2016 International Conference on Mechanics Design, Manufacturing and Automation (MDM 2016) ISBN: 978-1-60595-354-0

Analysis and Simulation of Trunnion-type Rotary Table

Zi-Xuan WANG1,a, Tian-Biao YU1,b, Ji ZHAO1,c,*, Qiang MA1,d, Shi-Xuan LIU2,e 1School of Mechanical Engineering and Automation, Northeastern University, NO. 3-11, Wenhua Road, Heping District, Shenyang, 110819, People’s Republic of China 2FAW-Volkswagen Automotive Co. Ltd., NO. 5, Anqing Road, Lvyuan District, Changchun, 130013, People’s Republic of China [email protected], [email protected], [email protected], [email protected], [email protected] *Corresponding author

Keywords: Trunnion type table, Finite element simulation, Statics analysis, Dynamics analysis, Kinematics analysis.

Abstract. The combination of trunnion type numerical control rotary table and three-axis machine tools can achieve the work of five-axis machine center. The key part of trunnion-type numerical control rotary table, trunnion, was studied by statics analysis, modal analysis and harmonic response analysis. The maximum deformation, vibration performance and other parameters, which may do harm to the accuracy, were investigated. Meanwhile, the dynamics and kinematics analyses of rotary table virtual prototype were conducted. The results of simulation and analyses provide theoretical basis and important references for the optimization design and manufacturing.

Introduction In recent years, machine tools need better properties, such as high speed, high precision, high efficiency and complex, to meet the high processing requirements [1-3]. The common machine tools fail to meet these demands. So five-axis center will lead the development trend of machine tools. Numerical control (NC) rotary table is one of the key components for five-axis machining center, which can fix in the direction of rotation and swing. Xu et al. [4] investigated the structure characteristics of two-axis rotary table and the application of torque motors on it. Gu et al. [5] built a mathematical model of NC rotary table transmission system, and provided some methods to improving the dynamic performance of table. Jiang et al. [6] investigated the modeling and simulation of virtual prototype for five-axis machine tools with rotary table. However, they didn’t take statics, dynamics and kinematics problems into account synthetically and discover the intrinsic laws. So in this work, the designed NC rotary table was modeled by Solidworks, and the statics and dynamics analyses for trunnion were conducted by ANSYS . Also, functions of rotary table virtual prototype were simulated and verified by Adams.

Model and Parameters The overall appearance and internal structure of trunnion type rotary table are shown in Fig. 1. It has two degrees of freedom: the swing of trunnion and the rotation of table. The parameters are shown in Table 1. Table1. Performance parameters of the table. Main parameters Units Values Table diameter [mm] Φ600 Maximum table load [Kg] 160 A-axis rotation angle [°] -120°~120° C-axis rotation angle [°] 0°~360° Rated torque of rotation motor [N. m] 1750 Rated torque of swing motor [N. m] 3050 A-axis maximum locking torque [N. m] 4477 C-axis maximum locking torque [N. m] 3414 The swing torque motor can drive trunnion and swing base swinging in space. The direct-drive technology of torque motor eliminates all mechanical transmission mechanism from motor to rotary table, which achieves zero transmission. The locking devices are responsible for the location of swing base and table with inputting hydraulic oil.

(a) Overall appearance (b) Internal structure Note: 1.cooling fan; 2.back cover; 3.base; 4.locking device; 5.swing torque motor rotor; 6.swing torque motor stator; 7.swing YRT bearing; 8. circular grating; 9.trunnion; 10.electric- hydraulic slip ring; 11.swing base; 12.rotary YRT bearing; 13.table; 14.rotation torque motor rotor; 15.rotation torque motor stator; 16.rotation circular grating; 17.rotation locking device; 18.cover Figure 1. Model of trunnion type numerical control rotary table.

Statics and Dynamics Analyses of Trunnion

Statics Analysis Trunnion is one of the key parts of rotary table, which combines base and swing section, so the statics and dynamics analyses on the trunnion model are very important. The loading limit of trunnion occurs in two cases. One is that when swing base stops at the limiting position (±90°), locking device provides locking force, and torque motor doesn’t output power. The maximum stress and deformation of trunnion concentrate on the contact area with locking device, at 12.32 MPa and 3.73×10-5 m respectively. The other one is that when swing base stops at limiting position and on the point of moving against the torque of swing section and workpiece, torque motor provides peak torque, and locking device is still locking. The maximum stress and deformation of trunnion are 12.22 MPa and 3.74×10-5 m respectively, and the concentration areas are similar as the first case. The deformation nephograms are shown in Fig. 2.

(a) The first case (b) The second case Figure 2. Trunnion deformation nephograms in two cases.

