Dynamic and Static Characteristics Analysis and Research for Key Components of the NC Lathe CK61125

Transcription

1 2017 Asia-Pacific Engineering and Technology Conference (APETC 2017) ISBN: Dynamic and Static Characteristics Analysis and Research for Key Components of the NC Lathe CK61125 Cheng Yang, Hongping Yang, Rongzhen Zhao and Weiqian Li ABSTRACT Based on the principle of static and modal analysis, carry on the static and dynamic characteristics analysis to the spindle of CK61125 machine tool using the finite element method (FEM). Then, got the static stress and deformation cloud, solve the first six order natural frequency and mode shape of the structure, provides a reference of engineering design and application for the machine tool spindle. INTRODUCTION The static and dynamic performance of spindle is the main factor that affects the machining accuracy of CNC. With the improvement of the speed and precision of CNC, the static and dynamic characteristics of the spindle is put forward higher design and processing requirements. Due to increased demand of aviation, aerospace, energy, and defense complex precision parts, prompting modern CNC are geared to the needs of rapid development direction of high speed and high precision. Dynamic and static characteristics of spindle is not only a main obstruction for machining precision increase, but also a main source of machining error for precision and ultraprecision machine tool. So extensive theoretical and experiments research has been conducted by many researchers. Charki[1] presents a methodology for the study of a hemispherical air spindle that takes into account not only a static and dynamic analysis but also a reliability evaluation, in addition, the reliability evaluation of a spindle supported by a fluid bearing is made using the Stochastic Response Surface Method. Matti[2] proposed a method for analysing lateral machine tool spindle vibrations based on a FEM and a contact-less dynamic spindle testing equipment, as well as study the effect of the gyroscopic moment and the speed dependent Yang Cheng 1,a, Yang Hong Ping 1,a, Zhao Rong Zhen 2,b, Li Wei Qian 3,c 1 School of Electromechanics and Automobile Engineering, Tianshui Normal University, Tianshui, China School of Mechanic and Electronic Engineering, Lanzhou University of Technology, Lanzhou, China Tianshui Spark Machine Tool Co.Ltd., Tianshui, China ) a kevinyang315@foxmail.com 1, b bobo_2002cn@163.com, c @qq.com 1 *Corresponding author: kevinyang315@foxmail.com 897

2 bearing stiffness on the system dynamics. Dong Hyeon Kim[3] presents the analysis of the static and dynamic characteristics and optimization design of a 40,000-rpm high-speed spindle, and used the response surface method to optimize the objective function and design factors. CAO[4] proposed a finite model updating technique based on frequency response function to identify the joint dynamics between the spindle and machine tool, the model can reasonably reflect the effects of the machine tool structure on the spindle and predict dynamic properties of the spindle system after mounting. Hung Jui-Pui[5] identified how the changing of drawbar force affects the dynamic characteristics of a spindle tool, provide a reference for setting the tool holder-spindle dynamic characteristics. Zhang[6] calculated and analyzed the dynamic stiffness of these types of spindles by finite element method, the spindle structure with optimization scheme is decided by comparing the stiffness and natural frequency. Chen[7] employed the finite element method to study the joint parts affecting HSK spindle system tool point frequency response, and proposed some anti-vibration solutions. This paper taking Tianshui Spark Machine Tool Co., Ltd R&D CK61125 type CNC lathe spindle as the research object, to analyze the spindle static and dynamic characteristics with the help of finite element method, then provide theory basis for optimal design of the CK61125 type CNC lathe spindle. STATIC AND DYNAMIC CHARACTERISTICS ANALYSIS MODEL Theoretical Basis Statics is calculated under fixed loading effect of the spindle structure, which not considering the influence of the inertia and damping, and do not change over time. Statics equations as follows: K x F where [K] is stiffness matrix, {x} is displacement vector, [F] is static load. Modal analysis is the linear time-invariant system vibration differential equations of physical coordinate change for modal coordinates, the equations of decoupling, as a set of modal coordinates and the modal parameters which is used to describe the independent equation, may thus be calculated the modal parameters of the system. Matrix transformation coordinate is modal matrix, each column is a modal vibration mode. Kinetic equation as follows: M x K x 0 (2) Free vibration of spindle is harmonic vibration, namely the displacement is a sine function x xsin t (3) Eq. 3 into Eq. 2 K 2 M x 0 (4) (1) 898

