Transmissions and Driveline

Transmissions and Driveline

6.1 Introduction

The most powerhl engine in the world is of little use unless the power from the engine can be safely and effectively transmitted to the ground. This, then, is the primary function of the transmission and driveline. In addition to being able to transmit the torque and power from the engine, the transmission and driveline also must allow the vehicle to operate over a wide range of speeds-from a standstill to the maximum speed of the vehicle. This implies that the system must inherently have some method of disconnecting the engine from the remainder of the driveline to allow the vehicle to remain stationary. Furthermore, the transmission also must be designed to satisfy the conflicting requirements of quick acceleration, high speed, and adequate fuel economy.

Figure 6.1 illustrates the need for a transmission. This figure shows the tractive force at the wheels plotted against vehicle speed. The individual curves have been generated by taking the basic engine torque curve and multiplying it by the appropriate gear ratio.

Force vs. Speed, Level Ground Resistive Force = Drag + Rolling Resistance

- 2ndGear 3rd Gear 4th Gear

- 5th Gear - 6th Gear

0 50 100 150 200 250

Vehicle Speed (mph)

Figure 6.1. Force versus speed.

236 1 Automotive Engineering Fundamentals

As shown in Fig. 6.1, a high torque multiplication is desired to accelerate the vehicle from a standstill. However, if first gear were all that were available, the maximum speed of the vehicle would be limited to 62 mph by the engine red-line. Although this might be an accept- able top speed for some, the penalty in fuel economy would be excessive. Figure 6.1 also plots the resistive force acting on the car, which is the sum of the aerodynamic drag and rolling resistance. As shown in Fig. 6.1, the car is capable of exceeding 62 mph by a large margin, but only by having more gear ratios available. At the other extreme, if the car had only sixth gear, any attempt to accelerate the car from a standstill inevitably would stall the engine or, at best, result in extreme clutch wear.

This chapter takes a logical progression from the engine flywheel to the drive axles. The first section deals with manual transmission systems and covers friction clutches, gear theory, and manual transmission operation and analysis. The next section discusses automatic transmission systems, including hydrodynamic torque converters, planetary gear analysis, general transmission operation, and gear ratio analysis. The chapter includes a brief discussion of continuously variable transmissions (CVTs). The power flow then is traced through the driveline and the differential to the drive axles. Although the case can be made for including tires and wheels in the driveline, for the purposes of this work, they will be treated as part of the vehicle control system. Thus, tires will receive mention under steering, vehicle dynamics, and braking, with a full discussion of tire nomenclature and design in Chapter 9. Chapter 6 concludes with a case study of a modem, five-speed, electronically controlled automatic transaxle.

6.2 Friction Clutches The friction clutch is the link between the engine and the transmission, and it exists to provide the operator with the ability to engage and disengage the engine from the transmission. The clutch consists of a cover, a pressure plate, and a disc with friction facings, as shown in Fig. 6.2. The cover is bolted to the engine flywheel; thus, it rotates with the engine at all times. Inside the cover is a pressure plate, which also rotates with the cover and the flywheel. Sandwiched between the pressure plate and the flywheel is the friction disc. This disc is connected to the transmission input shaft by means of splines.

Torque is transmitted to the transmission when the pressure plate is forced against the friction disc, thus squeezing the friction disc between the pressure plate and the flywheel. The axial force required to squeeze the disc is supplied by a series of springs arranged circumferentially around the pressure plate. Some clutches use coil springs, as shown in Fig. 6.2, although some manufacturers use a diaphragm spring (Belleville spring) for this function (Fig. 6.3).

The operation of a clutch may be explained by reference to Figs. 6.3 through 6.5. When the driver wishes to disengage the clutch, he or she does so by depressing the clutch pedal. Through a series of either mechanical linkages or hydraulics, this action causes the clutch fork to move against a release, or thrust, bearing. This bearing allows the axial force to be transmitted from the clutch fork to the diaphragm spring, while minimizing the wear that would exist if a stationary, solid piece of steel were used to contact the rotating spring. This action causes the

Flywheel


Adjusting Plate Shims

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Toggle Levers

Adjusting Plate

Plate Sleeve

Disk with Facings

Pressure Plate

Figure 6.2. Cross-sectional view of a coil spring clutch (TM 9-8000, 1983).

diaphragm spring to pull the pressure plate away from the friction disc. At this point, no torque can be transmitted to the transmission shaft, and the clutch is disengaged. Engagement of the clutch is produced when the driver releases the clutch pedal. The diaphragm spring now returns to its unloaded position, thus applying the necessary axial force to the friction disc and allowing torque to be transmitted

Pivot

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Pivot

Driving Plate

Diaphragm Spring

Driven Plate

Pivot Ring Retaining Bolt

Automotive Engineering Fundamentals

Engaged Disengaged

Figure 6.3. Operation of a diaphragm spring. Adapted from TM 9-8000 (1 985).

