1 rapid measurement system development

1.1 The principle of rapid measurement of the vortex height is the principle of measuring the height of the vortex body.

At every 18, the measurement contact points are taken in the radial direction on the top surface of the scroll body and the bottom surface of the tooth, so that 53 measurement points are respectively taken on the top surface of the tooth and the bottom surface of the tooth. During the measurement process, the height measuring instrument is driven along the X axis by the driving mechanism, and the scroll rotates on the precise rotating platform of the measuring system. When the rotation angle is 18, the measuring head is telescoped downward to complete one measuring point. measuring. The X axis and the rotary axis are linked to complete the measurement of all set measurement points. Under the premise that the measurement of the vortex angle of the top surface of the tooth and the bottom of the tooth is the same, it can be seen that the height of the wrap can be expressed as h(x,)=f(x 1,)-g(x 2,)

1.2 The composition of the rapid measurement system

The rapid measurement experimental platform is constructed based on Japan's Mitutoyo's cylindricity measuring instrument RA2000. It consists mainly of a rotating platform shaft, an X-axis moving along the direction of the polar axis, a scroll mounting fixture, and an MT60M length measuring instrument from Heiden hain, Germany. As shown. Measurement system and control system As shown, the control system is mainly composed of DC motor, stepping motor, motor controller, multi-axis control card PPCI7401, etc. The position detection of each axis adopts high-precision position encoder, and the whole detection and control process is performed by computer. carry out. The motion control adopts PID control. In order to ensure the rotation precision of the shaft, the rotating shaft rotates the coupling pair with air bearing, and also ensures the repeatability of multiple measurements. MT 60M measurement accuracy: 0.5m, measuring temperature range: 1040, probe resolution: 0.1m, measuring range: 60mm, measuring force: 1.0N. MT60M measuring rod is extended and retracted by internal motor control. It is also possible to connect the switch box and control the drive by an external signal. The MT60M measuring head height is measured using Heidenhain's IK220 counting card. The measurement system established above can realize the measurement points in the height direction at regular angles through the reciprocating telescopic control of the probe itself, which can meet the required measurement efficiency and measurement accuracy.

1.3 Rapid measurement system accuracy measurement

If there is a tilt error between the measuring platform and the X-axis, that is, the X-axis and the rotating platform plane are not parallel, the measurement system error has a great influence on the wrap height measurement result. Therefore, before measuring the wrap height, the system accuracy must be The measurement was carried out. The measurement scheme is as follows: 1) Fix a high-precision optical plane to the rotating platform with a plane accuracy of 50 nm and a diameter of 80 mm. The length measuring instrument is Heidenhain's CT6001, the measuring accuracy is 100 nm, the measuring range is 60 mm, and the measuring force is 1.0 N. The resolution of the probe is 10 nm; 2) The fixed rotating platform is set to drive the X-axis at a speed of 1 mm/s, and the CT6001 contact continuously scans the optical plane to collect the output value of the length measuring instrument. 3) Fix the length measuring instrument contact at 35 mm in the radial plane of the optical plane, set the rotation speed of the rotating platform to 10/s, rotate the optical plane 360, and collect the output value of the length measuring instrument during one rotation. The measurement results are as follows. Shown. The radial error range of the measurement system is 1m, the circumferential error range is <1m, and the accuracy of the measurement system meets the accuracy requirements of the scroll tooth height measurement.