3 The eigenvalue of Eq. 4 is ω i 2, ω i is the circular frequency of vibration, natural frequency of vibration f=ω i /2π, characteristic value of the corresponding eigenvectors {x} i is natural frequency of vibration f=ω i /2π of the corresponding vibration mode. In the process of cutting, the chip will produce elastic and plastic deformation, working condition is very complicated. Cutting moment of torque, axial force, cutting power are calculated by empirical formula: Cutting moment of torque M C d f K xm ym 3 M 0 M 10 (5) Axial force xf yf F CFd0 f KF (6) Cutting power n Pm M M (7) 30 In which C M, C F, x M, y M, x F, y F are coefficients to be determined from different cutting conditions and cutting materials; d 0 is bit diameter, mm; f is the feed per round, mm/r;k M, K F are cutting force correction factor. Figure 1. Spindle structure. Finite Element Model This paper taking Tianshui Spark Machine Tool Co., Ltd R&D CK61125 type CNC lathe spindle as the research object, the spindle of machine tool as shown in Fig. 1. The spindle is driven by a electromotor through synchronous belt directly. The design speed of spindle in the range of 200~600r/min, it also have stepless speed control function. The spindle is installed in the spindle box by four bearings, front of it are supported by a double row angular contact ball bearing and a conical dual-row roller bearing NN3032 which carry radial force and axial force, the backend of it is supported by a single-row cylindrical roller bearing NU1026 which carries radial force. To ensure the spindle have enough rigidity and rotation precision, install a conical dual-row roller bearing NN3028 which carries radial force in the middle of it. Build the 3D model of spindle by Solidworks, import the model into Workbench for mesh generation (Fig. 2). 899

4 Figure 2. The grid of spindle. STATIC AND DYNAMIC CHARACTERISTICS ANALYSIS OF SPINDLE The Grid Independence Test The grid independence test (Fig. 3) is essential in order to ensure the accuracy of the simulation results. When the spindle constraint remains the same, and grid quantity were 29938, 40626, 51557, 62377, the first-order modal natural frequency were Hz, Hz, Hz, Hz. The difference is about for the last two first-order modal natural frequency. So select the third grid to calculate in consideration of computational expense and precision. The first order modal natural frequency[hz] Grid quantity Figure 3. The grid independence test. Statics Analysis Statics analysis mainly includes the strength and stiffness computation. The material of spindle is No.45 steel which thermal refining. The material property as is shown in Table 1. TABLE 1. THE MATERIAL PROPERTY OF SPINDLE. Material Young modulus [GPa] Poisson's ratio Density [kg m -3 ] Yield strength [MPa] No.45 steel There are two types of boundary conditions of the spindle according to the actual working condition: constraint and load are presented below. (1) Constraint: enforce fixed support on fixed end of the spindle, constraint radial movement in the place of single-row cylindrical roller bearing NU1026, only keep rotation around the axis of spindle in the place of conical dual-row roller bearing NN3028 and conical dual-row roller bearing NN3032, constraint radial and axial movement in the place of double row angular contact ball bearing

5 Figure 4. Cutting force and turning moment. (2) Load: the torque of synchronous pulley M d =8000N m, to exert the torque upon working face of the keyway, meanwhile also have a force (F d =60000N) which included angle of 70 degrees with the axis of spindle, it is simplified to a concentrated force in the center of the fitting surface. Cutting the volume of cutting force and turning moment are simplified and then load it to the joint of spindle and three jaw chuck. Obtain the primary cutting forces F c =45000N, back force F p =12000N, feed force F f =25000N according empirical formula and actual working condition, cutting force and turning moment as shown in Fig. 4, point of force application in the center of joint surface of spindle and three jaw chuck, M c =22500N m, M p =6000N m, M f =8000N m. Statics analysis of the spindle as shown in Fig. 5. The largest equivalent stress(268.83mpa) occurred in the large end face of spindle. The yield strength of No.45 steel is 355MPa, so the spindle satisfies the requirement of strength. The maximum deformation (167.12μm) occurred in the tail of spindle; the deformation is too large. Figure 5. The result of statics analysis. Modal Analysis Little impact on lateral vibration damping because of enough axial rigidity. So only considering the radial support stiffness when finite element model of spindle is established. Simulating the bearing to use four spring along the circumferential uniformly. Spring installation as shown in Fig

