Analysis of the Food Processing Precision Grinder Bed Modal Based on ANSYS Workbench

This study describes the finite element analysis in the applications of food processing machine design, according to the actual application, using ANSYS Workbench software, food processing precision Grinding of Lshaped bed by the finite element model, based on the use of the property to define the parameters and boundary conditions, modal analysis and by the various vibration modes.


INTRODUCTION
With the continuous development of science and technology, the expansion of the grinding wheel speed range, spindle power increasing, the dynamic characteristics of food processing machine bed demand is higher and higher, exist in the traditional design method based on experience design cycle is long, large lathe bed weight, low reliability, need to be solved.Dynamic and static characteristics of food processing machine tools abroad research development soon, has a large number of finite element method is used to analyze and optimize the structure of food processing machine tool.Elbestawi et al. (2002) analyzes the processing method of combining high-speed milling and grinding and establish the CAD model by the Finite Element Analysis (FEA) to solve the components of each order modal vibration mode and vibration natural frequency.Lin et al. (2003) using the finite element model combined with the dynamic test method, in consideration of the case for pre-loaded speed food processing machine tool spindle coupling structure and thermal analysis.In recent years, the domestic application of the finite element method for analysis of the food processing machine structure in large numbers, (Xiaolong et al., 2014) by using BP neural network is put forward to optimize the structure of food processing precision grinder bed method, on the grinder bed size optimization.Ni et al. (2005) Using finite element method, the static and dynamic analysis of food processing machine tool bed and using progressive structural optimization algorithm based on the bed structure of the fundamental constraints and rigidity constrained topology optimization.

MATERIALS AND METHODS
Modal analysis of multi-DOF system: Set the system for the degrees of freedom is N linear time-invariant systems, the motion differential equation is: In the formula: M is the mass matrix system, C is the damping matrix system, K is the stiffness matrix of the system, they are (N×N) Order Matrix.X is the displacement of the point's system response vector; F is the point's system excitation force vector (Fu and Hua, 2000).The basic problem of modal analysis is to become the coupling equations, differential equations group of independent non-coupled.The Eq. ( 1) Pull conversion, you can get: In the formula: To pull transformation factor; X(s), F(s) respectively for the displacement response and the exciting force of pull transformation (initial conditions to zero): Let Z(s) = s 2 M+s 2 M+Sc+K, Z (s) as the N×N matrix, which is the formula (2) becomes: Let H (s) as Z (s) of the inverse matrix, then: For linear time-invariant systems, which left half plane pole in the complex plane, so can therefore be replaced by jω, get: In this case, the equation of motion for the system is: By the vibration theory knowledge, linear timeinvariant systems, the system response can be expressed at any point as a linear combination of each modal response, the response to l points can be expressed as: In the formula, φ lr is the first measuring point's l, the modal factor of R-modal.φ r as the first order modal vector r, it reflects the shape of the order vibration modes.

RESULTS AND DISCUSSION
The establish and modal analysis of food processing precision grinding bed finite element model: Food processing precision Grinding bed is made of gray cast iron as a whole, the overall L-shaped layout, long edge 1715 mm, short edge 1626 mm, width 846 mm, height 400 mm, bed surface collector tank for coolant return, there are eight pads Rail mounting holes, two lifting holes, bed inside the body as well-shaped ribs, its threedimensional structure as shown in Fig. 1.

CONCLUSION
This study describes the finite element analysis in food processing machine design applications and modal analysis and mathematical model of multi-freedom system was derived.Using ANSYS Workbench to L food processing precision grinding food processing machine lathe bed has carried on the modal analysis and each order modal are obtained.Through the simulation can indicate the direction for the actual food processing machine tool lathe bed structure design, reduce test times and shorten the design time.

Fig. 1 :
Fig. 1: Three-dimensional map of food processing precision Grinding bed

Fig. 2 :
Fig.2: The finite element model of food processing precision lathe bed grinder

Table 1 :
Finite element model parameter input table