Gears and Transmissions

Vehicle Engineering ME30217/ME50223 Gears, Clutches and Transmissions The powertrain and the need for gears

Richard Burke 1/37 2014

Gears, Clutches and Transmissions

Vehicle Engineering (ME30217/ME50223)

Semester 1 / 2014-15

Dr RD Burke

Contents

1 The powertrain and the need for gears .......................................................................................... 2 2 Gears ............................................................................................................................................... 5 3 Manual Transmissions .................................................................................................................. 16 4 Automatic Transmission ............................................................................................................... 21 5 Differentials ................................................................................................................................... 28 6 Clutches and Torque convertors ................................................................................................... 31 7 Further Reading ............................................................................................................................ 37 8 Recommended videos ................................................................................................................... 37



1 The powertrain and the need for gears

1.1 Powertrain components and layouts A powertrain refers to the complete propulsion system of a vehicle from the fuel in the tank to the tyres contacting the road. Conventional powertrains are based around an internal combustion engine which is supplied with liquid fuel from a tank via a hydraulic pumps and with combustion air by a more or less sophisticated air management system. The mechanical output shaft of the engine has linked to the wheels via a transmissions system comprising a gear box and differential. The transmission system is designed to match the work generated by the engine with that required to propel the vehicle. The onset of hybrid vehicle is making the job of transmissions more and more complex as they are required to control the flow of mechanical power between at least three but possibly more components (Engine, wheels, electric motor(s), mechanical flywheel,)

A separate section of this course is dedicated to hybrid vehicle layouts, while here we will focus on conventional layouts. The most common layouts for passenger and light commercial vehicles are illustrated below. Front wheel drive installation with transverse engine is the most common on smaller and lower cost vehicles as it is the cheapest installation. However, with larger engines and gearboxes, space constraints can become significant. Higher end cars and higher power vans will tend to have a rear wheel drive setup which reduces (somewhat) the space constraints, but increases the cost and the need for a driveshaft to the rear of the vehicle. There is also the need to a 90o change in power direction at the rear axle.

1.2 Why we need gears in a vehicle Gears in the powertrain fulfil a number of tasks that are vital for the operation of the vehicle. Firstly they transmit the mechanical power from one location to another. Secondly they allow for the change in direction of the vehicle (reverse gear). Combustion engines are directional components and can only operate in one direction, therefore gearing is required to allow for changing the

Rear Wheel Drive

Longitudinal installation

North/South

Front Wheel Drive Transverse installation

East/West

4 Wheel Drive

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Differential



direction of rotation at the wheels. Gears also change the rotational speed and the magnitude of transmitted torque depending on the relative sizing of the gears. In a typical saloon car, the engine will happily operate between 1000-6500rpm (petrol) or 1000-4500rpm (Diesel), generating a torque between 0-250Nm. At the wheels, the speed requirement will depend on wheel radius and rotational speed will typically very between 0-2000rpm (0-180km/h) whilst the required torque may reach 3000Nm for a steep hill pull away. The gears therefore allow the engine power to be modulated between different vehicle demands. In rear and 4 wheel drive applications, the gearing system allow for the change in angle of the shafts.

The selection of gear ratios is a complex problem that needs to take into account a number of vehicle level requirements:

Achieve pull away in worst case conditions (max vehicle weight including any towing, maximum gradients)

Achieve target acceleration in first gear Smooth progression of vehicle speed from stand still to cruising speed Good matching of engine operating points at typical cruising speeds to ensure good fuel

economy

At any operating condition, we can apply Newtons law of motions to a vehicle taking into account rolling resistance, aerodynamic drag, acceleration forces and gradient forces:

And

Where Ft is the tractive force (N),

m is vehicle mass (kg),

Cr is the rolling resistance coefficient,

is the air density, A is the vehicle frontal area,

Cd is the drag coefficient,

v is the vehicle velocity (m/s),

a is the acceleration (m/s2)

is the axle torque (Nm) is the rolling radius of the wheel/tyre (m)

An engine speed map is defined as the operating area of the engine in terms of speed and torque. An example is shown opposite for an engine that can operate between 800-5500rpm delivering a maximum torque between 100-140Nm.

This map can then be plotted onto a tractive force curve showing the possible operation of the vehicle for given gear ratios. The upper part of the tractive force curve plots the required tractive force against vehicle speed. Firstly, lines of constant power have been plotted between 10-130kW

Typical engine operating map

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Matching torque to pull-away requirements

Friction between tire and ground (rolling resistance)

Gradient force

Aerodynamics

Acceleration

Torque (axle)



these are the hyperbolic curves that are simply obtained as the product of speed and tractive force. Secondly, the required tractive force for gradients ranging from 0 to 100% have been plotted. These are almost flat lines but actually quadratic due to the squared term in the aerodynamic drag calculation. Finally, for each gear (6 in this case) the tractive force that would be obtained with maximum engine torque has been plotted. These 6 curves represent the highest tractive force that could be obtained by running the engine with that particular gear ratio. It should be noted that the engine does not have to run at its maximum torque level, and could operate anywhere below these lines. The bottom plot shows the engine speed as a function of vehicle speed for each gear. As the engine has a limited speed range (in this case 1000-5000rpm), there is a limitation in the vehicle speeds depending on the gear selection.

The selection of the first gear will primarily depend on the pull away requirements balanced with the need for the maximum speed in gear 1 not to be too low. The top gear can equally fairly easily be determined based on the maximum speed requirement of the vehicle. Both these are easily determined based on the tractive force diagram. Often other gear ratios are selected to promote fuel economy during cruising and often the highest gear would be labelled an economy gear. To illustrate the benefit of this we return to the engine operating map previously presented. Now we can plot on lines of constant vehicle speed (assuming the vehicle is running on a flat surface). These lines for different speeds indicated all the possibilities of engine operation point as we vary the transmission ratio. On top of these lines, we can plot the required engine torque to drive the vehicle across the engine speed range. This is represented for 5th gear by the solid line. The intersection of this line with the cruise speed lines is the operating point for that given gear ratio. The effect of including an additional 6th gear with a different ratio is to move the operation point for each of the cruises to a different place on the operating map. The aim of an economy gear would be to shift this point to a more favourable location in terms of fuel economy.

