Nonlinear Dynamic Behaviour Analysis of a Clutch System with Uncertainties Using Polynomial Chaos and the Constrained Harmonic Balance Method

Table 5

Comparison of the limit cycles of a clutch system with 6 DOF with different intervals of the friction coefficient (μ = 0.5; ).

Number of uncertain parameters r	1		2		5		8
Number of resolutions for the system of equations (see (13))	3		9		42		90
Friction coefficient variation Δμ	0.05	0.1	0.05	0.1	0.05	0.1	0.05	0.1
Maximum amplitude of displacements (10e − 4, rad)	304	310	304	310	306	310	306	312
Relative error of the maximum amplitude of displacements (%)	1.74	1.57	1.72	1.56	1.73	2.57	1.79	1.67
Minimum amplitude of displacements (10e − 4, rad)	290	282	290	282	290	280	286	280
Relative error of the minimum amplitude of displacements (%)	2.16	2.42	1.90	2.46	2.07	2.39	2.64	2.39
Maximum amplitude of velocities (rads^−1)	494	504	496	504	496	506	508	516
Relative error of the maximum amplitude of velocities (%)	2.26	2.10	2.24	2.10	2.26	2.11	2.24	2.21
Minimum amplitude of velocities (rads^−1)	470	458	470	456	470	456	460	450
Relative error of the minimum amplitude of velocities (%)	2.64	2.88	2.21	3.15	1.21	2.53	3.65	2.85