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Hybrid model for the analysis of the modal properties of a ball screw vibration system

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Abstract

In accordance with the vibration characteristics of ball screw feed systems, a hybrid modeling method is proposed to study its dynamic behavior. Partially, the ball screw is modeled as a continuous body, and the remaining components are considered lumped masses, allowing for a realistic description of the dynamics of the feed system. The axial, torsional, transverse, and bending vibration models of a ball screw carriage system are established via the Rayleigh-Ritz series method based on the Timoshenko beam assumption. The established model that added the Timoshenko beam assumption obtains the coupling vibration displacement between the transverse and bending vibrations of the lead screw, which is close to real situations. Numerical simulations are conducted to investigate the changes of the natural frequency and modal shapes of ball screw systems with carriage positions. Results show that the carriage position has significant influence on the amplitude and direction of axial and transverse vibrations, substantial influence on the direction of the bending vibration, and minimal influence on the amplitude and direction of torsional vibration. These results indicate that the proposed hybrid model performs well to predict the vibration characteristics of the feed system. Moreover, the carriage position and carriage load also have a remarkable effect on the frequency response of the feed system. These results, along with the modeling approach, provide an important basis for the further study of in-machining monitoring and vibration controller design.

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Abbreviations

E :

Young’s modulus

G :

Shear modulus

κ :

Shear coefficient of the section

s :

Lead of the ball screw shaft

J :

Moment of inertia of the ball screw

J m :

Moment of inertia of the motor

J c :

Moment of inertia of the coupling

η :

Damping loss factor

A :

Cross-section area of the ball screw shaft

ρ :

Density of the ball screw shaft

I x :

Moment of inertia of the cross section of the screw shaft around the x-axis

I y :

Moment of inertia of the cross section of the screw shaft around the y-axis

d :

Diameter of the ball screw shaft

l :

Length of the ball screw shaft

m c :

Weight of the table

k na :

Axial stiffness of the nut

k nr :

Radial support stiffness of the nut

k b :

Axial stiffness of the bearing

k c :

Torsional stiffness of the coupling

C b :

Damping coefficients of the bearing

C n :

Damping coefficients of the screw-nut interface

C c :

Damping coefficients of the coupling

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Acknowledgements

This work was financially supported by the National Natural Science Fund of China (Grant No. 51765039 and No. 51965037).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Qin Wu & Hua Huang

  2. Centre for Efficiency and Performance Engineering, University of Huddersfield, Huddersfield, HD1 3DH, UK

    Qin Wu, Fengshou Gu & Andrew Ball

Authors
  1. Qin Wu
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  2. Fengshou Gu
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  3. Andrew Ball
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  4. Hua Huang
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Corresponding author

Correspondence to Qin Wu.

Additional information

Qin Wu is a doctor of the School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou, China. She received her Ph.D. in Mechanical Engineering from Lanzhou University of Technology. Her research interests include mechanical vibration of CNC machine tools, nonlinear vibration and parameters identification.

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Wu, Q., Gu, F., Ball, A. et al. Hybrid model for the analysis of the modal properties of a ball screw vibration system. J Mech Sci Technol 35, 461–470 (2021). https://doi.org/10.1007/s12206-021-0104-4

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  • DOI: https://doi.org/10.1007/s12206-021-0104-4

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