Hinge Bolt

Spring

Throwout Fork

Figure 6.4. Clutch activation (TM 9-8000, 1985).

1

Primary Clutch Components 1 . Pilot Bearing 2. Facing 3. Fiction (clutch) Disc 4. Pressure Plate 7. Inner Pivot Ring 8. Diaphragm Spring 9. Outer Pivot Rinq 7


- 12. Clutch Cover 13. Release Fork 14. Release (Throwout) Bearing

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Figure 6.5. Exploded view of'a diaphragm clutch Adapted,fiom TM 9-8000 (1 985).

6.2.1 Torque Capability of an Axial Clutch

Figure 6.6 shows a typical friction disc. The disc normally has an annulus of friction material riveted or glued to both sides of the plate. The coil springs shown in Fig. 6.6 provide some measure of torsional flexibility to the plate, the better to extend its life when the operator is either learning to operate a clutch or is an aggressive driver.

The clutch designer must consider activating force, torque delivery, energy loss, temperature rise, and wear. Thus, the friction material must be selected to provide all of the following:

A uniform coefficient of friction over the surface A coefficient of friction that remains stable with temperature changes Good thermal conductivity Resistance to wear

Rivet Clutch Disk

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Figure 6.6. Clutch disc ~i th f lex ib le hub (TM 9-8000, 1985).


Resistance to thermal fatigue Good high-temperature strength

The torque capability of a clutch may be analyzed with reference to Fig. 6.7. There is some pressure operating over the face of the clutch; therefore, in general, the force on the clutch face is given by F = PA. Looking at a differential area on the face, this becomes dF = prdrd0. The total force on the clutch face may be obtained by integrating over the face of the friction material. However, some assumptions must be made regarding the pressure.

6.2.1.1 Uniform Pressure: p = pa

This assumption is valid if the surface of the friction material is truly planar. Thus, it is a good assumption in the analysis of a new clutch. The integral used to find the force is

Figure 6.7. Schematic of the friction material on a clutch surface.


which upon evaluation yields

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The frictional force on the face of the clutch is simply the normal force (F) times the coefficient of friction for the material (p). The torque transmitted by the clutch is found by integrating the product of the frictional force and the radius

Equation 6.3 gives the torque capacity of the clutch as a function of pressure. Amore conve- nient form for the designer results by solving Eq. 6.2 for the pressure (pJ, and substituting this expression into Eq. 6.3. This results in

242 I Automotive Engineering Fundamentals

which is the torque capacity of the clutch as a function of activation force (F). Note that this expression gives the torque capacity for a single friction surface. For multiple friction surfaces, Eqs. 6.3 or 6.4 must be multiplied by the number of friction surfaces (N).

6.2.1.2 Uniform Wear

Obviously, a clutch does not remain new for long. When the clutch has been broken in, the pressure distribution changes and permits uniform wear. The wear is a function of normal force and linear velocity, or

FVdt = pprwdAdt = constant

The implication of this is that the pressure is not constant, and the maximum pressure (pa)

occurs along the inner radius . Furthermore, the pressure at any other radius must be rl

inversely proportional to the maximum, or p = pa . The same procedure is followed to 9, L 1

determine the activation force on the clutch face

Again, the torque is the integral of the frictional force times the radius, and the torque capacity as a function of pressure is given by

Again, solving Eq. 6.5 for pa and substituting into Eq. 6.6 gives torque capacity as a function of activation force (F)

F P T = -(D + d) for a single surface and 4

F P T = N - (D + d) for multiple friction surfaces 4

Now, it appears by Eq. 6.7 that the torque capacity of the clutch would be maximized by allowing the inner radius to equal the outer radius (d = D). It would indeed generate maximum

torque because this gives the largest radius for the clutch. However, to do this would require infinite pressure to achieve any torque transfer. The proper way to maximize torque capacity is to take the appropriate partial differential of Eq. 6.6 (see problem 6.3 at the end of this chapter).


Another consideration in designing the clutch is the fact that the activation force provided by the springs must be overcome by the driver to disengage the clutch. Although the clutch pedal and linkages provide a mechanical advantage, another solution is to add centrifugal weights to the clutch assembly. Then, as the cover rotates, these weights can be used to increase the force on the pressure plate. This can be analyzed with reference to Fig. 6.8.

