Dynamic Balance Design of the Rotating Arc Sensor Based on PSO Algorithm

Transcription

1 016 International Conference on Advanced Manufacture Technology and Industrial Application (AMTIA 016) ISBN: Dynamic Balance Design of the Rotating Arc Sensor Based on PSO Algorithm Ji-zhong LIU 1, Wen-hu WU 1, Shun-feng ZHU 1, Jing HUA,* and Jian-xiong YE 3 1 Robot and welding automation key laboratory, Nanchang University, Nanchang , China School of Software, Jiangxi Agricultural University, Nanchang , China 3 School of M & E Engineering, Nanchang Institute of Technology, Nanchang , China *Corresponding author Keywords: PSO, Rotating arc sensor, PROE, Optimization design. Abstract. Dynamic balancing is a key issue for rotating arc sensor (RAS). It causes vibration during welding, and has an influence on reliable welding signal collection. It is a very significant thing to find a quick design methodology for RAS dynamic balancing structure, especially in restricted space. With the help of PROE and ADAMS virtual prototype technology, and the dynamic balancing analysis of the counterbalance, the unbalanced inertial force and the balance-weight-plane can be determined. Based on PSO (Particle Swarm Optimization) algorithm and the range of parameters according to RAS space dimension, the counterbalance dynamic balancing structure are achieved in which three parameters of the counterbalance are considered. It shows the optimized RAS structure has a lower vibration. The paper provides a novel dynamic balancing design methodology for RAS. Introduction Rotating arc sensor (RAS) is a key device in automatic welding. It combines welding procedure with welding signal collection and welding control perfectly. However, rotating arc sensor is a kind of conical pendulum which leads to the center of rotating parts deviation. The centrifugal force and vibration will occur when rotating arc sensor is working, which will influence the reliable welding signal collection and the final welding quality. In earlier design, the balancing structure in RAS was neglected [1,]. A lot of filtering methods were used [3-5] in order to decrease the noise. But it is a passive method for accurate welding signal collection. Actually, the dynamic balancing structure design of RAS is one of the most important measures for decreasing the vibration noise. Firstly, the trial method was used in RAS balancing structure design by changing the counterbalance thickness in the laboratory [6]. Later, based on spring-damper vibration model and ADAMS simulation, the RAS dynamic structure was optimized by changing the two parameters [7] or the three parameters [8] of the counterbalance. However, it is an ineffective process for the trial method. The optimization design based on ADAMS is also complicated. Based on PSO evolution algorithm and RAS dynamic balancing analysis, a novel RAS dynamic balancing design method is proposed. Structure of Rotating Arc Sensor and Dynamic Balancing Analysis Structure of Rotating Arc Sensor The structure of the rotating arc sensor is shown in figure 1. It is a kind of conical pendulum. Motor, self-aligning ball bearing 1 and two deep groove ball bearings are fixed on the shell. Conducting rod passes through the hollow shaft and connects to the shell by the self-aligning ball bearing 1 which is installed on its upper part. The self-aligning ball bearing is installed on its lower part, and it is fixed in the eccentric mechanism. As the eccentric mechanism and the hollow shaft are fixed together, the conductive rod will do the conical motion when the motor drives the hollow shaft to rotate. It will produce the unbalanced centrifugal force and cause the vibration. There are many components in the rotating part, and the installation space is limited for its compact size. Therefore structural parameters

