Performance Improvement of the LM Device and Its Application to Precise Measurement of Motion Trajectories within a Small Range with a Machining Centre
Hua Qiu, Yong Yue, Akio Kubo, Chao Lin, Kai Cheng, Dehong Huo, Dayou Li
1Department of Mechanical Engineering, Faculty of Engineering, Kyushu Sangyo University, Fukuoka City, Japan.
Advanced Manufacturing and Enterprise Engineering Department, School of Engineering and Design, Brunel University, Uxbridge, UK.
Department of Computer Science and Technology, University of Bedfordshire, Luton, UK.
Department of Mechanical Engineering, Faculty of Engineering, Kyushu Sangyo University, Fukuoka City, Japan.
Product Design and Engineering Department, School of Engineering and Information Sciences, Middlesex University, London, UK.
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, China.
DOI: 10.4236/mme.2012.23010   PDF    HTML   XML   4,309 Downloads   7,454 Views   Citations


In order to apply the LM device previously developed to precisely measuring small motion trajectories located on the different motion planes, three major improvements are successfully performed under the condition of completely maintaining the advantages of the device. These improvements include 1) development of a novel connection mechanism to smoothly attach the device to the spindle of a machining centre; 2) employment of a new data sampling method to achieve a high sampling frequency independent of the operating system of the control computer; and 3) proposal of a set-up method to conveniently install the device on the test machining centre with respect to different motion planes. Practical measurement experiment results with the improved device on a machining centre sufficiently demonstrate the effectiveness of the improvements and confirm several features including a very good response to small displacement close to the resolution of the device, high precision, repeatability and reliance. Moreover, based on the measurement results for a number of trajectories for a wide range of motion conditions, the error characteristics of small size motions are systematically discussed and the effect of the movement size and feed rate on the motion accuracy is verified for the machining centre tested.

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Qiu, H. , Yue, Y. , Kubo, A. , Lin, C. , Cheng, K. , Huo, D. and Li, D. (2012) Performance Improvement of the LM Device and Its Application to Precise Measurement of Motion Trajectories within a Small Range with a Machining Centre. Modern Mechanical Engineering, 2, 71-85. doi: 10.4236/mme.2012.23010.

1. Introduction

In recent years, with the advances of CNC machining technologies, especially in die manufacturing, more and more attention has been attracted from researchers and engineers on how to precisely detect and correctly evaluate the motion accuracy of Machining Centres (MCs) within a small area [1-10]. Several specific measuring devices have been developed for this purpose. For example, Kwon and Burdekin [1,2] developed a measuring device, which consists of a precision cube and two displacement sensors, to detect and evaluate the motion trajectories of both circular and linear interpolation motion within a small range for a MC. Kakino et al. [3] applied a cross grid encoder to measure small motion trajectories with a precision MC. Schmitz and Ziegert [4] produced an instrument combining three laser ball bars to evaluate the spatial CNC contouring accuracy within a relatively small area although the instrument needs a large installation space. Lee et al. [9] presented a measurement system, which included a fixture to mount multiple sensors and a target as the detecting object, to measure geometric errors of a miniaturized machine tool and further attempted to compensate these errors through a software-based method. Kono et al. [10] developed a device combining an optical flat and a laser displacement sensor to measure the geometric errors, associated with the feedback signal utilization of the servo axis from the control apparatus, and then successfully compensated the time-dependent components of these errors for a high-precision machine tool. However, problems exist to some extent in the practical applications of these devices, for example, the expensive price, the complex and time-consuming set-up process of the device on a machine tool, the orientation limitation to the motion planes or motion direction to be measured, and the limited application to specific objects. Nowadays, the most popular devices for detecting and evaluating MC motion accuracy are the double ball bar (DBB) [11] and the cross grid encoder whose commercial product is called as KGB [12]. Based on the principle and structure, a traditional DBB is unsuitable for measuring the motion trajectories within a small area. As an expensive device, the KGB can test a general motion trajectory located on a plane perpendicular to the MC spindle with a fairly high accuracy [13]; however, for a motion trajectory located on other planes, the operation to set up the device on a tested MC is not only difficult and time-consuming but also requires some specific apparatus and jig to ensure the alignment precision between the optical head and encoder [14]. Therefore, the problem of precisely assessing the accuracy in a small size motion has not yet been satisfactorily resolved, and there have been few publications of systematic research on the error characteristics and causes of the trajectory in small size MC motions.

The authors have successfully developed a device called the LM device, with a basic structure consisting of a double-bar linkage mechanism and two laser rotary encoders, for measuring motion accuracy of a MC with a vertical spindle previously [15,16]. The device is applicable to measuring the trajectory of a general planar motion located on a plane perpendicular to the MC spindle. The device has a simple and compact structure and yet provides a large working range with a high resolution. The cost to produce the device is fairly low. Both the installation process on the MC and the measurement operation are simple and convenient in practical applications. The LM device is able to measure small size motion trajectories of the MC; however, based on the mechanical structure feature and data acquisition method, some limitations in measuring performance exist to trajectories in a small area, especially when the motion is fed at a high speed.

