Error compensation techniques have been widely applied to improve multiaxis machine accuracy. However, due to the lack of reliable instrumentation for direct and overall measurements, all the compensation methods are based on offline measurements of each error component separately. The results of these measurements are static in nature and can only reflect the conditions at the moment of measurement. These results are not representative under real working conditions because of disturbances from load deformations, thermal distortions, and dynamic perturbations. This present approach involves the development of a new measurement system capable of dynamically evaluating the errors according to the six degrees of freedom. The developed system allows the generation of useful data that cover all machine states regardless of the operating conditions. The obtained measurements can be used to evaluate the performance of the machine, calibration, and real time compensation of errors. This system is able to perform dynamic measurements reflecting the global accuracy of the machine tool without a long and expensive analysis of various error sources contribution. Finally, the system exhibits compatible metrological characteristics with high precision applications.

The contribution of machine tools in the development of several industrial fields is demonstrated. However, during recent decades, the economic environment has forced the industry to new standards of performance in terms of quality, productivity, costs, and production time. These market constraints have evolved much faster than the performance of existing machines. The technology behind these machines is based on concepts dating back several decades and is almost to the limit of their potential. This relative stagnation is explained by the fact that technological developments in this sector are more motivated by the needs of users than by the manufacturer’s initiatives. This situation highlights the need to develop strategies to respond to these new challenges by improving the performance of the machines and making them evolved to a higher level of technology [

The loss of precision in the machine tools is due to the geometrical imperfections of the mechanical structure of the machine or follows the modification of this structure under static, thermal, and dynamic stresses. Even if some of these imperfections can be reduced by the improvement of machine design, it is nevertheless difficult to eliminate completely their effects. The technological limitations and the costs associated with this solution led to the introduction of the concept of errors compensation [

The objective of this paper is to develop a measurement system in real time to identify simultaneously all components of the volumetric error in the multiaxial machine tools. Indeed, the most recent advances in instrumentation have made possible the development of techniques for measuring performance both in terms of accuracy and in terms of speed and cost. The prototype is able to monitor and quantify the components of the error generated when moving along a main axis. Based on an optoelectronics structure, the proposed approach makes it possible to evaluate simultaneously the errors according to 5 of the 6 degrees of freedom of each machine head, regardless of the operating conditions. Moreover, this approach makes it possible to simplify in a substantial way the procedures of calibration and metrological performance evaluation of the machine tools. Compared with reference measurement techniques, this approach presents some significant advantages in terms of precision and in terms of manipulation speed and cost.

Recent advances in the instrumentation field made possible the development of new, powerful measurement techniques. The measurement approach, suggested during this research, is based partly on these innovations, combining the optical and electronic components to carry out a high precision system of measurement. A diagram of the device of measurement is presented in Figure _{1} and then reflected to photodetector PD_{1}. The second beam is projected on retroreflector RR and then directed to photodetector PD_{2}. The third beam is reflected to photodetector PD_{3} using 2 flat mirrors FM_{2} and FM_{3}. Any deviation of the mobile plate compared to the reference would cause variations of beam position on the photodetectors. These variations are obtained starting from the output signals of the photodetectors connected to an electronic circuit for conditioning and preprocessing. A computer is used for acquisition, treatment, and exploitation of various signals.

Disposition of measurement system components.

The He-Ne laser presents low-cost solution with good repeatability. The separators of the nonpolarized laser beam prevent polarization of the incident beam. Their low absorption allows these dielectric spacers to separate the beams by 50%. They are made from a substrate in high precision, having a thermal expansion factor of the order of 7.10^{-6°}C^{−1}, to minimize the distortion of the wavelength. Moreover, the inclination of the substrate avoids any possible back reflection to the laser. The position sensors are made of silicon photodiodes in a single crystal with a quadruple electrode. Compatible with low-power laser beams and other infrared beams, they allow obtaining accurate information on the linear positioning of the beam in both horizontal and vertical directions.

