Vibration mechanism analysis and algorithm optimization of contactor contact system

HUANG Kepeng， WANG Fazhan， ZHAO Mingji， GUO Baoliang， OU Daquan

(1. College of Mechanical and Electrical Engineering， Xi’an University of Architecture & Technology， Xi’ an 710055， China；2. Technology R&D Center， ABB Xinhui Low-Voltage Switchgear Co., Ltd.， Jiangmen 529089， China)

Abstract： In order to solve the problem of vibration bounce caused by the contact between moving and stationary contacts in the process of switching on, two-degree-of-freedom motion differential equation of the contact system is established. Genetic algorithm is used to optimize the pull in process of AC contactor. The whole process of contact bounce was observed and analyzed by high-speed photography experiment. The theory and experimental results were very similar. The iron core has collided before the contact is separated, which further aggravates the contact bounce. When the iron core bounces collided again, the bounce of the contact was not affected. During the operation of the contactor, the movement of the moving iron core will cause slight vibration of the system. The contact bounce time and the maximum amplitude are reduced. The research results provide a theoretical basis for further control and reduction of contact bounce.

Key words： electrical switch； contact bounce； two-degree-of-freedom motion differential equation； algorithm optimization； high-speed photography

0 Introduction

The contact is an important component which is widely used in electrical switching devices. It is a kind of nonlinear vibration behavior, in which the collision bounce between the moving and stationary contacts is an important factor affecting its dynamic characteristics[1-3]. The collision and bounce caused small distance separation of the contact parts, leading to the generation of arcs. Fusion bonding occur directly affects the electrical contact performance and service life[4-5]. Therefore, it is necessary to analyze the vibration mechanism accurately, and obtain the theoretical method to effectively reduce and suppress the contact bounce, which is an urgent need to improve the electrical life and reliability of electrical components.

Scholars have done a lot of useful work on the analysis of the dynamic process of the contact in recent years. Regarding the establishment of the contact bounce model, the coupling circuit Equation of motion was deduced[6]. The bouncing of the contact was analyzed, and the energy balance equation of the contact collision was established[7]. The collision and deformation were considered, and the control equations of the AC contactor were obtained by using Cauchy’s stress equation[8-9]. Contact system was proposed, and the zero current breaking control was studied[10-12]. Electromagnetic force was simulated during the closing process, and the influence of the magnetic ring and magnetic leakage was considered[13-17]. There are three main methods for measuring contact bounce. One is to record the bounce time by a measuring device[18]. Another is that the moving and static contacts were introduced into a DC circuit to reflect the bounce of the contactor during the closing process[19]. The last one is the high-speed photography technology to get the contact bouncing by shooting to observe the displacement of the mark[20].

In summary, scholars have done some useful work on the research of the contact bounce characteristics, but the vibration mechanism of contact bounce has not been studied. The large amount of work was to analyze the dynamic characteristics of electromagnets through simple coupled motion equations, circuit equation and magnetic circuit equation[21]. The mechanical vibration of the contact system of the contactor was used as the breakthrough point, and the two-degree-of-freedom coupling motion differential equation based on the vibration characteristics was established in this paper. Genetic algorithm is used to optimize the AC contactor pull in process. Finally, the high-speed photography technology is used to verify the experiment, which provides a theoretical reference for the optimal design of the contactor.

1 AC contactor

AC contactor is composed of contact system, electromagnetic system and contact bracket (Fig.1). The electromagnetic coil shall be energized first when the AC contactor works. When the electromagnetic force is greater than the force of the spring, the moving iron core makes the moving contact move downward through the contact bracket. Since the distance between the moving and static contacts is less than that between the moving and static cores, the moving contact will collide and bounce earlier than the moving iron core. At this time, the moving core continues to move downward until the static and moving cores collide, which makes the moving contact bounce again. Due to the collision between the moving and static iron cores, bouncing becomes more complicated. Therefore, analyzing the bounce of the moving and static contact before and after collision is the key and difficult point on the dynamic characteristics of the contactor.

Fig.1 AC contactor structure

2 Theoretical equation

The nonlinearity and discontinuity of the AC contactor make the dynamic characteristics appear abrupt change in the AC contactor system. Therefore, it is necessary to simplify them at the operating point based on special assumptions.

1) The moving parts of the contactor can only move along one direction, and there is no displacement or rotation in other directions.

2) The collision force between contact elements is caused by local contact deformation. The velocity and contact time before and after the collision are taken as the calculation parameters.

