Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: period-one motions

Al-Shyyab, Ahmad; Kahraman, Ahmet

doi:10.1016/j.jsv.2004.06.010

Cited by 93 publications

(55 citation statements)

References 21 publications

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“…Transmission error and backlash are considered in the nonlinear vibration model of shield TBM cutterhead driving system. Based on the gear mesh dynamic in [1][2][3][4][5][6], the relative position deviation function, elastic mesh force, and mesh torque can be obtained respectively, where e(t) and 2 i b is the transmission error and total backlash of the i-th gear pair respectively, y i (t) is the longitudinal (line-of-action or contact direction) vibration displacement of i-th pinion, and y i m (t) is the large gear's contact vibration displacement along line-of-action direction of i-th pinion.…”

Section: Preliminary and Preparationmentioning

confidence: 99%

“…In addition, the pinions and large gear's longitudinal SAVS, and pinions' longitudinal MVSA is increased, however large gear's longitudinal MVSA is reduced a little bit when large gear inertia is increased to 126.93 kgm 2 . Lateral ATMVS and VST of pinions and large gear will be reduced, and longitudinal ATMVS and VST of large gear will be reduced, however longitudinal ATMVS and VST of pinions is increased a little bit when large gear inertia is increased to 126.93 kgm 2 .36 mm/s, respectively, and lateral MVSA of pinions and large gear is about 11.22 and 2.07 mm/s, respectively when gear friction coefficient is increased to 0.08. Meanwhile the longitudinal and lateral SAVS of pinions and large gear are about 0.3294 and 0.0245 mm/s, and 0.0605 and 0.0046 mm/s respectively when gear friction coefficient is increased to 0.08.…”

Section: Physical Parameters' Effects On Dynamic Response Of Tdnltv Vmentioning

confidence: 99%

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Dynamic Two-Dimensional Nonlinear Vibration Modeling and Analysis for Shield TBM Cutterhead Driving System

Zeng

et al. 2014

Transactions of the Canadian Society for Mechanical Engineering

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This paper establishes a general dynamic two-dimensional nonlinear time-varying (TDNLTV) vibration model with multi-drive shaft for shield tunnel boring machine (TBM) cutterhead driving system. Multipleinput and multiple-output (MIMO) state-space vibration model of cutterhead driving system is also presented. TDNLTV vibration model is simulated, and physical parameters' effects on the vibration response are detailed investigated. A preliminary approach is proposed to reduce vibration or nonlinear vibration behaviors. Dynamic TDNLTV vibration model provides a basic foundation of fault detection and diagnosis (FDD) and health monitoring for cutterhead driving system. i-th induction motor rotor viscous damped after equivalent coupling-i J z,i inertia of the i-th coupling between motor-i and reducer-i b z,i viscous damped of the i-th coupling between motor-i and reducer-i J r,ii -th induction motor rotor inertia b r,i i-th induction motor rotor viscous damped J m large gear inertia b m large gear viscous damped r m large gear radius θ p,i angular displacement of i-th active pinion θ i angular displacement of i-th motor rotor θ m large gear angular displacement ω m large gear angular speed J c,

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Section: Preliminary and Preparationmentioning

confidence: 99%

Section: Physical Parameters' Effects On Dynamic Response Of Tdnltv Vmentioning

confidence: 99%

Dynamic Two-Dimensional Nonlinear Vibration Modeling and Analysis for Shield TBM Cutterhead Driving System

Zeng

et al. 2014

Transactions of the Canadian Society for Mechanical Engineering

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“…Viscous damped of the i-th coupling between reducer-i and pinion-i J p,i i-th pinion inertia; b p,i i-th pinion viscous damped T e,i i-th induction motor electrical magnetic torque ω p,i Angular speed of pinion-i ω i angular speed of induction motor-i The large gear's contact vibration displacement along i-th pinion's line-of-action direction T L Shield TBM cutterhead's load torque k f ,i , c f ,i elastic mesh force coefficient of pinion-i k t,i , c t,i elastic mesh torque coefficient of pinion-i i m,i gear transmission ratio T 1 The resistant torque of soil and rocks T 2 The friction torque of soil and rocks which chafe with the front of the cutterhead T 3 The friction torque of soil and rocks which chafe with the back of the cutterhead T 4 The friction torque of soil and rocks which chafe with bulkhead T 5 The stirring torque of soil and rocks by cutterhead stirring rod T 6 The friction torque of cutterhead bearings and sealed chamber…”

