To obtain the first two order modal parameters of the support of grating ruler which was bolted to the tool head, a modal test was carried out by LMS Test Lab. Then the stiffness of springs in the FE model of support was obtained by optimization. Topology optimization was accomplished with the stiffness obtained set to the model, and this result was difference from the result with fix boundary conditions. It’〖KG-*2〗s necessary to obtain the equivalent stiffness of bolted joint.