0 20 40 60 80 100 120 140 160 180 2000

5000

10000

15000

Vehicle Speed (km/h)

Trac

tive

Forc

e an

d R

unni

ng R

esis

tanc

e (N

)

0 20 40 60 80 100 120 140 160 180 200

0

2000

4000

6000

Vehicle Speed (km/h)

Eng

ine

Spe

ed (r

ev/m

in)

100%

80%

60%

40%

20%

0%

1st

6th

1st

2nd

2nd

3rd

3rd

4th

4th

5th

5th

10%10kW

30kW

50kW

70kW 90kW110kW

6th

130kW

Tractive Force plot

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Vehicle Engineering ME30217/ME50223 Gears, Clutches and Transmissions Gears


A factor that needs to be considered when selecting an economy gear is the torque margine. This is the amount of reserve torque available to the engine to allow the vehicle to accelerate from the cruise condition in the case of an overtaking manoeuvre, or that may be required if the vehicle is confronted with an uphill gradient. Typically engines operate more fuel efficiently nearer to their maximum torques (as engine friction becomes a lower proportion of total work), therefore a more economical operating point will typically result in a smaller torque margin.

In older vehicle applications, intermediate gears were selected typically around one of two criteria:

Arithmetic progression: Constant vehicle speed increase for each gear.

Geometric progression: Constant engine speed range for each gear.

However, with the importance of fuel economy for todays vehicles, intermediate gear ratio selection has become similar to the selection of economy gears in order to provide good fuel economy at intermediate cruising speeds. Typically these points will be chosen to match those required by the legislative procedures which in Europe will be the New European Drive Cycle.

2 Gears

2.1 Gears types and geometry Different types of gears exist and are suited to different applications. The simplest form are spur gears which have straight teeth and allow transmission between two parallel shafts. However helical gears are more commonly used in automotive gear boxes. Helical gears have the advantage that they can be used to transmit power between two non-parallel shafts; in automotive gearboxes they are used as they are less noisy than spur gears. One disadvantage is that they produce an axial loading on the shaft which must be supported by an appropriate bearing system.

5th Gear

Possible 6th

Gear

Torq

ue m

argi

n

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Disadvantage of 6th gear:

- lines were designed for flat surface and if driver encounters gradient, the torque margin reduces and therefore acceleration required for that gradient will not be possible



Bevel gears transmit power between two intersecting shafts using teeth on conical surfaces where the teeth can be straight or spiral. Hapoidal gears appear similar in shape, however they can operate between non-intersecting shafts. Worm gears are an additional example of transmission between non intersecting shafts and offer a high speed ratio (typically greater than 3), however they can only be driven from the worm to the wheel.

The main terminology for gear systems is shown in the figure below. The pitch diameter is the diameter of which a pure rolling action would transmit the same motion as the gear. The teeth are split into two parts by the pitch line: the addendum is the radial length between the pitch circle and the top land and the dedendum is the radial length between the pitch circle and the root circle.

Gear nomenclature

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Gear teeth shapes are most commonly involutes extending from the base circle. This ensures that the teeth are thickest at the root (giving good strength) and maintain a constant pressure angle (see below). The involute geometry is an unwinding of a cord of a circle and best described by considering a spool of wire. If a pen is attached to the end of the wire, and it is unwound whilst maintaining the wire taut, then the shape that will be drawn is an involute.

The number of teeth on a gear (N) depends on the diameter of the gear (D) and the size of the teeth. The circular pitch (p) is defined as the arc round the pitch circle between the same point on two teeth:

The diametral pitch (pd)is the number of teeth per unit diameter

And the module (m) is defined as

Standard modules exist in the metric system ranging from 0.5 to 6 and typically gears are designed with a minimum of 12 teeth.

The involute curve defining the shape of a gear tooth is obtained by unwinding a circle arc

Standard gear teeth sizes

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Assume diameter always refers to pitch diameter



2.2 Forces and Stresses in Meshing gears In a pair of mating gears, it is common to refer to the smaller gear as the pinion (the larger gear having no such special name). When the mating gears are operating, the speeds of the two gears are related by the gear ratio i as a function of speeds ( ), pitch diameters (d) or number of teeth (N):

Gear ratios are easily combined in gear trains as follows:

(

) (

) (

)

The forces acting on the gears are as follows if it is assumed that the larger gear is the driving gear:

A torque is applied to the input shaft. The meshing teeth cause a desirable force Ft at the interface which results in a torque on the output shaft.

A somewhat less desirable force Fs tends to separate the two shafts. It will be shown this is a result of the shape of the teeth and the angle of pressure

Finally, if the gears are helical, then opposing axial forces Fa will apply to each shaft.

Looking closed at the point of contact between the two gears, the force is transmitted along through the involute profiles at the point of contact along an axis at an angle with the tangent to the pitch circle at the point of contact.

If frictional losses are neglected, then the tangential force is related to the input and output torques:

The total force at the contact area is

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Therefore:

Torque 1/ Torque 2 = - R1/R2 = 1/i

But, in practice: Torque1 / R1 > Torque 2 /R2 due to friction losses



And

The power input is given by

And the output, where is the efficiency of the transmission

A simple efficiency model is the Tulpin efficiency which states:

{

(

)

(

)

Another important point is the effect gears have on the inertia of the total system perceived by one end of the drive chain, this is referred to as reflected inertia. If two shafts A and B, with total inertias IA and IB, support mashing gears with NA and NB teeth respectively, then the perceived inertia of the total system at shaft A is given by:

( )

Similarly, the total inertia perceived on shaft B will be given by

( )

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Why internal gears preferred over external gears?

- Contained in a sealed unit. This means theyre completely protected from water, dirt, road salt and grime- Internal gear hubs are easier to maintain than standard external gears- With an internally geared hub you can actually shift gears while stationary



During the operation of gears, two major key stress locations on the tooth can be identified: the contact stress on the face of the tooth and the bending stress at the root of the tooth.

