Vibration Characteristic Analysis of Spot-Welding Robot Based on ADAMS/Vibration

Transcription

1 2011 International Conference on Electronic & Mechanical Engineering and Information Technology Vibration Characteristic Analysis of Spot-Welding Robot Based on ADAMS/Vibration 12 Haitao Luo, *Yuwang Liu, ^ongguang Wang/Weijia Zhou 1. State Key Laboratory of Robotics, Shenyang Institute of Automation, CAS, Shenyang , P.R. China 2.Graduate School of the Chinese Academy of Sciences, Beijing , P.R. China {luohaitao, liuyuwang, hgwang, Abstract Aiming to improving the performance of high-power, heavy-load, high-speed and high-precision robots, this paper proposes a simulation method for analysis based on virtual prototyping technology. In ADAMS/Vibration, we first establish the rigid-flexible coupling system of a spotwelding robot, then solve the natural frequencies and modal shapes of the system, and finally calculate the frequency response under certain forced. In order to build system, the principle and simulation process of analysis are given by inputting sine sweep signal on end effector. With the help of the getting frequency response, we can avoid the failure of damage due to the resonance of the system and create the conditions for the optimal design and reliability research of a spot-welding robot. Keywords-Vibration analysis; ADAMS; Spot-welding robot; Rigid-flexible coupling; I. INTRODUCTION Spot-welding robot, combination of robotics technology and welding technique, is high-power, heavy-load, highspeed, high-precision, flexible-operation, large-workspace and so on. It is widely used in vehicles, ships and other engineering filed at the present stage. And the high performance is more and more needed. However, the quality of characteristic is an important factor to improve its performance [1]. Therefore, how to limit the effect so as to improve its anti- performance has become a key factor to the design. In the process of spot-welding, there are lots of sources on the robot, which caused by the low installation accuracy, transmission gap and uninterrupted impact loads and so on. And the s are common nonlinear and strong coupling. If the s pass to the machine, they will seriously affect the robot's dynamic characteristic, the working life and performance of the robot. Especially when the frequency of exciting force is equal or close to the natural frequency of the robot, and then resonance will happen [2-5], Which can seriously affect the quality of transmission system and result in key part's fatigue failure. Therefore, analysis has become an important and non-ignored indicator to evaluate the characteristic of spot-welding robot. In recent years, scholars from different country have done many valuable researches on the characteristic of industry robot. Jinwook and park put forward to the first order stiffness and analysis method based on geometric method and institutions of the stiffness and deformation [6]. Han made the test modal analysis of the robot by using hammer multi-point excitation method [7]. Kris.K calculated the characteristics of little degree of freedom robot using linear method [8]. Y Sakural analyzed the of cylinder block under firing conditions [9]. Zhang studied the dynamics characteristic of high speed machine tool [10]. These theory analyses above are mainly based on linear method, and ignore the impact of flexible body. However, the cost of experiment method is over high. So, we combine the advantages of these methods and give a more intuitive and accurate method. This paper mainly considers the impact and caused by the exciting force on the end effector of spotwelding robot. In ADAMS/Vibration, we first establish the rigid-flexible coupling system of a spot-welding robot, then solve the natural frequencies and modal shapes of the system, and finally calculate the frequency response under certain forced. In order to calculate the response of the end measuring point in the frequency domain, the external exciting force is used as an impact load. Through simulation analysis, we get the natural frequency and mode shapes which are negative to the system, and obtain frequency response curve of the robot. This provides scientific proof for the restraint of and the improvement of the robot's performance. II. VIBRATION ANALYSIS PRINCIPLE OF RIGID-FLEXIBLE COUPLING SYSTEM For simple system, the inherent characteristic of the system mainly refers to the natural frequency. For complex systems, the inherent characteristics included the different order natural frequencies, mode shapes, damping and so on [11]. The calculation and determination on inherent characteristics of the system, which can avoid system resonance at work on the one hand, on the other hand, it can also lay the foundation for further dynamic analysis. A. Vibration theory basis Differential equation of motion of single degree of freedom, second-order and damped linear mass-spring system is as follows: where, m mass; c damping coefficient; mx + ex + kx = F 0 sin cot, (1) 978-l /ll/$ IEEE August, 2011

