# Gear Shift Quality Improvement In Manual Transmissions Using Dynamic Modelling

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2 force or torque acting between components. Backlash and geometrical constraints are also taken into account. The external selector mechanism includes the shift lever, cables or rod, and any additional selector components outside the transmission. The masses, inertias, mechanical advantage, drag, damping, stiffness and backlash present in the system are modelled. The internal selector mechanism components typically include a selector rod, selector finger, selector rail, detents, selector fork and sleeve. Again all the relevant parameters that describe the system are used in the model generation. The transmission model varies depending upon the transmission layout. A typical front wheel drive system may include the clutch including torsional damper, input shaft, synchronised gear and output shaft. For small angles: F mesh + C mesh Where : = K mesh ( theta theta ( dtheta dtheta T = F gear1 mesh gear1 T = F mesh F mesh = Force generated at mesh point (N K mesh = Stiffness at mesh point (N/m C mesh = Damping at mesh point (Ns/m theta gear1 = Angular displacement of gear1 (rad dheta gear1 = Angular velocity of gear1 (rad/s theta gear2 = Angular displacement of gear2 (rad dheta gear2 = Angular velocity of gear2 (rad/s gear1 = Working pitch circle radius (m gear2 = Working pitch circle radius (m T gear1 = Torque applied to gear1 (Nm = Torque applied to gear1 (Nm T gear2 The driveline model also varies depending upon the application. Models of front wheel drive, rear wheel drive and four wheel drive have previously been developed. A typical front wheel drive system may include differential housing, differential bevel gears, drive shafts and wheels. A vehicle model may also be included. Figure 1 Simulink Model Top Level Schematic Two gears in mesh The torque between two gears is obtained by calculating the relative displacement at the gear mesh point. The angular displacement of the gears is converted into an linear displacement and the angular velocity is converted into relative linear velocity at the gear mesh point. The relative angular velocity and displacement are converted into a force at the mesh point. This force can then be converted to a torque and applied to each gear by the multiplication of the mesh force by the pitch circle radius. gear1 gear2 The synchroniser system employed in transmission systems varies greatly in configuration. These systems vary from single to multiple cones, asymmetric teeth, and location of blocker and engagement teeth. The synchroniser model includes provision for up shifts, down shifts asymmetric teeth and non-linear cone friction coefficients. The degrees of freedom modelled include individual degrees for each of the synchroniser cones, a degree of freedom for the sleeve and hub, and a degree of freedom for the gear. The synchronisation torque is generated from the axial force applied to the blocker ring from a combination of force applied by the pre-energisation strut and the force generated during sleeve to blocker ring tooth contact. This total axial force acts to resist the sleeve axial motion and is also converted into cone and index torque. Once the two sides of the synchroniser approach synchronisation the index torque (derived from the tangential component of the blocker axial force is greater than the cone torque. This causes the blocker ring to rotate out of the path of the sleeve allowing the sleeve to travel forward and approach the engagement teeth. The blocker force is calculated from the displacement of the blocker and sleeve teeth. This displacement and the corresponding velocity are used to calculate the force which is resolved into its axial and tangential components. Figure 2 Two gears in mesh. 2

