**4.4 Frequency analysis of GP**

Frequency analysis is implemented to find natural frequencies of the GP model and evaluate possible resonance in the case of external excitation. The same FE mesh for model as considered before is used. The contacts between assembly's parts are defined as bonded. The numerical solver FFEPlus of SW is used for calculations.

The obtained results show that the fundamental frequency of the GP is sufficiently high *f*1 = 170.47 Hz. The obtained mode shapes for the GP natural frequencies (*f*2 = 201.35 Hz, *f*3 = 264 Hz, *f*4 = 331.85 Hz) are shown on Fig. 16.

Shape Optimization of Mechanical Components for Measurement Systems 259

In this specific situation one of the solutions could be increasing the GP bracket cross-section thickness and changing the shape at the most stressed place. The cross-section shape for bracket's strengthening is defined by the 3 knot points (Fig. 18 a) of NURBS. Design parameters are coordinates of the knot points varied in the following ranges: 3 ≤ *X*1 ≤ 6; 2 ≤ *X*2 ≤ 5; 0 ≤ *X*3 ≤ 3. As a cross-section profile is defined, the 3D-shape is created using the path curve (Fig. 18 b). The same shape for strengthening is created on the second bracket of the GP frame component. A maximal von Mises stress in the bracket was minimized with

(a) (b) (c)

Fig. 18. Shape definition of bracket: (a) cross-section shape; (b) 3D- shape creation through

Von Mises stresses are compared in the design of the obtained shape and the initial shape (Fig. 19). There are 6 check points that show von Mises stresses distribution in the most stressed bracket cross-section. Volume of the obtained design is *v* = 770430 cm3. Change of

(a) (b) Fig. 19. Von Mises stress distribution in considered cross-section of: (a) initial design of GP

**4.6 Shape optimization of GP** 

constraint on the GP volume (*v* <770500 cm3).

path curve; (c) shape optimization result.

and (b) optimized design of GP.

Fig. 16. The mode shapes of the four lower natural frequencies of GP.
