2
Manual Transmissions

2.1 Introduction

The gear ratios discussed in Chapter 1 that match the engine outputs for optimized vehicle performance and fuel economy are realized by different types of transmissions. Manual transmissions (MT) are the oldest type and have a history as old as the automotive industry [1]. In a manual transmission, engine power is transmitted by gear pairs on fixed axes from input to output, and gear shifts are manually made by the driver. Although the basic structure and operation principles have remained almost the same ever since the advent of automobiles, manual transmissions have undergone an evolution of changes aimed at improving ease of operation and shift smoothness. The earliest manual transmissions used sliding gears for gear shifts [2]. To make a shift, the driver would separate a gear pair by pulling one of the gears out of mesh, and then pushing and sliding another gear into mesh. It was very difficult to make shifts this way and gear grinding was unavoidable during shifts. Later versions had constant mesh gear design in which gears responsible for shifts had a dogtooth ring attached. During a shift, the driver would push a sleeve with internal spline teeth on the transmission shaft and slide it into mesh with the dogtooth ring. Tooth grinding was still unavoidable since the speed of the sleeve and the dogtooth ring were different during shifts. It was in the 1930s that synchronizers were widely applied in manual transmissions [1,2]. The use of synchronizers greatly improved vehicle drivability and made driving much easier and more pleasant. To a certain degree, synchronized manual transmissions contributed to the wide spread of automobiles in the daily life of the populace.

The design of synchronized manual transmissions has not changed much for many decades, but advances in material and manufacturing technologies have made these products more durable and reliable. In comparison with automatic transmissions (AT) that offer better driver convenience, manual transmissions are less costly and generally more fuel efficient. For some drivers, manual transmission vehicles are the preferred choice because they offer sportier driving techniques and experience than the automatic counterparts. In addition, manual transmissions with multiple gear ratios are more suitable for heavy duty trucks due to their advantages in cost and fuel economy. For these reasons, it can be said that manual transmissions are a mature and everlasting product in the automotive industry.

The market share of manual transmissions varies with vehicle type and marketplace [3]. For passenger vehicles, manual transmissions have less than 20% market share in North America, but the number is closer to 80% in Europe. In the Chinese market, which is currently the world’s largest, manual transmission market share is about 60%. For trucks, including pickups and heavy duty vehicles, manual transmission share is well above 50% in all markets. For the world market as a whole, the manual transmission market share floats around 58%. These numbers indicate the significant status of manual transmissions in today’s automotive market.

The overall vehicle powertrain system includes the engine, transmission, transfer case for four wheel drive (4WD), drive shaft, final drive and differential, half shafts, universal or constant velocity joints, and driving wheels. The transmission is the core in the driveline from the engine output to the wheels. The focus of this chapter is on manual transmissions. Readers are recommended to study publications that provide technical details on other driveline components, such as transfer case, CV joints, and universal joints [4,5]. A manual transmission is a mechanical system that consists of dozens of components, including clutch, gears, shafts, synchronizers, bearings, and seals. This chapter starts with the general layouts of vehicle powertrains and the basic structures of manual transmissions, followed by the analysis on the power flow and transmission ratios. At the component level, the chapter focuses on the design and analysis of clutches and synchronizers which are specifically developed for automotive transmissions. A dynamic model will be introduced for the analysis of manual transmission shift dynamics. Detailed analysis on the synchronization process and synchronizer design are covered based on the model. Transmission gear design will be covered separately in the next chapter. It should be noted that this chapter uses example transmissions to demonstrate general principles and approaches, which are applicable for the design and analysis of all other manual transmissions.

2.2 Powertrain Layout and Manual Transmission Structure

Vehicle powertrain system layouts depend on whether the vehicle has front wheel drive (FWD), real wheel drive (RWD), or four wheel drive (4WD). For FWD vehicles, the transmission and the final drive, which contains the differential, are integrated into the same assembly. FWD vehicles usually have transversely mounted engines, with the engine crankshaft parallel to the drive axle, as shown in Figure 2.1a. A FWD vehicle can also have the engine mounted longitudinally as shown in Figure 2.1b, then a pair of spiral bevel gears or hypoid gears must be used to transmit the power to the driving wheels from the transmission output shaft which is perpendicular to the axle. In comparison with RWD layout, FWD layout offers lower manufacturing cost and better passenger room due to its compactness. It also offers somewhat better traction in cold weather conditions because the front axle has a larger portion of the weight distribution. Most passenger cars or vans today have front FWD layout because of these advantages.

Figure 2.1 Alternative front wheel drive layouts.

RWD vehicles always have longitudinally mounted engines. The transmission and the final drive are separate assemblies, as shown in Figure 2.2a, with a drive shaft connecting the transmission output and the final drive input. Universal joints (Hooke joints) are used at the two ends of the drive shaft to accommodate assembly condition and drive line flexibility. The final drive assembly in an RWD vehicle contains a pair of spiral bevel gears or hypoid gears that provide the final drive ratio and the differential that allows a speed difference between the two driving wheels. The weight distribution of RWD cars can be designed close to a perfect 50/50 between the front and rear axles. This optimized weight distribution leads to improved drivability and handling in comparison with that of FWD vehicles. There are drivers who prefer RWD cars because of the better drivability (at least as perceived by them) in steering and cornering. This may be one of the reasons why RWD is used for most of the luxury and sports cars. The RWD layout in Figure 2.2a is also used for the powertrains of light to middle duty trucks, such as pickups and delivery trucks. This layout can be conveniently modified to fit a 4WD system, as shown in Figure 2.2b. For 4WD vehicles, there are two final drive and differential assemblies, one for each drive axle. Other 4WD layouts may originate from an FWD configuration with transversely mounted engine. In a 4WD powertrain shown in Figure 2.2b, the transmission output is split by the transfer case to the final drives on the front and rear axles. The distribution of transmission output torque between the front and rear axles depends on the design and control of the transfer case.

Figure 2.2 Layouts for (a) RWD and (b) 4WD.

The vast majority of non‐commercial passenger vehicles have powertrain layouts as shown in Figures 2.1 and 2.2, perhaps with very few exceptions for fancy sports cars. Other powertrain system layouts can also be adopted to meet the requirements of different vehicle types and functions. For example, Figure 2.3a shows the typical powertrain layout for a semi‐truck with two drive axles in series. Standard cargo boxes are hooked to the semi‐trailer on top of the double axles that provide propulsion together. Spiral bevel gears or hypoid gears can be used in the final drives for the transmission of power from the longitudinal drive shaft to the axles. Both spiral bevel gears (with the pinion and gear axes intersected) and hypoid gears are used in the final drive of heavy duty trucks or buses. A pair of helical gears is sometimes used to provide an additional reduction ratio in the final drive assembly. The hypoid gear sets used in the layout shown in Figure 2.3a have the pinion axis offset above the axle, allowing the assembly of the differential at the center of the hypoid gear. Figure 2.3b shows the layout for a large passenger bus that has the engine longitudinally mounted in the rear. It should be noted here that either a manual transmission or an automatic transmission can be fitted to the same powertrain system layout of a vehicle.

Figure 2.3 Powertrain layouts for (a) semi‐truck and (b) commercial bus.

