基于多尺度分析的圆度误差在线检测研究
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摘要
本文采用多尺度分析方法对影响圆度误差在线检测精度的关键技术问题进行了深入地研究,并对适合圆度误差在线检测条件的误差分离技术进行了探讨。针对复杂的圆度误差在线检测信号的消噪滤波问题,提出了时域、频域相结合的多尺度消噪滤波算法;针对圆度误差评定问题,提出了多尺度遗传免疫优化算法,建立了圆度误差优化评定数学模型,并实现了圆度误差的统一评定;提出了基于改进反向法的误差分离方法用于分离圆度误差在线检测系统的主轴回转误差。
本文的研究结果提高了圆度误差在线检测精度,保证了在线检测结果的有效性。所提算法具有普遍应用价值,可推广到其它形位误差检测领域。
Roundness is one of the most important form errors and the foundation of measuring such form and position errors as cylindricity, coaxality and axis straightness, etc. It indicates the machining precision of rotating parts. Roundness on-machine measurement is a main direction of roundness measurement techniques, which can enhance the measuring efficiency, realize total quality control, and is especially suited to the measurement of large scale parts.
Besides the roundness error signals, the roundness on-machine measurement signals include many other undesired signals, such as the noise in workshop, high frequency signals and spindle error signals. To improve the measurement precision and make sure the on-machine measurement validity, effective denoising methods and error separation techniques should be employed to eliminate the noise and separate the spindle error, and then, an accurate method should be taken to evaluate the roundness.
There are obvious multiscale characters in roundness on-machine measurement signals and the process of roundness evaluating. Multiscale analysis methods can describe the problems with multiscale characters from various scales accurately. In this paper, multiscale analysis methods are employed to solve the key technique problems of improving the roundness on-machine measurement precision. After studying the error separation techniques both at home and abroad, a new error separation method based on IRM (improved reverse method) is proposed in this paper, which is suitable for roundness on-machine measurement. The main work can be summarized as follows:
1. Developing a roundness on-machine measurement system based on laser trigonometry principle.
Laser technique plays an important role in measurement fields for the advantages of non-contact, high speed and with strong anti-interference ability. On the base of common lathe, we set up a roundness on-machine measurement system. In the system, the spindle of the lathe is used to take the part to be measured to rotate; two CCD laser displacement sensors are employed for collecting data and error separation; a PC is used for data processing, results displaying, man-machine conversation, and so on; controller in charge of connecting different parts of the system.
The system is simple. The sensor size is small and with high sampling frequency, the measuring accuracy meets the precision demand. All these are suitable for roundness on-machine measurement conditions.
2. Building a denoising and filtering algorithm based on multiscale analysis
The roundness on-machine measurement signals are very complicated. The true roundness signals are being drowned in the noise. In this case, median filtering and Karman pre-filtering are employed for denoising in time domain, the former is used to wipe off the gross error, and the latter is used to pick up the roundness error from the noisy signals preliminary.
Many studies have shown that signals and noises have different multiscale features on different scales. Based on this feature, multiscale analysis method is introduced to the denoising procession in frequency domain. That is to decompose the signals to different frequency bands by wavelet package transform first, then to eliminate noise from multi-scales. During the multiscale denoising and filtering, the best wavelet function and the best layer of decomposition are studied. At last, the proposed method is compared with the exisiting method by examples.
The results show that the denoising and filtering algorithm based on multiscale analysis can recover the true roundness signals from the complicated on-machine measurement signals faster (about improve 60%) and more accurate (about improve 1.5%) than the multilevel roundness error separation algorithm, which sets a foundation for evaluating roundness well and truly.
3. Presenting an error separation method based on IRM (improved reverse method) for roundness on-machine measurement
The lathe spindle is used for roundness on-machine measurement, its rotationary accuracy can not satisfy the demand of measuring, and so, the error separation is necessary. After analyzing various roundness error separation techniques, we propose an error separation method based on IRM which is suited for roundness on-machine measurement conditions. This method can measurement and separate the roundness error from the spindle error with two sensors and one measurement.
The experiment results show that the measurement precision of the roundness on-machine measurement after error separation closes to the off-machine measurement precision of Coordinate Measurement Machine: the maximum absolute error less than 1μm,and the maximum relative error less than 2.4%。
4. Study on roundness uniform evaluation method based on multiscale analysis
There is an obvious multiscale analysis feature in the process of roundness optimization evaluating. On the basis of artificial immune optimization algorithm, a multiscale genetic and immune optimization algorithm (MSGIA) is built and the detailed flow of the algorithm is introduced. The mathematical model of the roundness optimization evaluation is established and the uniform evaluation of roundness is realized by MSGIA.
The affinity function, the region and the accuracy of search, the probability of crossover and mutation can be set with different scale automatically with the optimization deep going, which makes the roundness evaluating process fitted to the optimization mechanism. The results show that MSGIA is of global optimization and has many benefits compared with artificial immune optimization algorithm, the evaluating precision improves about 6%, and the convergence speed improves about 80%. These prove the practicability and the reliability of MSGIA.
5. Study on minimum zone evaluation of axis straightness
The mathematical model of axis straightness optimization evaluation is set up and the minimum zone evaluation is carried out by MSGIA proposed in this paper. The example shows that the algorithm has improved the precision about 11% and 8% respectively compared to least square method and artificial immune optimization algorithm. The test results confirm the robustness of the multiscale genetic and immune optimization algorithm.
