single-disc dry clutches for:
Passenger cars: β = 1.4 ... 1.9
Trucks: β = 1.5 ... 2.2
 for two-disc dry clutches of trucks: β = 2.0 ... 2.3;
𝐹𝑠𝑡 – is the total springs forces excreted on the pressure plate, N; 𝐹𝑠 is the force of one
spring, 𝑛𝑠 is the springs number, 𝑍𝑓 is the number of friction surfaces: For single-plate
clutch 𝑍𝑓 = 2; for a two-disk drive, 𝑍𝑓 = 4; for multi-disc 𝑍𝑓 = 2n (n is the number of
driven disc); 𝜇 - coefficient of sliding friction. Its value depends on the material of the
friction surfaces, their condition and processing, the relative sliding speed of the disc,
pressure and temperature. For various types of friction linings, 𝜇 limits various from
𝜇 = 0.23 to
0.27
Rc - radius of location of the resultant friction forces:
𝑅𝑐 = (𝐷𝑜𝑢𝑡 3 − 𝑑𝑖𝑛 3 )/3(𝐷𝑜𝑢𝑡 2 − 𝑑𝑖𝑛 2 )
(3)
Where D and d are the outer and inner diameters of the friction lining respectively, m
The friction area of one lining of the driven disc can be calculated by ,
𝐴𝑓 = 0.25 𝜋 (𝐷𝑜𝑢𝑡 2 − 𝑑𝑖𝑛 2 )
(4)
𝜋(𝐷𝑜𝑢𝑡 3 − 𝑑𝑖𝑛 3 )
𝑅𝑐 =
12 𝐴𝑓
(5)
The outer diameter 𝐷𝑜𝑢𝑡 of the friction lining is limited by dimensions of the flywheel.
Internal diameter 𝑑𝑖𝑛 of the friction lining is set from the ratio:
𝜆𝑛 =
𝑑𝑖𝑛
𝐷𝑜𝑢𝑡
(6)
For passenger cars: 𝜆𝑛 = 0.67 ± 0.07
For trucks:
𝜆𝑛 = 0.55 ± 0.05
When calculating adhesion, the specific (permissible) pressure on friction disc
𝑃𝑜 = 𝐹𝑠𝑡 /𝐴𝑓
(7)
Substituting
𝐹𝑠𝑡 = 𝛽 ∗ 𝑀𝑒𝑚𝑎𝑥 / 𝑍𝑓 ∗ 𝜇 ∗ 𝑅𝑐
13
(8)
𝑃𝑜 =
=
𝛽 ∗ 𝑀𝑒𝑚𝑎𝑥
12 ∗ 𝛽 ∗ 𝑀𝑒𝑚𝑎𝑥
=
=
𝑍 ∗ 𝜇 ∗ 𝑅𝑐 ∗ 𝐴𝑓
𝜋 ∗ 𝑍 ∗ 𝜇(𝐷𝑜𝑢𝑡 3 − 𝑑𝑖𝑛 3 )
12 ∗ 𝛽 ∗ 𝑀𝑒𝑚𝑎𝑥
𝜋 ∗ 𝑍 ∗ 𝜇 ∗ 𝐷𝑜𝑢𝑡 (1 − 𝜆ℎ 2 )
≤ [𝑃𝑎𝑙𝑙 ]
(9)
The value of the allowable pressure [𝑃𝑎𝑙𝑙 ] for asbestos-free polymer of the lining friction is
selected in the range of [𝑃𝑜 ] = 0.15 ... 0.30 MPa. Smaller values correspond to the clutches
of light cars and buses. Thus, the safety factor β estimates the possibility of adhesion in
when transmission torque, and the specific pressure 𝑃𝑜 ≤ [𝑃𝑎𝑙𝑙 ] on friction lining and the
reliability of the lining in terms of wear resistance.
Determination of Clutch Slipping Work 𝒘𝒔𝒍 , Specific Slipping Work and the
temperature of Clutch Parts during Slipping 𝑻𝒔𝒍
The clutch is a heat-volumetric mechanism that converts part of the engine power into heat
when engages. Clutch slipping work 𝒘𝒔𝒍 and slipping power 𝑵𝒔𝒍 reach the highest values
when the car starting from the rest.
The clutch slip work 𝒘𝒔𝒍 is calculated based on a two-mass dynamic model (Figure 1).