The bending stress can be estimated using Lewis formula:

Where:

is the tangential force on tooth (N) is the face width is the Lewis Form Factor is the module is the dynamic factor

The dynamic factor can be estimated simply from:

The Lewis Form Factor is given from tables:

N Teeth Y N Teeth Y 12 0.22961 28 0.34791 13 0.24317 30 0.35511 14 0.25531 34 0.36731 15 0.26622 38 0.37727 16 0.27611 45 0.39093 17 0.28508 50 0.39861 18 0.29327 60 0.41047 19 0.30078 75 0.42283 20 0.30769 100 0.43574 21 0.31406 150 0.44931 22 0.31997 300 0.46364 24 0.33056 Rack 0.47897 26 0.33979

Contact Stress on tooth face

Bending Stress at tooth root

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The contact stress can also be calculated from the empirical formula

Where

The dynamic factor accounts for the impact of the teeth as they mate, even during steady speed running. This is caused by the inevitable clearance between the gears. As two mating pairs separate there will no longer be any force transmitted between the two gears and the driven gear will decelerate until the next pair come into contact. It is this impact that is being accounted for. Although a simple equation is suggested above, this factor depends strongly on the quality of the gear and the pitch line velocity and charts are available based on gear quality classification.

In Helical gears, there is an additional axial force induced by the angle of the gears. Although this geometry can reduce impact effects which will both reduce noise and can improve durability, it is more expensive and the axial force must be supported by a suitable bearing system. These gears create an axial force on the shaft such that:

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EXAMPLE

A gear A has a diameter of 50mm with module 2.5mm and a face width of 30mm. An input torque of

100Nm is applied to the shaft. Assuming low speed operation, what is the bending stress on the

tooth? What would the bending stress be if the input speed was 5000rev/min?

When the speed is low, the dynamic factor Kv1

The tangential force is given by:

The number of teeth is given by:

Hence from the table, the Lewis ford factor is 0.30769

At 5000rev/min,

( )

So

Therefore the bending stress would become

It should be noted that the bending stress is above that for mild steel meaning careful selection of materials and heat treatments are required.

Now, let gear B, meshing with gear A, have a diameter D=100mm, assuming all other conditions are

equal, calculate the contact stress.

Firstly we calculate the ratio of diameters, h in the contact stress equation



Then, taking values from the previous calculation

The contact stress is three times greater than the tooth bending stress

The stresses in gears cause different failure modes, the most common being pitting of the surface and root cracking of the teeth. Both were discussed in more detail in the Tribology section of this course. It should be noted that quite often root cracking will be initiated at a point of pitting where the surface has already been damaged.

The gap between the teeth that causes the need for dynamic factors when calculating the stresses can also cause errors in motion when gears change direction. This gap must be closed before force can be transferred in the new direction, and causes a level of hysteresis where the driving gear will move without any response from the driven gear.



2.3 Gear Materials A range of materials can be used for manufacturing gears for a range of applications in the vehicle from the transmissions gears in the powertrain to small gears in a servo motor controlling the actuator of a VGT mechanism. The material of choice depends strongly on the applications and the table below summarises different materials that have been used for gears.

Non metals Material Notes Applications

Acetal (Delrin) Wear resistance, low water absorption Long life low load up to commercial quality

Phenolic laminates Low cost, low quality, moderate strength High production, low quality to moderate commercial quality Nylons No lubrication, absorbs water Long life and low loads with commercial quality PTFE Low friction and no lubrication Special low friction gears to commercial quality

Ferrous Metals Material Notes Applications

Cast Iron Low Cost and easy to machine with high damping Large to moderate power in commercial applications

Cast Steels Low cost and reasonable strength Power gear with medium rating to commercial quality

Plain Carbon Steels Good machining and can be heat treated Power gears with medium rating to commercial/medium quality

Alloy Steels Heat treated to provide highest strength and durability Highest power requirement in precision and high precision applications

Stainless Steel (Aust) Good corrosion resistance and non-magnetic

Corrosion resistance with low power rating up to precision quality

Stainless Steels (Mart)

Hardenable, Reasonable corrosion resistance, magnetic

Low to medium power ratings, up to high precision quality

Non- Ferrous Metals Material Notes Applications

Aluminium Alloys Light weight, non-corrosive and good machinability Light duty instrument gears up to high precision quality

Brass Alloys Low cost, non-corrosive, excellent machinability Low cost commercial quality gears up to medium quality

Bronze Alloys Excellent machinability, low friction and good compatibility with steel For use with steel power gears. Quality up to high precision

Magnesium Alloys Light weight but poor corrosion resistance Light weight low load gears. Quality up to medium precision

Nickel alloys Low coefficient of thermal expansion. Poor machinability Special gears with thermal application with commercial quality

Titanium alloys High strength, low weight, good corrosion resistance Special light weight, high strength gears to medium quality

Di Cast Alloys Low cost with low precision and strength High production, low quality gears to commercial quality Sintered powder alloys Low cost, low quality, moderate strength

High production, low quality to moderate commercial quality



The surface hardness of the gear determines the limiting contact stress that can be tolerated. For metal gears, various treatments can be applied to modify the properties of the gear for particular applications. These are listed in the table below.

Surface treatment

Suitable base metal Description

Typical hardness

(Vickers Hv) Typical size Advantages and disadvantages

Carburising Steels less than 2% carbon

Carbon content of surface layer increased using solid, liquid or gaseous medium

800 0.5mm depth

Nitriding Nitriding steels Diffusion of Nitrogen in the surface (520-560oC) 900-1150 0.3mm depth

Increases surface hardness and leaves residual compressive stresses in surface. Give good resistance to scuffing

Plasma Nitriding Alloy Steels

Bombarding surface with nitrogen ions at 400-600oC

900-1250 0.3mm with surface groth of 25m

As for nitriding. Also give low distortion

Sulfinuz

All ferrous metals including stainless

Salt bath treatment at 540-600oC introducing carbon, nitrogen and sulphur

400

Size change from -5m to +3m. Effective 4-25m

Gives good scuffing resistance and some reduction in friction but reduces corrosion resistance

Boriding Steels, cast irons

Formation of borides in surface layer at 800-900oC

1200-1760 30m to 0.3mm Gives good sliding wear resistance

Electroplated Chromium All metals Electroplating 950

Thickness increased 0.01-0.5mm

Appropriate plating conditions are needed to avoid cracks in the plating which are undesirable and any detached particles become abrasive

The material selection for transmission gears requires a number of factors:

- Hard and wear resistant surfaces - Resistance to tooth root bending fatigue - Resistance to surface fatigue to avoid pitting - A tough core - Dimensional accuracy to reduce noise, vibration and harshness through smooth meshing - Ability to transmit high loads within sensible size and weight constraints.