2 k spring stiffness; x displacement; F 0 amplitude of harmonic excitation force; Solution of equation under harmonic excitation: FJk Va-A 2 ) 2 +(2a) 2 2 l q> = arctan l-a 2 A = co I co n is the frequency ratio, C, = c I c n is the damping ratio. Differential equations for damped system expressed by complex number are as follows: (2) mx + ex + kx = F a e lc (3) Using the relationship of exponential and trigonometric functions, the frequency response function can be obtained as follows: H(a)) = Xe~ FJk 1 l-a 2 +i2cjl The most practical mechanical systems and mechanical structure are continuous and non-uniform elastic body. To be able to analyze, they are always equivalent to finite degree of freedom system under meeting accuracy requirements. Equations of motion of discrete multi-freedom system are: (4) [m]{x} + [c]{i} + [k]{x} = {F 0 (t)} 9 (5) here, [m], [k], [c] is respectively the system mass matrix, damping matrix and stiffness matrix; {x}, {^0(0} respectively displacement response and excitation of the system. So system frequency response function matrix is: [H(w)] = H U ((D) H 12 (CD) H^ico) H 2l (co) H 22 {coi) H 2j (co) H a (co) H l2 (co) H U {G>) here, FL^co) represents frequency response function between the excitation point / and j. When i = j, it represents the origin frequency response function; when i ^ j, it represents cross-point frequency response function. B. Representation of flexible-body In ADAMS, flexible body is generated by using a combination method of finite element analysis and modal analysis. The discretization result of the finite element is not directly imported to ADAMS, but firstly generated a modal neutral file (.mnf file) by modal analysis in ANSYS. The file (6) ls includes lots of information about mass, center of mass, inertia, frequency and mode shape of flexible-body [12-13]. By calculating the deformation in dynamic simulation process and the forces on connecting nodes using modal superposition method, we can introduce flexible-body to dynamics model, and improve the simulation accuracy of the mechanical system. In ADAMS/Vibration module, flexible body is added constraint, exerted force and measured the dynamic characteristics by using the coordinate point [14]. Shown in Fig.l, the position vector of flexible body at any node can be expressed as: = X+B A { S p+ U p)> (7) where, G BA transformation matrix of coordinate system B relative to coordinate system G ; s p position of point P under coordinate system B when body is non-deformed; u direction vector of point P' on deformed body with respect to point P on nondeformed body; x position vector of object coordinate system B under base coordinate system; Among them, u =( & p q, O represents modal matrix sub-block corresponding to the node translational degrees of freedom. The Velocity of node P is: = [J-U{S P +U P )B G BA%]4: (8) where, tilde indicates the position vector is non-symmetrical matrix; matrix B is defined as first-order derivative of Eulerian angle relative to time or angular velocity transition matrix. So the kinetic and potential energy can be expressed T = \-\pv T vdv = h T M(Z)%. (9) v = v g (4)+-4 T K4. (io) Establish the differential equation of motion of flexible body using Lagrange multipliers method: M +M%- 1 dm S + KZ+f+D + here, K modal stiffness matrix; D modal damping matrix; / generalized gravity; Q generalized external force; A = fi(ll) 692

3 X Lagrange multiplier of constraint equation; and cylinder rod and corresponding parameters must be specified. The spring stiffness is \tfnlm, damping is 10* N/(m / s 2 ) and preload value is N. Figure 1. Moving schematic of flexible-body on node P In this study, the response value is obtained by using corresponding marker's measurement on output channels. III. VIBRATION MODEL OF SPOT-WELDING ROBOT Based on the theory above, we establish the structural model in ADAMS, and create the system model in ADAMS/Vibration. With the combination of the two models, we can smoothly run the simulation analysis. A. Structural model The structural model of spot welding-robot is as shown in Fig.2. B. System Model Vibration test system mainly consists of excitation source, model, input channels, and output