3 Blocker Force Generation The force is resolved into axial and tangential components. Pitch F = F (sinγ + sign( dx µ cos λ axial sleeve teeth θ modified F tan gential where = F (cosγ sign( dx sleeve µ teeth sin γ θ index γ Blocker d xsleeve = sleeve axial velocity (m/s µ teeth = teeth contact friction coefficient X2 X1 sleeve The first contact between the blocker and sleeve teeth is governed primarily by the index angle which is a function of the synchroniser design. The angle through which the sleeve can rotate in relation to the blocker teeth is governed by the axial position of the sleeve. Figure 3 Blocker to Sleeve Contacts The blocker force is calculated from the relative angular position of the blocker ring and sleeve. F = K x + C dx where: and x where: and θ modified where: K = Normal contact stiffness (N/m C = Normal damping coefficient (Ns/m dx = Normal contact velocity (m/s = (( blocker abs ( θ cos sl γ θ br θ modified θ sl = Sleeve angular displacement (rad θ br = Blocker ring angular displacement (rad blocker = Pitch circle of blocker ring teeth (m γ = Blocker to sleeve teeth contact angle (rad = θ index Neutral (( x1 x2 tanγ 2 bloc ker θindex = index angle x 1 = sleeve travel from neutral to first blocker teeth contact (m x 2 = sleeve travel from neutral to instantaneous position (m 2 The impact force between the sleeve and gear engagement teeth is modelled in a similar manner to that of the blocker teeth. However the speed difference between the gear and synchroniser hub are much greater at the start of the shift and as there is no physical constraint between the two components the relative displacement can be very large resulting in incorrect contact displacements. To overcome this a remainder function is used which calculates the position of one sleeve tooth in relation to two adjacent gear engagement teeth. Use of the model The model can be used in a number of ways. The first example is to investigate a current gearshift quality problem e.g. large second load, nibble, partial clash. For this type of investigation an objective gear shift quality assessment would be performed to analyse the problem when the vehicle is driven under operating conditions. This would give an experienced transmission engineer an insight into the problem but it can be difficult to pinpoint the causes. Any potential improvement has then to be tested on a vehicle. This can be costly and time consuming. The problem may be related to more than one area and the interaction of different parameters may be overlooked. A dynamic model of the entire system can be used to identify potential problem areas allowing quick and cost-effective investigations of potential solutions both in isolation and their interaction with other parameters. To perform parameter studies it is preferred to start with a correlated model. Correlation of a model poses several problems. The first problem is the driver. A driver can shift in a subconscious closed loop manner where he/she modifies the force and velocity profile exerted on the shift lever based upon the feedback at the lever. A skilled driver may be able to find a problem with every shift or avoid the problem entirely. It is also very difficult to accurately model a driver. For these reasons an open loop approach 3

4 to this problem has been adopted. The test method uses a known velocity profile electro-servo actuator which acts on the gear lever inside the vehicle through double acting springs. The velocity of the actuator and the spring rates can be modified to give variable peak input force levels to the system. The vehicle is motored on a chassis dynamometer to give a repeatable vehicle velocity for the test. The actuator shifted data is compared with the hand shifted data to ensure a high degree of correlation. Spring rates and actuator velocities can be modified to achieve representative shifts. As the shift process is random 50 shifts are typically taken for each shift. The Ricardo GSQA system is used to log the handball position, handball force, transmission input and output speeds. 50 shifts are performed at three force levels and at three different vehicle speeds resulting in a total of 450 gearshifts for each shift type. The model results can then be correlated to the test data. As the model is numerical it will give the same results for a given set of parameters. To overcome this variability is introduced into the model to simulate the effects of randomness. This is achieved by adjusting the relative position of the sleeve and engagement teeth at the start of each simulation. This is performed 15 times for a given peak input force and vehicle speed with the relative position varying between the pitch of the engagement teeth. Correlation allows the tuning of the model to take into account unknown parameter data such as damping etc. Once correlation has been achieved, problem areas can be investigated in detail, looking at the interactions between components and the causes of specific events. Potential solutions can be assessed for cost, practicality and then simulated. A pre-processor has also been created which allows batch running of multiple parameter changes for investigations of the performance of potential solutions. The gearshift quality model can also be used for initial concept design. The basic geometry of the synchroniser, the target selector masses, stiffness and backlash, the driveline stiffness, backlash and inertia can be predicted to give an indication of how a gearshift system may perform. The model can be updated when real information is available, throughout the concept and development phases of a project right through to production intent sign off. Another use of a shift quality model is to predict how an existing transmission may perform in a different vehicle, driveline or selector mechanism application, or to identify potential cost savings. The entire gearshift process is the combination of several stages. Using dynamic modelling it is possible to understand how each sub-system performs and how a subsystems individual performance affects other systems. The following paragraphs refer to figures 4 & 5, and explain what problems can arise at each stage of the gearshift process. This example is for an up-shift. Figures 4 & 5 both show three subplots of a 4 th to 5 th gearshift at 140kph for a front wheel drive car as predicted by a dynamic model. The top display shows the gear and input shaft velocities (rads -1 V's, the centre display shows the handball force (N V's and the lower display shows synchroniser sleeve axial position (m V's. stage 1: Out of gear taking up the backlash in the system, the sleeve moves forward towards next gear. The sleeve velocity is reduced through drag and friction in the selector system and detent loads. stage 2: The sleeve comes out of gear and drag begins to take effect on the clutch side of the synchroniser and begins to reduce the velocity of the upstream components. stage 3: The sleeve picks up the pre-energisation strut, which has the effect of wiping oil from the cones. The axial force begins generates cone torque, which results in a change in gradient of the gear velocity. The blocker ring is rotated to the indexed position. These events happen prior to blocking to prevent push through clash while the friction coefficient is low due to the oil film between the cones. stage 4: The sleeve and blocker teeth contact and as there is a speed difference between the cones the sleeve cannot push though towards the engagement teeth. The handball force builds up during synchronisation. The output shaft velocity trace shows an increase in velocity as the driveline is accelerated by the cone torque causing the driveline components to rotate from the coast to the drive flanks. The velocity stabilises but there is a level of torsional windup in the driveline. The level of wind-up in the driveline is dependant upon the level of torque generated during synchronisation. PROBLEMS DURING THE GEARSHIFT PROCESS 4