Most of the manual transmissions used for passenger cars and vans today have five or six forward gears and one reverse. Only a few sports cars or high end models are equipped with transmissions with six or more forward speeds for fuel economy and performance. Manual transmissions are a mature product in the automotive industry that shares similar structures. Figure 2.4 shows the section view of a typical five‐speed FWD manual transmission that fits to the powertrain layout in Figure 2.1a for passenger cars. Key components in the manual transmission are marked in the drawing. The gear pairs for different speeds and synchronizers are laid out on the input shaft and the output shaft. All gears except the reverse gears are cylindrical helical gears. There are six gears on each shaft since there are five forward and one reverse gears. Both the input and output shafts are supported on cylindrical roller bearings on the engine side and on deep groove ball bearings on the outside. The whole output shaft and a section of the input shaft are hollow to reduce weight and mass moment of inertia. The 1st gear and the 5th gear are on the two ends of the shaft, close to the bearings, to minimize shaft deflection. The synchronizer for the first and second gears is on the output shaft. The 3–4 synchronizer and the 5th synchronizer are mounted on the input shaft. The reverse gear is realized by a sliding idler between the input and output shafts. This requires a little more effort than shifting into a forward gear, but has little effect on drivability since reverse gear is always engaged when the vehicle is at rest. The output gear for reverse is attached to the 1–2 synchronizer assembly and is machined on the sleeve of the 1–2 synchronizer. The input gear of the final drive is machined on the output shaft, and the ring gear (final drive output) is bolted to the differential carrier, which is supported on both sides by tapered roller bearings that resist thrusts. Each of the two side gears of the differential is connected to the driving wheel via a haft shaft, which is coupled to the side gear and the wheel hub by CV joints. The transmission housing consists of two pieces bolted together with sealing and is attached to the engine assembly by bolts. The housing is designed with an empty space on the input side, called clutch well, for the clutch assembly. Note that the axes of the shafts, the final drive, and the sliding idler are actually not within a plane, but at angles with respect to each other for assembly and compactness considerations.

Figure 2.4 Section view of a FWD five‐speed manual transmission.

A typical five‐speed manual transmission for an RWD passenger vehicle is shown in Figure 2.5. This transmission fits the powertrain layout in Figure 2.2a. There are three shafts in this transmission design. The input shaft is supported on the housing by a deep groove ball bearing and at the center of the engine flywheel by a pilot bearing. To minimize shaft deflection, both the counter shaft and the output shaft are supported at three locations. The counter shaft carries all of the gears on it and is supported by a cylindrical roller bearing on the engine side, a double row roller bearing on the supporting wall of the housing, and a ball bearing at the other side. The output shaft is supported by ball bearings on the supporting wall and on the output side, as well as by a roller bearing at the center of the input gear. The first, second, and 5th gears are located by the bearing to minimize shaft deflections. The reverse gears are constantly meshed and the reverse gear is engaged by the R‐5 synchronizer. All three synchronizers are mounted on the output shaft and thus all gears freewheel on the output shaft unless engaged. The housing is designed with an extra space on the output side for the assembly of the shifting mechanism and speedometer gear or speed sensor. There are variations of RDW manual transmissions with five or six speeds based on improvements from the one shown in Figure 2.5. In the newer versions [6], the supporting wall in the transmission housing and the bearings on it are eliminated because sufficient rigidity and strength are guaranteed by new materials and manufacturing technologies for the housing.

Figure 2.5 Section view of an RWD five‐speed manual transmission.

The structure of a manual transmission, or any other mechanical systems in general, can be illustrated by a simple and intuitive sketch, commonly termed as “stick diagram” in the automotive industry. A stick diagram uses a set of symbols to represent various components and interconnections between them in a mechanical system or machinery. The symbols used in a stick diagram are easily identifiable and are used consistently to represent powertrain components throughout this book. A list of symbols for powertrain components is shown in Figure 2.6.

Figure 2.6 Symbols for common powertrain components.

The stick diagrams for the five‐speed FWD manual transmission in Figure 2.4 and the five‐speed RWD manual transmission in Figure 2.5 are shown in Figures 2.7a and 2.7b, respectively. Clutches are not shown in the stick diagrams for clarity of the drawing. These two stick diagrams provide a clear picture for the structural layouts of the two manual transmissions and are easy to understand because of the intuitive feature of the symbols. The numbers of teeth for each gear are also labeled in the stick diagrams for the identification of power flows and gear ratios, which are discussed in the next section. The first of the two subscripts indicates the speed and the second indicates the shaft that the gear is on. For example, N_4i is the number of teeth of the 4th gear on the input shaft. For the FWD MT, the integrated final drive is a pair of helical gears labeled as N_ai and N_ao. The RWD MT has two stages of gears for each speed, which shares a common input gear pair labeled as N_i and N_c.

Figure 2.7 Stick diagrams for (a) five‐speed FWD MT and (b) five‐speed RWD MT.

2.3 Power Flows and Gear Ratios

It is fairly straightforward to figure out the power flow in each gear for a manual transmission. With the numbers of teeth labeled with the subscripts as shown in Figure 2.7, the power flow can be identified directly from the input to the output. For example, the power flow in each forward gear for the FWD MT in Figure 2.7a is shown as follows:

• 1st gear: Input shaft (gear N_1i) Output shaft (gear N_1o and gear N_ai) Final drive output (gear N_ao)
• 2nd gear: Input shaft (gear N_2i) Output shaft (gear N_2o and gear N_ai) Final drive output (gear N_ao)
• 3rd gear: Input shaft (gear N_3i) Output shaft (gear N_3o and gear N_ai) Final drive output (gear N_ao)
• 4th gear: Input shaft (gear N_4i) Output shaft (gear N_4o and gear N_ai) Final drive output (gear N_ao)
• 5th gear: Input shaft (gear N_5i) Output shaft (gear N_5o and gear N_ai) Final drive output (gear N_ao)

It should be noted that, in each gear, only the concerned gear in the power flow is coupled to the shaft by the synchronizer, and gears not in the power flow freewheel on their shafts. The power flow in reverse gear differs from forward gears and involves an idler gear between the input and output shafts, shown in the following:

In all manual transmissions, the reverse gear is realized by the reverse idler. Due to their being one more external mesh than the forward gears, the reverse idler gear will reverse the direction of rotation of the output shaft without contributing to the gear ratio. When the vehicle travels in a straight path, the final drive output, i.e. the ring gear of the final drive, will rotate at the same angular velocity as the two driving wheels. The differential allows speed difference for the two driving wheels on the driving axle when the vehicle travels on curves. The power flow for the RWD five‐speed MT shown in Figure 2.7b can be found in a similar fashion. All forward gears, except the 4th gear, involves two stages of gearing, as follows:

• 1st gear: Input shaft (gear N_i) Counter shaft (gear N_c and gear N_1c) Output shaft (gear N_1o) Final drive
• 2nd gear: Input shaft (gear N_i) Counter shaft (gear N_c and gear N_2c) Output shaft (gear N_2o) Final drive
• 3rd gear: Input shaft (gear N_i) Counter shaft (gear N_c and gear N_3c) Output shaft (gear N_3o) Final drive
• 5th gear: Input shaft (gear N_i) Counter shaft (gear N_c and gear N_5c) Output shaft (gear N_5o) Final drive

The 4th gear is a direct drive, with the output shaft coupled to the input shaft gear N_i by the 3–4 synchronizer. All gears freewheel in the 4th gear. The reverse gear power flow involves an idler gear as follows:

Similar to all other gearboxes, the gear ratios of an automotive transmission are defined as the ratio between the input angular velocity to the output angular velocity, by the following general formula:

(2.1)

where n is the number of external meshes in the power flow path. Clearly, if n is odd, then the output angular velocity will be opposite to the input. For the FWD MT in Figure 2.7a, the value of transmission ratio in each gear and the final drive gear ratio are calculated by the following equations:

(2.2)

It should be noted here that the transmission ratio in a FDW transmission refers to the ratio between the input angular velocity and the output angular velocity that is also the input angular velocity of the final drive. For the transmission in Figure 2.7a, there are two external meshes in the power flow of forward gears from the transmission input shaft to the final drive output, so the direction of rotation for the input shaft and the driving wheels is the same. But in the reverse gear, there are three external meshes in the power flow, so the direction of rotation of the driving wheels is opposite to that of the input shaft and the vehicle moves backward, as illustrated in Figure 2.8.

Figure 2.8 Reverse idler gear.

For the RWD MT in Figure 2.7b, there are more than one pairs of gears involved in the power flows, with the exception of the 4th gear, as mentioned previously. Using Eq. (2.1), the five forward ratios and the reverse ratio are determined in terms of the tooth numbers of involved gears in the following:

(2.3)

The minus sign for the reverse gear ratio indicates that the rotational direction of the output shaft in reverse gear is opposite to that of the forward gears. In this RWD MT, the 4th gear is a direct drive with a ratio of one and the 5th gear is an overdrive with a ratio below one. In the automotive industry today, some passenger vehicles are also equipped with FWD or RWD six‐speed manual transmissions with typical layouts shown in Figure 2.9.