This paper presents further developments and improvements for applying the LM device to precisely measuring small size motion trajectories located on different planes. Moreover, as a practical application of the device, a case study, in which the accuracy of a small size motion is detected and evaluated for the MC texted, has been performed. Section 2 describes the improvements performed, including an original connection mechanism, a new data sampling method and a set-up method to install the device on the MC with respect to different motion planes. Section 3 presents and discusses in detail the experiment results with the improved device for the measurement of small size circular and linear interpolation motion trajectories which are located on the X-Y, Y-Z and X-Z planes of the MC respectively. The experiment results sufficiently demonstrate the effectiveness of the improvements. At the same time, based on the measurement results for a number of motion trajectories performed under a wide range of motion conditions, the error characteristics and related causes are verified for the small size motion with the MC. Section 4 draws conclusions on the work presented.

2. Improvements of Measurement Device

Figure 1 shows a schematic diagram of the LM device consisting of a double-bar linkage and two laser rotary encoders which are set at the root end on Link 1 and Link 2 to detect the rotation angles of the links. The device base is fixed on the table of the MC with a vertical spindle. The tip of Link 2 is attached to the spindle with a connection mechanism. The rotation planes of both links are parallel to each other and perpendicular to the rotation axis of the spindle.

Before starting the measurement, a measuring coordinate frame can be set up through a simple operation [15]. The X, Y and Z axes are parallel to those of the MC respectively, and the Z axis coincides with the rotation axis on the root side of Link 1. Therefore, in the coordinate frame, the coordinates (X, Y, Z) of a measured point, which is defined as the intersection point between the spindle rotation axis and the X-Y plane, is given by the following equation:

Figure 1. Schematic diagram of the LM device.

where L1 and L2 are the link lengths, which is 100 mm in the LM device, and q1 is the rotation angle of Link 1 relative to the positive direction of the X axis and q2 is the rotation angle of Link 2 relative to Link 1. The resolution for both q1 and q2 is 1 second due to the used laser rotary encoders, Canon K-1, and interpolators, Canon IU-16. The entire working range of the LM device is located on the X-Y plane and has a disc shape around the origin O whose inner radius is 10 mm and outer radius is 190 mm. The LM device has the position resolution of less than 0.5 mm at the radial direction and less than 1 mm at the argument direction for any measured point within the working range [15].

In order to precisely measure the motion trajectory in a small area with a high feed rate, three major improvements have been performed on the previous device. One is to develop a novel connection mechanism attaching the tip of Link 2 to the MC spindle. The other is to employ a new data acquisition method. The third is to design a simple set-up jig that enables the device to measure trajectories located on different motion planes.

2.1. The New Connection Mechanism

In the previous device, a conventional coupler was used to connect the tip of Link 2 and the MC spindle to be measured. Some potential errors such as the flatness error on the table surface of the MC or the assembly errors of the device itself may lead to the movement of the tip of Link 2 along the Z direction in the measurement. Such movement is forcedly absorbed by the coupler and hardly affects the measuring results for a trajectory in a large size motion or in a small size motion but with a low feed rate. However, the movement may have some negative effect on the rotation of links and result in undesired errors in the measuring results for a small size motion with a high feed rate.

In order to solve this problem, a novel connection mechanism as shown in Figure 2 has been developed. A precision steel ball is fixed at the tip of a stroke ball bearing pin and the stroke bearing is assembled on Link 2. The clearance of the stroke bearing is carefully adjusted at 0 by the manufacture. The pin can freely rotate around the axis and slide along the axial direction. A stopping ring mounted at the bottom of the pin limits the sliding displacement within 3 mm. A connecting bar, at whose tip a magnet piece is fixed, is attached to the MC spindle. During the measurement, the ball is connected to the magnet piece via a supporter consisting of three small precision balls. Because the magnetic force in the connection

Figure 2. Connection mechanism between the improved device and the spindle of MC.

is considerably larger than the friction in the stroke bearing, no relative sliding happens between the steel ball and the supporting balls in the measurement. By applying the mechanism, not only a very small relative displacement between the device and the spindle can be smoothly achieved but also the influence of the movement of Link 2 tip along the Z direction can be naturally absorbed. Furthermore, the set-up operation of the improved device on the MC becomes simpler and easier than the previous device.

2.2. The Data Sampling Method

The software of the previous device was constructed on the MS-DOS platform. The sampling command was sent one by one from a personal computer to the counter board at each sampling time. With this method, it is very difficult to ensure a sampling period in the ms order under the WINDOWS environment. As an effective solution to this problem, a high-speed counter board, Contec CNT32-8M (PCI), is employed in the improved device. Through the utilization of a sampling function based on the board’s clock, a sampling period of 50 ms, which is independent of the operating system of the personal computer, is achieved.