Therefore, the piecewise model can be used to establish the piecewise linear vibration differential equation.

2.1 Model establishment

During the operation of AC contactor, it can be equivalent to a damped forced vibration system with two degrees of freedom, as shown in Fig.2. Wherem1andm2are the mass of the moving iron core and moving contact;x1andx2are the length of the moving iron core and the displacement of the moving contact;c1andc2are the equivalent damping of the electromagnetic mechanism and contact system;k1andk2are the stiffness coefficients of the reaction spring and contact spring;piandpcare the contact force when the contact and core collide, andFxis the electromagnetic force.

The closing motion process of the contactor can be divided into three stages. First, when the moving and static contacts have not yet collided and contacted. Second, the moving and static contacts have first collided. Third, contacted, but the moving and static iron cores have not yet collided, and the moving and static iron cores first collide. The differential equations were obtained as

(1)

(2)

(3)

2.2 Electromagnetic force

The force of the moving contact and iron core are simplified, wherexiandxcare the total stroke of the moving contact and iron core, respectively, and the force model is shown in Fig.3.

Fig.3 Force model

The closing force process is divided into two stages. In the first stage, when there is no contact between the moving contact and the static core, the moving contact and the moving iron core move downward together, because they are connected through the contact bracket. In the second stage, when the static and dynamic contacts are in contact and the core is not in contact, the moving contact is separated from the moving core, and only the moving core moves downward. The differential equations were obtained as

(4)

(5)

Considering the Eqs.(4) and (5), the electromagnetic force of the moving iron core can be solved.

2.3 Contact force

The contact belongs to an elastic body, so the collision will cause periodic bounce during the closing process. The physical process of the contact bounce is shown in Fig.4.

Fig.4 Contact bounce model

(6)

piti=m2v2-m2v1.

(7)

For the Eqs.(6) and (7),Kis the contact recovery coefficient, andtiis the contact time.

Similarly, the iron core collision is presented as

(8)

(9)

2.4 Equation solution

In order to solve the equation, ABB A9-30-10 electromagnetic contactor is taken as an example. The parameter values at different stages are given in Table 1.

Table 1 AC contactor parameters

(10)

Taking the data from Table 1 into Eq.(10), it can be got that the equation with the larger difference in the coefficient matrix values on the right side of the equation group is a slightly stiff differential equation. Considering the influence of nonlinearity, the system is allowed to have high error tolerance, and the MATLAB command ODE23 is used to solve it.

The mass option of ODESET is used to specify mass matrix, and ABSTOL and RELTOL options are used to specify the absolute error tolerance and relative error tolerance. The Events property is set to a function and a corresponding function is created. Since the equation is segmented, the ODE can be solved through ODE23. It passes the predefined value of the previous equation to ODEFCN to solve the next equation. At the same time, parameters outside the function are defined and these parameters are passed when specifying the function handle.

Using the above settings to solve Eqs.(1)-(3), the results are shown in Fig.5 and Table 2.

The beginning of the AC contactor closing to the first contact is the closing time. The time from the first bounce to the end of the second bounce is the bounce time. The time from the beginning of the contactor to the end of the second bounce is contact stabilization time.

According to Fig.5 and Table 2, it can be got that the contact closing time corresponds to Eq.(1). The time from the first bounce of the contact to the first bounce of the core is the Eq.(2). The time from the start of the first bounce of the core to the end of the second bounce of the contact is the Eq.(3).

Fig.5 MATLAB result curve

Table 2 MATLAB results

The contact bounces earlier than the iron core, but ends after the iron core. The bounce amplitude of the contact is greater than the iron core. This is due to that the distance between the moving and static contacts is smaller than the distance between the moving and static iron core. The iron core mass is much larger than the contact mass. The contact has not been separated after the collision, and the iron core has collided at the same time, which further intensified the bounce of the contact and increased its bounce displacement.

The start and end time of the second bounce of the iron core are earlier than the contact.When the second bounce of the iron core occurs, the bounce of the contact is not significantly affected. This is due to that the second bounce amplitude of the iron core is much smaller than the first one, which is consumed by the system itself and not transmitted to the contacts.

Contact stabilization time and maximum bounce amplitude of the contact are larger than the iron core. This is due to that the contact area of the iron core is larger. When the iron cores hit, it further prevents the iron core from bouncing again.