Vehicle Engineering ME30217/ME50223 Gears, Clutches and Transmissions Manual Transmissions


The manufacturing process for gears requires a combination of forging, machining, heat treatment and surface treatments. This complex route is continuously put under pressure to reduce costs by:

- Better prediction of the distortion effect of heat treatment to eliminate hard machining - Reducing heat treatment times by using higher temperatures - Improving machinability

Equally, the manufacturing process must provide materials that have:

- Controlled hardness: ensuring repeatability of mechanical properties - Controlled low silicon steels: improve the bending fatigue life by reducing internal oxidation

during carburising - Optimised sulphur content: balances the conflicting benefits of low sulphur for improved

bending fatigue and high sulphur for improved machinability - Inclusion modified steels: improve machining throughput rates with reduced tool wear - Clean steels: provide good fatigue resistance from a low overall inclusion content.

3 Manual Transmissions

3.1 Overview Manual transmissions are transmissions where the driver has full control over the gear change both in selecting when gear changes should occur and in providing the actions and forces to undertake the gear changes. These gearboxes have a high mechanical efficiency and are relatively cheap to manufacture. They also can be made relatively small and light weight. The fact that the driver has control over the gear changes can be a highly subjective topic, however the driver dependency of the system requires more involved learning to use the machines (gear change is a complex manoeuvre) and this can result in a tiring driving experience. In addition, the gear ratios which are set to deliver good fuel economy and emissions will be somewhat compromised if the driver selects the wrong gear for any given driving conditions. Finally, manual gear changes means the driver becomes a factor in drivability of the vehicle: firstly, this can limit the total number of gears to 6 using a selector fork mechanism and secondly this compromises the gear ratios as it should be avoided the need to up shift too frequently during acceleration.

3.2 Layout and Components Manual gearbox design is usually made up of two or three shafts. In a single stage gearbox, the gear ratio is undertaken with a single set of gears for each gear. In a double stage, the gearbox will incorporate a third layshaft and each gear ratio will be made up of one fixed gear ratio and one variable. The example below shows a double stage layout where an initial fixed ratio exists between the engine input and the layshaft, followed by the selectable ratio. All of the gears are then constantly meshing, but not all rigidly linked to the output (or lay) shaft. In the example below, when the vehicle is stopped and in neutral, but the engine idling, all of the gears will spin on the stationary output shaft. When 1st gear is selected and the vehicle moving, the 1st gear on the layshaft will be engaged with the output shaft and drive it; the other gears will all be spinning depending on their respective ratios with the layshaft, however they will all be slipping on the output shaft.



A gear ratio of 1 is referred to as direct drive, where the output shaft of the gearbox is rotating at the same speed as the engine input shaft and in this case power is typically not passed through the layshaft (although it does continue to rotate). Gear ratios of less than 1, where the output shaft rotates faster than the input shaft are referred to as overdrive.

An excellent demonstration of a manual gearbox is available at: https://www.youtube.com/watch?v=vOo3TLgL0kM

A key point in the design of manual transmissions is the selector mechanism. In road vehicles, the conventional route is to use a synchromesh which synchronises the speed of the gearbox input shaft with the output shaft (linked to vehicle speed) before the gears are engaged. Transmissions without a synchromesh do exist, using a crash or dog engagement where the engager is forced into the gear directly. The output torque for both options is shown below during a gear change:

In both cases, the initial gear selected is gear1, giving a similar torque output.

Synchromesh engagement: First the clutch pedal is depressed, causing a drop in torque and an eventual torque reversal. The clutch remains depressed throughout the synchronisation process whilst the shafts in the gearbox and the output plates of the clutch are accelerated or decelerated depending on the ratio of the gear being selected. Note, the torque to accelerate/decelerate the input shaft comes from the shift force. After synchronisation and engagement, the clutch can be re-engaged giving a smooth torque recovery. This processes results in a smooth change which reduces noise and wear in the gear box and improves the vehicle ride.

Dog engagement transmission: The clutch is again depressed causing a drop in output torque, however with the dog transmission, the engagement must happen very quickly to ensure the teeth are forced into the gears correctly. In this type of transmission, the clutch is also not fully depressed and is reengaged very rapidly. This causes a spike in torque due to the inertia of the engine and rotating parts, because they change speed quickly top match that of the output shaft. This inertia

Example layout of a manual transmission

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spike can be used to positively accelerate/decelerate the vehicle and also reduces the time when no acceleration occurs due to clutch disengagement which is useful in racing applications. However, this results in a harsher and noisier gear change.

The performance effect of a Dog engagement vs. synchromesh is shown below: The synchromesh transmission causes a noticeable halt in the vehicle acceleration that can be avoided by the faster shifts with the dog engagement.

When the vehicle is moving in a particular gear, as it has already been described, the selected gear is locked with the output or layshaft. When a gear change is required, the current gear is disengaged, however the new desired gear is sliding on the shaft, and this gear and the engaged shaft need to be accelerated or decelerated to the same speed as the output shaft. This is the role of the synchromesh that acts somewhat like a clutch.

The synchromesh is formed of a number of key parts as shown below. Firstly, the gears are rigidly attached to a ring of drive dogs and an external cone, these are usually one part. The mating external cone is usually a separate part called a baulk ring and may typically be made of bronze. The baulk ring is attached to the hub of the synchromesh and rotated with the hub and shaft. An outer sleeve with mating dogs moves towards the gears, compressing the baulk rings and then engages with the drive dogs.

Comparison of transient performance of a

synchromesh transmission and a crash

engagement transmission



Disengaged position

Engaging

Engaged Position

In the disengaged position, for example neutral of an alternative gear selector, the hub of the synchromesh is rotated with the shaft on which it is mounted and the gears slide on this shaft at different speeds depending on their relative sizes.

As the sleeve is moved towards the gear, it engages with and compresses the baulk ring against the gear, engaging the cone clutch. This provides a high torque for a given axial load to accelerate or decelerate the gear and connected shaft.

As the sleeve moves further towards the gear dogs, it engages fully with these due to the chamfers on the dog teeth. This ensures the final stage of the gear engagement and locks the gears together for power transmission allowing for the clutch to be re-engaged.



Some improvements to the synchromesh can be implemented to improve its performance and are described below.