It is important to note the degrees of freedom principle. In a linear constraint, displacement along a known axis leads to the elimination of 5 of the 6 degrees of freedom of the moving part compared to the guidance support. The movement in the direction of the remaining degree of freedom is controlled with precision using a suitable control device. A linear displacement of the moving part along a specific axis involves deviations according to three directions: three translations (positioning and straightness errors) and three rotations (yaw, pitch, and roll). Consequently, the three beams obtained from the principal beam must be aligned in the direction of the moving axis so that the considered beams are received by the photodetectors. The principle and the method of calculation of the position of each beam on a photodetector are presented in Figure _{1} receives the beam reflected by flat mirror FM_{1}, with its positions (_{2}, which receives the beam reflected by the retroreflector RR, are sensitive to the straightness errors in the horizontal and vertical plans. The beam position is reflected by 2 flat mirrors FM_{2} and FM_{3} (oriented at 45°) and represented by the positions (_{3}. This constitutes the cumulative effects of the angular errors (pitch and roll) as well as the straightness in the horizontal plane. Based on the dimensional and geometrical configuration of the measurement system and interactions between data from the photodetectors, some arithmetic relations were established to calculate the various errors. Thus, for each relative movement between the two plates (mobile and references plates), six coordinates are available to evaluate the five components of error. Redundant measurement can be used as checking criterion. In the case of the machine tool, measurements obtained in this manner reflect the real position of the tool related to the part and make it possible to evaluate the deviations that it undergoes compared to its programmed trajectory. These deviations can be caused by geometrical, static, thermal, and dynamic sources. Once the _{2}, the deviation in the horizontal plan is regarded as a horizontal straightness error while any deviation in the vertical plan is considered a vertical straightness error

Calculation of beam position.

With the aim of analyzing the responses of the new measurement system in order to determine its metrological characteristics, a coordinate measurement machine (CMM) is used to carry out evaluation tests. The diagrammatic representation of the experimental setup is illustrated in Figure

Schematic representation of the experimental setup.

Preliminary tests were carried out in order to optimize the utilisation conditions of the measurement system. In fact, it seems important to maximize the precision and the stability before starting the measurement validation. The obtained results show clearly that environmental conditions (light, vibrations, draught, and moisture) have a negative influence on the quality of the system responses. To evaluate the impact of these phenomena, an analysis of sensitivity was performed. This study made it possible to determine their actions and the mechanisms of their interactions and to release the conditions allowing the reduction of their effects. Thus, the two parts of the measurement system were covered so as to reduce the effects of the external sources of light. The use of the covers made it possible to improve substantially the stability and the luminosity of the beams. Figure

Responses of photodetectors based on different conditions.

Preheating curve of laser source.

To calibrate the system and to reduce the effect of environmental conditions, artificial neural networks present an interesting solution. In fact, models based artificial neural networks (ANN) are commonly used to compensate for the effects of temperature and relative humidity. The integration of these models in the compensation is easy and simple to implement. However, the model cannot be generalized for all surfaces of the position detector, because of nonlinearity due to the geometrical shape of the position detector. To overcome these limitations, it is necessary to calibrate the position sensor by developing an algorithm to estimate the horizontal and vertical positions while correcting for nonlinearity due to the concave shape of the surface position sensors. This algorithm must take into account the position of the beam on the projection surface from the position detector by combining all of the environmental factors. To get a rough estimation of the resolution readings, calibration tests were performed. During these tests, the mobile plate is mounted on the displacement member of the CMM related to the fixed plate so as to bring the laser beam to the center of each photodetector position. This position is then the reference position for position sensor calibration. A scan of the entire surface of the position detector is made to generate the necessary data for modeling. The pattern of data acquisition is shown in Figure

Calibration data pattern.

The positions

ANN model architecture of positions prediction.

Figures ^{2} for ^{2} for the ^{2} for the ^{2} for the

Comparison of training and validation performances.

Training | Validation | |
---|---|---|

MSE ( | 76.15 | 277.71 |

MSE ( | 92.81 | 240.27 |

Variance (^{2}) | 0.601 | 1.797 |

Variance (^{2}) | 0.650 | 1.795 |

Residual error of training stage.

Residual error of validation stage.