Modal Analysis Modality reflects the inherent attribute of mechanical structure. Modal analysis of mechanical structure includes modal shape, inherent frequency and damping ratio [7]. Modal analysis is the first step of other complex dynamics analyses, such as harmonic response analysis, spectral analysis, transient dynamic analysis, etc. The modal analysis of trunnion was conducted based on the statics analysis. Six lowest order inherent frequencies obtained by computing are 333.23 Hz, 490.61 Hz, 508.71 Hz, 534.59 Hz, 671.93 Hz and 672.8 Hz. The modal shapes of them are shown in Fig. 3.

Figure 3. The modal shapes of six lowest order.

In the first order modal shape, the axis region of trunnion vibrates under the effect of locking device. The edge of the axis region and plate region are more sensitive. In the second order modal shape, the axis region pulls back and forth from the plate region, and the center of plate region is more likely to be damaged. In the third and forth order modal shapes, the edge of plate region twists alternately, which is weaker than other areas. In the fifth and sixth order modal shapes, the axis region of trunnion swings up and down, and the top edge and lower edge of axis region may be damaged. For trunnion, the vibration source is rotation torque motor. The revolving speed of motor can increase with the drop of motor torque. The revolving speed range is 110 r/min~2000 r/min, so the vibration frequency range is 2 Hz~35 Hz, which is lower than the inherent frequency of each order. So it is unlikely to cause vibration for the operation of motor. Harmonic Response Analysis Harmonic response analysis can show the influence of exciting force on machining accuracy more clearly. Rotation torque motor could produce exciting force, which was like harmonic vibration generated by rotary unbalance mass. An exciting force was applied to trunnion along Y direction, which was estimated to 500 N and its phase angle was 0°. According to the results of modal analysis, the frequency range was set from 0 to 800 Hz including 50 substeps, i. e. computing response every 16 Hz. The frequency response curves in X direction, Y direction and Z direction obtained by computing are shown in Fig. 4 to Fig. 6.

Figure 4. The frequency response Figure 5. The frequency response of X direction. of X direction.

Figure 6. The frequency response Figure 7. Total deformation of 330 Hz. of Y direction. The simulation results show that the maximum amplitudes in X, Y and Z directions are 6.6×10-6 m, 5.1×10-10 m and 1.4×10-6 m, respectively. The maximum value occurs at 330 Hz in X direction, under which the total deformation was shown in Fig. 7. The center region of trunnion plate has the maximum deformation, so dynamic load and revolving speed should be adjusted to avoid resonance during machining.

Kinematics and Dynamics Analyses of Virtual Prototype The kinematics and dynamics analyses of trunnion type rotary table virtual prototype were conducted by Adams, which could verify the feasibility of motion. The swing of trunnion and the rotation of table can cause the coupling of revolving speed, torque, etc. Ten fixed Joints, two revolute pairs and two cylindrical pairs were applied to the model in order to achieve the motion of rotary table in two degrees of freedom. Two drives were applied to the motion of swing base and the rotation of table respectively. Eq. 1 and Eq. 2 show the velocity functions. Three loads were applied to the Adams model, including gravity, torque on workpiece and torque on swing base. They could simulate torques on table generated by cutters.  Time  cos((  )  ) . (1) 222  Time  cos(( ) ) 322. (2) Kinematics Simulation Analysis The angular accelerations of swing base and table are shown in Fig. 8 and Fig. 9. It can be seen that the curves are smooth, so the movement process of rotary table is stable. It meets the requirement of machining.

Figure 8. The angular acceleration Figure 9. The angular acceleration of table. of swing base.

Dynamics Simulation Analysis Fig. 10 shows the output torque of swing motor. The output torque peak is 2103 Nm only when swing base moves, and the value is 2103 Nm as well when the table revolves around two axes. In addition, they have the same trend, so coupled motion almost has no influence on swing motor’s output torque.

Figure 10. Output torque of swing motor. Figure 11. Output torque of rotation motor.

Fig. 11 shows the output torque of rotation motor. The output torque peaks of both only rotation and two axes revolving are 1425 Nm, but the trends of curves have a big difference, so the output torque of rotation motor is more sensitive for coupled motion.

Summary This work conducts statics and dynamics analyses on trunnion, and kinematics and dynamics analyses on the virtual prototype of rotary table. The conclusions are as follows: (1) Statics analysis shows the maximal deformation areas and values of trunnion. The modal shapes of trunnion and its inherent frequency are obtained from modal analysis. Harmonic response analysis gained the maximal deformation caused by outside vibration. These provide the theory basis and important reference for further study. (2) The angular acceleration curves of table and swing base from kinematics analysis verify that virtual prototype of rotary table can work stably. The output torque curves of the two motors from dynamics analysis verify that the performance of torque motor meet the requirement during the coupling movement of swing base and table possess.

Acknowledgement This research was financially supported by the Key Science and Technology Program of Liaoning Province, China (No. 2012220031).

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