2 Measurement error separation based on adaptive chaotic particle swarm optimization

2.1 Measurement results and error analysis

The underside of the scroll and the top surface of the tooth were measured by the developed measuring system, and the measurement results were compared with those of the coordinate measuring machine. It was found that the measurement results of the vortex height of the rapid measurement system contained large periodic errors. Draw a three-dimensional scatter plot of the measurement results of the underside of the CMM and the rapid measurement system, as shown. It can be found that there is a large inclination error in the measurement results of the rapid measurement system, which is mainly due to the installation inclination error between the scroll body and the positioning fixture during the measurement. In the process of calculating the tooth height through the measurement data of the tooth bottom surface and the tooth top surface, if the measured points are the same in the XY coordinate plane, there is no periodic error in the measured scroll tooth height. However, from the previous measurement principle, the measurement point of the top surface of the tooth and the bottom surface of the tooth are the same, and there is a certain distance in the radial direction, so that there is a periodic error in the measurement result of the spiral tooth height. When evaluating the high profile of the wrap, it is necessary to find the optimal datum plane, and change the evaluation coordinate system through the optimal plane, thereby separating the measurement error caused by the positioning tilt error.

2.2 Adaptive chaotic particle swarm optimization algorithm

There are two shortcomings in the basic particle swarm optimization (PSO) search process: 1) the randomness of the initialization process and the randomness of the particle evolution process, so that the current optimal position P id and the historical optimal position P gd are updated with certain Blindness affects the convergence of the evolutionary process.

2) Particles update their speed and position, which is actually a positive feedback process, so the algorithm is easy to fall into the local optimal solution. The chaotic particle swarm optimization algorithm combines the advantages of fast convergence of particle swarm optimization and ergodicity of chaotic algorithm. It can improve the ability of standard particle swarm optimization to get rid of local extremum points, thus improving the convergence speed and accuracy of optimization algorithms. The basic idea of â€‹â€‹chaotic search in chaotic particle swarm optimization algorithm is: firstly, a set of identical chaotic variables are generated based on the number of optimized variables, chaos is added to the optimization variables by means of carrier-like, and the chaotic traversal range is extended to the optimization variables. Range of values, then search directly using chaotic variables.

From the PSO particle search feature, it can be found that the particle searches faster when starting the search and slower at the later stage of the search.

At the same time, near the local extremum point, the particle velocity update is controlled by the inertia weight. Usually, the inertia weight of the PSO algorithm is <1 (=097), and the particles are premature. The inertia weight is adaptively adjusted based on the premature convergence degree of the group and the individual fitness value, and the calculation accuracy of the local search and the convergence speed of the global search can be considered simultaneously. Therefore, it is important to correctly evaluate the premature convergence degree of the particle swarm for adaptively adjusting the inertia weight. Here, the following indicators are used to evaluate the premature convergence degree f of the particle group as the average value of the current fitness values â€‹â€‹of all the particles, m is the particle swarm size, and fi is The current fitness value for each particle. Suppose that the fitness value of the group optimal particle is fg, and the fitness value of all fitness values â€‹â€‹better than f avg is averaged, assuming it is f

Avg, avg| is a parameter for evaluating the degree of premature convergence of the particle group, and the smaller the particle group, the more premature convergence of the particle group.

In order to balance the global convergence and convergence speed of the algorithm, the group is divided into three subgroups according to the fitness value of the individual. The particles with smaller inertia perform local search to improve the convergence speed; the particles with larger inertia perform global search to avoid premature convergence.

Through the above analysis, the main processes of the adaptive chaotic particle swarm optimization algorithm (ACPSO) adopted in this paper are as follows: 1) Initially set the relevant parameters of the chaotic particle swarm optimization algorithm (including inertia weight, learning factor, maximum iteration number or fitness error threshold). 2) Calculate the fitness value of the subgroup, select the M solutions with better performance as the initial solution, and randomly generate M initial velocities; 3) If the particle fitness value is better than the local extremum p Best, then the local The extreme value p Best is set to the new position; 4) if the particle fitness value is better than the global extreme value g Best, the global extreme value gBest is set to the new position; 5) the premature convergence degree of the particle group calculated by the formula % changes the current Inertia weight, the speed and position of the particle are updated by adaptively modified inertia weights. 6) Chaotic optimization of the optimal position Pg = (p g1, p g2,, p gd) to obtain P(n)g = (p(n)g1, p(n)g2,, p(n)gd) (n=1, 2,). Substituting P(n)g into its fitness value, taking the best feasible solution P; 7) using P

Replace the position of any one of the particles in the current group; 8) If the number of iterations or calculation accuracy is met, the global optimal position is output, otherwise return to step 3). Stop the search until the condition is met.