The analysis model was used to evaluate the influence of temperature on the position. On average, a temperature variation of about ±0.5°C causes a change in the beams position of 1

Influence of temperature on the positions.

Horizontal position ( | Vertical position ( | |
---|---|---|

| 1 | 1.5 |

| 3.25 | 5 |

| 5 | 9 |

Effect of relative humidity (RH) on the positions.

Horizontal position ( | Vertical position ( | |
---|---|---|

±0.5% RH | 0.15 | 0.20 |

±1% RH | 0.45 | 0.65 |

±2% RH | 0.75 | 1.10 |

The last phase of this project is to evaluate the metrological characteristics of the new measurement system (NMS) and validate their performances using a multiaxial machine tool by comparison with a precision interferometer laser (Renishaw-ML10). A protocol for the referencing and installation of the measuring system on the machine is built up to facilitate the alignment procedures and reduce setup time. To get a good estimation of the 5 error components along the main displacement axis, a laser interferometer (ML10) with an accuracy of about 0.1

The validation tests are conducted on the CMM. The reference plate of the NMS is placed on the machine frame, while the mobile plate is fixed on the machine displacement head. The NMS is aligned according to an alignment protocol. Since the interferometer laser uses an elementary measurement approach, it cannot, however, validate more than one error component at each test. It is necessary to mount in parallel with the NMS while respecting the proposed configurations for each measure.

Figure

Measurement of horizontal straightness.

Figure

Measurement of vertical straightness.

The statistical analysis performed was used to compare the correlation between the two curves (front and back). A comparative study of the performance curves according to the displacement cycle is conducted. Regarding the sequence “front” the residual error between the curves obtained with the two techniques is on the order of 11.130

Figure

Measurement of yaw.

Figure

Measurement of pitch.

It is also interesting to compare the two approaches by calculating the mean square error (MSE) and variance. Concerning the yaw, the variance is more pronounced between the two curves than between the front and back cycles. The MSE is about 0.331 arcsec for the front cycle and on the order of 1.204 arcsec for the back cycle. The variance is around 0.016 arcsec and 0.045 arcsec for the two cycles, respectively. As for pitch, the MSE are comparable and are of the order of 0.151 arcsec and 0.170 arcsec for the two cycles, respectively. The variances are comparable to the variances of the measures taken by the ML10.

The roll measurement is illustrated in Figure

Measurement of roll.

The new measurement system consists of an optoelectronics structure able to measure simultaneously and dynamically 5 of the 6 components of the error of displacement. This system enables the identification and the compensation of error in real time regardless of the operating conditions. The tests carried out show that the precision of the system is advantageously comparable with that obtained by recognized measurement techniques. In addition to its precision, the system of measurement proposed is also characterized by its speed, its facility of use, and its cost. Moreover, by its dynamic character, it makes it possible to integrate geometrical, thermal, and dynamic effects and to include them in the same measurement operation. The NMS is developed and designed for the simultaneous and direct evaluation of five geometrical errors on a multiaxial machine tool using a combination of various optical and electronic components. The optimal arrangement of these elements in the existing system was used to measure the positions of the laser beam on the position sensors and convert these positions into real errors. This configuration allows the quantification of linear deviations or horizontal straightness and vertical straightness and three angular errors, yaw, pitch, and roll.

The new measurement system required a sensitivity analysis to study the behavior over time of the signals from the three position sensors. This analysis helped to reveal the impact of environmental conditions on the measurements. Although it helped to stabilize variations in a temperature range between 17°C and 25°C, it is not possible to remedy the convex nature of photodetector. The model was developed to characterize the horizontal and vertical positions of the beam according to each parameter’s influence. The developed model helps to calculate the horizontal position (

The characterization of the metrological parameters of the NMS was needed to determine operating conditions and characteristics in terms of accuracy and resolution. The statistical analysis was used to study the accuracy and fidelity in different points. In addition, tests performed on the CMM were used to validate the performances of the new measurement system using a precision laser (ML10). The developed measurement system is characterized by its speed, accuracy (about ±1.5

The authors declare that they have no competing interests.