Investigation of Rotating Disk Stability

Loss of stability of a flat form of equilibrium of large diameter saw blades that operate at high speeds is the main cause of failure. The loss of stability occurs as a result of high heating up of saw blade outer contour when sawing logs. However, in the scientific literature there is no complete solution of this problem, including the heat task. In this study, the problem of determining the stationary temperature field arising in a rotating disk while heating up its outer contour is solved. Cooling a saw blade is due to convective heat exchange on the outer surface of the disc. The resulting temperature distribution is used to solve the stability problem. Arising in the disk forces depend both on heating up and on rotation. Stability problem of a flat form of equilibrium of rotating disk is solved in a static setting, i.e., the temperature of the disk outer contour is determined by method of initial parameters depending on the rotating speed when the new contiguous forms of equilibrium arise. The research results allow choosing the cutting modes that preclude wave formation of the saw blade.

References

[1] Lykov A.V. Teoriia teploprovodnosti [The theory of heat conduction]. Moscow, Vysshaia shkola publ., 1967. 600 p.

[2] Niki forov A.F., Uvarov V.B. Spetsial funktsii matematicheskoi fiziki [Special functions of mathematical physics]. Dolgoprudnyi, Intellekt publ., 2007. 343 p.

[3] Dem’ianushko I.V., Birger I.A. Raschet na prochnost’ vrashchaiushchikhsia diskov [Calculation of the strength of rotating disks]. Moscow, Mashinostroenie publ., 1978. 247 p.

[4] Alfutov N.A. Osnovy rascheta na ustoichivost uprugikh system [Basis for calculating the stability of elastic systems]. Moscow, Mashinostroenie publ., 1991. 336 p.

[5] Biderman V.L. Mekhanika tonkostennykh konstruktsii. Statika [Mechanics of thinwalled structures. Statics]. Moscow, Mashinostroenie publ., 1977. 488 p.

[6] Frieze P.A., Dowling P.J., Hobbs R.E. Ultimate load behavior of plates in compression. Steel Plated Structures. Proc. Int. Conf. on Steel Plated Structures, Crosby Lockwood Staples, London, 1977, pp. 24 – 50.

[7] Guide to stability design criteria for metal structures. Third Ed. Edited by Bruce G. Johnston . New-York, John Wiley and Sons, 1976. 616 p.