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

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Abstract

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 

Nomenclature

I

inertia, kg·m2

K

component stiffness, N·m/rad

k

component stiffness, N/m

C

component damping, N·m·s/rad

c

component damping, N·s/m

r

component radius, m

θ

angular displacement, rad

θ

angular velocity, rad/s

θ

angular acceleration, rad/s2

δ

teeth deflections, m

fd

dynamic coefficient of friction

fs

static coefficient of friction

fn

normal load distribution, N/m

Ftr

traction force, N

Fn

normal force, N

Frr

rolling resistance force, N

g

function characterizing the road conditions

h

film thickness of lubrication, m

kФ

pressure-sinkage parameter

n

rolling resistance constant

Nf

number of friction pair

P0

engagement pressure, MPa

TE

engine torque, N·m

T0

averaged engine torque, N·m

TC

clutch torque, N·m

Tac

asperity contact torque of clutch, N·m

Thd

hydrodynamic torque of clutch, N·m

TINT

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

TLT

lock-up clutch torque, N·m

Tb

braking torque, N·m

u

internal friction state

vr

relative velocity, m/s

vs

Stribeck relative velocity, m/s

V

vehicle motion velocity, m/s

α1, α2

pressure angle, rad

ε

tolerance of velocity calculation, rad/s

φf, φfs

shear stress factors

μ

traction coefficient

μc

Coulomb friction coefficient

μs

static friction coefficient

σ0

rubber longitudinal lumped stiffness, N/m

σ1

rubber longitudinal lumped damping, N·s/m

σ2

viscous relative damping, N·s/m

Subscripts

E

engine

F

flywheel

CD

clutch drum

CH

clutch hub

G

gear set

S

sun gear

pi

planetary gear (i = 1, 2, 3)

P

planet carrier

R

ring gear

DS

drive shaft

D

differential

W

wheel

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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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