The cone surface can be threaded to allow for the removal of oil from between the two surfaces. Special channels can also be manufactured to allow better oil flow. The surface is manufactured to have a high coefficient of friction and surface treatments such as paper or metal spraying can be used to enhance friction further or control wear.

The torque that is achieved from the cone surface is provided from the axial force provided by the driver and dictates the time required to accelerate or decelerate the system before gear engagement. It is therefore often desirable to increase this torque either to reduce the effort from the driver or to reduce the synchronisation time and hence the shift time. This can also be achieved by reducing the inertia of the clutch and shaft assemblies, but this will be limited by the power transmission requirements of these components. To increase the synchronisation torques, a number of routes are possible:

1. Increase the diameter of the synchroniser: This increases torque but is usually difficult due to space constraints

2. Increase the lever ratio: This produces more shift force from a given driver effort, however it will increase the travel distance of the lever

3. Change in lubrication oil: this can be impractical as single lubrication oil also lubricates gears and transmission bearings

4. Increase friction of surface: increasing the cone friction is beneficial, but is usually a trade-off with wear resistance

5. Use a twin or triple cone synchro: This increases the number of friction surfaces and is very effective, however it does increase complexity and number of parts (and hence cost).

With manual transmission, if the effectiveness of the synchroniser is increased too greatly and it can make shifting too easy which may result in inappropriate gear selection from the driver.

Comparison of single and triple cone synchromesh

Vehicle Engineering ME30217/ME50223 Gears, Clutches and Transmissions Automatic Transmission


4 Automatic Transmission

4.1 Overview and types of transmissions Automatic transmissions are transmission systems where the shifting of gears or the varying of gear ratio is controlled by an automated process with no direct input from the driver. By removing the need for the driver to change gears, the driving experience can be made more relaxing and cause less fatigue, especially during city driving where gear changes occur frequently. By removing the driver input, the gear shifting can be set by the vehicle manufacturer and used as a way of improving fuel consumption and emissions by better matching the engine operating point to the vehicle requirements. This may seem surprising as conventionally automated transmission were known for poor fuel economy compared to manual. However, this was a result of the limited gear ratios in older automatic transmissions which were limited to 3 or 4 ratios. However the latest gear boxes for passenger cars have 8 or 9 gears- this number of gears would be difficult to implement in a manual setup using a conventional shifting mechanism. Various types of automatic transmissions exist for passenger vehicles and each will be discussed separately:

- Conventional automatic - Automated manual transmission (AMT) - Dual Clutch transmission - Continuously variable transmission (CVT)

4.2 Automated Manual transmission As the name suggests, this type of transmission is based on a manual transmission as described above, however the clutch and shift forks are actuated by an electronic or hydraulic control system. This approach maintains the high efficiency of the manual transmission but adds the ability to dictate gear selection. The system is relatively inexpensive as the base manual transmission can be used with an add-on automation system. The complexity of the automated manual transmission stems entirely in the control of the gear changing process. The control system of an automated manual transmission has to cope with the highly non-linear behaviour of the clutch yet still provide a smooth transition. This is difficult enough for human drivers and is made more complex through the aging of oils and clutch plates. Particularly challenging aspects can be hill starts and avoiding aggressive launches. The clutch control during shifting is also of concern, and the tine required to smoothly control the clutch is directly felt by the driver as an interruption in available torque from the engine.

Renault Quickshift and Opel Easytronic are examples of automated manual transmissions



4.3 Dual clutch transmission Dual clutch transmissions have, at some location within them, a dual shaft arrangement whereby the even gears are connected to one shaft and the odd gears to the other. Each shaft can be connected to the engine via a dual clutch arrangement. In this way the gear box has two possible power paths. An example layout is shown beside.

Consider the situation where first gear is selected and we will shortly be moving to 2nd gear. In this case, the 1st clutch is engaged and the second clutch depressed. The engine is therefore providing power to the odd gear group and as the 1st gear is engaged on the layshaft, power is transferred through this gear. The other gears are all slipping on the layshaft as with a manual transmission. As the engine speed increases and the transmission controller anticipates an upshift to 2nd gear, this gear can be engaged on the layshaft whilst still transmitting power through the first gear. As the second gear is engaged, it will start to drive the even gear group which is free to turn as the 2nd clutch is depressed. In the layout above, the even group will then slip around the odd gear group shaft. With second gear pre-selected, the actual gear change consists simply of disengaging the 1st clutch and engaging the 2nd clutch simultaneously. The final step of the upshift is to disengage 1st gear in anticipation of engaging 3rd gear for the next upshift.

The advantages of the dual shift transmission are clearly a very quick shift time with little or even no torque interruption. It gives very good drivability such as a conventional automatic transmission, but with the efficiency of a manual transmission. The down side is that these transmissions are expensive, complex to build and the control of the two clutches can be problematic. Some example designs are shown below.

Example Audi and Mercedes dual clutch transmissions

Output shaft

2nd clutch

1st Clutch

LuK PSG (Parralel Shift Gearbox)

Transmission



4.4 Conventional Automatic Conventional automatic transmissions are typically built around planetary gear systems. These planetary gear systems are made up of or a sun and ring gears contained within a ring gear. In some cases more complex plant arrangements are designed to vary further the ratios. Planetary gears arrangements have very high torque densities due to the large number of meshes.

The three shafts connected to the sun, carrier and annulus (ring) can all rotate at different rotational speeds s, c and a. The ratio of speeds between the three axes is given by:

Where

Typically

The transmitted torques can be obtained by considering conservation of power and balancing of torques on the device which if efficiency is assumed to be 100% is given by

If the carrier is clamped to the casing, then we have:

The input to output speed ratio is given by:

The output torque is therefore given by

And the clamping torque on the carrier



Similar expressions can be derived by considering the cases where the sun or annulus is clamped to the casing. For each of these cases, the torque relationship is given by:

If two of the rotating elements are clamped together, then the transmission behaves as a direct drive. For example, if the sun is clamped to the planet carrier:

A variety of other ratios are available using different combinations of locking of the planetary gears. The following table list 6 possibilities where one of the shafts is held stationary with respect to the casing.

