The ARMA(p,q) time series model can be transformed into two special cases: the MA(q) model and the AR(p) model. Because the autoregressive AR model is relatively simple to build, the calculation is small, and the model parameters are estimated accurately, it is suitable for the thermal error compensation modeling of CNC machine tools. In addition, the ARMA model can be approximated by an inverse function using an AR model that may be infinite order. So choose to use the AR model to fit the thermal error of CNC machine tools.
The data is required to be a stationary random sequence of zero mean. The stationary sequence should have mean, variance, and autocorrelation functions that do not change over time, and its autocorrelation function is only related to the time interval, regardless of the position of the endpoint of the interval. The stationarity of the sequence can be verified by statistical methods. For time series with defined components, the deterministic part should be separated before modeling, and then the remaining stationary random sequence should be modeled.
The following is a time series modeling analysis of a turning machining center at the factory site, where data is collected during actual machining on the turning center, including the four temperature values ​​on the machine and the actual machining dimensions of the workpiece. Since there is a significant change trend between the thermal error value of the machine tool and the four temperature values, it is obviously a non-stationary sequence. If the multi-linear regression least squares model is used to fit the prediction, the deviation is often large. Therefore, the sequence must be smoothed, that is, the non-stationary trend part is separated, and then the remaining part is fitted with the correlation model of the time series analysis.
Thermal error compensation system As shown, the compensation control system consists of four resistive thermal sensors (positioned at the critical temperature point of the turning center after thermal sensor optimization arrangement analysis), adjustment board with bridge circuit, A/D board and Combined with the controller of the turning center. The temperature signal of the turning center is first collected in real time by means of four temperature sensors arranged on the turning center. Then, the signal is adjusted by the adjustment board (the specially manufactured adjustment board is composed of only some simple bridge circuits, its main function is to convert the resistance signal to the voltage signal), and then the A/D board enters the turning center controller through amplification, adjustment and the like. The controller calculates the compensation value based on the thermal error timing analysis mathematical model, and performs real-time control on the additional motion of the tool holder to correct the error caused by the thermal deformation of the machine tool. Modification of the mathematical model can be done simply by keyboard input from the turning center controller, if desired.
Thermal error compensation results The time series analysis model is used for compensation processing on multiple turning centers with the same type and specifications. The improvement of the model compensation accuracy is obvious because the time series analysis model is an autocorrelation and autoregressive model. The latest data information is corrected. For the four key point temperature changes used for modeling at the turning center, it can be seen from the figure that the turning center temperature also changes as the workpiece is machined (data acquisition interval 2 min).
Conclusion Through the above analysis, it can be seen that the time series model as a dynamic model not only considers the past values ​​of the sequence under study, but also has a memory function; it can also reflect the randomness and statistical characteristics of the sequence, and has a predictive function. Based on the dynamic machining characteristics of CNC machine tools, this paper applies the time series analysis modeling method to the real-time compensation of machine tool thermal error, and has achieved good results. The modeling is flexible and has excellent compensation function, which greatly improves the machining accuracy of the machine tool.
(Finish)
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