Thermoelastic Whirling Analysis of Cylinders During Grinding

Cylinder grinding has been the subject for an intensive research, because delay-type resonances, commonly known as chatter-vibrations, have been reason for serious surface quality problems in industry [1]. As a result of this activity there is available a simulation platform, on which the complete grinding process including delay-resonances can be driven [2]. This platform consists of models for the grinder, for the cylindrical work piece and for the stone-cylinder grinding contact. The elastic cylinder model is based on analytical eigenfunctions in bending vibrations, which basis has been used to present the rotordynamic equations of cylinder in modal coordinates. Stone-cylinder interaction mechanism has been derived by combining the rules of mass and momentum transfer in the material removal process. The contribution of this paper is to update the platform to include the thermal effects of the work body. Following the method to use the eigenfunctions of a non-supported beam to describe the rotordynamic motion of the work body, a promising method could be to use in a similar way the eigenfunctions of a thermally isolated cylinder to solve the temperature distribution of the cylinder. The temperature distribution and terms related to the non-homogeneous boundary conditions will then be the input to the thermoelastic problem. It can be shown that the eigenfunction basis consists of trigonometric functions in axial and circumferential directions while the radial eigenfunctions are Bessel functions. The stone-cylinder interface has to be updated also to include thermal effects. A portion of the mechanical power is transferred to the work piece. The rest goes to the stone, to the material, which is removed and to the cutting coolant. On the other hand, thermal deformations modify the grinding forces, which are loading the work piece. The solution of the coupled thermal and thermoelastic problem will be done in terms of modal coordinates corresponding to the eigenfunction basis. This leads to numerical time integration of two groups of differential equations, the solution of which can be used to perform the temperature distributions and the corresponding thermal deformations.