channels, as shown in Fig.3. External excitation is regarded as the signal source of test, the input channels are used to define the position and direction of input and output channels are used to measure the response [15]. Because the deformation of some components is not too large under external force, but little effect on the welding precision, so these parts of the robot can be considered as rigid bodies. In addition, the flexible body of model has a great influence to simulation speed, so in order to improve simulation process, only the more important components can we transformed to flexible body, while other elements remain rigid body. From the structure of spot-welding robot, we can see upper arm and forearm are its major parts, which have a great influence to the welding accuracy of end effector. So we mainly considered part 5 and part 6 as flexible body to form a rigid-flexible coupling system of entire model. Figure 3. Vibration system model 1-base; 2-waist; 3-cylinder block; 4-cylinder rod; 5-upper arm flexible body; 6-forearm flexible body; 7-wrist; 8-end effector Figure 2. Rigid-flexible coupling model of Spot-welding robot In the finite element analysis software ANSYS, we make upper arm and forearm of spot welding-robot become flexible-body, and then in ADAMS, read the modal neutral file generated in ANSYS, respectively replace the rigid upper arm and forearm of multi-rigid-body dynamics model with flexible body, so the rigid-flexible coupling dynamics model of spot-welding robot is generated Where, adding a fixed pair between the base and earth and six revolute pairs on rotational joints. In addition, a revolute pair is added between balance cylinder rod and upper arm and a translational pair is added between cylinder block and cylinder rod. In order to prevent the generation of redundant constraints, an inline pair need to be built between cylinder block and lug. To simulate the role of balance cylinder, a spring should be added between cylinder block In order to effectively simulate the impact caused by the welding load, we selected the sine sweep signal as the external excitation. As a result of large excitation power and high signal-to-noise ratio of sine sweep, we can obtain more accurate measurements. Sine sweep signal have the steady amplitude and increasing frequency, when the sine signal acted on the model, we only provide the initial amplitude and phase angle. The expression of sine sweep signal in time domain is: here, f(t) f(t) = F[cos(o)t + 0) + js'm(a)t + 6)], (12) is the time domain form of forced signal on frequency domain equation; F is the amplitude of excitation force; co is the circular frequency; 6 is the phase angle. IV. DYNAMICS SIMULATION ANALYSIS OF SPOT- WELDING ROBOT Free analysis mainly calculates the natural frequency and solves the each order's mode shape of system. ADAMS/Vibration transformed the simulation model into a 693

4 linear matrix by using Laplace transform in a state point, and calculated the natural frequency and damping ratio of system through eigenvalues. A. Free The real and imaginary coordinates of eigenvalues are as shown in Fig.4. Table I shows the top 10 natural frequencies, damping ratios and corresponding mode shapes description of spot-welding robot system. Figure 4. System modes given by using displacement response value of X, Y, Z and spatial synthesis direction, thus the graph of frequency response can be created. When the robot system is excited by external fore, frequency response curve of 0-200Hz can be obtained in post-processing module of ADAMS. The response curve of X direction is as shown in Fig.5 (a). The frequency response of end measuring point in X direction is 25Hz and the maximum displacement response amplitude is 0.017mm. The response curve of Y direction is as shown in Fig.5 (b). The frequency response of end measuring point in Y direction is 37Hz and the maximum displacement response amplitude is 0.085mm. The response curve of Z direction is as shown in Fig.5 (c). The frequency response of end measuring point in Z direction is 25Hz and the maximum displacement response amplitude is 0.115mm. The response curve of spatial synthesis direction is as shown in Fig.6 (d). The frequency response of end measuring point in this direction is also 25Hz and the maximum displacement response amplitude is 0.088mm. TABLE I. NATURAL FREQUENCY, DAMPING RATIO AND VIBRATION MODE OF SYSTEM Order frequency (Hz) 1.59E E E E E E E+002 Damping ratio 1.72E E E E-002 Mode shape side-to-side up and down face-to-back variation torsional As can be seen from the table above, the top 6 shape modes only show slight, and the began to intensify from the 7th-order. In practical work of spotwelding robot, modal tests should be completed combined with damping sheet attached to suppress the excitation of corresponding order's mode and ensure the welding accuracy of end effector. B. Forced Applied the excited force on end position of the robot and analyzed with the analysis method of sine sweep, the value of amplitude is 2000 N, the direction is vertical, and the initial phase is zero. Response of end measuring point is 694