Section: Nomenclature Nmentioning

confidence: 99%

“…Based on the gear mesh dynamic, [1][2][3][4][5][6] the relative position deviation function, elastic mesh force, and elastic mesh torque can be obtained where y i (t) is the contact direction (line-ofaction) vibration displacement of i-th pinion, and y i m (t) is the large gear's contact vibration displacement along contact direction of i-th pinion.…”

Section: Preliminary and Preparationmentioning

confidence: 99%

Study on Linear Vibration Model of Shield TBM Cutterhead Driving System

Li¹,

Yu²,

Zeng³

et al. 2014

IJAV

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In this paper, a general linear time-varying multiple-axis (LTVMA) vibration model of shield tunnel boring machine (TBM) cutterhead driving system is established. The corresponding multiple inputs and multiple outputs (MIMO) state-space model is also presented. The linear vibration model is analysed, and the vibration-torque transfer function matrix and the vibration-torque static gain matrix are obtained. The linear vibration model is simulated, and the physical parameters' effects on the vibration response are investigated. A preliminary approach is proposed to reduce vibration by increasing motor rotor inertia and viscous damped. The LTVMA vibration model provides a solid foundation for fault detection and diagnosis (FDD), as long as the health monitoring of cutterhead driving system. NOMENCLATURE nThe number of cutterhead driving motors; q the reducer speed reduction ratio The large gear's contact vibration displacement along i-th pinion's line-of-action directionThe resistant torque of soil and rocks T 2The friction torque of soil and rocks which chafe with the front of the cutterhead T 3The friction torque of soil and rocks which chafe with the back of the cutterhead T 4The friction torque of soil and rocks which chafe with bulkhead T 5The stirring torque of soil and rocks by cutterhead stirring rodThe friction torque of cutterhead bearings and sealed chamber

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“…In fact, the mesh stiffness and mesh damped are the time-varying system parameters. Based on gear mesh dynamic in [19][20][21][22][23][24], the relative position function, elastic mesh force, and mesh torque are obtained, respectively. Where ( ) and 2Δ are the transmission error and total backlash of the th gear pair, respectively,…”

Section: Preliminary and Preparationmentioning

confidence: 99%

Research on Dynamic Models and Performances of Shield Tunnel Boring Machine Cutterhead Driving System

Yuan

et al. 2013

Advances in Mechanical Engineering

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A general nonlinear time-varying (NLTV) dynamic model and linear time-varying (LTV) dynamic model are presented for shield tunnel boring machine (TBM) cutterhead driving system, respectively. Different gear backlashes and mesh damped and transmission errors are considered in the NLTV dynamic model. The corresponding multiple-input and multiple-output (MIMO) state space models are also presented. Through analyzing the linear dynamic model, the optimal reducer ratio (ORR) and optimal transmission ratio (OTR) are obtained for the shield TBM cutterhead driving system, respectively. The NLTV and LTV dynamic models are numerically simulated, and the effects of physical parameters under various conditions of NLTV dynamic model are analyzed. Physical parameters such as the load torque, gear backlash and transmission error, gear mesh stiffness and damped, pinions inertia and damped, large gear inertia and damped, and motor rotor inertia and damped are investigated in detail to analyze their effects on dynamic response and performances of the shield TBM cutterhead driving system. Some preliminary approaches are proposed to improve dynamic performances of the cutterhead driving system, and dynamic models will provide a foundation for shield TBM cutterhead driving system's cutterhead fault diagnosis, motion control, and torque synchronous control.

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Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: period-one motions

Cited by 93 publications

References 21 publications

Dynamic Two-Dimensional Nonlinear Vibration Modeling and Analysis for Shield TBM Cutterhead Driving System

Dynamic Two-Dimensional Nonlinear Vibration Modeling and Analysis for Shield TBM Cutterhead Driving System

Study on Linear Vibration Model of Shield TBM Cutterhead Driving System

Research on Dynamic Models and Performances of Shield Tunnel Boring Machine Cutterhead Driving System

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