6 Spindle Spring Bearing outer ring Bearing inner ring Natural frequencies/hz Mode order Figure 6. Spring installation. Figure 7. The preceding six steps natural. Using Spring to simulate bearing in Workbench, and utilizing Cylindrical Support to provide axis constraints in the place of conical dual-row roller bearing NN3032. The constrained modal analysis is performed, then obtain the preceding six steps natural frequencies under the constrained modal analysis as shown in Fig. 7. The preceding six steps mode shape of the structure as shown in Fig. 8. The first and third mode shape are radial extension on account of chuck located effect. Radial extension has great influence on bearing pre-tightening and fit. The second, third, fifth, sixth mode shape are flexural vibration along the two orthogonal radial. The second, third and the fifth, sixth order frequency are similar, so the frequency are repeated root which mutually independent and orthogonal. The actual working conditions of the spindle will not reach the first modal frequency because of the spindle natural frequency is higher. Figure 8. The preceding six steps mode shape of the structure frequencies. SUMMARY This paper taking Tianshui Spark Machine Tool Co., Ltd R&d CK61125 type CNC lathe spindle as the research object, to analyze the spindle static and dynamic characteristics with the help of finite element method, the main results are as follows: 902

7 (1) Obtain the largest equivalent stress (268.83MPa) and the maximum deformation(167.12μm) by static analysis. (2) Obtain the first six order natural frequency and mode shape of the structure by modal analysis, provides a reference of engineering design and application for the machine tool spindle. ACKNOWLEDGEMENTS This project is supported by National Natural Science Foundation of China (Grant No ), National Natural Science Foundation of Gansu Province (Grant No.1506RJZE113), The Department of Education of Gansu Province (Grant No. 2015A-134) and Postdoctoral Foundation of Gansu Province. REFERENCES [1] Abdérafi Charki, David Bigaud, Fabrice Guérin. "Behavior analysis of machines and system air hemispherical spindles using finite element modeling, " Industrial Lubrication and Tribology. Papers 65(4), (2013). [2] Matti Rantatalo, Jan-Olov Aidanpää, Bo Göransson, et al." Milling machine spindle analysis using FEM and non-contact spindle excitation and response measurement, International Journal of Machine Tools and Manufacture. Papers 47(7-8), (2007). [3] Dong Hyeon Kim, Choon Man Lee, Hyun Jin Choi. "Static and Dynamic Analysis and Optimization Design of rpm HighSpeed Spindle for Machine Tools, Transactions of the Korean Society of Mechanical Engineers. Papers 37(1), (2013). [4] Cao Hongrui, He Zhengjia. "Dynamic Modeling and Model Updating of Coupled Systems between Machine Tool and Its Spindle, Journal of Mechanical Engineering. Papers 48(3), 88-94(2012). [5] Jui Pui Hung, Lai Yu Sheng, Luo Tzuo Liang, et al. "Effect of Drawbar Force on the Dynamic Characteristics of a Spindle-Tool Holder System, International Scholarly and Scientific Research and Innovation. Papers 8(5), (2014). [6] Zhang XueLing, Man Jia, Chai Shufeng, et al. Improving Measures of Dynamical Stiffness for Grinding Machine Spindle Based on Modal Analysis, Modular Machine Tool and Automatic Manufacturing Technique. Papers (11), 95-98(2013). [7] Chen Jian, Tian Liang, Shang Hongmo, et al. Effects of Joint Part on HSK Spindle Dynamic Performance, China Mechanical Engineering, 26(9), (2015). 903