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TECHNICAL BRIEFS

# Dynamics of a Rotating Shaft Subject to a Three-Directional Moving Load

[+] Author and Article Information
Huajiang Ouyang1

Department of Engineering, University of Liverpool, Liverpool L69 7ZF, UKh.ouyang@liverpool.ac.uk

Minjie Wang

School of Mechanical Engineering, Dalian University of Technology, Dalian 116023, China

1

Corresponding author address: Department of Engineering, Room 1.04, Chadwick Tower, University of Liverpool, Liverpool L69 7ZF, UK.

J. Vib. Acoust 129(3), 386-389 (Jan 05, 2007) (4 pages) doi:10.1115/1.2731402 History: Received March 07, 2006; Revised January 05, 2007

## Abstract

This paper presents a dynamic model for the vibration of a rotating Rayleigh beam subjected to a three-directional load acting on the surface of the beam and moving in the axial direction. The model takes into account the axial movement of the axial force component. More significantly, the bending moment produced by this force component is included in the model. Lagrange’s equations of motion for the modal coordinates are derived based on the assumed mode method and then solved by a fourth-order Runge-Kutta algorithm. It is found that the bending moment induced by the axial force component has a significant influence on the dynamic response of the shaft, even when the axial force and speed are low and, hence, must be considered in such problems as turning operations.

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## Figures

Figure 1

Rotating shaft subjected to a moving load with three perpendicular forces

Figure 2

Torque and bending moments generated from the three force components translated to shaft centerline

Figure 3

Dynamic response of the shaft subjected to three force components moving at different speeds (Px=0.2Pcr and no Mz): (a)vp∕vs at β=0.15 and (b)vp∕vs at β=0.03

Figure 4

Dynamic response of the shaft subjected to three force components moving at different speeds (Px=600N and no Mz): (a)vp∕vs at β=0.15 and (b)vp∕vs at β=0.03

Figure 5

Dynamic response of the shaft subjected to three force components and the induced bending moment Mz moving at different speeds (Px=600N): (a)vp∕vs at β=0.15 and (b)vp∕vs at β=0.03

Figure 6

Dynamic responses obtained using realistic axial speed and axial cutting force: (a)vp∕vs at u=2m∕s and β=0.15 and (b)vp∕vs at u=2m∕s and β=0.03

Figure 7

Logarithm of power spectrum for Figs. 6 (left) and 6 (right) in Hertz with Mz

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