5 Figure 5. Frequency response of marker point in every direction From the graphs above, we can see the maximum frequency response happened on the 25Hz in the Z direction, when the robot subjected to V excitation force. High frequency components have little effect on the system, it can be ignored. Through the analysis of frequency response, we can reasonably improve anti design of the robot by changing the relevant parameters of virtual prototype, such as center of mass, spring stiffness and damping etc. V. CONCLUSION This paper deals with simulation analysis of characteristics in ADAMS, a practical and effective method was put forward to improve the dynamic performance of spot-welding robot. In order to create rigid-flexible coupling system of entire model, we considered upper arm 5 and forearm 6 as flexible body in ADAMS/Flex module. Then in ADAMS/Vibration module, we obtained the natural frequencies and mode shapes under free, and got the displacement response of end measuring point under the external excitation force. Simulation analysis has drawn the following conclusions: 1) All eigenvalues have the negative real-parts under free analysis, which indicate that the system is stable. From the beginning of the 7th-order frequency 25.8Hz, the system appeared obvious. 2) Within the range of 0-200Hz, when welding pliers subjected to an excitation force with the frequency 25Hz and amplitude 2000 N, the displacement response of end measuring point is maximal in vertical direction, and the maximum displacement value is mm. 3) High frequency components (61 Hz above) have little effect on the system, which can be ignored. [I] Yimin Song, Yueqing Yu, Ce Zhang etc, "Flexible-robot dynamic analysis and Control review,". Journal of machine design. J. Vol. 20(4), pp. 1-5,2003. [2] Lijuan Zhao, Chengyun Wang, "Modal Parameter Identification and Vibration Analysis of complex rigid-flexible coulping system,". Manufacturing Automation. J. Vol. 31(4), pp , [3] Xiangrong Xie, Xiang Yu, Shijian Zhu. "Anti- performance analysis of flexible foundation system based on ADAMS,". Journal of Vibration and shock. J. Vol. 29(3), pp , [4] Chunxia Zhu, Lida Zhu, Yongxian Liu, "Simulation of Vibration Characteristic and Optimization for Parallel Robot Based on ADAMS,". Journal of System Simulation. J. Vol. 20(14), pp , [5] Lijuan Zhao, Tao Xu, Jie Liu, "Modeling and Analysis on Vertical Vibration of Mill Using ADAMS/Vibration,". Journal of System Simulation. J. Vol. 18(6), pp , [6] Jinwook Kim, Park, F C Mumsang Kim, "Geometric design tools for stiffness and analysis of robotic mechanisms," International Conference on Robotics & Automation. Piscataway, NJ, USA: Institute of Electrical and Electronics Engineers Inc. C. pp ,2000. [7] Qingkai Han, Tao Yu, Wu Du, "Modal experiment and dynamics analysis of six-bar paralle robot,". Journal of Vibration Engineering. J. Vol. 16(3), pp ,2003. [8] Kris K, Imme E, William, "Locally linearized dynamic analysis of parallelmanipulators and application of input shaping to reduce s,". Journal of Mechanical Design (S ). J. Vol. 126(1), pp ,2004. [9] Y Sakural, H Hoshino, and Y Goino, "Simulation technique of cylinder block under firing conditions,". The ninth international pacific conference on automotive engineering, Indonesia. pp , [10] Yaoman Zhang, Xudong Wang, Guangqi Cai, and Libo Teng, "FEA and dynamics characteristic experiment of high speed machine tool,". Modular Machine Tool & Automatic Manufacturing Technique. J. Vol. 1(12), pp ,2004. [II] Yinmin Zhang, Mechanical. M. Beijing: Tsinghua University Press, [12] Junwen Xing, MSC.ADAMS/Flex and AutoFlex training courses. M. Beijing: Science Press, [13] MSC Software Corporation. "ADAMS/View," Version2005. SantaAna: Mechanical Dynamics. K. Inc [14] Youfang Lu, Flexible multi-body system dynamics. M. Beijing: Higher Education Press, [15] MSC.Software Corporation, MSC.ADAMS/Vibration training courses (ADM720), ACKNOWLEDGMENT This work was supported by the National Science and Technology Major Project on High Grade CNC Machine Tool and Fundamental Manufacturing Equipment under Grant 2009ZX REFERENCES 695