The coupling part of rotating systems is a very important factor in determining their static/dynamic stiffness. To ensure the correct performance of the machine tool, the static/dynamic stiffness of the rotating system must be predicted. Various parameters of the coupling section in rotating systems, such as the spring element, the node number and the bias, affect the characteristic of rotating system.
This study focuses on the prediction of the static and dynamic stiffness of the rotating system with coupling section using the finite element (FE) model. To represent the coupling section of the rotating system, finite element method (FEM) calculations were performed on the preload effect and the spring element arrangement. The preload effect on the coupling section was estimated based on the HERTZIAN contact theory.
An FE model of a sixteen-node couple section was constructed using MATRIX 27. Comparisons between FEM predictions and experimental results were made in terms of static and dynamic stiffness.
Introduction
- Motivation
- Analytical method for prediction of static/dynamic stiffness
- Experimental method
- Finite element method
Structure spectrum such as model complexity and variety of new product development time/cost explosion. The structural/thermal analysis of the automation of small and medium-sized enterprises should alleviate the lack of a rotation system of skilled workers. However, the FEM has hardly performed the prediction of the unit and the rotating system based on the original shape of the coupling section due to contact problems.
It uses data in the form of time series to develop discrete difference equations that represent the dynamic properties of the machine tool structure at the measurement points. They have conducted the study on the different configuration of spindle cutter system in a high speed milling cutter[23-25]. Research by Zhang and Huang et al.[7] show that about 60% of the total dynamic stiffness and about 90% of the total damping in an entire evaluation structure originates from the joints.
Recently, many of the researchers carried out the coupling section, because when the coupling sections were considered, the rotating system of feature could have been presented. However, many of the papers did the investigation of load for liner guile and bolt.[28-31] The rotating unit was the one of the important parts in the rotating system.[32-34] It still remained an early stage. for the coupling section. until now day.
Coupling section modeling of rotating systems
General type of the coupling section
Coupling section modeling
The simple design of the coupling section for rotary units consisted of an inner race, an outer race and a spring element. One of the key points was the inner and outer race that the true bearing has. The stress value is taken from the sampling section that is close to the tie point.
For the simulation, the construction of a simple bearing model had to go to the next step, that is, how to define the stiffness property of the spring element according to the bearing stiffness. Because the stiffness of the bearing meant the overall stiffness of a simple bearing model, which consists of a set of spring elements. He told us that bearing stiffness and spring stiffness were different ideas due to the fact that bearing stiffness relates directly to the spring element.
The study investigated MATRIX 27 because of the important factor in developing the coupling section. According to the position of the spring in radial direction, the stiffness matrix considered the position effect as the bearing stiffness is uniformly distributed in the simple bearing model. The simple bearing model consisting of the combination 14 expressed the bearing stiffness in the case of rotation of the model in typical axes such as x, y and z.
Another weakness was that the additional part in the simple bearing model was created in axial direction to assign the axial stiffness in the case of the angular contact bearing. The influence of preload classified the geometric calibration and the characteristic of bearing stiffness.[36-38] The characteristic of bearing stiffness under preload was more important than the geometric calibration on static and dynamic stiffness. Because the coupling part is composed of the spring element which is dependent on bearing stiffness, the preload effect considered the relationship between preload and bearing stiffness.
Assume that the contact forces on each ball in the ball bearing are equal when the roller bearing is under load F. Where Q is the contact force for each ball, α is the contact angle, n is the ball number. A finite element model of the rotating unit with coupling section was created in the first step for angular contact ball bearings.
To simulate the stiffness and damping of the coupling section in the rotating unit, the spring element used MATRIX 27 because the angular contact ball bearing had axial and radial stiffness. The coupling section of the property was defined in five cases to verify a wide range of coupling section.
Experimental verification
The experimental procedure was that the roll cell generates displacement at the bottom of the shaft within 0.2 mm. Many of the small companies need simulation forecasting for their equipment because they have limitations to get the simulation department. If the user makes a stiffness matrix for MATRIX 27, many of the procedures are performed on each element.
The paper has studied the static and dynamic stiffness of rotating unit with coupling section in the FE model. Preload has significantly affected the static and dynamic stiffness, so it had to consider the prediction of the procedure. During the machining process, a large amount of heat tool parts such as electric motor, roller bearings and cutters are generated.
Heat is transferred to different parts of the machine tool by the methods of thermal conduction, convection and radiation, which leads to different temperature rise and thermal expansion for different parts of the machine tool. Thus, the exact relative position of the cutter and the workpiece is affected by thermal expansion, which eventually affects the machining accuracy. Kang, Y., et al., Integrated “CAE” strategies for the design of machine tool spindle bearing systems.
Altintas, Modeling of spindle bearings and machine tool systems for virtual simulation of milling operations. Zhang, G.P., et al., Predicting the dynamic behavior of a complete machine tool structure based on computer-aided engineering. Mi, L., et al., Effects of joint preloads on the dynamic stiffness of a machine tool overall structure.
Stone, The Optimization of the Dynamic and Static Efficiency of Spindle Systems, in International Mechanical Engineering Congress and Exhibition (1994:Perth, W.A.)1994, Institution of Engineers, Australia: Barton, A.C.T. Wu, Identification of natural frequencies and damping ratios of machine tool structures by dynamic data system approach. Janota, Simulation of the dynamic properties of an axis and tool system coupled to a machine tool frame.
Lee, A Review on Rolling Bearing Preload Technology for Machine Tool Spindles.