3 Improved genetic algorithm

3.1 Genetic algorithm

Genetic algorithm imitates biological genetics and evolution. Its essence is to evaluate the merits and demerits of the solution according to the fitness function value, so as to search the solution space. Due to its strong robustness and efficient global search capabilities, genetic algorithm has been successfully used to solve engineering practical optimization problems such as multi-peak, nonlinearity and high complexity[22]. It can be described by a five-dimensional vector group as

GA=[Npop,Ngen,P,feval,fset],

(11)

whereNpopis the population;Ngenis the number of iteration;fevalis the population size;fsetis the regeneration selection rule;Pis a genetic operator.

3.2 Optimization variable

The contact bounce and iron core bounce are the result of multiple factors. According to the moving analysis, the factors that affect the bounce of contact and iron core mainly includes the moving contact, the moving iron core, the moving and static contact stroke, moving and static iron core stroke, contact spring stiffness coefficient, reaction spring stiffness coefficient, equivalent damping of the contact system, equivalent damping of the electromagnetic mechanism, contact force, iron core collision force and electromagnetic attraction.

Therefore, nine parameters that have a greater impact on the contact bounce as the optimized variables of this contactor are selected. The derivative ofXcan be defined as

(12)

3.3 Objective function

The contact bounce generates arc and ablation, which is the key to impacting the electrical life of the contactor[23]. Contact closing and contact bounce time are taken as the optimization target, which can be defined as

minf(X)=[T(X),ΔT(X)],

(13)

whereT(X) is the contact closing time, andΔT(X) is the contact bounce time.

3.4 Fitness function

The AC contactor optimization problem is a multi-objective optimization problem. In general, there is no optimal solution for a multi-objective optimization problem, so that each optimization goal is optimized at the same time. So the corresponding weight can be set for each goal. According to the linear weighting method, the multi-objective optimization problem is transformed into a single-objective optimization problem for solution[24].P(X) is defined as

(14)

wherew1andw2are the weighting factor of the objective function;T0andΔT0are the value of each objective function before optimization. Letw1=0.1,w2=0.9,w1+w2=1.

3.5 Restrictions

In order to ensure that a reliable and reasonable solution can be obtained for the algorithm, constraints must be imposed on the parameters of the AC contactor model[25].

1) In order to ensure a certain initial pressure when the contacts are in contact, the core spacing must be greater than the contact spacing. The expression can be obtained as

xc-xi>0.

(15)

2) In order to ensure the restraint of the attraction and reaction force characteristics, the electromagnetic attraction force must be greater than the spring reaction force. The expression can be expressed as

Fx-(k1xc+k2xi)>0.

(16)

3.6 Optimization process

The parameters of AC contactor such as contact quality, iron core quality, contact spring and electromagnetic coil turns are optimized, and the algorithm running process is shown in Fig.6.

Fig.6 Algorithm flow chart

1) Setting the initial parameters of the algorithm such as coding type, initial population size, number of genetic iterations and cross mutation probability.

2) Using the solution space uniform sampling method to generate the initial population pool uniformly and randomly, and selecting the initial population.

3) Calculating the fitness of the initial population, and using the elite retention strategy to directly maintain the top 10% of the outstanding individuals in the initial population to the offspring. Judging whether the population satisfies the convergence condition, if so, output the result, otherwise returning to 4).

4) Selecting 80% of the parent individuals for genetic operations. Calculating the individual’s cross-mutation probability according to the individual fitness value in the population, and performing cross-over and mutation operations.

5) Adopting the elite retention strategy, and the random generation mechanism. The individuals produced by selection, crossover and mutation constitute a new population.

6) Judging whether the genetic algebra of the population exceeds the set value, if so, output the result, otherwise return to 1).

3.7 Optimization result

The own GA toolbox of MATLAB does not consider the mathematical characteristics of the contactor optimization problem. So the C language is used to write related program optimization programs. According to the key influencing factors of contact bounce, the strategies of chromosome structure, crossover, mutation and other processes are specifically added. Using the VC++6.0 debugger to compile and add the program to generate related files, and realize the registration of the self-compiled algorithm to MATLAB.

After the algorithm is optimized, the newly obtained values are assigned to specific parameters for MATLAB. After setting the parameters, the fitness function is used as the performance evaluation to optimize the prototype model. The optimization result is shown in Fig.7.

