Ashley R. Crowther

Analysis and simulation of clutch engagement judder and stick-slip in automotive powertrain systems:

Abstract Clutch engagement judder and stick—slip are investigated analytically and numerically to examine the influencing factors on these phenomena. Models are developed for a four degree-of- freedom (4DOF) torsional system with slipping clutch and for a powertrain with automatic transmission system. Stability analysis is performed to demonstrate that clutch judder is dependent on the slope of the friction coefficient and the analysis is verified with numerical simulations. An algorithm for modelling stick—slip is developed and is used in numerical simulations which show that the likelihood of stick—slip is increased by clutch pressure fluctuations, judder approaching engagement, and external torque fluctuations. Numerical simulations for second to third gear up shifts demonstrate that the likelihood of stick—slip to occur from clutch engagement is increased by clutch applied pressure fluctuations, judder approaching engagement, and external torque fluctuations and that the likelihood of stick—slip occurring is decreased dramatically by applied pressure ramps proximus to the engagement point.

A finite element method for the dynamic analysis of automatic transmission gear shifting with a four-degree-of-freedom planetary gearset element

Abstract A dynamic model of a passenger car automatic transmission and driveline is developed for simulating transient torsional vibration in gearshifts. A finite element method is proposed for presenting the transient dynamics of the parametric system, element matrices are defined and then global inertial, stiffness and damping matrices are formulated corresponding to the defined global coordinate vectors. A four-degree-of-freedom matrix element is developed that describes the rigid body dynamics of the planetary gear set and is then integrated with the driveline system; this element captures the parametric change while the transmission speed ratios vary over gearshifts. Free vibration analysis and a transient 2-3 upshift simulation are discussed and results presented.

Identification and quantification of stick-slip induced brake groan events using experimental and analytical investigations.

To describe the brake creep-groan phenomenon and several types of stick-slip motions, we propose both analytical and experimental investigations for an automatic transmission equipped vehicle. A lumped torsional model is employed to approximate the dynamics of the real mechanical system. This model assigns inertia to the drive, brake rotor, brake caliper and tire/vehicle, and by appropriate algorithms the simulation time histories include the effects of the friction non-linearity coupling brake and rotor. We consider how to force this particular system, from what physical state, and finding appropriate parameters and solutions. Important computational issues, as related to the stick-slip or slip-stick transitions, are addressed with the algorithms. Driving forces are assigned with two functions, one appropriate for comparison with the test and the other to study stick-slip orbits, which have been found to have various types of motion depending on the controlling brake actuation parameters. Since the groan features a discontinuous friction force and finite-repeating motions some comparisons are made in the frequency and time-frequency domains. These demonstrate the expected stick-slip frequency and multiple orders.

Transient Clunk Response of a Driveline System: Laboratory Experiment and Analytical Studies

