mproving of cutting process is one of the most important requirements that are expected from the machining methods in the recent years. In some machining processes, the positive effect of ultrasonic waves to improve the cutting process is used. The cutting process efficiency depends on the structure of excitation system which generates ultrasonic waves. One of the most important elements of this system is the ultrasonic waveguide. The role of waveguide is the transfer of ultrasonic vibration energy from ultrasonic transducer to the tool cutting edge interacting with the workpiece (ultrasonic assisted machining-UAM). The UAM system performance depends on well-designed ultrasonic waveguide. The most important aspects of waveguide design are a resonant frequency, amplification factor and the determination of waveguide resonant wavelength - usually integer multiple of half wavelength. The effect of geometrical parameters of stepped waveguide on dynamical properties is presented in this paper.

The relationship between the functional dimensions of the furniture and a user’s anthropometric dimensions is crucial for safety and functionality. The weight and dimensions of the user’s body significantly affect the functional dimensions of the furniture, especially for overweight users. This paper is focused on the concept of chair structural design, which is suitable for bariatric users, including the application of additional reinforcing structural components. Such components are expected to improve the stiffness and strength properties of the chair structure, and it provides the possibilities to a chair design with improved ergonomic parameters. To increase rigidity and reinforce the frame structure of a chair for obese users, the side stretchers, middle braces inserted under seat and armrests are used. The main goal of the different structural designs of chair frames is to minimize internal forces acting in the structural components of the chair. The finite element method (FEM) was used to determine the internal forces and stress-strain state in the structural elements of the chair, starting with the standard design of the chair frame and comparing different design variants. A synergistic effect is obtained, making the bariatric chair durable and ergonomic, without stigmatizing its users.

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The various excitation effects are affecting the machining tools during the machining process. Cutting speeds, cutting forces, chip-making manner, the stiffness of MTW (machine-tool-workpiece) system are predominant effects affecting the dynamics of MTW system and also influencing the machining process (roughness of the machined surface, tool wear, tool or workpiece damage, noise generated by the machining process, etc.). In many cases, to achieve of adequate dynamic properties of the tool, the change of modal properties (mode shapes, natural frequencies) of the body tool must be performed using structural modification. The main objective of this paper will be to formulate, analyse and evaluate the proposed methods and procedures for structural modifications of the tool, represented as a beam. A modification of modal properties by insertion of non-uniform cross-section reinforcing core into body tool is studied and the effect of material properties and geometrical parameters of core on modal properties is analysed. The applications of structural modifications of tool body are leading to better conditions in the cutting process.

Dynamical properties of circular discs are investigated in this paper. One of the techniques of the disc modifications to achieve the required dynamic properties is to initiate pre-stress in disc plane. To obtain appropriate in-plane stress either roll-tensioning of disc surface or volume transformation of disc segment can be used. The role of in-plane stresses is assessed from the change in natural frequencies and modal shapes. The natural frequency characteristics for various rolling position and various rolling depth of the annulus are obtained by modal analysis using Finite Element Method (FEM). The fundamental considerations and derivation of equations of motion are based on Kirchhoff 's assumptions. The assumptions are valid only for thin circular disc. The field of displacements in the cylindrical coordinates r, φ, z, using Kirchhoff plate theory, can be written as˜ r ∂φwhere: u(r, φ), v(r, φ), w(r, φ) -displacements of point laying on neutral plane of the circular disc in coordinate directions.Generally, the stress-strain relations under consideration of initial stresses and initial strains are given bywhere: σ, ε -stress and strain vector, σ 0, ε 0 -initial stress and initial strain vector, D -elasticity matrix.Using the finite element formulation (ZIENKIE-WICZ, TAYLOR 2000), the equation of motion for a free vibration of in-plane stressed disc is described by expressionwhere: M -mass matrix, K -tiffness matrix, K σ -stiffness matrix resulting from stress distribution induced by rolling, ü, u -vector of nodal accelerations and vector of nodal displacements, respectively.We note, that the mass distribution of circular disc after rolling is not changed, but the bending stiffness is considerably changed.Equations (3) can be transformed to modal coordinates using the transformation equationswhere: φ -modal vector, q(t) -normal coordinate of the system.After applying the above transformation, the equation of motion (3) can be used to determination of the natural angular frequencies and mode shapes of the circular disc with roll-tensioning induced residual stress distribution. We obtain the following eigenvalue problemwhere: In order to calculate the modification of disc stiffness K σ after rolling, we must know the residual stress distribution in a disc plane. To determine the residual stress distribution, the method of thermal stress loading is used (KURATANI, YANO 2000). The thermal expansion induces a stress distribution, which is analogous to the stress distribution initiated by rolling. The dependence between temperature and depth of roll-tensioning is approximately described by equationwhere: µ -Poisson number, α -temperature expansion coefficient, h -disc thickness, ∆z -depth of roll-tensioning. 81The matrices M, K and additional matrix K σ , which follow from stress distribution arising from rolling (in this model analogy with thermal expansion is used), are calculated automatically by ANSYS (ANSYS 2001). Solution processes for determination of natural angular frequencies and modal shapes ...