Figure 2.9 Six‐speed MTs for (a) FWD and (b) RWD.

2.4 Manual Transmission Clutches

As mentioned in Chapter 1, internal combustion engines cannot provide stable output torque below the idle speed. When a vehicle is being launched from rest, the vehicle speed is zero but the engine speed must be above the idle. This means that there must be a launch device that allows slippage while transmitting the engine torque to the transmission input during vehicle launch. The slippage ends at the time when the vehicle speed has gradually increased to the value that satisfies Eq. 1.21. In a manual transmission vehicle, the clutch functions as the launch device that bridges the gap between the engine RPM and the vehicle speed. The clutch has another important function in a manual transmission vehicle. When disengaged, it provides a disconnection between the engine output and the transmission input. During a shift, the clutch is briefly disengaged to cut off power supply to the transmission so that the disengagement of the current gear and the engagement of the next gear can be carried out smoothly by the driver. Most of the clutches in manual transmissions are actuated manually through clutch pedal depression by the driver, but some are automated hydraulically or electrically for ease of operation

2.4.1 Clutch Structure

Manual transmission clutches are friction devices that require a clamping force or normal force on friction surfaces for the generation of friction. The clamping force is generated by the compression of springs. There are two types of springs used in manual transmission clutches, coil springs and Belleville or diaphragm springs. Coil spring clutches have higher torque capacity and are thus mainly used for trucks. Belleville clutches are mainly used for passenger vehicles due to structural simplicity and compactness. The structure of a coil spring clutch is illustrated by a section view in Figure 2.10.

Figure 2.10 Structure of coil spring clutch (a) engaged (b) disengaged.

As shown in the Figure 2.10, the clutch assembly consists of the friction disk, pressure plate, clutch cover, release lever, coil springs, and release bearing. Friction is generated on the two faces of the friction disk that is splined to the transmission input shaft and sandwiched between the pressure plate and the engine flywheel which is machined with a flat contacting surface. The friction disk is assembled with a torsional spring damper that is designed to cushion the dynamic impacts caused by clutch actuation and engine output harmonics. The pressure plate is attached to the clutch cover by flexible links as shown in Figure 2.10. The flexible links carry the pressure plate in rotation with the clutch cover that is bolted to the flywheel and meanwhile allow the pressure plate to move slightly in the axial direction. A set of coil springs is installed circumferentially between the pressure plate and the clutch cover. Compression in the coil springs is generated in assembly when the clutch cover is bolted to the flywheel. This compression is adjustable by the tightness of the assembly bolts. The clutch is normally engaged since sufficient magnitude of clamping force is generated by the coil spring at assembly. This clamping force is applied by the pressure plate to the friction disk. Engine torque is transmitted by the friction generated on the two contacting faces of the friction disk – one between the disk and the flywheel, and the other between the disk and the pressure plate – to the transmission input shaft. The disengagement of the clutch and the control of the clamping force (i.e. the clutch torque) are realized through symmetrically mounted release levers, each of which is on the central line between two coil springs, pivoting about a pin joint on the clutch cover. The upper end of the release lever contacts the pressure plate and the lower end contacts the release bearing. The engaged position and the disengaged position of the clutch are shown in Figures 2.10a and 2.10b respectively. Before the vehicle is launched, the driver will first depress the clutch pedal fully to disengage the clutch through the clutch actuation linkage. The release bearing moves leftward and the pressure plate moves rightward as the clutch pedal is depressed, placing the clutch in the disengaged position as shown in Figure 2.10b. As the vehicle is being launched, the driver will gradually lift the clutch pedal so that the release bearing moves rightward due the spring force and the pressure plate moves leftward until the clutch is engaged as shown in Figure 2.10a. Clutch operation during transmission shifts is the same as for vehicle launch. The clutch in Figure 2.10 uses one friction disk. To increase the torque transmission capacity, two or more friction disks may be used, with an extra pressure plate between the two for additional friction faces.

Figure 2.11 Diaphragm spring and structure of Belleville clutch (a) engaged (b) disengaged.

As shown in Figure 2.11, the structure of the Belleville or diaphragm clutch is similar to that of coil spring clutches, but only differs in the spring that generates the clamping force. In a Belleville clutch, the conically shaped diaphragm spring serves as both the clamping force generator and the release lever. Multiple slots are machined on the diaphragm spring so that its inner side forms touching fingers to contact the release bearing. These slots are also conducive to uniform deformation of the inner side along the axial direction when pushed by the release bearing. The diaphragm spring is attached to the clutch cover by pins that fit into the holes on the upper side of the slots. Two circular rings are placed on the rivet pins, on each side of the diaphragm spring. These two circular rings retain the position of the diaphragm spring and also allow it to pivot about the pins. The outer side of the diaphragm spring is attached to the pressure plate. This attachment allows for a slight relative motion between the diaphragm spring and the pressure plate. Before the clutch cover is bolted to the engine flywheel, the diaphragm spring is not deformed and there is a small gap between the clutch cover and the flywheel even though the flywheel, the friction disk, and the pressure plate touch each other. When the clutch cover is bolted to the engine flywheel, the small gap is eliminated and the diaphragm spring is therefore deformed in the axial direction, generating the clamping force on the pressure plate. This results in bending in the upper portion of the diaphragm spring and an axial deflection at the pivoting point that is equal to the gap. By design, this deflection of the diaphragm spring generates sufficient clamping force to fully engage the clutch at assembly. The friction disk is then clamped tightly between the pressure plate and the flywheel. When the clutch needs to be released, the clutch actuation linkage pushes the release bearing to the left, carrying the diaphragm spring inner side to the left also. The leftward deflection at the inner side reduces the clamping force on the pressure plate due to the lever effect of the diaphragm spring itself. If the release bearing moves to the left sufficiently, then the combined effect of spring deformation and leverage will pull the pressure plate completely out of contact with the friction disk, fully disengaging the clutch. Note that the axial stiffness of the diaphragm spring – i.e. the relation between the axial spring deflection and the axial force applied by the release bearing on the spring inner side – can be analytically formulated and validated by experiments.

The clutch actuation mechanism is fairly simple in structure. The release bearing is actuated by the clutch release fork which pivots about a joint attached to the clutch well of the transmission housing. This fork straddles over the groove on the release bearing and is connected to the clutch pedal by either a cable or a linkage. In some designs, the clutch fork is connected to the clutch pedal by a hydraulic hose with a master cylinder on the driver side and a slave cylinder on the clutch side. The slave cylinder can also be mounted with the release bearing on the transmission input shaft for compactness, with the piston pushing the release bearing directly. A mechanical advantage is designed between the clutch pedal and the clutch release fork to reduce the effort of the driver’s foot on the clutch pedal.

2.4.2 Clutch Torque Capacity

The clutch for a manual transmission must be capable of transmitting the maximum engine torque; in other words, the clutch torque capacity must be higher than the maximum engine torque. As mentioned previously, clutch torque is generated by the friction on the friction disk due the clutch clamping force. It is therefore clear that the clutch torque capacity depends on several factors: the friction coefficient of the friction disk, the clamping force, and the dimensions of the disk. In formulating the clutch torque capacity, an assumption must be made about the distribution of the normal pressure generated by the clamping force on the disk face. One assumption is that the clamping force is evenly distributed over the disk. The other assumes that the clamping force is distributed in such a way that the power of friction per disk area is a constant from the inner radius to the outer radius. This assumption is equivalent to uniform wear on the disk face and is termed accordingly. The following equation quantifies the uniform wear assumption:

(2.4)

where μ is the friction coefficient of the friction disk, p_n is the distribution of the clamping force or the normal pressure in or psi. v is the speed at a point on the disk friction face. C_f is the friction power per unit area that is a constant with a unit of or . Here, W is watts. Based on this assumption, the clamping force distribution or the normal pressure is then described by:

(2.5)

where r is the radius of a point on the disk friction face, as shown in Figure 2.12. C is also a constant since the term is constant for a given disk at a given angular velocity ω. Therefore, the maximum normal pressure p_max occurs at the inner radius and the constant C is equal to . The distribution of the clamping force is thus expressed as . The clamping force and the friction torque on one friction face are then determined by integration through the following equations:

(2.6)

(2.7)

where d and D are the inner and outer diameters of the friction disk respectively. Since each disk has two faces, the clutch torque for a clutch with n disks is determined by:

(2.8)

For a given clutch, is a constant. The friction coefficient depends on the lining material and can be considered as a given value in clutch design. For ceramic lining, the friction coefficient is about 0.25, and for an organic lining, it is about 0.30. In real world applications, the value of friction coefficient is affected by clutch temperature to some degree and gradually fades away with the clutch service life. The dominating parameter in the clutch torque is the clamping force F generated by the clutch spring. Note that Eq. (2.8) will also be used to model the torque in wet clutches in automatic transmissions where the clamping force F is generated by hydraulic pistons.