INPUT OUTPUT LOCKED RATIO TYPICAL RANGE

Sun Carrier Ring

Sun Ring Carrier

Carrier Sun Ring

Carrier Ring Sun

Ring Carrier Sun

Ring Sun Carrier

Automatic transmissions make use of a number of these components arranged in sequence. In manual transmissions, each gear ratio has its own corresponding meshing pair of gears. In an automatic transmission, the gear ratios are achieved by restricting the motion of certain gears in different sequences using clutches. A good example of a how the clutches are varied in a 6 speed automatic gearbox is available at https://www.youtube.com/watch?v=1ByVBBfEXWk. Some examples are shown below and specifically notice the 4-wheel drive transmission (you should be able to identify the Torsen Differential after reading all of these notes!).

The input to output speed ratio is given by:

The sun torque is 0Nm as this is not connected to an output. Therefore:

https://www.youtube.com/watch?v=1ByVBBfEXWk



The automatic transmission also requires a flexible coupling between the transmission and engine to allow modulation of engine speed as the clutches selecting the gear ratio are varied. Such device is usually a torque convertor or a fluid flywheel which will be described later.

4.5 Continuously variable transmission CVTs are special types of transmissions that allow stepless changes in gear ratio without torque interruption over a range of ratios. As all ratios can be achieved, it is possible for the transmission to hold the engine at a constant operating speed throughout the vehicle acceleration. As such, CVTs offer improved benefits over automatic transmissions by increasing the number of ratios further. Equally, the gear changes are automatic and therefore do not require driver intervention. However, CVT drives are less efficient than gear systems and this offsets somewhat the benefits from operating the engine at a high efficiency point. They are also more complex than gear systems and result in an unconventional driving experience (vehicle accelerates at constant engine speed).

Two main types of mechanical CVTs exist: Traction drives and belt drives. Other forms of CVT can be implemented through hydraulic or electrical couplings.

An illustration of the principle of a traction drive is shown below. Torque is transmitted through elasto-hydrodynamic lubrication between the rollers and the input/output discs and no metal to metal contact should occur. Under these lubrication regimes the fluid viscosity increases significantly due to high pressures of the magnitude of 0.7-3.5GPa which cause it to behave somewhat like a solid. So high are the pressures that the metal parts also deform locally to provide elliptical contact patches.

Example modern automatic transmissions



The area of operation of the traction CVT can be plotted on a curve similar to the stribek curve seen in the tribology section of the course. With low contact pressures, the rotating discs are able to form a relatively large film thickness that corresponds to hydrodynamic lubrication. Under this regime, the parts are well lubricated, and the traction coefficient is low. The coefficient of traction is identical to the coefficient of friction, that is:

That is to say in a CVT, that the coefficient of traction determines, for a given clamping force holding the rotating members together, the maximum torque that can be transmitted. It is always possible to transmit lower torques, however if it is attempted to transmit a higher torque, the transmission will slip causing unwanted shearing of the traction fluid resulting in heat losses.

As the fluid film is reduced by applying further contact pressure, the coefficient of traction begins to rise to allow the transmission of power. It continues to rise throughout the hydrodynamic regime. The coefficient of traction can rise further in the boundary lubrication regime; however operation in this regime will result in contact and wear between components.

In a belt drive CVT, the variation in transmission ratio is achieved by varying the diameters of the pulleys as shown below. The V shaped pulleys can be pushed closer together or further apart to change the size of the pulleys. As one increases in size, the other will reduce as the belt cannot be stretched. In order to have the necessary strength to transmit the engine power, the belt is made from steel consisting of flexible bands supporting trapezoidal plates.

Traction CVT in speed reducing setting Traction CVT in speed increasing setting

The variation of film thickness and traction coefficient

with contact pressure for traction CVT.



Another category of CVTs are infinitely variable transmissions which allow the transmission to pass through zero and to reverse the output speed. They are typically achieved by combining a CVT with an epicyclic transmission and these transmissions allow for the vehicle clutch or torque convertor required for vehicle launch to be omitted. It is in fact the clutch within the epicyclic gear that allows for the pull away characteristic.

The major disadvantage for the CVT system is that is has lower efficiency than a manual transmission. Crucially, the efficiency of the transmission typically varies with the gear ratio with a maximum which can approach the efficiency of a manual transmission. This lower efficiency tends to offset the gains in engine performance from the CVT.

There have been a number of CVT applications in vehicles. The most high profile perhaps being in 1993 Williams F1 tested a CVT system in their all-conquering 1992 car. This employed a belt drive system and the key limit in development was building a belt strong enough to take the full engine power. This could have changed the way the sport sounded with the cars continually operating at

Belt driven CVT varies the transmission ratio using varying diameter pulleys. The belt is made from steel as it

needs to be strong enough to transmit full engine power

Efficiency of a CVT as a function

of gear ratio and transmitted

torque

Vehicle Engineering ME30217/ME50223 Gears, Clutches and Transmissions Differentials


high engine revs. However, the technology was banned before even getting to a race through two rule regulations: The first imposing that cars have between 4 and 7 distinct ratios and subsequently explicitly banning CVTs.

https://www.youtube.com/watch?v=x3UpBKXMRto

Other areas receiving current interest include the application of CVT systems to auxiliary components such as superchargers, water and oil pumps where the power transfer is not so great. Also, CVT are being trialled in turbo compounding applications, where the CVT links a turbine in the exhaust system to the output shaft in order to capture otherwise waste heat from the exhaust gases. In this case, the lower efficiency of the device is less problematic than without this system, the efficiency of exhaust heat recuperation would be 0%.

5 Differentials The differential is a key component that allows two wheels on the same axle to rotate at different speeds whilst both being able to receive power from the engine. This is crucial to allow different wheel speeds during cornering for the inner and outer wheels. Before differentials, a single wheel would be connected to the drive shaft, otherwise one of the wheels would be forces to slip on the road during cornering.

A typical differential is shown below. The differential incorporates the final drive ratio through the relative sizes of the drive pinion and the ring gear (also called crown gear). The ring gear is rigidly

The Williams belt driven CVT could have revolutionised Formula One. Rule changes meant it never saw

competitive racing.

