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

Table 2

Comparison of calculation time of N limit cycles of a clutch system with 6 DOF.

	Number of direct simulations of the initial system	Number of CHBM direct calculations of the initial algebraic equation (13) for one set of parameters	CHBM direct calculation time of the initial algebraic equations for one set of parameters (s)	Calculation time of stochastic modes (s)	Calculation time of N limit cycles with the «» method (s)	Total calculation cost to obtain N limit cycles (s)
Results 1 («MC» method)	N	—	—	—	«MC» method 17.71N	17.71N
Results 2 («Sim + ngPC» method) with	31	—	—	41	«Sim + ngPC» method 3.96N	(17.7131) + 41 + (3.96N)
Results 3 («CHB» method)	—	1	1.43	—	«CHB» method 0.002N	((11.43) + 0.002)N
Results 4 («CHB + ngPC» method) with	—	3	1.98	7e − 4	«CHB + ngPC» method 0.0023N	(31.98) + 7e − 4 + (0.0023N)