2 Optimization function value optimization based counterbalance design is needed for the space confined dynamic balancing problem. Figure 1. Structure of rotating arc sensor. Figure. Force analysis and balance calculation. Analysis of Dynamic Balancing Because the vibration of the rotating arc sensor is caused mainly by the unbalance of the rotating part, it is necessary to find the unbalanced centrifugal force and its location. As show in figure 1, the centrifugal force generated by the rotating parts is delivered by the deep groove ball bearings which are matched with the hollow shaft. Suppose that the load of the deep groove ball bearing 1 caused by the rotary unbalancing parts is -F 1, and the load of the deep groove ball bearing is -F, we can get the force values based on the RAS PROE model and ADAMS simulation. According to the law of action and reaction, the forces that the deep groove ball bearing 1 and the deep groove ball bearings exert on the rotate arc sensor are equal in value and opposite in direction. So they are F 1 and F respectively as shown in figure. We translate the force F 1 and F to plane X 1 O 1 Z 1, which parallels to the plane XOZ, and let F 1 AO 1 =F BO 1. (1) Since F 1 and F are opposite in direction, the couple M 1 and M generated by F 1 and F translation are cancelled out (because they are equal in value and opposite in direction.) according to theoretical mechanics. That is: M 1 = -M. () If we design a counterweight at the extension line of the resultant force of F 1 and F in the plane X 1 O 1 Z 1 (that is F 0 as shown in figure 4.) with the value of F 1 + F, the RAS is dynamic balanced. Structure of Counterbalance Figure 3. Structure of counterbalance Generation Figure 4. Average convergence curves. The counterbalance is designed as sector- annular structure as shown in figure 3 because of the cylindrical structure of the sliding sleeve. B stands for the width of the counterbalance (mm), R stands for the outer radius of the counterbalance (mm), stands for the central angle ( ), stands for the rotation angle to the reference plane ( ). H stands for the distance from the width center plane of the

3 counterweight to the bottom of sliding sleeve (mm). They have their limit value ranges because of the structure size of the rotating arc welding sensor. If we choose the intersecting line of the arc symmetry-center-plane and the width-center- plane of the counterweight as the extension line of the resultant force of F 1 and F in the plane X 1 O 1 Z 1, the parameter =0, and at the same time the parameter H is a constant according to theoretical mechanics and force translation theory. Two parameter variables can be reduced in optimization. The optimized variables of counterbalance in RAS dynamic balancing are 3 structure parameters of B, R and. Optimization Model of Counterbalance Suppose the density of the counterbalance is ρ (kg/m 3 ) and the outer radius of the slider sleeve is r (mm, it equals to the inner radius of counterbalance), we can get the mass of the counterbalance (m) and the center of mass (O ) [8]. OO where 4R S1 sin S S S S 1 R, S r r sin (3) m ( S1 S ) B (4) O is the center of slider sleeve circle; r is known. The centrifugal force of counterbalance is: F m RF m( n / 60) R F (5) is the angular velocity of RAS and is known; R is the turning radius of the center of F counterbalance mass (O ) in the plane X 1 O 1 Z 1. R F ( OO - e) (6) e is the eccentric distance in the plane X 1 O 1 Z 1 (the turning radius of RAS in the plane X 1 O 1 Z 1 ) and e is known. The optimization objective is to minimize F+ F 0. That is to minimize F - F 0. F, F 0 are force vectors. And there are only B, R and unknown structural parameter variables. PSO Algorithm Based Optimization Design PSO Algorithm Particle Swarm Optimization (PSO) algorithm is an evolution algorithm for nonlinear optimization. The swarm is typically modeled by particles with a position and a velocity, where each particle represents a candidate solution to the optimization problem. During the optimization procedure, particles communicate good positions to each other and adjust positions according to their history and the experience of neighboring particles. Due to the nature of individual memories and information sharing, particles can reach the best solution quickly [9]. The general Particle Swarm Optimization algorithm is as equation (7) and equation (8) [10] : v id ( id 1 1 id id gd id n n 1) v ( n) c r ( p ( n) x ( n)) c r ( p ( n) x ( )) (7) xid ( n 1) xid ( n) vid ( n 1) (8) where v is the velocity of each particle, x is the position of each particle, the subscript i and d denotes the particle index and particle dimension index, n is the index of recursive computation, c 1 and c are the system control parameters, r 1 and r are the random numbers in (0, 1), P id is the current best