Figure 2.12 Distribution of clamping force on disk face.

2.4.3 Clutch Design

The clutch for a manual transmission must be capable of transmitting the maximum engine torque. This means that the clutch torque capacity must be designed to be higher than the maximum engine torque with some reservation, i.e. .As can be observed in Eq. (2.8), there are only three design parameters, which are the inner and outer diameters of the friction disk and the clamping force. The friction coefficient is considered as a constant and its value depends on the lining material, as already mentioned. The inner and outer diameters must guarantee both sufficient friction surface area and enough room in the radial direction for the assembly of the spring damper. In addition, the outer diameter is also limited by the centrifugal stress at the disk perimeter at high RPMs and the availability of assembly room in the clutch well. The magnitude of the clamping force depends on the maximum contact stress allowed for the disk lining material. The contact stress is in magnitude equal to the normal pressure p_n. After the normal pressure p_n is determined based on friction disk material properties, the disk dimension, namely the inner and outer diameters can then be designed according to the required torque capacity and assembly conditions. Note that the clutch spring has to be further deformed at the fully disengaged position. The spring force at the fully disengaged position is usually designed to be about 15% larger than the spring force F at the engaged position. This means that the spring stiffness is equal to , with δ as the pressure plate travel between the engaged and disengaged positions. Knowing the spring forces at the two clutch positions and the spring stiffness, clutch designers can then select the springs from product inventories of spring suppliers. In the automotive industry today, manual transmission clutches are mature products and can be readily supplied by clutch manufacturers according to the required torque capacity.

2.5 Synchronizer and Synchronization

Gear shifting in a transmission involves coupling together two components or assemblies that turn at different angular velocities in the same direction. This is dynamically similar to the case when an object moving linearly is collided behind by another object moving collinearly at a higher speed. If the rotational speeds of the two components during a gear shift are not brought to the same value, i.e. not synchronized, before they are coupled together, a collision will occur between them, resulting sharp noises, gear grinding, and even component damage. It is possible to make synchronized shifts, or nearly synchronized shifts, in a manual transmission without synchronizers if the driver is highly skilled. But for an average driver, it is a very difficult (if not impossible) job to operate a vehicle equipped with a non‐synchronized manual transmission. The vast majority of manual transmissions today are equipped with synchronizers, with a few exceptions for heavy duty trucks. Note that the synchronization issue during shifts is also important for automatic transmissions. In an automatic transmission, synchronization during shifts is realized by controlling the slippage in hydraulically actuated clutches, as discussed in Chapter 6.

2.5.1 Shift without Synchronizer

In the following qualitative analysis, the five‐speed MT in Figure 2.7b is used as the example to demonstrate the 3–4 upshift and the 4–3 downshift processes in the absence of synchronizers. Other upshifts or downshifts are similar in nature, so the example can be extended to all other manual transmissions for generality.

3–4 Upshift: The 3–4 upshift involves the disengagement of the 3rd gear and the engagement of the 4th gear. This is realized by moving the 3–4 shifter or the 3–4 synchronizer sleeve, illustrated in Figure 2.13, from the 3rd gear position to the 4th gear position along the output shaft so that the internal teeth on the 3–4 shifter engage the dog teeth ring on the input gear (the 4th gear) N_i. When the vehicle is driven in 3rd gear at speed v, the 3rd gear N_3o is engaged by the 3–4 shifter to the output shaft and turns with it at the angular velocity determined by:

(2.9)

where i_a is the final drive ratio and r is the tire rolling radius. The 4th gear, i.e. the input gear N_i on the input shaft, turns at an angular velocity higher than the output, that is, since . If the driver decides to make a 3–4 upshift, the clutch is first disengaged to cut off the engine power and then gear N_3o is decoupled from the output shaft by the 3–4 shifter, which is now at the neutral position. While the 3–4 shifter stays at neutral, both angular velocities, ω_i and , decrease since there is no power supplied to the transmission. However, ω_i decreases at a much higher rate than because the 3–4 shifter turns with the output shaft that is coupled to the whole vehicle mass. Therefore, the two angular velocities, ω_i and , will become equal themselves at some time. The driver can then actuate the shift stick to engage the 4th gear at or near that time, making a synchronized shift without the help of a synchronizer. Clearly, to make this happen, the driver needs high skill and must know the right time to engage the target gear.

Figure 2.13 Synchronizer assembly and gear with dog teeth.

4–3 Downshift: In downshifts, the next gear turns at higher speed than the current gear, contrary to upshifts. For the five‐speed MT in the example, a 4–3 downshift involves the disengagement of the 4th gear N_i and the engagement of the 3rd gear N_3o through the 3–4 shifter. When the vehicle is driven in 4th gear at speed v, gear N_i is coupled by the 3–4 shifter to the output shaft and both turn at the output angular velocity determined by:

(2.10)

The 3rd gear N_3o turns at a lower angular velocity determined by:

(2.11)

When a 4–3 downshift is initiated, first the clutch is disengaged and then the 4th gear N_i is decoupled by the 3–4 shifter, which now stays at the neutral position for a fraction of a second. While the 3–4 shifter stays at the neutral position, both angular velocities, and ω_N3o, decrease since power is cut off. However, decreases at a much lower rate than ω_3o for the same reason as mentioned previously in the analysis for the 3–4 upshift. This makes it impossible for the two angular velocities to become equal by themselves because is already higher than ω_3o before the 4–3 shift is initiated and drops at a much lower rate than ω_3o at the neutral position. Therefore synchronized downshift will not happen without driver’s intervention. In this case, the driver can use a so‐called “double declutching shift” technique to make synchronized or near synchronized downshifts. In double declutching, the driver will briefly engage the clutch and step on the gas pedal while the shift stick is at neutral position. This action will quickly increase angular velocity ω_3o to be above as the engine RPM flares. The driver then disengages the clutch again. Now that ω_3o is higher than but drops at a much higher rate than while the 3–4 shifter is still in the neutral position, the two angular velocities will become equal at some point of time as in the 3–4 upshift example. An experienced driver would then be able to make a synchronized downshift by actuating the shifting stick at the right time.

2.5.2 Shift with Synchronizer

It can be seen from this analysis that even though synchronized shifts are possible for transmissions without synchronizers for well‐experienced drivers, driving such vehicles will still be a very difficult and unpleasant endeavor for an average driver. This is the reason why manual transmissions for today’s passenger vehicles are all synchronized. To understand how synchronizers work, it is helpful to first take a look at the structure of a typical synchronizer, as shown in Figures 2.13 and 2.14.

Figure 2.14 Exploded view of a synchronizer.

