Vertical Stand

Description

The vertical stand represents a structural part of a machine tool. On one of its surfaces there are guide rails located. On these rails a tool slide is moving due to the machining process the slide has to perform by the machine tool on top. The machining process producing a certain amount of heat which is transported through the structure into the vertical stand. This heat source will be considered as an temperature input at the guide rails. This transfered heat amount will lead to deformations within the device induced by the prevailed temperature field. The evolution of this field is modeled by the heat equation [File:Staender_Geom_white.jpg name|12p]

$c_p\rho \frac{\partial \theta }{\partial t}=\mathrm{\nabla }.(\lambda \mathrm{\nabla }\theta )=0$

with the boundary conditions

$\lambda \frac{\partial \theta }{\partial n}=q$ on the surface where the tool slide is moving on the guide rails and

$\lambda \frac{\partial \theta }{\partial n}\theta =\kappa (\theta -{\theta }_{ext})$ on the remaining boundaries, which describes the heat transfer to the ambience.

Contact information:

User:Lnor