Here 𝛪𝑒 is the flywheel moment of inertia and translated to it moment of inertia of the
rotating and translating moving engine parts, and clutch driving parts (engine moment of
inertia) ; 𝛪𝑎 is the moment of inertia transfers to the engine crankshaft "equivalent to the
translational moving masses of the car 𝑚𝑎 and the trailer 𝑚𝑡𝑟 " , 𝑀𝑒 is the engine torque,
𝑀𝜓 – is the road resistance moment to the movement of the car reduced to the engine, 𝑀𝑠
– twisting moment realized through the clutch 𝜔𝑒 and 𝜔𝑔 - engine and input shaft of the
gearbox (or driven clutch shaft) angular velocities, respectively
In general, 𝑀𝑒 and 𝑀𝑐 are nonlinear functions of time, depending on many factors (position
of the fuel pedal, speed of clutch engagement, engine performance, etc.). Respectively
angular velocities 𝑤𝑒 and 𝑤𝑝 will be nonlinear functions of time.
14
To simplify calculations, the following assumptions are made:
1) The torques 𝑀𝑒 and 𝑀𝜓 acting on the system are constant, i.e. 𝑀𝑒 = 𝑀𝑒 𝑚𝑎𝑥 = const,
and 𝑀𝜓 = constant
2) The law of change in the angular speeds of the crankshaft of the engine 𝑤𝑒 and input
shaft of the gearbox 𝜔𝑝 from the time of engaging the clutch linear.
3) At the initial moment of time (t = 0) the angular velocity of the crankshaft motor is 𝜔𝑒
equal to its angular speed at maximum torque 𝜔𝑒 = 𝜔𝑚 , and the angular speed of the
input shaft of the gearbox 𝜔𝑝 = 0
The schematization of the laws of change of the above parameters is given on car
acceleration diagram (Figure 2)
Based on experimental overclocking research car, it was found that when normal clutch
engagement rate the frictional moment 𝑀𝑐
increases along linear law from 0 to 𝑀𝑐 =
β 𝑀𝑒 𝑚𝑎𝑥
The process of slipping the clutch in during the time interval from 0 𝑡𝑜 𝑡2 , conditionally
divided into three intervals:
1) 𝑡𝑜 𝑡1 ) - friction moment 𝑀𝑐 increases, but the input shaft of the box gear is still
motionless. By the end interval 𝑀𝑐 = 𝑀𝜓 = and the car starts to move from rest.
2) (𝑡0 𝑡𝑜 𝑡1 ) - friction moment continues to increase and towards the end interval reaches
the maximum value 𝑀𝑐 = 𝛽 ∗ 𝑀𝑒𝑚𝑎𝑥 . Ends of the clutch engaging
15
3)
(𝑡1 𝑡𝑜 𝑡2 ) - friction moment 𝑀𝑐 maximum, the clutch is engaging and to the end
interval, its slipping ends. The clutch engagement time is usually 1 ... 2 s,
so for simplifications of calculations assume that the clutch engages instantly and torque
realized through the clutch, 𝑀𝑐 = 𝛽𝑀𝑒𝑚𝑎𝑥 = const. 𝜔0 is the angular velocity of the
masses of the dynamic system after the end of slipping and 𝑡2 = 𝑡𝑠𝑙 - Clutch slipping time.
Slipping time calculation
𝑡𝑠𝑙 =
𝜔𝑚 𝛪𝑒 𝛪𝑛
𝛪𝑒 (𝑀𝑐 − 𝑀𝜓 ) − 𝛪𝑛 (𝑀𝑒 − 𝑀𝑐 )
(10)
𝑀𝑐 ∗ 𝜔𝑚 ∗ 𝑡𝑠𝑙
2
(11)
Slipping work
𝑤𝑠𝑙 =
Substitution of the expression for 𝑡𝑠𝑙 into this equality determines
2
𝑀𝑐 𝜔𝑚
𝛪𝑒 𝛪𝑛
𝑤𝑠𝑙 =
2[𝛪𝑒 (𝑀𝑐 − 𝑀𝜓 ) − 𝛪𝑛 (𝑀𝑒 − 𝑀𝑐 )]
To assess the influence of the coefficient of adhesion safety 𝛽 =
(12)
𝑀𝑐
𝑀𝑒 𝑚𝑎𝑥
on time and
work of slipping clutch need to convert the formula. For starting at rest on a horizontal
16
paved road the moment of resistance to the movement of the car 𝑀𝜓 can be neglected,
then:
2
𝜔𝑚
∗ 𝛪𝑛
𝑤𝑠𝑙 =
2[1 + (𝛪𝑛 ⁄𝛪𝑒 ) + 𝛪𝑛 (1 − 1/𝛽)]
(13)
Thus, with an increase in the
coefficient of safety factor 𝛽 , the
slipping work 𝑤𝑠𝑙 and slipping time
𝑡𝑠𝑙 decreases (Figure 3) and thereby
increases the durability of the clutch
and the acceleration of the vehicle is
improved.
