Abstract
Modified HBM (Harmonic Balance Method) with AFT (Alternating Frequency Time) method is utilized to obtain steady-state response of an automotive clutch system with piecewise-linear stiffness. The stability analysis for the obtained response is performed via perturbation technique and Floquet multipliers. The considered system shows a flip and fold bifurcation, and variation of system parameters can exhibit abnormal clutch vibration such as a rattling phenomenon.
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Abbreviations
- C :
-
Viscous damping
- h 1,h 2 :
-
Non-dimension 1st, 2nd stage angle of drive side
- I :
-
Equivalent mass moment of inertia ofI 1 andI 2
- I 1 :
-
Equivalent mass moment of inertia of flywheel, clutch cover, crank shaft, connecting rod
- I 2 :
-
Equivalent mass moment of inertia of input gear and clutch hub
- K :
-
Torsional spring stiffness ofK 1 andK 2
- K 1 :
-
Torsional spring stiffness of clutch pre damper
- K 2 :
-
Torsional spring stiffness of clutch main damper
- q :
-
Diffrence angle betweenθ 1 andθ 2
- q 1,q 2 :
-
1st, 2nd stage angle of drive line
- Q n :
-
Harmonic component
- γ:
-
Crank radius
- t :
-
Time
- T :
-
Combined torque per one cylinder
- T c :
-
Torsional torque of clutch
- T c * :
-
Nondimensional torsional torque of clutch
- T E :
-
Engine fluctuation
- y :
-
Nondimensional displacement
- α:
-
Nondimensional viscous damping
- β,β 2 :
-
Nondimensional equivalent stiffness
- δ:
-
Nondimensional gap
- ξ:
-
Nondimensional damping
- η,η 1 :
-
Nondimensional frequency
- θ:
-
Nondimensional time
- θ 2,θ 2 :
-
Angle
- λ:
-
Eigenvalue
- ν:
-
Subharmonic ratio
- σ:
-
Stiffness ratio
- ω,ω 1 :
-
Angular velocity
References
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Department of Mechanical Engineering
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Kim, Y.B., Lee, H.B. Periodic response and nonlinear vibration behavior for automotive clutch. KSME International Journal 12, 1073–1078 (1998). https://doi.org/10.1007/BF02942580
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DOI: https://doi.org/10.1007/BF02942580