All the above discussion indicates that the denoising algorithms and the roundness evaluation method based on multiscale analysis and the error separation technique based on the improved reverse method improve the roundness on-machine measurement precision, ensure the validity of on-machine measurement results, and prove the multiscale analysis method has a bright future in error measurement field.
本文的研究结果提高了圆度误差在线检测精度,保证了在线检测结果的有效性。所提算法具有普遍应用价值,可推广到其它形位误差检测领域。
Roundness is one of the most important form errors and the foundation of measuring such form and position errors as cylindricity, coaxality and axis straightness, etc. It indicates the machining precision of rotating parts. Roundness on-machine measurement is a main direction of roundness measurement techniques, which can enhance the measuring efficiency, realize total quality control, and is especially suited to the measurement of large scale parts.
Besides the roundness error signals, the roundness on-machine measurement signals include many other undesired signals, such as the noise in workshop, high frequency signals and spindle error signals. To improve the measurement precision and make sure the on-machine measurement validity, effective denoising methods and error separation techniques should be employed to eliminate the noise and separate the spindle error, and then, an accurate method should be taken to evaluate the roundness.
There are obvious multiscale characters in roundness on-machine measurement signals and the process of roundness evaluating. Multiscale analysis methods can describe the problems with multiscale characters from various scales accurately. In this paper, multiscale analysis methods are employed to solve the key technique problems of improving the roundness on-machine measurement precision. After studying the error separation techniques both at home and abroad, a new error separation method based on IRM (improved reverse method) is proposed in this paper, which is suitable for roundness on-machine measurement. The main work can be summarized as follows:
1. Developing a roundness on-machine measurement system based on laser trigonometry principle.
Laser technique plays an important role in measurement fields for the advantages of non-contact, high speed and with strong anti-interference ability. On the base of common lathe, we set up a roundness on-machine measurement system. In the system, the spindle of the lathe is used to take the part to be measured to rotate; two CCD laser displacement sensors are employed for collecting data and error separation; a PC is used for data processing, results displaying, man-machine conversation, and so on; controller in charge of connecting different parts of the system.
The system is simple. The sensor size is small and with high sampling frequency, the measuring accuracy meets the precision demand. All these are suitable for roundness on-machine measurement conditions.
2. Building a denoising and filtering algorithm based on multiscale analysis
The roundness on-machine measurement signals are very complicated. The true roundness signals are being drowned in the noise. In this case, median filtering and Karman pre-filtering are employed for denoising in time domain, the former is used to wipe off the gross error, and the latter is used to pick up the roundness error from the noisy signals preliminary.
Many studies have shown that signals and noises have different multiscale features on different scales. Based on this feature, multiscale analysis method is introduced to the denoising procession in frequency domain. That is to decompose the signals to different frequency bands by wavelet package transform first, then to eliminate noise from multi-scales. During the multiscale denoising and filtering, the best wavelet function and the best layer of decomposition are studied. At last, the proposed method is compared with the exisiting method by examples.
The results show that the denoising and filtering algorithm based on multiscale analysis can recover the true roundness signals from the complicated on-machine measurement signals faster (about improve 60%) and more accurate (about improve 1.5%) than the multilevel roundness error separation algorithm, which sets a foundation for evaluating roundness well and truly.
3. Presenting an error separation method based on IRM (improved reverse method) for roundness on-machine measurement
The lathe spindle is used for roundness on-machine measurement, its rotationary accuracy can not satisfy the demand of measuring, and so, the error separation is necessary. After analyzing various roundness error separation techniques, we propose an error separation method based on IRM which is suited for roundness on-machine measurement conditions. This method can measurement and separate the roundness error from the spindle error with two sensors and one measurement.
The experiment results show that the measurement precision of the roundness on-machine measurement after error separation closes to the off-machine measurement precision of Coordinate Measurement Machine: the maximum absolute error less than 1μm,and the maximum relative error less than 2.4%。
4. Study on roundness uniform evaluation method based on multiscale analysis
There is an obvious multiscale analysis feature in the process of roundness optimization evaluating. On the basis of artificial immune optimization algorithm, a multiscale genetic and immune optimization algorithm (MSGIA) is built and the detailed flow of the algorithm is introduced. The mathematical model of the roundness optimization evaluation is established and the uniform evaluation of roundness is realized by MSGIA.
The affinity function, the region and the accuracy of search, the probability of crossover and mutation can be set with different scale automatically with the optimization deep going, which makes the roundness evaluating process fitted to the optimization mechanism. The results show that MSGIA is of global optimization and has many benefits compared with artificial immune optimization algorithm, the evaluating precision improves about 6%, and the convergence speed improves about 80%. These prove the practicability and the reliability of MSGIA.
5. Study on minimum zone evaluation of axis straightness
The mathematical model of axis straightness optimization evaluation is set up and the minimum zone evaluation is carried out by MSGIA proposed in this paper. The example shows that the algorithm has improved the precision about 11% and 8% respectively compared to least square method and artificial immune optimization algorithm. The test results confirm the robustness of the multiscale genetic and immune optimization algorithm.
All the above discussion indicates that the denoising algorithms and the roundness evaluation method based on multiscale analysis and the error separation technique based on the improved reverse method improve the roundness on-machine measurement precision, ensure the validity of on-machine measurement results, and prove the multiscale analysis method has a bright future in error measurement field.
引文
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