The VanDyne SuperTurbo 1. Exhaust Manifold 2. Turbine 3. High speed drive 4. Compressor 5. CVT 6. Engine connexion https://www.youtube.com/watch?v=DMz4MATUJxE

https://www.youtube.com/watch?v=x3UpBKXMRtohttps://www.youtube.com/watch?v=DMz4MATUJxEhttps://www.youtube.com/watch?v=DMz4MATUJxE



connected to the housing, but free to rotate along the axles. The housing supports the differential pinions which engage with the side gears. If the vehicle is moving straight with equal traction on both wheels, then the pinions will not rotate about themselves but instead act as a rigid bevel gear with both axles, rotating them at the same speed. If the vehicle encounters a corner, then the wheel on the inside will slow down. This will cause the housing and ring gear to rotate about this axle. The arrangement of the differential pinions will therefore accelerate the opposing axle which is driving the wheel on the outside of the corner. The whole process is automatic requiring no external control and this design is called an open differential.

The principle is best illustrated through a video and it is recommended to visit: https://www.youtube.com/watch?v=K4JhruinbWc

However, in the situation where one of the wheels encounters a low traction situation, for example an ice patch, the open differential will direct torque to that wheel as it will represent the path of least resistance. In extreme cases, it can be imagined that the high traction wheel could stall whilst the low friction wheel spins freely on the low traction surface.

To solve this issue, limited slip differentials have been invented. These allow for some difference in angular velocity between the output shafts, but impose some mechanical limits on the difference in speeds. The basic design is similar to that of an open differential, however an additional mechanism is incorporated that resists the relative motion of the two axles. This resisting force can be provided in a number of ways:

- Clutch mechanism between the axle gears and the differential housing. This mechanism can be spring loaded (fixed slip limit), passively activated (varying slip depending changes in driving torque) or electronically actuated.

- Viscous effects (tends to give a limiting response relative to shaft speed), although these systems are more gradual than mechanical clutches, they tend to be less reliable and wear out sooner.

Layout of an open differential. This allows wheels to rotate at different speed which is useful when cornering,

however if one wheel loses traction, the differential will promote wheel spin

https://www.youtube.com/watch?v=K4JhruinbWc



A special type of limited slip differential is the Torsen (TORque SENsing) differential. As with other types of limited slip differentials, the limiting slip is provided by a frictional force between the axles when rotating at different speeds. This device uses a series of helical gears that create axial loads on the different shafts of the differential depending on the level of torque being transmitted through the differential These axial loads tend to push the different shafts against each other or against the supporting housings. The resulting frictional forces tend to limit the slip between the axis. The limiting slip ratios can be defined by the friction characteristics of the different surfaces and the shapes of the helical gears (that affect the magnitude of the axial forces). There are four major sources of friction as shown below:

1. Between Worm gear and worm wheel teeth 2. Between Worm Wheel face and differential housing (Between axle and diff housing) 3. Between Worm wheel face and worm wheel face (directly between axles) 4. Between the spur gears on the layshafts and the differential housing.

Limited slip differentials have a mechanism to induce friction between the two axles and the housing to

limit speed difference between axles and avoid wheel spin in low traction environments that is

encountered with open differentials

Worm wheels cause faces of spur gears to be

pushed against differential housing

Worm gears cause their faces to be pushed against each

other (both axles) or against the differential housing

Worm gears and worm wheels engage and slide

against each other

The TORSEN differential is a purpose built limited slip differential

Vehicle Engineering ME30217/ME50223 Gears, Clutches and Transmissions Clutches and Torque convertors


An alternative way to achieve a similar effect to a limited slip differential is to use the vehicle braking system to independently brake one of the wheels. Although this is less complex from a differential perspective, it does result in brake wear.

Finally, for off road vehicles which encounter low traction environments more often, fully locking differentials can be implemented. These mechanisms effectively stop the differential from behaving like a differential by linking the motion of the two shafts. Some systems may need to be manually engaged by the driver whereas other system may use electronic or mechanical control systems to engage the locking automatically if excessive slip is detected between the two axles.

6 Clutches and Torque convertors

6.1 Friction Clutches Clutches and torque convertors are required in manual and automatic transmission to fully or partially disengage the engine from the gearbox to allow shifting.

In a manual transmission vehicle, a clutch, controlled by the driver, allows for the smooth transition of engine speed during gear changes and for the vehicle to start from rest. The clutch is composed of a number of friction plates that are splined to the gearbox input shaft. These plates rub against mating surfaces attached to the engine flywheel. Spring clamps compress these plates together when the clutch is released to link the plates together and transmit the engine torque.

The driven plate is splined to the input shaft to transmit the engine torque when engaged. This driven plate should be designed to have minimal inertia to improve pick up from the engine but also it is this inertia that must be overcome by the synchromesh during gear changes. The plate also incorporates torsional damper springs that provides a level of compliance during engagement and reduces shock loadings on the gear box.

Further springs are installed between the plate and the friction material. These springs assist in the modulation of torque during engagement giving a progressive increase in torque. Older clutches to not have these features and are noticeably vicious to modern drivers.

Layout of a typical friction clutch used in

conjunction with manual transmissions



Clutches can be either wet or dry. Dry clutches offer better friction because the oil used in wet clutches reduces the coefficient of friction. However, this oil also reduces the wear of the clutch during slipping and offers liquid cooling of the clutch. Wet clutches are more controllable than dry clutches, meaning they are often used in automated transmissions.

The torque capacity of a clutch can be calculated if the friction coefficient, clamping load and dimensions are known.

Where Torque capacity is in Nm, is the friction coefficient, N is the number of friction surfaces

(normally 2 per plate), F is the axial load (N) and Rm

is the effective radius of the friction lining.

The mean effective radius is given as a function of the inner and outer radius of the lining material, Ro and Ri respectively:

When designing a clutch, clearly it needs to be able to transmit the maximum torque of the engine without slipping. If a clutch was designed to exactly meet the maximum engine torque, it would be said to have a cover factor of 1. However, in practice engine torque fluctuates as individual cylinders fire and the instantaneous peak torque is somewhat larger than the average peak torque over a number of firing cycles. The problem is accentuated at lower engine speeds where more time occurs between firing. Typically a cover factor of 2 is sensible.

To influence the torque capacity of a clutch, the designer can:

- Vary the number of plates: in practice, increasing the number of plates can have an adverse effect on the clamping force because of wedging and friction between them and their holders. Therefore clutches with more than 6 plates (N=12) are uncommon.

- Increase clamping load: In a dry clutch this is a spring load that must be overcome by the driver when depressing the clutch pedal. In a wet clutch this is often provided by a hydraulic piston and is therefore related to the area of the piston and the supplied pressure. Although there a less limits on the pressure, the friction material will have a limit not to be exceeded.

