Error Correction of Radial Displacement in Grinding Machine Tool Spindle by Optimizing Shape and Bearing Tuning
In this article, the radial displacement error correction
capability of a high precision spindle grinding caused by unbalance
force was investigated. The spindle shaft is considered as a flexible
rotor mounted on two sets of angular contact ball bearing. Finite
element methods (FEM) have been adopted for obtaining the
equation of motion of the spindle. In this paper, firstly, natural
frequencies, critical frequencies, and amplitude of the unbalance
response caused by residual unbalance are determined in order to
investigate the spindle behaviors. Furthermore, an optimization
design algorithm is employed to minimize radial displacement of the
spindle which considers dimension of the spindle shaft, the dynamic
characteristics of the bearings, critical frequencies and amplitude of
the unbalance response, and computes optimum spindle diameters
and stiffness and damping of the bearings. Numerical simulation
results show that by optimizing the spindle diameters, and stiffness
and damping in the bearings, radial displacement of the spindle can
be reduced. A spindle about 4 μm radial displacement error can be
compensated with 2 μm accuracy. This certainly can improve the
accuracy of the product of machining.
[1] B. G. Choi, B. S. Yang, Optimum shape design of rotor shafts using
genetic algorithm, Journal of Vibration and Control 6 (2000) 207-222.
[2] Y. H. Kim, A. Tan, B. S. Yang, W.C. Kim, B. K. Choi, Y. S. An,
Optimum shape design of rotating shaft by ESO Method, Journal of
Mechanical Science and Technology 21 (2007) 1039-1047.
[3] M.A. Alfares, A.A. Elsharkawy, Effect of axial preloading of angular
contact ball bearings on the dynamic of a grinding machine spindle
system, Journal of Material Processing Technology, 136 (2003) 48-59.
[4] W. Jacobs, R. Boonen, P. Sas, D. Moens, The influence of the lubricant
film on the stiffness and damping characteristics of a deep groove ball
bearing, Mechanical Systems and Signal Processing, 42 (2014) 335-350.
[5] B. S. Yang, S. P. Choi, Y. C. Kim, Vibration reduction optimum design
of a steam-turbine rotor-bearing system using a hybrid genetic
algorithm, Struct Multidisc Optim 30 (2005) 43-53.
[6] F. Straub, M. Inagaki, J. Starke, Reduction of vibration level in
rotordynamics by design optimization, Struct Multidisc Optim 34 (2007)
139-149.
[7] M. Aleyaasin, R. Whalley, M. Ebrahimi, Error correction in hydrostatic
spindles by optimal bearing tuning, International Journal of Machine
Tools & Manufacture 40 (2000) 809-822.
[8] N. Ozawa, T. Sugano, Y. Yoshida, Measuring method of central position
of spindle rotation 2nd report, evaluation of new method and
experimental results of hydrostatic bearing spindle, Transaction of The
Japan Society of Mechanical Engineers, C 60 (572) (1994) 1387–1390.
[9] D. E. Goldberg, Genetic algorithm in search, optimization & machine
learning, Addison Wesley, New York (1989).
[10] M. Lalanne, B. G. Ferraris, Rotordynamics prediction in engineering,
Wiley, New York (1998).
[11] T. Yamamoto, Y. Ishida, Linear non-linear rotordynamics a modern
treatment with applications, John Wiley and Son, New York (2001).
[12] M. I. Friswell, J. E. T. Penny, S. D. Garvey, A. W. Lees, dynamic of
rotating machine, Cambridge University Press, New York (2010).
[1] B. G. Choi, B. S. Yang, Optimum shape design of rotor shafts using
genetic algorithm, Journal of Vibration and Control 6 (2000) 207-222.
[2] Y. H. Kim, A. Tan, B. S. Yang, W.C. Kim, B. K. Choi, Y. S. An,
Optimum shape design of rotating shaft by ESO Method, Journal of
Mechanical Science and Technology 21 (2007) 1039-1047.
[3] M.A. Alfares, A.A. Elsharkawy, Effect of axial preloading of angular
contact ball bearings on the dynamic of a grinding machine spindle
system, Journal of Material Processing Technology, 136 (2003) 48-59.
[4] W. Jacobs, R. Boonen, P. Sas, D. Moens, The influence of the lubricant
film on the stiffness and damping characteristics of a deep groove ball
bearing, Mechanical Systems and Signal Processing, 42 (2014) 335-350.
[5] B. S. Yang, S. P. Choi, Y. C. Kim, Vibration reduction optimum design
of a steam-turbine rotor-bearing system using a hybrid genetic
algorithm, Struct Multidisc Optim 30 (2005) 43-53.
[6] F. Straub, M. Inagaki, J. Starke, Reduction of vibration level in
rotordynamics by design optimization, Struct Multidisc Optim 34 (2007)
139-149.
[7] M. Aleyaasin, R. Whalley, M. Ebrahimi, Error correction in hydrostatic
spindles by optimal bearing tuning, International Journal of Machine
Tools & Manufacture 40 (2000) 809-822.
[8] N. Ozawa, T. Sugano, Y. Yoshida, Measuring method of central position
of spindle rotation 2nd report, evaluation of new method and
experimental results of hydrostatic bearing spindle, Transaction of The
Japan Society of Mechanical Engineers, C 60 (572) (1994) 1387–1390.
[9] D. E. Goldberg, Genetic algorithm in search, optimization & machine
learning, Addison Wesley, New York (1989).
[10] M. Lalanne, B. G. Ferraris, Rotordynamics prediction in engineering,
Wiley, New York (1998).
[11] T. Yamamoto, Y. Ishida, Linear non-linear rotordynamics a modern
treatment with applications, John Wiley and Son, New York (2001).
[12] M. I. Friswell, J. E. T. Penny, S. D. Garvey, A. W. Lees, dynamic of
rotating machine, Cambridge University Press, New York (2010).
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:71272", author = "Khairul Jauhari and Achmad Widodo and Ismoyo Haryanto", title = "Error Correction of Radial Displacement in Grinding Machine Tool Spindle by Optimizing Shape and Bearing Tuning", abstract = "In this article, the radial displacement error correction
capability of a high precision spindle grinding caused by unbalance
force was investigated. The spindle shaft is considered as a flexible
rotor mounted on two sets of angular contact ball bearing. Finite
element methods (FEM) have been adopted for obtaining the
equation of motion of the spindle. In this paper, firstly, natural
frequencies, critical frequencies, and amplitude of the unbalance
response caused by residual unbalance are determined in order to
investigate the spindle behaviors. Furthermore, an optimization
design algorithm is employed to minimize radial displacement of the
spindle which considers dimension of the spindle shaft, the dynamic
characteristics of the bearings, critical frequencies and amplitude of
the unbalance response, and computes optimum spindle diameters
and stiffness and damping of the bearings. Numerical simulation
results show that by optimizing the spindle diameters, and stiffness
and damping in the bearings, radial displacement of the spindle can
be reduced. A spindle about 4 μm radial displacement error can be
compensated with 2 μm accuracy. This certainly can improve the
accuracy of the product of machining.", keywords = "Error correction, High precision grinding,
Optimization, Radial displacement, Spindle.", volume = "9", number = "9", pages = "1674-5", }