Dynamics Analysis of Torsional Vibration Induced by Clutch and Gear Set in Automatic Transmission

  • Meng Li
  • Michael KhonsariEmail author
  • Ruzhou Yang


The torsional vibration generated during clutch engagement directly affects the shifting quality of automatic transmissions, where the noise source stems from both the clutch and the gear set. To predict the dynamical response and driveline oscillation, a comprehensive mathematical model of the vehicle powertrain equipped with automatic transmission is developed with consideration of nonlinearities in the clutch and the planetary gear set. For the clutch, the dynamics of stickslip is described for the transition between the slipping to locked states. The gear backlash model is used to analyze the rattle noise of the planetary gear set. Based on extensive powertrain simulations for the clutch engagement process, the magnitude of vibration propagation in the driveline are predicted to identify the primary factors of noise generation.

Key words

Powertrain Transmission Planetary gear backlash Clutch engagement 



inertia, kg·m2


component stiffness, N·m/rad


component stiffness, N/m


component damping, N·m·s/rad


component damping, N·s/m


component radius, m


angular displacement, rad


angular velocity, rad/s


angular acceleration, rad/s2


teeth deflections, m


dynamic coefficient of friction


static coefficient of friction


normal load distribution, N/m


traction force, N


normal force, N


rolling resistance force, N


function characterizing the road conditions


film thickness of lubrication, m


pressure-sinkage parameter


rolling resistance constant


number of friction pair


engagement pressure, MPa


engine torque, N·m


averaged engine torque, N·m


clutch torque, N·m


asperity contact torque of clutch, N·m


hydrodynamic torque of clutch, N·m


clutch torque at the instant of zero relative speed, N·m


lock-up clutch torque, N·m


braking torque, N·m


internal friction state


relative velocity, m/s


Stribeck relative velocity, m/s


vehicle motion velocity, m/s

α1, α2

pressure angle, rad


tolerance of velocity calculation, rad/s

φf, φfs

shear stress factors


traction coefficient


Coulomb friction coefficient


static friction coefficient


rubber longitudinal lumped stiffness, N/m


rubber longitudinal lumped damping, N·s/m


viscous relative damping, N·s/m







clutch drum


clutch hub


gear set


sun gear


planetary gear (i = 1, 2, 3)


planet carrier


ring gear


drive shaft






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Copyright information

© The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringLouisiana State UniversityBaton RougeUSA

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