However,
with
increasing the safety factor 𝛽
increases
pedal
disengagement
effort
the
when
clutch
(by
increasing forces on the pressure
Figure 3. Dependence of work 𝑤𝑠𝑙 and slip time
𝑡𝑠𝑙 from the coefficient adhesion margin 𝛽
plate 𝑃𝑠𝑡 ), also deteriorates the protection of the vehicle transmission from overloads by
inertial torque If we take 𝑀𝑐 = 𝑀𝑒 𝑚𝑎𝑥 , then:
0.5𝐼𝑎 𝑀𝑒𝑚𝑎𝑥 𝜔𝑒2
𝑤𝑠𝑙 =
𝑀𝑐 − 𝑀𝛹
(14)
Where 𝐼𝑎 - is the flywheel moment of inertia, replacing the progressively moving mass of
the vehicle, kg × m2, MΨ – is the moment of road resistance to vehicle motion brought to
the engine crankshaft, N. m
The flywheel moment of inertia, which replaces the progressively moving mass of the
vehicle, is calculated by the formula:
𝐼𝑎 =
𝐼𝑚 . 𝐼𝑏
𝐼𝑚 + 𝐼𝑏
(15)
Where: 𝐼𝑎 - is the moment of inertia of the conventional flywheel, kg × m2 , 𝐼𝑚 - is the
moment of inertia of the engine flywheel, kg × m2; 𝐼𝑚 = 0.13, 𝐼𝑏 - is the moment of inertia
of the conventional flywheel reduced to the gearbox drive shaft, kg . m2
17
The moment of inertia of the conventional flywheel brought to the drive shaft of the gearbox
is calculated using the formula:
𝐼𝑏 =
𝑀𝑎 ∗ 𝑟𝑤 2
𝑖𝑔 ∗𝑖𝑓
, 𝑘𝑔. 𝑚2
(16)
Where 𝑀𝑎 − is the total mass of the vehicle, kg; 𝑟𝑤 is the rolling radius of the wheel, m;
𝑖𝑔 − is the gear ratio of the first gear stage; 𝑖𝑓 –is the final drive gears ratio The angular
velocity of the engine crankshaft, 𝜔𝑒 rad / s can be determined by the formula
𝜔𝑒 =
2π n
60
Where n is the engine speed, rpm
The moment of road resistance to motion of the car, reduced to the crankshaft of the engine,
is calculated assuming that the rolling radii of all the wheels of the car are equal by the
formula
𝑀𝜓 =
𝑀𝑎 ∗ 𝑔 ∗ 𝑟𝑤 ∗ 𝜓
𝑖𝑔 ∗ 𝑖𝑓 ∗ ɳ𝑡𝑟
(17)
Where - 𝑔 is the gravity of acceleration, 𝑚/𝑠 2 ɳ𝑡𝑟 - transmission efficiency and is the road
resistance coefficient (𝜓 = 0.02)
The heating of the drive disk with one pulling away is calculated by the formula:
∆𝑇 =
γ ∗ 𝐿𝑏
M𝑑 ∗ 𝐶𝑑
(18)
where ΔT is the temperature of the drive disk, °C; γ is the heat of fraction absorbed by the
disk; M𝑑 is the pressure disc mass, kg; C𝑑 - specific heat capacity of steel,
C𝑑 = 481.5 , 𝐽/𝑘𝑔. °C , and steel density, 𝜌𝑠𝑡 = 7700, 𝑘𝑔/𝑚3
Wide application for determining the work and slip time couplings have also found the
formulas obtained as a result of processing and analysis of a large number of experimental
data of the starting process vehicles in the most typical operating conditions:
ℎ 𝐼𝑎 𝑀𝑒𝑚𝑎𝑥 𝜔𝑒2
𝑤𝑠𝑙 =
0.67 𝑀𝑒𝑚𝑎𝑥 − 𝑀𝛹
(19)
𝜔𝑚 𝛪𝑛
0.67 𝑀𝑒𝑚𝑎𝑥 − 𝑀𝛹
(20)
and
𝑡𝑠𝑙 =
18
Here ℎ is a coefficient characterizing the type of engine.
 For diesel engines ℎ = 0.72, ω𝑚 = 0.75 · ω𝑚𝑁 ,
 For gasoline engines ℎ = 1.23, ω𝑚 = 𝜔𝑚 𝑀 /3 + 50π or (ℎ = 1.25, ω𝑚 = 0.5 · ω𝑚𝑁 (
According to formulas (12 and 19), the slip work is determined:
 For cars, buses and road trains (trucks with trailers and semi-trailers) when starting off
with full load in 1st gear in the gearbox (or in 1st highest gear if there is divider

For single trucks - in 2nd gear (or 1st top gear in the presence of a divider
 For all wheel, drive vehicles - in 1st gear in the gearbox and top gear in the transfer case.
As follows from the analysis of the presented formulas, the work of slipping increases
significantly with increasing initial engine angular velocity 𝜔𝑒 ; when starting off in higher
gears in gearbox (due to an increase in 𝛪𝑎 ), on the rise or on the road with high rolling
resistance coefficient ψ and when driving with trailer.