Fig.7 Optimization curve

It can be seen from the Fig.7 that the moving contact reaches a stable closing state after three consecutive small bounces. The time required for the moving contact closing is 23.32 ms, and the maximum displacement is 0.021 mm, and the total time for the bounce is 0.98 ms. Compared with curve of Fig.5, it can be seen that the total contact bounce time is reduced by 37% through the genetic algorithm, the maximum displacement is reduced by 92%, and the overall performance of the contactor is greatly improved.

The various parameters of the contactor before and after optimization are shown in Table 3. It is obvious that the mass of the moving iron core is reduced, and the mass of the moving contact is increased after optimization. The contact distance and the iron core distance are reduced, and the equivalent damping of electromagnetic mechanism and contact system are increased. The stiffness coefficient of reaction and contact spring is increased, and the electromagnetic force is decreased, and the dynamic characteristics of the prototype are greatly improved.

Table 3 Optimization results comparison

4 Experiment and discussion

In order to get the whole dynamic process of contact bouncing intuitively, the high-speed photography technology (EoSens-mini2 system) is firstly adopted to take photographic measurement of the same group of contacts of ABB’s A9-30-10 electromagnetic contactor.

The bounce time of the contact during the closing process of the AC contactor is very short, generally only 2 ms-6 ms. In order to ensure that the camera can accurately capture the whole process of bounce, 128×128 pixels were selected. The shooting speed was 43 540 frames per second. Figs.8 (a) and (b) are the layout of the contactor prototype and experimental equipment.

As shown in Fig.8, a measuring hole is opened on one side of the contactor directly facing the position of the contact group. The high-speed camera is aimed at the contact. The head position of the moving contact is marked and monitored by the high-speed camera. The shooting parameters of the camera are adjusted and the camera is started for shooting.

Fig.8 Shooting layout

Fig.9(a) is the screenshots of the moving and static contacts which have not yet collided. Fig.9(b) is that the moving and static contacts have collided. Fig.9(c) is that the moving and static iron cores collided.

Fig.9 Contact of bounce process

The processing program is applied to process the above-mentioned collected images in MATLAB. The mainly steps are shown in Fig.10.

Fig.10 Data processing flowchart

1) The collected images are processed by denoising and enhancing, then the geometric information of image feature points are extracted and recorded.

2) According to the characteristics of black and white pixels in the image, the dynamic and static contact components are highlighted, as shown by the dot mark in Fig.9. The program is used to identify and binarize the marked points. The image coordinate system is extracted.

3) The binary image retrieval is used to extract the image coordinates. The least square method is used to fit the coordinates of the marked points.

4) The diameter calculation of the mark center circle is transferred to the linear relationship of the two coordinate systems. The processing results of each image are arranged according to the collected time series, and the real-time displacement data of the marked points can be obtained.

The MATLAB calculation result curve of the contact is compared with the experimental curve. The results are shown in Fig.11.

Fig.11 Experimental and theoretical curves comparison

It can be seen from Fig.11 that the overall trend of the experimental and theoretical curves are similar. The contacts have two obvious bounces, but the experimental curve is not smooth in the first bounce of contact. It is due to that the movement of the moving iron core will cause a slight jitter. Furthermore, the experimental and the theoretical curves do not fit perfectly in the contact stabilization time. This is due to that the multiple contact structures are simplified to one group in the modeling of contactors without considering the influence of contact bridge structure.

The specific numerical values of experimental and theoretical results are shown in Table 4. It can be seen that the start time, end time, closing time, bounce time, contact stabilization time, and maximum bounce amplitude error of the experimental and theoretical contacts are all within 5%. The experimental and theoretical results are highly consistent. The accuracy and reliability of the theory are verified.

Table 4 Theory and experiment comparison

5 Conclusions

In this study, from the point of view of vibration, considering the nonlinear electromagnetic force and impact contact force, the two-degree-of-freedom coupled motion differential equation is established. The vibration model of contactor is analyzed and verified by high-speed photography experiment. The conclusions are obtained as follows.

1) The first bounce of the contact is earlier than the iron core and later than the end of the iron core. Before the contact is separated after collision, the iron core collides, which further aggravates the contact bounce.

2) For the starting and ending time of the second bounce, the contact is later than the iron core. The iron core does not affect the bounce of the contact. The contact stability time and maximum bounce amplitude of the contact are greater than the iron core.

3) The bounce time, contact stabilization time and maximum bounce amplitude of the contact are all greater than the iron core. In addition, during the operation of the contactor, the movement of the moving iron core will cause a slight vibration of the contactor system.