5 stage5: In this particular example the static friction coefficient is lower than that of the dynamic and as synchronisation is approached the cone torque drops below the index torque and blocking release begins. The blocker ring is indexed allowing the sleeve to move through the blocker ring towards the engagement teeth. Once blocking release has occurred, drag can act on the upstream components introducing a speed difference across the synchroniser with the gear velocity dropping below that of the output shaft. The sleeve travels towards the engagement teeth of desired gear. The selector mechanism has been compressed during the synchronisation process storing energy in the system. This is released and the sleeve travels towards the selected gear at a greater velocity than the input to the system. The driveline also has stored energy in the system and begins to unwind. The combination of these three phenomena contribute to second load problems ranging from double bump (single second load to nibble (multiple second load with teeth passing. As the sleeve moves forward its stored energy is reducing. It is possible for the sleeve to stop once this energy has been expended. The sleeve remains stationary until the rest of the selector mechanism has moved sufficiently to close the backlash in the system. The effect of drag post synchronisation is a reduction in gear speed below that of the secondary shaft. The extent of desynchronisation depends on the drag and inertia of the system and also the length of time the gear remains unconstrained to the sleeve. Another problem arises postsynchronisation. As the driveline unwinds the output shaft velocity reduces and then increases with an oscillatory response. The sleeve and gear engagement teeth impact resulting in the sleeve moving away from the gear, force being transmitted to the handball and an additional speed modification. This particular example shows a single second load spike. The sleeve is not forced away form the gear engagement teeth past the point of tip to tip contact. The sleeve is then pushed though to final engagement. The relative angular position that the engagement teeth impact each other post synchronisation is random with differing effects depending on which flank is hit and the direction of the relative motion. There are therefore several potential problem areas, which must be overcome. The driveline unwind as the driveline is unloaded must not happen at a point where the engagement teeth can contact. The driveline torsional effect must also be small. The sleeve should travel towards the engagement teeth as fast as possible so as to minimise the effect of transmission drag. The sleeve must not stop part-way into engagement while the selector mechanism catches up with the sleeve. stage1 stage2 stage4 stage5 stage3 Figure 4 Model results for a 4 th to 5 th gearshift at 140kph Handball force (N Speed (rad/s Sleeve axial position (mm Gear and input shaft veloity Vs time handball force Vs time stage Sleeve axial position Vs time Figure 5 Zoom on stages 4 and 5 of Figure4 5

6 60 Test data 4th to 5th gearshift at 100kph 40 Force (N Input shaft and gear velocity (rpm Figure 6 Example of test data CONCLUSIONS Past experience has shown good correlation between model parameter modifications and vehicle tests. Modifications have ranged from increasing sleeve mass, reducing shift fork stiffness and improvements of spline qualities. Additional improvements can be made if improvements to the driveline are performed. Gearshift dynamic modelling can give a much clearer picture of how the physical interactions of transmission components influence the shift quality. ACKNOWLEDGMENT The author wishes to thank the directors of Ricardo for allowing the publishing of this paper. REFERENCES [1] Socin R.J. and Walters L.K 1968 Manual Transmission Synchronizers SAE [2] Sykes L.M The Jaguar XJ220 Triple Cone Synchroniser - A case study SAE

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