- Choice of friction material: This is highly specialised and the subject of much research. Sintered metals offer food heat and wear resistance and can withstand high clamping loads. Other materials are used that combine different fibres and fillers that can produce higher friction coefficients, better static to dynamic friction ratio and help reduce clutch judder.

During clutch engagement, heat will be generated owing to the friction whilst slipping occurs. The heat is generated by the transfer or torque between the slipping plates of the clutch. This can be calculated by calculating the friction work done on the clutch plates during engagement. In dry clutches, conduction to the casing and ultimately external convection is the cooling route. If



excessive temperature levels are reached in the clutch (high heat generation and low external cooling), then the friction material can degrade and the pressure plate can warp. In wet clutches the oil is a considerable cooling route.

The total heat generated during a slipping manoeuvre will depend on the shift time. The shift time is typically a target time for a given manoeuvre and determines the acceleration required through the gearbox. If the input to the gearbox is spinning at a constant speed and the driven side is initially spinning at a different speed , then to achieve a shift time , the output must be accelerated at a rate given by:

If the shaft to be accelerated has an inertia I, then the required acceleration torque will be given by:

The total torque to be transmitted through the clutch during the engagement must also include any loading on the shaft due to friction in the engine or due to tractive force on the vehicle.

EXAMPLE

During a downshift, the engine is to be accelerated from 2000rpm to 2500rpm in a shift time of 0.3s. The engine has a total inertia of 0.4kgm2 and a friction torque at these speeds of 30Nm.

In this case, the acceleration torque is to be transmitted from the wheels, driveline and gearbox to the engine and its flywheel. The acceleration torque is given by

Hence

The total torque to be transmitted is given by:

Now, during a vehicle pullaway, the gearbox input is to be accelerated by the engine from rest to 1000rpm in 2s. The driveline has an equivalent inertia at the flywheel of 0.5kgm2 and a torque of 3Nm is required to overcome rolling resistance.



Again the acceleration torque is given by:

And the total torque by

The heat generated in the clutch during the manoeuvre is simply equated to the friction work on the clutch during the manoeuvre

Where the friction work can be equated as

With

Assuming as with the case above that the acceleration torque is constant, then the actual speed over an engagement manoeuvre is given as a function of time t by:

Combining the above equations yields:

(

)

And therefore the heat generated during the manoeuvre is given by

(

)

And assuming that all torques are constant with respect to time

( ) (

)



EXAMPLE

Calculate the heat generated during the downshift event described above.

( ) (

)

Calculate the heat generated during the pull-away manoeuvre above

( ) (

)

During this manoeuvre, around 3kJ of heat is generated in the clutch which must be dissipated by the respective cooling mechanism. Increasing the duration of the engagement has only a small effect on the overall heat loss due to prolonged exposure of the clutch to the rolling resistance torque. This is because the longer engagement time is accompanied with a lower acceleration torque. However, prolonged engagement times usually occur when trying to make a smoother engagements and this will also require a higher synchronisation speed. In this case the acceleration torque will remain of similar magnitude but over a longer engagement time. With an engagement speed of 2400rpm and an engagement time of 6s the heat generated would become 15.2kJ. During gear shifting, the difference between initial and sync speed is much smaller than at pullaway, resulting in much lower heat generation.

A key component that works in tandem with the clutch to damp out vibrations for the engine powertrain are dual mass flywheels. As the name suggests, these are composed of two masses, linked by a spring damper system. The output from the engine is linked to one mass whilst the other forms part of the clutch and is ultimately linked to the input to the gearbox. The aim of the device is to produce a much damped torque to the gearbox and in achieved by carefully setting the two masses, spring stiffness and damping rate. These devices can be very effective and the benefits include a smoother torque delivery which improved comfort but also durability of the gearbox

Dual mass flywheels damp torque vibrations

from the engine



6.2 Fluid couplings and Torque Convertors Fluid couplings are a transmission which uses a fluid to transmit power between the input and the output. The input shaft is connected to an impeller which causes fluid flow whilst the output shaft is connected to a turbine which is driven by the flowing fluid. Because there is no mechanical link between the two, it is possible to stall the output shaft whilst the input shaft continues to rotate. There will be a small residual load on the input under these conditions. An improvement to the fluid coupling can be achieved if an additional stator is included between the output of the turbine and the input of the impellor. The additional stator creates an additional torque on the turbine that increases its output torque. The torque convertor, like all fluid couplings, operates with a level of slip between input and output, that is the output shaft rotates slower than the input. The advantage of the torque convertor is that it recovers some of this slip as a torque and therefore acts as a reduction gear ratio.

Torque convertors have a peak efficiency of around 85% and therefore cause losses during cruising. To avoid these losses, an additional locking clutch can be included which engages for the final 15% or slippage and ensures a 100%, no-slip 1:1 transmission between input and output shafts.

Engine cyclis operation causes significant torque variations at the crankshaft. Without a Dual

mass flywheel these are transmitted to the gear box and can cause discomfot and damage. Using

a Dual mass flywheel reduces these pulsations

Basic operation of a torque convertor

Vehicle Engineering ME30217/ME50223 Gears, Clutches and Transmissions Further Reading


7 Further Reading

Advanced Vehicle Technology, H. Heisler, ISBN 075651318, Lib loc: 629.2.HEI

8 Recommended videos Manual Transmissions: https://www.youtube.com/watch?v=vOo3TLgL0kM

Differentails: https://www.youtube.com/watch?v=gIGvhvOhLHU

https://www.youtube.com/watch?v=K4JhruinbWc (a little old)

Torsen Diff: https://www.youtube.com/watch?v=Z9iPqIQ_8iM

Automatic Transmission: https://www.youtube.com/watch?v=1ByVBBfEXWk

Layout of a torque convertor with lockup clutch and powerflows in turbine mode and

lockup mode

https://www.youtube.com/watch?v=vOo3TLgL0kMhttps://www.youtube.com/watch?v=gIGvhvOhLHUhttps://www.youtube.com/watch?v=K4JhruinbWchttps://www.youtube.com/watch?v=Z9iPqIQ_8iMhttps://www.youtube.com/watch?v=1ByVBBfEXWk

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Gears and Transmissions