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Pressure Plate

Clutch Plate Force

rnro*

Weight

Clutch Cover

I

Spin Axis Clutch Spring Force

Figure 6.8. Schematic of a clutch with centrifugal weights and free-body diagram of afinger.

2 Summing moments about point A in Fig. 6.7 yields Fpma = rnro b , or

which is the additional activation force on the clutch face.

6.3 Gear Theory Before explaining the operation of a manual transmission, the fundamentals of gear operation will be examined. Gears are most often used to transmit power, as well as to change angular velocity and torque, because the teeth provide a positive driving action (i.e., no slippage). The nomenclature, design, fabrication, and analysis of gears are governed in the United States by standards bodies such as the American Gear Manufacturers Association (AGMA). For this information, the student is directed to any good machine design textbook such as Shigley

and Mischke (2001). This book is concerned with the application of gears and their use in automobiles.

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Almost every type of gear can be found in an automobile. The most common varieties are discussed next.


6.3.1 Straight-Tooth Spur Gears

Figure 6.9 shows an example of this type of gear. Straight-tooth spur gears have straight teeth parallel to the axis of rotation. When the teeth engage, they do so instantaneously along the tooth face. This sudden meshing results in high impact stresses and noise. Thus, these gears have been replaced with helical gears in most transmissions. However, these gears do not generate axial (or thrust) loads along the shaft axis. Furthermore, they are easier to manufac- ture and can transmit high torque loads. For these reasons, many transmissions use spur gears for first and reverse gears. This accounts for the distinctive "whine" when a car is reversed rapidly.

Figure 6.9. Spur gears.

6.3.2 Helical Spur Gears

Figure 6.10 shows an example of a helical gear. Helical gears have teeth that are cut in the form of a helix on a cylindrical surface. As the teeth begin to mesh, contact begins at the leading edge of the tooth and progresses across the tooth face. Although this greatly reduces the impact load and noise, it generates a thrust load that must be absorbed at the end of the shaft by a suitable bearing.

Figure 6.1 0. Helical gears (TM 9-8000, lY8S).

6.3.3 Straight-Tooth Bevel Gears


These gears, shown in Fig. 6.11, have straight teeth cut on a conical surface. They are used to transmit power between shafts that intersect but are not parallel. They are used in differen- tials. Similar to straight-tooth spur gears, they will be noisy. However, in the differential, they rotate only when the axles are rotating at different speeds.

245

Figure 6.11. Straight-tooth bevel gears (TA4 9-8000, 198.5).

6.3.4 Spiral Bevel Gears

These gears have teeth cut in the shape of a helix on a conical surface. They can be used for final drives to connect intersecting shafts (Fig. 6.12).

Figure 6.12. Spiral bevel gears (TM 9-8000, 1985).

6.3.5 Hypoid Gears

These gears have helical teeth cut on a hyperbolic surface (Fig. 6.13). They are used in final drives to connect shafts that are neither parallel nor intersecting. These gears have high tooth loads and must be lubricated with special heavy-duty hypoid gear oil because greater sliding occurs between the teeth. The sliding increases with the amount of offset between the shaft axes. With zero offset, a spiral bevel gear results, whereas the maximum offset corresponds to a worrdwheel configuration. Despite having a lower efficiency than spiral bevel gears,

Figure 6.13. Hypoid gears (TM 9-8000, 198.5).

hypoid gears allow the driveshaft to be lowered, thereby requiring a smaller "transmission tunnel" in the body.


The relationship between two meshed gears can be derived from Fig. 6.14, which shows a schematic of two meshed gears and a free-body diagram of both the gear and the pinion. Summing moments about the center of the input gear yields

247

and by the same process on the output gear

Ti(

C din

Figure 6.14. Schematic of the gear mesh and free-body diagram of each gear.

248 ( Automotive Engineering Fundamentals

Because the tangential force at the mesh must be equal and opposite at the point of meshing,

Furthermore, for any gear, the pitch diameter is proportional to the number of teeth (N), and an analysis of angular velocity also shows that the speeds of the gears are inversely related to the diameter. Combining this leads to what is commonly known as the gear law

The negative sign in Eq. 6.9 accounts for the reversal of rotation in a single mesh. Equation 6.9 also assumes no friction loss in the mesh. In reality, there is a slight loss on the order of 1 to 2%.

The gear law can be extended to multiple gear meshes such as the one shown in Fig. 6.15. In this case, the gear train is analyzed by

where N is the number of gear meshes.

N4

Driver

Figure 6.15. Gear train.