Figure 2.13 illustrates the assembly of a typical synchronizer with a gear on each side. This assembly consists of several key components: synchronizer hub, shifting sleeve, two blocking rings (one on each side of the hub), and inserts (or sliders) that are located between the synchronizer hub and the shifting sleeve. The hub has both internal splines and external splines. The internal splines couple the hub to the shaft so the hub and the shaft always turn together. The external spline teeth of the hub mesh with the internal spline teeth of the shifting sleeve. This allows the shifting sleeve to slide over the hub during a shift, while turning with it. Gears are located on each side of a synchronizer and always freewheel on the shaft unless engaged by the shifting sleeve. For the example transmission, we can imagine that the 4th gear is on the left side of the synchronizer and the 3rd gear is on the right side, as shown in Figure 2.13. The engagement of a gear is through the mesh between the dog teeth on it and the internal teeth of the sleeve. The dog teeth form a ring with the same pitch radius as the internal spline teeth on the sleeve. Power is transmitted by the regular gear teeth once the related gear is engaged by the shifting sleeve. The two blocking rings, placed between the gear and the hub on each side, both have a ring of teeth with the same pitch radius and other tooth element proportions as the internal spline teeth of the shifting sleeve. Clearly, the shifting sleeve has to slide over the blocking ring to engage a gear. The blocking rings are usually made of bronze to enhance wear resistance and are both machined with an internal conical surface that contacts the external conical surface on the gear. It is the friction generated between the two contacting conical surfaces that realizes the synchronization during a shifting process. Double friction cones can be designed to minimize synchronization time for quicker shifts, as in sports car applications. Without the blocking rings, the assembly is just a plain gear shifter that disengages and engages gears during shifts without synchronization.

The exploded view in Figure 2.14 offers a better understanding on the structure and operation of synchronizer. As shown in the figure, three symmetrically arranged gaps are machined on the external spline of the hub (4). The three inserts (3) have the same width as these gaps and are placed in them. There is a small ridge at the middle of each insert that fits into a notch on the internal spline of the sleeve (2). Two ring‐shaped springs (5), one on each end of the insert, fit into the corners of the three inserts and push them outward against the sleeve internal spline. There are also three symmetrically arranged gaps on each of the blocking rings (1). The three inserts (3) are longer than the gaps on the hub, therefore the two ends of these inserts extend into the gaps on the two blocking rings in the assembly. The blocking ring gaps are slightly wider than the width of the inserts, so a small relative rotation is allowed between the blocking ring (1) and the inserts (3). The teeth on the two blocking rings (1) have the same pitch radius and tooth element proportions as the internal spline teeth of the sleeve (2). The tooth space on the blocking ring and the tooth on the sleeve internal spline are aligned by design only when the inserts are exactly located at the middle of the gaps on the blocking ring. This is the only relative position between the blocking ring and the sleeve that will allows the sliding of the sleeve over the blocking ring. When the vehicle is driven in any particular gear, the insert contacts one side of the gap on the blocking ring by the gear that is not engaged and carries the blocking ring in rotation with the synchronizer assembly and the shaft.

3‐4 Upshift: When the vehicle is driven in 3rd gear, the sleeve of the 3–4 synchronizer, i.e. the 3–4 shifter, engages the 3rd gear N_3o and couples it to the output shaft. The inserts contact the two blocking rings at the lower end of the gap on it, as shown in Figure 2.15a. The blocking rings are thus carried by the inserts to rotate with the output shaft and the 3–4 synchronizer assembly at angular velocity ω_sleeve that is equal to ω_out, as determined by Eq. (2.9). When a 3–4 upshift is initiated, the clutch is firstly disengaged to cut off engine power and meanwhile the 3rd gear N_3o is disengaged by the sleeve, or the 3–4 shifter. The sleeve is now temporarily at the middle position, i.e. the neutral position, and the inserts still contact the blocking ring at the same point as in 3rd gear operation, as shown in Figure 2.15a. As the driver pushes or pulls the shift stick continuously, the sleeve is forced to move leftward by the shifting force F and tends to carry the inserts in this motion due to the combined effects of the ridge on the inserts and the friction between the inserts and the addendum of the spline teeth. This quickly leads the left end of the inserts to contact the blocking ring and applies a force on it in the axial direction. Contact force and friction with it are then generated between the friction cones of the 4th gear and the blocking ring.

This friction then turns the blocking ring quickly through a small angle in the direction as carried by the 4th gear since it turns faster than the 3rd gear and as allowed by the width difference between the gap and the inserts, until the inserts contact the other side of the gap on the blocking ring, as shown in Figure 2.15b. At this position, there is no relative rotation between the blocking ring and the sleeve, but the sleeve keeps moving leftward as pushed by the shift force F until the teeth on the sleeve internal spline contact the teeth on the blocking ring as shown in Figure 2.15b. Since the inserts are located at the end side of gaps on the blocking ring, the tooth space on the blocking ring is not aligned with the tooth space of the sleeve internal spline. As a result, the teeth of the blocking ring and the teeth of the sleeve internal spline contact against each other at the blocked position shown in Figure 2.15b. Note that the blocking ring must turn quickly enough so that the insert reaches the other side of the gap on the blocking ring before the sleeve slides to the blocked position. The ends of the blocking ring teeth and the sleeve internal spline are machined with round‐up surfaces that form an arrow shaped tip, so that at the contact point between the blocking ring teeth and sleeve internal spline teeth, contact force N_t and friction force μ_tN_t will be generated on an inclined side surface on the tooth end as the sleeve is pushed by the shifting force F.

Meanwhile, the friction cone on the blocking ring will be pressed against the friction cone on the 4th gear, and friction is generated due the existence of the normal contact force on the conical surfaces and the relative motion between the two cones. At the blocked position, the blocking ring is subject to the friction between the friction cones of the 4th gear and the blocking ring itself, and at the contact between itself and the sleeve, the contact force N_t and friction force μ_tN_t. The resultant of contact force N_t and friction force μ_tN_t has a component in the tangential direction of the blocking ring as shown in Figure 2.15b and Figure 2.16b, forming a torque about the axis of the synchronizer that tends to rotate the blocking ring to make way for the sleeve to slide over. This effect is resisted by a resistant torque generated by the friction between the two friction cones on the blocking ring. This resistant torque is reactive and is by design larger than or equal to the torque formed by the resultant of contact force N_t and friction force μ_tN_t. Therefore, the sleeve is blocked by the blocking ring at the blocked position.

While the sleeve is at the blocked position, the friction between the two friction cones acts against the 4th gear and decelerates its angular velocity ω₄. As time goes by, the angular velocity of the 4th gear decreases to be equal to that of the sleeve, i.e. . When these two angular velocities are synchronized, the friction between the two friction cones disappears due to the lack of relative motion. The shift force F, contact force N_t and friction force μ_tN_t still exist because of the driver’s actuation on the shifting stick. Now that there is no friction between the two friction cones to resist the torque formed by the resultant of contact force N_t and friction force μ_tN_t in the tangential direction, the blocking ring will turn slightly so that the inserts will be positioned at the middle of the gap to align the tooth space on the blocking ring and the internal sleeve spline teeth, allowing the sleeve to slide over the blocking ring, as shown in Figure 2.15c. After the sleeve slides over the blocking ring, its internal spline teeth then contact the dog teeth on the 4th gear at the round‐up tooth ends. Now that the angular velocity of the 4th gear and the sleeve are the same, the dog teeth can be engaged quickly and smoothly, as shown in Figure 2.15d.

Figure 2.15 Synchronization process for an upshift.

4–3 Downshift: The 4–3 downshift, or any other downshifts, are basically similar to the 3–4 upshift analysed above. There are some general differences between downshifts and upshifts. Before a 4–3 downshift is initiated, the 2–3 synchronizer sleeve engages the 4th gear N_i, as shown in Figure 2.15d. In the 4–3 downshift process, the 4th gear is firstly disengaged and the sleeve is then at the neutral position, as illustrated in Figure 2.15a. Unlike the 3–4 upshift, the inserts remain at the position in the blocking ring gap as shown in Figure 2.15a during the synchronization process. The friction between the friction cones of the 3rd gear and the blocking ring on the right side (not shown in Figure 2.15) of the 3–4 synchronizer speeds up the angular velocity of the 3rd gear N_3o on the output shaft and synchronizes it with the angular velocity of 3–4 synchronizer sleeve. The 4–3 downshift is otherwise the same as the 3–4 upshift.

