Abstract
The paper relates to the design of machine tool spindles for optimal static stiffness using computer simulation. Current trends are to have computer algorithms which are reliable and allow efficient and accurate programming. In particular, algorithms which may be repeatedly applied to model complex systems, by gradually building up to the final system, are extremely useful. The algorithms described allow the analysis of complex statically indeterminate spindles and provide stiffness values and deflected shapes. The algorithms may also be used with nonlinear bearing stiffnesses thus enabling the resulting nonlinear static stiffness of the spindle system to be predicted. The algorithms are also fast compared to normal methods and therefore allow the designer to investigate a range of design possibilities interactively.
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Abbreviations
- A :
-
area of cross-section
- E :
-
Young's modulus
- F :
-
applied force
- G :
-
shear modulus
- I :
-
second moment of area
- L :
-
length of shaft element
- M :
-
bending moment
- y :
-
horizontal direction perpendicular toX,Z-plane
- x :
-
position along shaft
- γ:
-
slope resulting from shear
- λ:
-
shear factor for section
- ϕ:
-
slope resulting from bending
- α:
-
static receptance after addition of bearing
- β:
-
static receptance after addition of shaft element
- γ:
-
static receptance of existing shaft system
References
R. E. D. Bishop and D. C. Johnson, The Mechanics of Vibration, Cambridge University Press, London, 1960.
S. J. Potter and B. J. Stone, “The calculation of the response of spindle-bearing systems to oscillating forces”, MTIRA Research Report 55, 1974.
R. J. Lambert, A Pollard and B. J. Stone, “Some characteristics of rolling element bearings under oscillating conditions”, MTIRA Report VI, December 1981.
B. J. Stone, “The state of the art in the measurement of the stiffness and damping of rolling element bearings”, Keynote Paper, Annals CIRP, 31(2), 1982.
S. J. Lacey, F. P. Wardle and S. Y. Poon, “A high speed bearing arrangement for CNC machine tool spindles”, RHP Bearings 1981.
M. P. Soon and B. J. Stone, “A knowledge-based system for the design of machine tool spindles”, International Journal of Advanced Manufacturing Technology (submitted).
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Soon, M.P., Stone, B.J. The stiffness of statically indeterminate spindle systems with nonlinear bearings. Int J Adv Manuf Technol 14, 787–794 (1998). https://doi.org/10.1007/BF01350763
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DOI: https://doi.org/10.1007/BF01350763