In the case presented in Fig. 6.15, the center gear has no effect on the overall torque ratio. However, it causes the output shaft to rotate in the same direction as the input shaft. This gear is called an idler. Thus, it can be seen that stringing several gears together is no way to gain

large increases in torque. The final torque ratio is governed solely by the first and last gears in the train. The only way to gain a larger torque ratio is to go to a compound gear train, in which two of the gears are connected by a common shaft, as shown in Fig. 6.16. In this case,


the torque relationship is given by

249

C

N3 N5

Figure 6.16. Compound gear train (Krutz et al., 1994).

Note that gears 2,4, and 5 in Fig. 6.16 are driving gears, whereas gears 3,5, and 6 are driven gears. This leads to the definition of a train value, e, as

Product of driving tooth numbers e =

Product of driven tooth numbers

By observation, the train value is the inverse of the gear (or torque) ratio and is equal to the speed ratio for a gear train. With this knowledge, it is now possible to analyze the manual transmission.

6.4 Manual Transmissions The earliest transmissions were sliding gear types, in which the gears were splined to the appropriate shafts and were engaged and disengaged by the driver. They were used univer- sally through the late 1920s but have since been replaced in passenger cars by synchronized, constant-mesh transmissions. Figure 6.17 shows a photograph of a four fonvard-speed plus reverse transmission, with a schematic of the transmission. At this point, the discussion is

Clutch Gear 3-4 Synchronizer Third Gear (27 teeth) Second Gear (33 teeth) Second Synchronizer Sleeve and First Reverse Driven Gear (40 teeth) Second Gear Synchronizer Hub Mainshaft Countergear First Gear (1 8 teeth) Countergear Second Gear (25 teeth) Countergear Third Gear (31 teeth) Countergear Shaft Gear (35 teeth)

250

Figure 6.17. A four-speed transmission.


limited to analyzing gear ratios and will not delve into the operation of the linkages and safety devices. Furthermore, the operation of the synchronizer will be discussed in the next section.

The transmission has three shafts: the input shaft, the countershaft, and the output shaft (or mainshaft). The clutch gear (1) is an integral part of the transmission input shaft and always rotates with that shaft. The countershaft gears normally are machined from a single piece of steel and sometimes are referred to as the cluster gears. These are mounted to the countershaft on roller bearings, and the countershaft is fixed in place so it does not rotate. The gears on the output shaft, called speed gears, also are mounted on roller bearings. They are always meshed with the cluster gears and continuously rotate around the main shaft. The speed gears are locked onto the main shaft by the action of the synchronizers and, when locked, transmit torque to the output shaft. (Synchronizer operation will be discussed in the next section.)

6.4.1 Transmission Power Flows


Now it is possible to outline the flow of power through the transmission shown in Fig. 6.17, as well as to calculate the gear ratio for each gear.

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6.4.1.1 First Gear

Torque flows through the input shaft to the clutch gear (23 teeth) and then to the countershaft via the cluster gear (35 teeth) (Fig. 6.18). The countershaft torque then is transmitted through the countershaft first gear (18 teeth) to the second gear synchronizer sleeve (40 teeth). The second gear synchronizer sleeve is splined to the main shaft through its hub, and torque is transmitted to the main shaft. Applying the gear law to this gear train, the torque ratio (or gear ratio) is

Tout - 35 40 GR, =----=3.38 Ti, 2318

40 teeth

35 teeth

Figure 6.18. Ponw.,flor~~ i t~ , f ir .~t gear

6.4.1.2 Second Gear

Torque flow again is from the input shaft to the clutch gear and countershaft. In second gear, the rear synchronizer has moved forward, locking the second speed gear onto the main shaft (Fig. 6.19). Torque flows through the countershaft second gear (25 teeth) to the second speed gear (33 teeth). The gear ratio is thus

252 1 Automotive Engineering Fundamentals

Figure 6.19. Power,flow in second gear.

6.4.1.3 Third Gear

The torque flow again is input shaft, clutch gear, and countershaft. In this case, the forward synchronizer has moved to lock the third speed gear onto the main shaft (Fig. 6.20). Torque flow from the countershaft is to the countershaft third gear (3 1 teeth) to the third speed gear (27 teeth). The gear ratio is

27 teeth

31 teeth 35 teeth

Figure 6.20. Powerflow in third gear.

6.4.1.4 Fourth Gear

In fourth gear, the forward synchronizer has moved forward and locked the clutch gear onto the main shaft (Fig. 6.2 1). This results in power flowing directly from the input shaft to the main shaft, and the gear ratio thus is 1: 1. In other words, in fourth gear, there is no torque

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Transmissions and Driveline