**3.4 Shape optimization of cross section of the ellipsoidal disk**

The shape of cross section of the disk is optimized, taking into account only centrifugal load. The constructive restrictions allow changing the disk cross section shape only at one side and in radial direction at range 150 mm to 300 mm from ellipse center. The section of the disk at radial distance 0-150 mm has constant thickness b = 10 mm. Three methods are used to define the cross section shape (Fig. 12): a) with NURBS knot points, b) with NURBS polygon points and c) with points that are connected with straight lines. Four parameters are stated to define the shape. Parameters are varied in the following ranges: 4 ≤ X 1 ≤ 10; 4 ≤ X 2 ≤ 10; 5 ≤ X 3 ≤ 12; 3 ≤ X 4 ≤ 5 for variants "a", "c" and 3 ≤ X 1 ≤ 10; 0.5 ≤ X 2 ≤ 20; 5 ≤ X 3 ≤ 25; 2 ≤ X 4 ≤ 5 for "b". The design of experiments is calculated with MSE criterion for 4 factors and 70 trial points. This design of experiment is also available on the web: http://www.mmd.rtu.lv.

So the 70 strength studies are calculated for each considered method. SW Simulation results (volume, maximal von Mises stress, axial displacement of the disk etc.) are entered into EDAOpt for approximation and subsequent global search.

Some optimization and approximation characteristics are shown in Table 4. Results of variants "a" and "b" are obtained with second order local polynomial approximation. Third order local polynomial approximation is used for variant "c". Gaussian kernel coefficient was varied for least value of crossvalidation error (4).


Table 4. Quantitative data of approximation and shape optimization of the ellipsoidal disk cross section.

The obtained metamodels are used for optimization of factors. The ellipsoidal disk volume is minimized by taking into account the specified constraints on displacement and stress level. The obtained shapes are presented in Fig. 12. As shown in table 4, the best results are obtained for variant "b" (Fig. 13), where the volume is lower by 8.2 % in comparison to variant "a" and on 2.6 % - to "c". All 3 variants give significant advantage in volume (28.1 – 33.9 %), comparing to variant "d"- the initial shape design with constant 10 mm thickness.

Shape Optimization of Mechanical Components for Measurement Systems 255

In this section designing the mechanical part of an automotive vehicle gage panel is discussed. Automotive vehicle gage panels (GP) must meet many requirements - such functional characteristics as appropriate stress levels under loads, eigenfrequencies, stiffnesses, weight, accuracy etc. and last but not least they must have minimal environmental pollution during service lifetime. The 3D geometrical models of the gage panel are elaborated using SW. Static and dynamic responses of the gage panel are calculated using SW Simulation and impacts to environment are evaluated using SW Sustainability that include such indices as total energy consumed, carbon footprint, air acidification and water eutrophication. The stationary and transient behaviors of the gage panel under dynamic excitation as well as stress distribution under static loading are investigated. Due to the complexity of the gage panel FEM models, the appropriate metamodels are elaborated based on design of experiments. These metamodels are used for multiobjective optimization using a global search procedure. Partial objectives are aggregated in the complex objective function for optimization purposes. Dynamic behavior of the gage panel is then verified by solution of the full FEM models in case of random

A constantly pressing problem is the development of safe and environmentally friendly engineering objects with high functional properties, attractive style and competitive price. We should try to take into account not only precisely measurable functional indices, but also

The Industrial Designer Society of America defines industrial design as the professional service of creating and developing concepts and specifications that optimize the function, value, and appearance of products and systems for the mutual benefit of both users and manufacturer. In fact, industrial designers focus their attention upon the form and user interaction of products. There are five critical goals (Ulrich & Eppinger, 2008): 1) Utility: The product`s human interfaces should be safe, easy to use, and intuitive. Each feature should be shaped so that it communicates its function to the user. 2) Appearance: Form, line, proportion, and color are used to integrate the product into a pleasing whole. 3) Easy maintenance: Product must also be designed to communicate how they are to be maintained and repaired. 4) Low costs: Form and features have a large impact on tooling and production costs, so these must be considered jointly by the team. 5) Communication: Product design should communicate the corporate design philosophy and mission through the visual qualities of the products. The practical concept selection methods (Ulrich & Eppinger, 2008) vary in their effectiveness and include the following: 1) External decision: Concepts are turned over to the customer, client, or some other external entity for selection. 2) Product champion: An influential member of the product development team chooses a concept based on personal preference. 3) Intuition: The concept is chosen by its feel. Explicit criteria or trade-offs are not used. The concept just seems better. 4) Multivoting: Each member of the team votes for several concepts. The concept with the most votes is selected. 5) Pros and cons: The team lists the strengths and weaknesses of each concept and makes a choice based upon group opinion. 6) Prototype and test: The organization builds and tests prototypes of each concept, making a selection based upon test data. 7) Decision matrices:

**4. Automotive vehicle gage panel** 

vibrations.

**4.1 Specific requirements** 

such a difficult-to-formalize index as style of GP.

Fig. 12. Results of optimization of ellipsoidal disk. Shape of cross section is defined by (a) NURBS knot points, (b) NURBS polygon points, (c) points that are connected with straight lines.

Fig. 13. Half of 3D model of optimal shape disk and real von Mises stresses distribution in it.

#### **3.5 Summary**

The proposed equipment allows using the standard wheel pair with removable measurement equipment as a tensometric wheel pair that considerably reduces material and time expenses required for preparing testing. By means of size and shape optimization, the total volume of the mounting disk of railway vehicle measurement system is reduced by ~64 % in comparison with the initial design. The method based on NURBS polygon points gives the shape with at least 3% better objective (volume) than other used methods.