A laboratory experiment is designed to examine the clunk phenomenon. A static torque is applied to a driveline system via the mass of an overhanging torsion bar and electromagnet. Then an applied load may be varied via attached mass and released to simulate the step down (tip-out) response of the system. Shaft torques and torsional and translational accelerations are recorded at pre-defined locations. The static torque closes up the driveline clearances in the pinion/ring (crown wheel) mesh. With release of the applied load the driveline undergoes transient vibration. Further, the ratio of preload to static load is adjusted to lead to either no-impact or impact events. Test A provides a ‘linear’ result where the contact stiffness does not pass into clearance. This test is used for confirming transient response and studying friction and damping. Test B is for mass release with sufficient applied torque to pass into clearance, allowing the study of the clunk. A set of non-linear differential equations describe the experiment and the applicable dry friction coefficients are experimentally found. Various test conditions (corresponding to no impacts, and single-sided or double-sided impacts) are successfully simulated. Numerical and experimental time histories compare well. INTRODUCTION Clunk is an impulsive response in the powertrain which is typically initiated by a sharp torque reversal such as from throttle (and engine torque) tip-in or tip-out [1]. The torsional vibration response at the lowest mode, or ‘driveline shuffle or surging’, causes the gears to impact after they pass through the clearance between their backlashes. The oscillation frequency is under 10 Hz and varies with transmission ratio [1-2]. Also, in relation to the size of the torque step there is a corresponding mean change in rigid body motion [2]. Some results (at the vehicle and drivetrain level) are available for clunk experiments [1-3]. Likewise simulations have been used to study clunk, e.g. [4] where the combined effect of transients in engine torque, braking and road load are considered. In this paper we report a test device reduced in complexity so as to isolate clunk from additional non-linear sources, however friction needed to be considered. Faced with results from any of these experiments, the nature of non-linear response may be difficult to fully understand. Correct diagnosis usually requires numerous tests. Benefits in terms of time and cost reduction could be realized by using analytical studies. We thus apply a non-linear mathematical simulation technique [2] to understand the physics related to the impact event. Any simulation model is limited by its simplifying assumptions so the bench experiment needs to be designed and conducted. In this paper, the steps involved in experiment, rig and model development and findings are discussed. The laboratory experiment helps to refine and then correlate the mathematical model with measured results. DEVELOPMENT OF AN EXPERIMENT FOR TRANSIENT The driveline set-up is shown in Figure 1 and includes driveshaft, rear axle and axle shafts. The axle flanges are rigidly attached to the test-bed. The front end of the driveshaft is connected to the torsion bar and supported by a bearing. The torque is measured via a Wheatstone bridge at each end of the driveshaft and at each axle. The length and section of the torsion bar were selected to give a driveline shuffle frequency of around 2-3 Hz. This is similar to 1 gear in a typical vehicle. The significant clearances in the set-up are in the pinion/ring gear mesh and in the differential gears. The torque is applied to the set-up via masses suspended on an electromagnet attached to the end of the torsion bar (Figure 2). The mass of the torsion bar and magnet provides a mean (static) load, and suspended masses provide an applied load, , giving total preload, s T1

Development of a Clunk Simulation Model for a Rear Wheel Drive Vehicle With Automatic Transmission

A reduced model is developed for transient analysis of gear rattle in an automatic transmission (AT) powertrain. Linear modal analysis for the reduced order model compares well with a detailed model that includes planetary gear dynamics. Clearance type lash functions are used for the reduced geared coordinates of the automatic transmission and final drive. Impacts within the gear pairs are affected by the engine surging, shaft stiffness, component inertias, engine harmonics, drag torques, braking, viscous damping and vehicle load. The occurrence of these impacts, or clunk, from shuffle and axle oscillations is demonstrated under typical driving conditions.

