Detection of machine tool contouring errors using wavelet transforms and neural networks

The accuracy and precision of computer numerical control (CNC) machine tools directly affect the dimensional accuracy of machined parts. Fast detection of machine tool contouring errors is required to guarantee the accuracy of the manufacturing process and, further, to eliminate errors through error compensation techniques. In this paper, several typical contouring error patterns of CNC machine tools (i.e., cyclic, backlash, scale mismatch, etc.) are presented. Detection of machine tool contouring errors is conducted in two steps using wavelet transforms (WT) and neural networks (NN). In the first step, wavelet transform is applied to contouring error signals to extract error features. In the second step, wavelet coefficients are grouped into proper input units for neural networks; that is, data were compressed by omitting unnecessary details. In this study, cascade-correlation (CC) neural networks are selected to recognize the seven basic patterns of CNC contouring errors. Multiple contouring errors can also be identified quantitatively in the WT-NN approach.Computer numerical control (CNC) machine tools are widely used throughout the manufacturing industry. Accuracy and good machining conditions are critical to the dimensional accuracy of parts produced using these tools. In general, CNC machine tool errors can be classified into four types:

1. Geometric errors of machine components and structures,

2. Errors induced by thermal distortions,

3. Deflection errors caused by cutting forces, and

4. Other errors-for example, those caused by servo errors of machine axes (for example, tracking errors) or numerical control interpolation algorithmic errors.1

Currently, two approaches exist for improving the accuracy of CNC machine tools: error avoidance and error compensation. The error compensation technique, which is an economical way to improve machine tool accuracy, was first applied by Hocken on a Moore NS CMM.2Error compensation identifies machine errors through either direct mapping or indirect modeling. Direct mapping of machine errors is accomplished through the use of precision artifacts and measurement instruments. Indirect modeling is performed using a kinematic model to express the error of tools relative to the position of parts. This technique was successfully applied to a multiaxis machine tool' and a CMM.4

The fundamental step in error compensation is the error identification technique, which can be classified as either direct or indirect. The feature-based error identification technique involves the measurement of machined parts. It involves tools such as pattern recognition, fuzzy systems, decision trees, expert systems, and neural networks.5 After the machine tool errors are detected with a feature-based method, inverse kinematic techniques and statistical methods can be used to identify individual machine error components. An adaptive error identification method was proposed by Mou.6,7 In this method, a feature-based comparison method is used to correlate the dimensional and form errors of a manufactured part to the systematic machine tool errors.

Compared with direct error component measurement, feature-based error identification is a more efficient way of estimating the components of machine tool error. Further, it is more useful for shop-floor applications of error identification.

The objective of this study is to develop an approach that can effectively detect the composition and amplitudes of error patterns from the machine tool contouring error signals. This approach is developed based on two techniques, wavelet transformations (WT) and neural networks (NN). The following sections describe the details of this approach.

Measurement and Classification of Machine Tool Contouring Errors

Accuracy and good machining conditions are critical to the dimensional accuracy of parts produced using CNC machine tools. Various machine errors affect the dimensions and forms of the resulting parts. Every type of machine error (such as backlash, axis reversal characteristics, vibration, nonsquareness, scale mismatch, and so on) can be reflected through how well a machine can interpolate a circle. Thus, machine errors can be revealed by measuring the circular cutting path of a CNC machine and comparing the path to predetermined reference error patterns.