Clutch slip power
𝑁𝑠𝑙 = 𝑤𝑠𝑙 ⁄𝑡𝑠𝑙 = ℎ ∗ 𝑀𝑒𝑚𝑎𝑥 ∗ 𝜔𝑚
(21)
The clutch specific work (𝑤𝑠 , 𝑁/𝑚) of slipping, by which wear resistance is assessed vehicle
clutches, and slip power density are also calculated for starting conditions:
𝑤𝑠𝑙
𝑤𝑠𝑙
𝑤𝑠𝑝 =
=
A𝑓
π(𝑅𝑜𝑢𝑡 2 − 𝑅1𝑛 2 )
(22)
And
𝑁𝑠𝑝 = 𝑁𝑠𝑙 ⁄A𝑓
Where: 𝑤𝑠𝑙 – is the slipping work, N.m
(23)
A𝑓 - is the surface area of one side of the friction
lining, m2
Specific work 𝑤𝑠𝑝 and power 𝑁𝑠𝑝 of slipping should not exceed:
 for passenger cars with an engine capacity of up to 1.2 litters, from 1.2 to 1.8 litters and
over 1.8 litters ,[𝑤𝑠𝑝 ] = 270, 370 and 470 𝐽/ 𝑐𝑚2 , [𝑁𝑠𝑝 ] = 95, 125 and 150 𝑊/ 𝑐𝑚2 ,
respectively
 for trucks with gasoline engines:
[𝑤𝑠𝑝 ] = 460 𝐽/ 𝑐𝑚2 , [𝑁𝑠𝑝 ] = 100 𝑊/ 𝑐𝑚2
 for trucks with diesel engines and single-disk and double-disc clutches, respectively:
19
[𝑤𝑠𝑝 ] = 350 and 170 𝐽/ 𝑐𝑚2 , [𝑁𝑠𝑝 ] = 110 and 95 𝑊/ 𝑐𝑚2
Springs Design
The clutches are cylindrical, conical or diaphragm springs made of alloy and carbon steel
grades (Figure 4)
Coiled coil springs
To avoid misalignment of the pressure disc when disengaging the clutch, their number
should be a multiple of the number of levers clutch release and is from 8 to 20.
Figure 4. Composite coil springs, installed one
inside other
Calculation of twisted cylindrical springs is performed for torsion in the following
sequences
1) Estimated force per spring with the clutch engaged
𝐹𝑠 = 𝐹𝑠𝑡 /𝑛𝑠
Where 𝑛𝑠 is the springs number
20
When choosing the number of springs, it must be borne in mind that the design force on
one spring 𝐹𝑠 should not exceed 800 N.
2) Wire diameter, mm
𝑑 = √8 ∗ 𝐹𝑠 ∗ 𝑘 ∗
𝑐
∗𝜏
𝜋 𝑎𝑙𝑙
Here c = 4, 6, 8, 12 - spring index; k = (4S + 2) / (4S - 3) - coefficient, taking into account
the curvature of the coils of the spring; 𝜏𝑎𝑙𝑙 = 750 MPa – permissible torsional stress in the
coils of the spring.
The calculated value of the diameter 𝑑 of the wire is rounded along a number of normal
linear dimensions.
3) Average spring diameter, mm
𝐷0 = 𝑑 ∗ 𝑐
4) Settlement (deformation)of one spring coil under the calculated load, mm
8 ∗ 𝐹𝑠 ∗ 𝐷0 3
𝛿𝑠 =
𝐺 ∗ 𝑑4
where G = 8104 MPa is the modulus of rigidity for steel.
5) The required number of working coils of the spring (determined under the condition that
when the clutch is disengaged, the calculated force on the spring increases by 1.2 times)
𝑛 = 𝑆⁄0.2𝛿𝑠
Where 𝑆 is the retraction of the pressure plate when the clutch is disengaged?
S = 2 to 3 mm – for single plate clutches (lower value for clutches with rigid axial
direction driven discs, more - with flexible discs.)S = 4 mm - for double disc clutches.
6) The total number of coils of the spring
𝑛𝑡 = 𝑛 + (1.1 𝑡𝑜 2)
7) Spring rate, N / mm,
𝐹𝑠
𝐺 ∗ 𝑑4
𝐶𝑠 =
=
𝑛 ∗ 𝛿𝑠 8 ∗ 𝐷0 3
8) Height of the spring in working condition (with the clutch engaged)
𝐻𝑤 = 𝑛(𝑑 + 𝛿𝑠 ) + 𝑆
Where δ = 1 ... 2 mm is the gap between the coils of the spring with the clutch disengaged.
21
9) Height of the spring in a free state
𝐻𝑓 = 𝐻𝑤 + 𝛿𝑠 ∗ 𝑛
22