2.6 Dynamic Modeling of Synchronization Process

A lumped mass model is shown in Figure 2.16a for the dynamic analysis of the synchronization process during manual transmission shifts. The model is based on a 3–4 upshift for the example 5‐speed RWD MT, shown again in Figure 2.17 for readers’ convenience, but is generally applicable for all shifts in other manual transmissions. As shown in Figure 2.16, F is the shifting force transferred from the shifting stick, N is the contact force between the two friction cones, and M_c is the friction torque generated by the friction cones about the shaft. The geometry of the friction cones is defined by the mean radius r_c and the cone angle α. The pitch radius of the sleeve internal spline and the blocking ring are the same, denoted as r_r in Figure 2.16b. The to‐be‐synchronized component in the 3–4 upshift is the input gear or 4th gear N_i and its angular velocity is denoted as ω₄. In the 3–4 upshift, ω₄ is to be reduced by the friction torque M_c to be synchronized with ω₃, which is the angular velocity of the 3–4 synchronizer sleeve. It should be noted that the 3–4 synchronizer sleeve and the output shaft rotate together at the same angular velocity since the 3–4 synchronizer is coupled with the output shaft.

Figure 2.16 Dynamic model for synchronization process.

When a manual transmission makes a shift, the angular velocity of the output shaft is related to the vehicle speed and is almost unchanged because the vehicle has a huge inertia in comparison with the to‐be‐synchronized component. The angular velocities of synchronizers that are splined to the output shaft and gear pairs rotating with the output shaft are also almost unchanged. All other components, including gears, shafts, and synchronizers that rotate separately from the output shaft, will change angular velocity and need to be synchronized as a lumped mass. As shown in Figure 2.16a, the equivalent mass moment of inertia of this lumped mass is denoted as J_e, and the equivalent mass moment of inertia of the vehicle and components coupled to the output shaft is denoted as J_o.

Figure 2.17 Example five‐speed RDW MT.

2.6.1 Equivalent Mass Moment of Inertia

Note that the components that rotate separately from the output shaft are always the same during all shifts for the same transmission. To find the equivalent mass moment of inertia, the first step is to identify those components in the transmission whose angular velocities change during shifts. These components can be easily identified by observing the stick diagram. For the example transmission in Figure 2.17, the output shaft and the three synchronizers on it are coupled to the vehicle inertia and therefore do not change angular velocity. All other components, including the input shaft with the clutch friction disk on it, the counter shaft with all gears on it, the reverse idler and reverse gear that freewheels on the output shaft, and all gears that freewheel on the output shaft during shifts, do change angular velocity and need to be accounted for in the equivalent mass moment of inertia. The second step in finding the equivalent mass moment of inertia is to identify the component that is to be synchronized directly by the synchronizer. The directly synchronized component varies for different shifts. For the example MT in Figure 2.17, the component to be synchronized directly is the input shaft with gear N_i in a 3–4 upshift. But for a 4–5 upshift, the component to be synchronized directly is gear N_5o. The equivalent mass moment of inertia to be synchronized is lumped on the component that is to be synchronized directly by the synchronizer. The determination of the equivalent mass moment of inertia is based on the condition that the kinetic energy of the equivalent mass moment of inertia must be same as the sum of kinetic energies of all individual components that change angular velocity during a shift, i.e.

(2.12)

(2.13)

where ω_s is the angular velocity of the component to be synchronized directly, ω_i and J_i are respectively the angular velocity and the mass moment of inertia of each component that changes angular velocity during the shift. The summation is for all those components that need to be synchronized as lumped masses. In summary, the equivalent mass moment of inertia can be determined for any shift by following steps:

• Assuming the transmission output speed remains the same, identify all the components in the transmission that will change angular velocities during shifts. These components are the same for the same transmission in all shifts.
• Identify the component, which can be a gear or a shaft, to be synchronized directly in the shift of interest.
• Use Eq. (2.13) to find the equivalent mass moment of inertia for the shift.

For the 3–4 upshift in the example transmission shown in Figure 2.17, ω_s is the angular velocity of the 4th gear N_i, i.e. ω₄ as shown in Figure 2.16a. ω_i is the angular velocity of each individual component that changes angular velocity, including the input shaft, the counter shaft with all gears on it, the reverse idler, and all gears that freewheel on the output shaft during shifts. The summation is for all of these individual components. The angular velocity ratios in Eq. (2.13) depend on the tooth numbers of related gears. For the 3–4 upshift in the example, the equivalent mass moment of inertia is determined by:

(2.14)

(2.15)

In Eq. (2.15), J_CS is the mass moment of inertia of the counter shaft assembly that includes all of the gears that rotate with it. All other mass moments of inertia are for each individual gear as indicated by the subscripts. The equivalent mass moment of inertia for other shifts can be found similarly by replacing the angular velocity of the component to be synchronized directly, ω_s in Eq. (2.13) accordingly. For example, for 4–5 shift, the component to be synchronized directly will be the fifth gear N_5o and ω_s is replaced by ω_5o in Eq. (2.13) to find the equivalent mass moment of inertia in a 4–5 shift. Note that if the component to be directly synchronized is the same, then the equivalent mass moments of inertia are also the same regardless of shifts. For example, the equivalent mass moment of inertia for 3–4 upshift and 5–4 downshift is the same as determined by Eq. (2.15).

The location of the synchronizers affects the number of components whose angular velocities will change during shifts and the equivalent mass moment of inertia. For example, the 3–4 synchronizer is located on the counter shaft for the six‐speed RWD MT in Figure 2.9. This arrangement will reduce the number of components to be synchronized during shifts. In this case, the counter shaft is the component to be synchronized directly by the 3–4 synchronizer in any shift whose target gear is 3rd or 4th. In general, putting a synchronizer on the counter shaft for an RWD MT reduces the equivalent mass moment of inertia, but increases the angular velocity difference to be synchronized during shifts.

The equivalent mass moment of inertia coupled to the vehicle, J_O, can be determined in similar fashion. For the 3–4 shift in the example, J_O is determined on the output shaft as follows:

(2.16)

The equivalent mass moment of inertia coupled to the vehicle is far larger than the mass moment of inertia to be synchronized. Therefore, it is reasonable to assume that the angular velocity of those components that are coupled the output shaft is unchanged during synchronization.

2.6.2 Equation of Motion during Synchronization

Referring to Figure 2.17, the equation of motion for the equivalent mass moment of inertia during the 3–4 upshift is represented in the following based on Newton’s second law:

(2.17)

Since the synchronization time is fairly short, the equation above can be approximated by its finite form as:

(2.18)

where Δω₄ is the change of angular velocity before and after shift of the input shaft with the fourth gear N_i, which is the component to be synchronized directly in the 3–4 upshift, and Δt is the synchronization time. Clearly, larger equivalent mass moment of inertia, bigger change in the angular velocity during shift, and shorter synchronization time correspond to a larger friction torque being required for synchronization. The angular velocity difference in the 3–4 upshift can be calculated by:

(2.19)

As can be observed in this equation, the angular velocity difference that needs to be synchronized is proportional to the difference of the gear ratios between the current and next gears. It is also proportional to the vehicle speed v at which the shift is made. In addition, the angular velocity difference to be synchronized in upshifts, such as the 3–4 upshift in the example, is always negative. This means that the component to be synchronized directly in upshifts is always slowed down. As shown in Figure 2.17, the contact force between the friction cones generated by the shift force F is equal to . The friction torque M_C generated in the friction cones is thus determined by:

(2.20)

where μ is the friction coefficient of the friction cones and . For a given synchronizer, the friction torque M_C depends on only the shift force F. As can be observed from Eq. (2.18), the magnitude of the shift force directly affects the synchronization time Δ_t, which should be below half a second so that a shift, including actuations for disengagement, engagement, and synchronization, can be completed within a second. Shorter synchronization time requires a larger shift force F, which originates from the driver’s hand pushing or pulling the shifting stick. Although a mechanical advantage is designed into the shift mechanism between the driver’s hand and the shift sleeve, the shift force F should be kept within an appropriate range since a large mechanical advantage needs a large travel of driver’s hand on the shifting stick. To reduce the effort and enhance the shifting feel of the driver, the shift force on the synchronizer sleeve should be below 100 N for passenger cars, and below 300 N for trucks. Before synchronization is achieved, the friction torque M_C has two crucial effects for the synchronization process, one of which is to reduce the angular velocity of the fourth gear and the other is to prevent the blocking ring from turning by the tangential resultant F_t of the contact force N_t and friction force μ_tN_t at the contact point between the blocking ring and the sleeve, as shown in Figures 2.16a and 2.16b. The friction torque M_C exists only when there is relative motion between the two friction cones. At the synchronization point, the relative angular velocity Δω₄ is equal to zero and the friction torque becomes zero also, as observed from Eq. (2.18), even though the shift force F still exists because the driver pulls or pushes the shifting stick continuously during the shift.