2.3 Vortex height optimization calculation model

Two important steps of the adaptive chaotic particle swarm optimization algorithm are to encode and determine the fitness function. Real number coding is used here. It can be known from the previous measurement principle of the vortex tooth height that the tooth top surface and the tooth bottom inclination error fitness function hT based on the adaptive chaotic particle swarm algorithm is the tooth top surface fitness function; h B is the tooth bottom surface. The fitness function; A, B, and C are the least square plane coefficients of the measurement data of the top surface and the bottom surface of the tooth; A, B, and C are the parameters to be determined by the adaptive chaotic particle swarm algorithm respectively; sik is the measurement point to the most The minimum distance of the excellent plane, then s ik = |Ax i +By i +Cz i | A 2 +B 2 +1 i=1,2,,n

The adaptive chaotic particle swarm algorithm step is used to search and optimize the fitness function in the formula. The number of particles is 20, the dimension of the particle is 3, and the search stop condition is 100 times of iteration.

Through the adaptive chaotic particle swarm optimization algorithm, the optimal measurement of the inclination error of the top surface and the tooth bottom surface of the tooth top surface and the tooth bottom surface respectively is obtained, and the inclination angles of the tooth top surface and the tooth bottom surface along the X-axis and Y-axis directions are calculated.

3 compensation results and their comparison

The measurement results of the rapid measurement system are compensated and corrected by the positioning inclination angle calculated by the above-mentioned tooth bottom surface, and in order to verify the correctness of the measurement result, the same scroll body is compared and measured by a coordinate measuring machine. After the adaptive chaotic particle swarm optimization algorithm is used to locate the tilt error compensation, the measurement results of the bottom surface height profile are shown in Fig. 6. It can be found that after the inclination compensation, the measurement result of the rapid measurement system on the underside of the tooth is basically the same as that of the coordinate measuring machine. In the same way, the measurement results of the top surface of the tooth can also be corrected and compensated. The above-mentioned adaptive chaotic particle swarm optimization algorithm is used to optimally evaluate the bottom surface of the tooth and the top surface of the tooth, and then calculate the wrap height from the measurement principle. After the optimal evaluation, the measurement results of the wrap height are as shown.

At the same time, in order to verify the stability of the rapid measurement system, the rapid measurement system is used to perform three repeated measurements on the tooth height of the scroll. The repeatability error of the rapid measurement system is 0.4m, which can meet the requirements of actual measurement. The comparison can be obtained: 1) After obtaining the optimal evaluation coordinate system by the adaptive chaotic particle swarm algorithm, the measurement results of the rapid measurement system are basically consistent with the measurement results of the coordinate measuring machine; 2) for the single-piece vortex tooth height Measurement, the total measurement time of the rapid measurement system is 355s, and the total measurement time of the CMM is 1047s. Therefore, with the rapid measurement system, the measurement efficiency of the wrap height is significantly improved; 3) The rapid measurement system can meet the requirements. The measurement environment of the processing site, and the measurement principle adopts the exhibition method. By further developing the rapid measurement system, it can be directly used for online measurement of the scroll body processing, which can improve the processing precision of the scroll body.

4 Conclusion

Based on the principle of the exhibition method, the rapid measurement system of the scroll tooth height was developed using the MT60M high-precision length measuring instrument. The optimal evaluation plane of the vortex height is obtained by the adaptive chaotic particle swarm optimization algorithm. After the compensation of the positioning inclination error of the measurement result, the measurement results of the fast measurement system and the coordinate measuring machine are compared: 1) Measurement of the rapid measurement system The results are basically consistent with the measurements of the three-coordinate measurement; 2) the measurement time is reduced from the original 1047s to 355s; 3) The newly developed rapid measurement system can be used for on-line measurement of scroll machining.

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