Nonlinear dynamic evolution and sensitivity analysis of marine parallel propulsion system: theory and experiment

doi:10.1007/s10483-026-3427-9

Abstract

Abstract:

The parallel propulsion system is the primary choice for power systems of large-scale ships. However, its operational state is influenced by multiple parameters, and unclear dynamic mechanisms critically restrict its navigation stability and reliability. This study develops a coupled lateral-torsional-longitudinal nonlinear dynamic model to establish the mapping between the key system parameters and the transmission vibration amplitude as well as the gear meshing state. Through the global sensitivity analysis, this study investigates the main effect sensitivity, total effect sensitivity, and interaction effect sensitivity of different parameters on the transmission structure, identifying the dominant factors affecting meshing vibration for different gear pairs. Subsequently, both full-scale ship vibration tests and small-scale prototype experiments are conducted to thoroughly investigate the influence patterns of various parameters on the vibration, acoustic, and power efficiency characteristics of the system. The research results provide essential technical support for a reasonable parameter configuration in such systems and for proactively mitigating the risk of abnormal vibrations.

Key words: nonlinear dynamic evolution, parallel propulsion system, global sensitivity analysis, multi-dimensional parameter, multi-source excitation

2010 MSC Number:

O322

Jianghai XU, Yudie TAO, Zhongliang XIE, Chunxiao JIAO, Donglin ZOU, Zhushi RAO, Guilin SHE. Nonlinear dynamic evolution and sensitivity analysis of marine parallel propulsion system: theory and experiment. Applied Mathematics and Mechanics (English Edition), 2026, 47(9): 2063-2088.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-026-3427-9

https://www.amm.shu.edu.cn/EN/Y2026/V47/I9/2063

Figures/Tables 26

Table 1

Fig. 1

Table 2

Table 3

System parameters adopted in the analysis"

Power parameter	Value range	Structural parameter	Value range
$ω ¯ e$	0-2	$L O$ /m	0-1
$λ f$	0-1	b_m/μm	0-200
$f O$	0-0.1	$ζ I$	0-10
$f m$	0-0.01	$ξ m$	0-2

Table 3

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Table 4

Ranked influence of various parameters on the vibration amplitude based on S1"

Sensitivity	Gear pair	1	2	3	4	5	6	7	8
S₁	$GP 12 ⁢ L M$	$f O$	$ζ I$	$ξ m$	$f m$	$L O$	$b m$	$ω ¯ e$	$λ f$
	$GP 34 ⁢ L M$	$ζ I$	$L O$	$f O$	$ξ m$	$f m$	$λ f$	$b m$	$ω ¯ e$
	$GP 12 ⁢ L A$	$ξ m$	$f O$	$ζ I$	$L O$	$f m$	$λ f$	$b m$	$ω ¯ e$
	$GP 34 ⁢ L A$	$ζ I$	$L O$	$ξ m$	$f O$	$f m$	$b m$	$ω ¯ e$	$λ f$

Table 4

Table 5

Ranked influence of various parameters on the vibration amplitude based on ST"

Sensitivity	Gear pair	1	2	3	4	5	6	7	8
S_T	$GP 12 ⁢ L M$	$λ f$	$ω ¯ e$	$b m$	$L O$	$f m$	$ξ m$	$ζ I$	$f O$
	$GP 34 ⁢ L M$	$b m$	$ω ¯ e$	$ξ m$	$λ f$	$f O$	$f m$	$L O$	$ζ I$
	$GP 12 ⁢ L A$	$ω ¯ e$	$λ f$	$f m$	$b m$	$ζ I$	$L O$	$f O$	$ξ m$
	$GP 34 L A$	$ω ¯ e$	$b m$	$λ f$	$f m$	$f O$	$ξ m$	$ζ I$	$L O$

Table 5

Fig. 14

Fig. 15

Fig. 16

Table 6

Mapping between the theoretical parameters and experimental control variables"

Theoretical parameter	Experimental control variable	Conversion relation
$λ f$ (load ratio)	$λ T$ (torque ratio between motors)	$λ f = λ T$
$f O$ (average load)	I (control current)	$f O = (p 1 ⋅ I + p 2) ⋅ r O / (L c ⁢ J O ⁢ ω n 2)$
$ω ¯ e$ (dimensional meshing frequency)	R (motor rotational speed)	$ω ¯ e = z ⁢ (2 ⁢ π ⁢ R / 60) / ω n$ with z being tooth number of $GP 12 ⁢ L M$
$J O$ (output-flywheel rotational inertia)	$J out$ (flywheel rotational inertia)	$J O = J out$

Table 6

Fig. 17

Fig. 18

Fig. 19

Fig. 20

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Prior work	Previously validated	Genuinely new in this paper
Ref. [5]	Theory-experiment consistency under symmetric and moderately asymmetric power inputs	Unified Sobol evaluation integrating power and structural parameters, systematic interaction rankings, global sensitivity mapping across power and structural parameters
Ref. [24]	Vibro-acoustic characteristics with unsymmetrical input power
Ref. [25]	Nonlinear vibration mechanism and control analysis