2.6.3 Condition for Synchronization

As shown in Figure 2.16b, the sleeve of the 3–4 synchronizer is blocked by the blocking ring and is in equilibrium before the synchronization is achieved, therefore,

(2.21)

(2.22)

where β is the contact angle at the tooth tips of the blocking ring and the sleeve internal spline, as shown in Figure 2.16b. Note that the contact force N_t and the friction force μ_tN_t are at the contact between the blocking ring teeth and the sleeve internal spline teeth, and the contact force N and friction force μN are at the contact between the two friction cones. All of these forces originate from the shift force F. The tangential component F_t is the sum of the projections of the contact force N_t and the friction force μ_tN_t in the tangential direction of the blocking ring, determined as:

(2.23)

As discussed previously, the tangential force component F_t in the equation above tends to turn the blocking ring in the direction to yield for the sleeve to slide over it. The critical condition for achieving synchronization is that the blocking ring remains at the blocked position before the synchronization point. To satisfy this condition, the friction torque generated by the friction cones must be larger than the torque generated by the tangential force component on the blocking ring, i.e.

(2.24)

(2.25)

The inequality (2.25) is the condition for guaranteeing that the blocking ring does not turn before synchronization is achieved and is therefore the condition for synchronization. The shift force F does not appear in this inequality since it is a common factor for both M_C and F_t in inequality (2.24) and cancels itself out. It can be observed from inequality (2.25) that the friction coefficient μ_t at the contact between the blocking teeth and the sleeve internal spline teeth makes the right‐hand side smaller. Neglecting μ_t makes the right‐hand side larger and strengthens the synchronization condition. The strengthened synchronization condition is then represented by the following inequality:

(2.26)

To satisfy the synchronization condition, the cone angle α should be as small as possible to increase the contact force N for a larger friction torque M_C. But it has to be above a minimum value to avoid the locking of the friction cones. This minimum cone angle depends on the friction coefficient of the friction cones and is equal to the friction angle, i.e. . The friction coefficient μ is about 0.1 as mentioned previously, therefore the minimum cone angle to avoid friction cone locking is about 6°. In synchronizer design, the cone angle is usually above 6° for a factor of safety. The ratio between the friction cone mean radius and the blocking ring pitch radius is about 0.85. Thus the contact angle β is in the neighborhood of 35°. It should be noted that the friction coefficient μ depends on many factors, such as temperature and lubrication, and is impossible to be accurately determined. The synchronization condition and the analysis in this paragraph provide only a guideline for synchronizer design, so experimental data and experience of existing production synchronizers are crucial to the selection of the related design parameters. Synchronizers are mature products in today’s automotive industry and can usually be ordered from suppliers from existing inventories based on transmission specifications.

As long as the synchronization condition is satisfied, the angular velocity of the to‐be‐synchronized component during a shift, ω₄ in the 3–4 shift of the example transmission, will be synchronized to be the same as the coupling component, the 3–4 synchronizer sleeve in the example, as described by Eq. 2.17. As soon as synchronization is achieved, the friction torque M_C disappears and the blocking ring is then turned slightly by the tangential force component F_t, aligning the tooth space of the blocking ring with the teeth of the sleeve internal spline. The shift force F further pushes the sleeve over the blocking ring and eventually engages the sleeve with the dog teeth of the fourth gear.

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Example 1.1

The stick diagram of a five‐speed FWD MT is shown in Figure 2.7a. The tire radius of the vehicle is R (ft). The numbers of teeth are labeled in the drawing.

1. Determine the equivalent mass moment of inertia to be synchronized in a 1–2 upshift and a 5–4 downshift respectively, in terms of the gear tooth numbers and mass moments of inertia of the involved parts.
2. A 1–2 upshift is to be made at a vehicle speed of v (mph). Assuming the synchronization time is Δt and the angular velocity change is uniform during synchronization, determine the friction torque to be generated by the synchronizer friction cones.
3. Determine the work done by the friction in the process of synchronization for the shift in (b).
4. The synchronizers used in the transmission are the same, and the angular velocity change during synchronization is assumed to be uniform. Find the ratio between the magnitude of the shift force in a 4–5 upshift, F₄₅, and the magnitude of the shift force in a 5–4 downshift, F₅₄. Both shifts are made at the same engine speed and within the same synchronization time.

Solution:

1. For this transmission, the following components need to be synchronized during shifts: the input shaft assembly that includes gears N_1i, N_2i, N_ri and the 3–4 and 5th synchronizers, gears N_1o and N_2o. In a 1–2 shift, gear N_2o is directly synchronized by the 1–2 synchronizer that turns with the output shaft. In a 5–4 shift, the input shaft is directly synchronized by the 3–4 synchronizer to rotate at the same angular velocity as gear N_4i. The equivalent mass moments of inertia for the 1–2 shift and 5–4 shift are determined respectively in the following by using Eq. 2.13.

   

   

2. 

   The angular velocity of gear N_2o before and after the 1–2 shift is:

   

   

   With J₁₂ determined in (a), the friction torque can be determined using Eq. (2.18) as:

   

3. Friction work is equal to the change of kinetic energy. Therefore:

   

4. The equivalent mass moment of inertia for the 4–5 upshift and 5–4 downshift is the same since the component to be synchronized in both shifts is the same. As observed in Eq. (2.18) and Eq. (2.20), the shift forces in the 4–5 upshift and the 5–4 downshift are proportional to the angular velocity differences to be synchronized in the two shifts.

   

   

   Since the shifts are made at the same engine speed, the shift force ratio is:

Figure 2.18 Shifting stick and shift pattern.

2.7 Shifting Mechanisms

The shifting mechanism of a manual transmission must fulfill the following functional requirements:

1. Fully engage the synchronizer sleeve internal spline teeth with the gear dog teeth and keep the gear engaged without dropping out.
2. Prevent different gears from being engaged at the same time.
3. Differentiate the engagement of reverse gear from that of forward gears.
4. Be able to produce an appropriate mechanical advantage between the shift stick and the synchronizer sleeve to reduce the driver’s effort during shifts.

The functions above are realized through the external shifting mechanism and internal shifting mechanism which are interconnected in kinematics by either a connection rod or cables. Shifts in the vast majority of, if not all, manual transmissions today are realized through the shifting stick that has two motions if actuated by the driver, a horizontal motion for gear selection and a fore and aft motion for gear engagement in a so‐called H pattern. The internal shifting mechanism may have multi‐rail design or single (or main) rail design. The following text uses a main‐rail design as the example for analysis. The design and operation of multi‐rail the shifting mechanism is similar in principle.

The external shifting mechanism shown in Figure 2.18 is typical for RWD manual transmissions, as shown in Figures 2.7b and 2.9b. The low end of the shifting stick (1) is connected with the main shifting rail (6) (or the single shifting rail if designed so) in the internal shifting mechanism, shown in Figure 2.19, by the shift link rod (3). The shifting stick pivots on a ball and socket joint mounted on the gear shifter support (4) rigidly attached to the transmission housing. Force and motion originated from the driver’s hand are transmitted to main shift rail through the shift link rod (3). The joints at the two ends of the shift link rod allow the main shifting rod to rotate and move axially. The shift stick is blocked from moving into the reverse gear position unless it is lifted by the driver at the neutral position to release the blocking first. The joints on both ends of the shift link rod (3) are enclosed by rubber boots (2) and are lubricated at assembly. The ball and socket for the shifting stick is also lubricated at assembly and enclosed in rubber root that serves both sealing and cosmetic purposes.