An Explanation for Brake Groan Based on Coupled Brake-Driveline System Analysis

Brake creep-groan is studied via a friction coupled torsional model consisting of driveline and brake subsystems. The model captures the main torsional modes of interest while a suitable reduction of higher degree-offreedom models allows selection of appropriate parameters. Numerical simulations are programmed that capture groan response with stick-slip friction and transient brake pressure. The vehicle is initially at rest and the groan may build into a steady state limit cycle, depending on the brake force actuation. For automatic transmission (AT) the driving torque is at the torque converter. For manual transmission (MT) the vehicle is on a slope and the driving torque is due to weight of the vehicle. On-vehicle tests provide time and frequency domain measured accelerations for comparison. INTRODUCTION Creep-groan may occur as a vehicle starts to move from rest. For AT vehicles the torque converter impeller is applying small torque on the stationary turbine and hence the rest of the powertrain. The driver may wish to slowly move some small distance and stop (e.g. in stopgo traffic, at traffic lights, in garage maneuvers). With slow pedal release the brake friction torque will be overcome by the driving torque (impeller) and the brake rotor will start to slip against the brake pad. This initial slip excites vibration of the driveline and brake subsystems, allowing a condition where the rotor and pad may stick again. In practice this stick-slip motion may repeat until the rotor and pad reach some steady-sliding state, or stick and halt the vehicle. The motion is highly dependent on pedal actuation. For MT the vehicle is on a slope, with clutch disengaged and the driver is easing the car from rest. The reasons for the onset of groan are similar but the driving torque is due to weight of the vehicle. In theoretical models, depending on conditions, it can be shown to repeat forever in a stick-slip limit cycle. Many parameters affect this creep-groan phenomenon, including, but not limited to, system modes, damping, friction characteristics, driving torque magnitude, rate and magnitude of brake release, rate and magnitude of brake reapplication and hydraulic system dynamics. Groan may also occur on brake application as reported by Brecht [1]; it typically can be a long event for brake release on takeoff and a short event for vehicle braking to stop. Jang et al. [2], suggest approaches to minimize the vibration by increasing damping or inertia of the rotating bodies and by reducing system compliance. The problem is related to many in the large body of literature for friction research, Martins et al. [3] give a lengthy review that includes most relevant material. The brake creep groan problem remains a complex engineering problem that has yet to be fully understood or analyzed. We propose an analytical investigation of four-degree-of-freedom torsional model (as shown in Figure 1). It includes driveline and brake torsional subsystems, with friction interface through the brake rotor and pad. This model should conceptually describe the brake creep-groan phenomenon and several types of stick-slip motions, and yet it could be easily extended. Note that two dynamic sub-systems are coupled by a friction interface, an important aspect of the non-linear model (as illustrated by Figures 1-2). The frequency ratio for the sub-system modes dominating the stick-slip motions is not near zero (or infinite), hence neither the brake or powertrain sub-systems may be considered as a rigid body. Specific objectives of this paper are as follows: a) Demonstrate the model of two dynamic subsystems coupled with friction interface for the brake groan problem; b) Describe briefly the identification of relevant system parameters; c) Formulate and obtain solutions to the creep-groan response for AT and MT cases; d) Conduct analogous vehicle experiments and show a preliminary correlation between theory and experiment. BRAKE GROAN MODEL The reduced order dynamic model of Figure 1 is designed so as to be applicable to a vehicle with either automatic or manual transmission. Further, it could be employed to study both transient and stick-slip periodic motions. Since brake groan is induced by the stick-slip phenomenon the equations of motion are given below in matrix form where the friction torque introduces a piecewise non-linearity: ) , ( t θ T Kθ θ C θ J = + + (1) Here J, C and K represent inertia, damping and stiffness matrices respectively, T is the external torque vector and θ is the angular displacement vector. Under the slipping condition the governing system of Fig. 1 is of dimension four and is given by and, { } t b r d θ θ θ θ = θ [ ] d r b t diag J J J J = J ; 0 0 0 0 0 0 0 0 d d

Limitations of Smoothening Functions for Automotive Vibro-Impact Problems

Nonlinear torsional models are used to analyze automotive transmission rattle problems and find solutions to reduce noise, vibration and dynamic loads. The torsional stiffnes s and inertial distribution of such systems show that the underlying mathematical problem is numerically stiff. In addition, the clearance nonlinearities in the gear meshes introduce discontinuous functions. Both factors affect the efficacy of time domain in tegration and smoothening functions are widely used to overcome computational difficulties and improve the simulation. In t his paper, alternate smoothening functions are studied for their influence on the numerical solutions and their impact on global convergence and computation times. In particular, four smoothening functions (arctan, hyperbolic-cosine, hyperbolic-tan an d quintic-spline) are applied to a five-degree-of-freedom g eneric torsional system with two backlash (clearance) elements. Each function is assessed via a global convergence metric across an excitation map (a design of experiment). Regions of the excitation map, along with multiple solutions, are studied and the implicat ions to assessing convergence are critically examined. It is obser ved that smoothening functions do not lead to better convergence in many cases. The smoothening parameter needs to be carefully selected, or over-smoothened solutions may be found. The system studied is representative of a typical automotive rattle pr oblem and it was found that benefits were limited from applyin g such smoothening functions.

Development of a Novel Wireless Transducer for Measuring the Transient Torque of an Automotive Powertrain

This paper presents the development of a specific wireless torque measurement system that is used to obtain the transient torque of automatic transmissions. Strain gauges are put on the surface of components that rotate and transfer power. The gauges are connected to a circular printed circuit board (PCB), which is mounted on the rotating component next to the strain gauges. The PCB contains an amplifier, low pass filter, A/D converter, microcontroller, digital RF transceiver and the power supply. The transmitted torque data is received by a stationary antenna and transceiver, which is interfaced to a PC to process, display and save the data.