4 position of particle i, and P gd is the current global best position of all the particles (the swarm). The particle position x id (n) is updated using its current value and the newly computed velocity v id ( n 1). The minimum of the optimization function is obtained after N steps recursive computation. Commonly, the average or the best of several N steps computation results is the final result of the optimization. Several can be denoted as M. M and N are often chosen according to experiential knowledge or convergence curve of the optimization function. Structural Parameters Optimization In the designed rotating arc sensor, the known parameters and the range of the optimizing variables are as follows: The known parameters: F 0 : 8.07(acquired by PROE model); n: 40 r/min; e: 0.70 mm; r: 18 mm; : 7.85*10 3 kg/m 3. The range of the optimizing variables: B: 6-14mm; R: 19-mm; : According to equation (3), (4), (5) and (6), the optimization function is: min 3 3 R r n 40 R r F F 0 min B( ) sin e F R r (8) Calculation parameters: N: 100; M: 5; Particle number: 0; Particle s dimension: 3 (because of 3 variables). The PSO based parameters optimization procedure is as follows: 1) Produce a random initial value to each particle (The value is in the variable range); ) Calculate the value of the optimization function and find out the best particle of the swarm; 3) Take the current best particle as a base particle to produce a new swarm according to equation (7) and (8), do () and (3) again until N steps; take the best particle of the Nth step as the solution of this N-step calculation; 4) Repeat 1) - 3) step M times, and choose the best solution of the M times as the final solution. Optimization Results Analysis So we choose the best of the 5 times 100 steps calculation as the final result. 6 final results are listed in table 1. The 3 average convergence curves of 5 times 100-step calculation are shown in figure 4. Table 1. The optimized structure parameters and the result with N=100. Optimized B/mm R/mm /degree Value Table. The optimized structure parameters and the result with N=00. Optimized B/mm R/mm /degree Value

5 It can be seen from table 1 and figure 4 the optimized counterbalance structure parameters can make the rotating arc sensor dynamic balanced. When particles reach 80 or more generations, the average value curve of optimization function tends to be stable. PSO algorithm is a kind of stochastic optimization algorithm. If the particle exceeds the variable s range in calculation, we give a random value in the range and let N=00. We can get more choices with better results of parameters for counterbalance. The 5 results are shown in table. Summary A structural parameters optimization method is proposed for rotating arc sensor s counterbalance design in the paper. Based on particle swarm optimization design, there are many advantages in RAS dynamic balancing problem s solving. 1) Based on the RAS PROE model, the PSO methodology can quickly get the counterbalance parameters according to the centrifugal force to be balanced. ) For completed RAS, it is easy and feasible to get the loads of the two deep groove ball bearings, and furthermore the centrifugal force to be balanced. It is also a convenient methodology for completed RAS counterbalance design. 3) PSO algorithm is a kind of stochastic optimization algorithm. It can provide more choices for counterbalance s parameters. It is helpful for space confined RAS design and dynamic balance problem solving. 4) It shows PSO based counterbalance parameters design methodology provides a simple and practical method for rotating arc sensor dynamic balancing problem. Acknowledgement Thanks to the reviewers for the valuable comments. The work is supported by the Foundations of Jiangxi Provincial Department of Science and Technology under the grant no. 013BAB0608 and 013BAB References [1] Li Xiang-Wen, Hong Bo, Pan Ji-luan, etc., Design and simulation of sensor for rotating arc with stepless adjustment eccentric, Electric Welding Machine, 43(013): [] Chen Hai-Jun, Zhang Hua, Structure design of rotating arc sensor with air curtain, Mechatronics Technology, 3(011): [3] Ye Jian-xiong. Rotating arc sensor and its signal processing, Journal of Shanghai Jiaotong University, 44 Sup(010): [4] Zeng Zhi-Ying, Zhang Hua, Ye Yan-hui, etc., Signal collection and processing of rotating are sensor weld seam tracking, Welding Technology, 41(01): 17-. [5] G.Y. Lee, Suck Oh Myong, S.-B. Kim. Development of high speed rotating arc sensor system for tracking complicate curved fillet welding lines, Int. J. Precis. Eng. Man., 4(003): [6] Jia Jian-Ping, Li Hong-Li Sun Peng. Structure design of rotating arc sensor with TIG welding, Transducer and Microsystem Technologies, 9 (010): 1-13, 133. [7] Ye Yan-Hui, Zhang Hua, Qin Qing-wen, etc. The optimization design of rotating arc sensor structure, Modern Manufacturing Engineering, 11(014): [8] Zhu Shun-feng. Vibration Analysis and Structural Optimization of the Rotating arc Sensor. Nanchang: Nanchang University, 015.

6 [9] J. Liu, B. Wang, J. Ao, etc., An Immune-Swarm Intelligence Based Algorithm for Wireless Sensor Networks Deterministic Coverage Problems. J. of Cent. South Univ., 11(01), [10] Y. Mo, J. Liu, Wang B., etc., Application of Particle Swarm Optimization in Cylinder Helical Gear Multi-objective Design. Key Engineering Materials, (011): 9-33.