Figure 2.19 Internal shifting mechanism of main‐rail design.

The internal shifting mechanism is shown in Figure 2.19, including an internal shift rod (2) which is used to support the 3–4 shifter fork (19) and the 5‐R shifter fork (4). The 1–2 shifter fork (3) is supported on the main shift rail (18) itself. The shift finger (11) and shift pin support (5) are rigidly attached to the main shift rail (18) by bolts. Spring (15) is mounted on the main shift rail between the spring seat (16), which is retained axially by a snap ring (17) and spring support (6) that is mounted on the housing. Note that the 3–4 shifter and the 5‐R shifter can also be mounted on the main shift rail in a single rail design that does not need the auxiliary shift rod (2). In either design, the shifter forks are supported on the shift rail by multiple race ball bearings (1) which minimize friction for linear motion. The shifter fork straddles over the groove of a synchronizer and maintains a fixed angular position as designed. The main shift rail is supported on both ends also by multiple race bearings. During a shift, the main shift rail has two motions: rotation for selection and axial motion for gear engaging. When the main shift rail rotates in the selection motion, the shift finger (11) on it will be aligned with the receiving notch on the selected shifter or selector fork. Since the angular position of the shifter is fixed, there is only one rotational angle for the main shift rail to align its shift finger with the receiving notch of the shifter. Meanwhile, only at this position, will the shift pin on the shift pin support (5) be aligned with the shift gate (13) for the selected gear. The shift gate guarantees that only the selected gear will be engaged and also provides the effect of guiding the engaging motion of the shifting stick and keeping the angular position of the main shift rail at an engaged position. Once a gear is selected during a shift – that is, the shift finger (11) is received and connected with the selected shifter and the shift pin is aligned with the gate for the selected gear – the driver will push or pull the shifting stick to actuate an axial motion for the main shift rail to engage the selected gear.

The axial positions of the main shift rail (18), namely the left position for 1–3–5 gears and the right position for 2–3–R gears, as shown in Figure 2.19, are locked by the shift rail locking mechanism (8). Three shallow ball‐shaped or V‐shaped races, are machined on the left end of the main shift rail which fit into a hole in the transmission housing. The center distances between these three races are equal to the travel of the shifters to fully engage the gear dog teeth. A ball is seated on top of a spring inside a hole drilled on the transmission housing, as shown in Figure 2.19. This ball is jacked up by the spring and fits into the races when the main shift rail is located at the three positions corresponding to the synchronizer sleeve or the shifter, locking the main shift rail in these positions unless the driver pulls or pushes the shifting stick, and therefore, keeping gears engaged without dropping out. In addition, the locking mechanism, designed appropriately, will yield a “clicking” or “sucking in” feel when a gear is disengaged or engaged. The spring (15) is not deformed at the neutral position and helps return the main shift rail to the neutral position. It also provides a damping feel for the driver while moving the shifting stick. In reverse gear, an actuating pin (9) will close the reverse warning light circuit to signal the driver and the pedestrians around the vehicle. The locking plate (12) and reverse interlock (14) double guarantee that only one gear can be engaged at a time.

Other designs for the shifting mechanism are also applied for manual transmission, depending on assembly and cost considerations. For example, three shift rails can be used, each for two gear positions and each with a locking mechanism. In this design, the shifters are fixed to the rails and move with the rails axially during shifts. Interlocks using balls and pins are placed between the three shifting rails, allowing only one rail to move axially at a time. The three receiving notches on the rail ends are arranged in a row with a distance between each. The shift finger on the lower end of the shifting stick is directly received and connected by a receiving notch on the rail for the selected gear. Other aspects for the shifting mechanism and operations are similar to those already discussed. Note that in manual transmissions for FWD vehicles, shift cables are often used instead of a shift rod, due to the peculiar assembly conditions. Usually, two cables contained in steel tubes are used, one for selection motion and the other for engaging motion. Since the cables are contained in steel tubes, both push and pull motions during shifts will be transmitted from the shifting stick to the shifting levers attached to the transmission housing. The shifting levels then complete the gear selection and engage for the intended shift. The details of these shifting mechanisms can be found in technicians’ manuals for most passenger vehicles [6] in the market, which can be referred to for further studies on the subject.

References

1. 1 Gott, P.G.: Changing Gears: The Development of the Automotive, Society of Automotive Engineers, 1991, ISBN 1‐56091‐099‐2.
2. 2 Manual transmission – Wikipedia https://en.wikipedia.org/wiki/Manual_transmission.
3. 3 Transmission type market share – global car production 2017 https://www.statista.com/statistics/204123/transmission‐type‐market‐share‐in‐automobile‐production‐worldwide/.
4. 4 Fenton, J.: Handbook of Automotive Powertrain and Chassis Design, Professional Engineering Publishing, 1998, ISBN 1‐86058‐075 0.
5. 5 Lechner, G.; Naunheimer, H.: Automotive Transmissions: Fundamentals, Selection, Design and Application, Springer, 1999. ISBN 3‐540‐65903.
6. 6 Ford Parts and Service Division, Technical Training: Aerostar Electronic Four‐Wheel Drive and Scorpio MT‐75 Manual Transmission, 1989, Ford Motor Company.

Problems

1. The stick diagram of a six‐speed RWD MT is shown Figure 2.9b. The tire radius of the vehicle is R (ft) and the final drive ratio i_a is 3.25. The numbers of teeth are labeled in the drawing. Some gear ratios are given as: 1st gear (3.92), 2nd gear (2.76), 3rd gear (1.91), 4th gear (1.41). The number of teeth of gears N_i and N_c are 19 and 23 respectively.
   1. Determine the equivalent mass moment of inertia to be synchronized in a 1–2 upshift and a 5–4 downshift respectively, in terms of the mass moments of inertia of the involved parts and the labels for the tooth numbers.
   2. A 2–3 upshift is to be made at a vehicle speed of V (mph). Assuming the synchronization time is Δt and the angular velocity change is uniform during synchronization, determine the friction torque to be generated by the synchronizer friction cones.
   3. Determine the work done by the friction and the angle of rotation of gear N_4c in the process of synchronization for the shift in (b).
   4. The synchronizers used in the transmission are the same and the angular velocity change during synchronization is assumed to be uniform. If the magnitude of the shift force in a 2–3 upshift, F₂₃, is 10 N, determine the magnitude of the shift force in a 1–2 upshift, F₁₂. Both shifts are made at the same engine angular velocity ω_e and within the same synchronization time Δt.
   Note: In your answers for (a), (b), and (c), only the equivalent mass moments of inertia are allowed to contain labels for tooth numbers.
2. The stick diagram of a six‐speed FWD MT is shown in Figure 2.9a. The tire radius of the vehicle is R (ft). The numbers of teeth are labeled in the drawing for clarity. The gear ratios from the 1st to the 4th gears are: 1st gear (3.92), 2nd gear (2.76), 3rd gear (1.85), 4th gear (1.35). The numbers of teeth of the final drive gears are: N_Fi = 21, N_Fo = 66.
   1. Determine the equivalent mass moment of inertia to be synchronized in a 1–2 upshift and a 4–3 downshift respectively, in terms of the mass moments of inertia of the involved parts.
   2. A 2–3 upshift is to be made at a vehicle speed of V (mph). Assuming the synchronization time is Δt and the angular velocity change is uniform during synchronization, determine the friction torque to be generated by the synchronizer friction cones.
   3. Determine the work done by the friction and the angle of rotation of gear N_4i in the process of synchronization for the shift in (b).
   4. The synchronizers used in the transmission are the same and the angular velocity change during synchronization is assumed to be uniform. If the shift force in a 2–3 upshift, F₂₃, is 10 N, determine the shift force in a 1–2 shift, F₁₂. Both shifts are made at the same engine speed and within the same synchronization time.
   Note: Your answers must not contain the gear tooth labels.