The major role of temperature sensors in a machine tool thermal error compensation system is the improvement of machining accuracy through the supply of reliable temperature data on the machine structure. This paper presents a new method for the fault diagnosis of temperature sensors along with the recovery of faulty data, thereby protecting the reliability of a thermal error compensation system. The proposed method of detecting a fault and its location is based on the correlation coefficients among the temperature data produced by the sensors. Thereafter, a multiple linear regression model, prepared using the complete normal data, is used for the recovery of faulty data. The effectiveness of this method was tested by comparing computer simulation results with measured data from a CNC machining center.

Keywords: Thermal Error Compensation System, Fault Diagnosis, Recovery, Correlation Coefficient, Multiple Linear Regression Model

Introduction

The major role of temperature sensors in a machine tool thermal error compensation system is the improvement of machining accuracy through the supply of reliable temperature data for a thermal error model of the machine structure. However, contrary to previous expectations, malfunctions or faults in temperature sensors during the working of a compensation system can in fact increase the machining inaccuracy.1,2 Whereas the intuitive detection of faults in temperature sensors is very difficult during machining, there is also a serious financial implication to attaching an additional monitoring device for detecting sensor faults through an acceptance or rejection test of finished workpieces.

Accordingly, a fault detection and recovery technique for temperature sensors is necessary to improve the reliability of a thermal error compensation system. Plus, such a technique is also crucial to produce stable machining, prevent accidents, and improve productivity.

Previous research on the detection of system malfunctions and faults has been characterized by the target system; therefore, an influence diagram,3,4 artificial neural network,5 fuzzy algorithm,6,7 and statistical technique8 have all been applied.

The most serious fault patterns in a thermal error compensation system for CNC machine tools are the breaking of wires and the inclusion of noises. The lack of independence between the temperature sensor outputs is one of the basic characteristics of temperature sensors because the temperature variation in a machine structure is highly correlated.

This paper proposes a new method for fault diagnosis and the recovery of faulty sensor output in a thermal error compensation system. This method considers the characteristics of a thermal error compensation system for CNC machine tools. The correlation coefficients from the temperature data produced by the sensors are used for the fault diagnosis. The fault and its location are detected using a combination of a statistical hypothesis and test on the correlation coefficients. Thereafter, a multiple linear regression model, prepared using the complete normal data, is used for the recovery of faulty data.

The effectiveness of this method was tested by comparing computer simulation results with measured data from a CNC machining center.

Fault Diagnosis and Recovery Algorithm

Quantification of Correlation Among Temperature Variables

Because the temperature data from sensors in a thermal error compensation system can be prescribed as random variables, they are quantified as correlation coefficients. If the statistical correlation between temperature variables is quantified by correlation coefficients, there are several advantages.

First, the cause-and-effect relation between temperature variables can be converted to a simplified input-output relation. Therefore, the complicated physical relation between temperature variables need not be considered.

Second, the correlation coefficients for all the temperature variables can be easily obtained using a simple calculation.

Third, because the cause-and-effect relation between one variable and other variables is consistently determined, the location of a faulty sensor can be easily detected.