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Effects of spindle speed-dependent dynamic characteristics of ball bearing and multi-modes on the stability of milling processes

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Abstract

To predict the stable cutting regions of high speed milling, one needs to know the frequency response function of tool tip, which is usually obtained by the modal test or finite element from a static spindle. The dynamic characteristics of high speed spindle which is commonly supported by ball bearing, however, change dramatically during high speed rotation. In this paper, the speed dependent dynamic characteristics of ball bearings are investigated and the speed-dependent variable bearing stiffness’s are determined. By considering the effects of speed-dependent dynamic characterisitics, and then the influences on the modal parameters of tool tip, a set of differential equations with variable mass, stiffness, and damping is set up to describe the dynamics of a multiple mode milling system in two orthogonal directions. Semi-discretization method is used to determine the stability boundaries related to chatter. Results indicate that the effects of variable bearing stiffness and higher order modes of spindle cannot be ignored to predict the stability of the milling processes.

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Abbreviations

α 0 :

Designed contact angle of bearing

δ :

Deflection of ball

Q :

Normal contact load at ball race way interface

f :

r/D b

A :

Distance between race way groove curvature centers

ω m :

Orbital speed of ball

B :

A/D b

d :

Raceway diameter

d m :

Bearing pitch diameter

F c :

Centrifugal force

N :

Number of balls

D b :

Ball diameter

ψ j :

Angular position of ball j

α j :

Contact angle of bearing ball j

r :

Radius of raceway curvature

M g :

Gyroscopic moment

λ :

Constant for the raceway control

ω b :

Angular speed of ball about its own axis

ω :

Speed of rotating ring

φ n :

Normal rake angle

η :

Helix angle

μ :

Cutting friction coefficient

k t :

Specific cutting energy

k n :

Proportionality constant

c :

Refers to cage

j :

Refers to the jth ball

o :

Refers to outer raceway

i :

Refers to inner raceway

r :

Refers to radial direction

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Acknowledgments

The authors gratefully acknowledge the support by the National Key Basic Research Program of China (973 Program, 2011CB706803), NSFC (No. 11172167), and SKL Fund MSV-MS-2010-11.

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Authors and Affiliations

  1. Institute of Vibration, Shock, and Noise, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan RD, Shanghai, 200240, People’s Republic of China

    Xinhua Long & Yingang Chai

  2. Beijing Institute of Astronautical Systems Engineering, #1 Nandahongmen RD, Beijing, 100076, People’s Republic of China

    Dehao Meng

Authors
  1. Xinhua Long
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  2. Dehao Meng
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  3. Yingang Chai
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Correspondence to Xinhua Long.

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Long, X., Meng, D. & Chai, Y. Effects of spindle speed-dependent dynamic characteristics of ball bearing and multi-modes on the stability of milling processes. Meccanica 50, 3119–3132 (2015). https://doi.org/10.1007/s11012-015-0183-3

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  • DOI: https://doi.org/10.1007/s11012-015-0183-3

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