2.3. The Set-Up Method of the LM Device on the MC to Measure Trajectories Located on Different Motion Planes

As explained above, the LM device was developed for measuring the motion trajectory on a parallel plane to the standard surface of the device, i.e. the table surface of the MC to be tested. To detect trajectories on other motion planes, for example, a vertical plane for a MC with vertical spindle, a suitable standard to set-up the device on the MC is necessary. For this purpose, a simple jig is designed, as shown in Figure 3. The jig consists of two main parts: a rectangular part with a right angle and a block with good parallelism between the upper face and

Figure 3. Setting up the LM device on the table of MC.

bottom face. The rectangular part is placed on the upper face of the block to provide a standard surface to set the device. Thus, once the device is fixed on the setting plane of the rectangular part, the rotation planes of Link 1 and Link 2, and then the motion plane, where a trajectory to be measured is located on, are restricted to be parallel to the setting plane. Moreover, in order to prevent the collision between the device and spindle in the measurement, the connection mechanism is attached to the spindle through an inclined bar fixed on the spindle.

It should be noticed that strict parallelism accuracy between the setting plane and motion plane is not required because of the feature of the connection mechanism, i.e. if a small parallelism error exists, the effect is smoothly absorbed by the mechanism. From the results of the measurement experiments, it has been verified with the improved device that limiting the parallelism precision within 50 mm/100 mm is sufficient to ensure the measuring accuracy of motion trajectory in practical applications.

In addition, if a part available to freely adjust the angle of the setting plane is built in the jig instead of the rectangular part, the motion trajectory on a general plane can be readily measured by the LM device. In such situation, based on the same reason presented above, a strict setting accuracy for the setting plane relative to the motion plane is not required.

3. Results and Discussions of Measurement Experiments

In order to verify the effectiveness of the improvements, measurements of small size motion trajectories are performed on the MC with the improved LM device under a wide range of motion conditions. Furthermore, in order to examine the reliability of the measured results, following the ISO standard, ISO 230-1:1996 [17], the measured trajectories are compared with the profile of the work pieces machined under the same motion conditions. Based on the measured results of the motion trajectories, the error characteristics of small size motions are discussed and their causes verified with the tested MC. Because a cutter path for machining a complex contour is usually generated through an interpolation operation of circular arcs or linear segments in industrial practices, the trajectories to be measured are restricted to a circular or linear interpolation motion in this research.

A vertical-spindle MC with a control system of semiclosed loop, Wasino WMC-4, is tested. The movable range of the MC is 900 mm in the X direction, 450 mm in the Y direction and 510 mm in the Z direction, respectively. The NC system is FANUC Series 0-MC, the number of simultaneously controllable axis is 2.5 and the minimum input increment is 1 mm. The basic structure of the MC consists of a Z axis column and a XY table with a hydraulic slideway, where the X table is ridden on the Y table. The maximum feed rate of cutting is 5000 mm/min. In the experiments, the origin of the measuring coordinate frame is set at the central position of the movable range of the MC.

3.1. Circular Motion Trajectories on the X-Y Plane

The experiment conditions are presented in Table 1. The centre of circular motions to be measured is set at point (100, 0) in the measuring coordinate frame as shown in Figure 4. For every condition, the trajectories with respect to a single revolution and to three consecutive revolutions in both clockwise (CW) and counter clockwise (CCW) directions are measured and recorded, respectively. The number of measured points along a full circle trajectory is 800 ~ 2000. The trajectory errors are illustrated in the form of roundness deviation calculated by the least squares criterion in the following if no notation is given.

Figure 5 shows the measured results for the circular motion with a radius of 1 mm and feed rate of 1000 mm/min, where the trajectory in (a) corresponds to the

Conflicts of Interest

The authors declare no conflicts of interest.


[1] H. D. Kwon and M. Burdekin, “Development and Application of A System for Evaluating the Feed-Drive Errors on Computer Numerically Controlled Machine Tools,” Precision Engineering, Vol. 19, No. 2, 1996, pp. 133-140.
[2] H. D. Kwon and M. Burdekin, “Adjustment of CNC Machine Tool Controller Setting Values by an Experimental Method,” International Journal of Machine Tools & Manufacture, Vol. 38, No. 9, 1998, pp. 1045-1065.doi:10.1016/S0890-6955(97)00058-8
[3] Y. Kakino, Y. Ihara, S. Lin, S. Hayama, K. Kawakami and M. Hamamura, “Measurement of Motion Accuracy and Improvement of Machining Accuracy on Ultra-High Precision NC Machine Tools by Using Cross Grid Encoder Test,” Journal of the Japan Society for Precision Engineering, Vol. 62, No. 11, 1996, pp. 1612-1616.doi:10.2493/jjspe.62.1612
[4] T. Schmitz and J. Ziegert, “Dynamic Evaluation of Spa- tial CNC Contouring Accuracy,” Precision Engineering, Vol. 24, No. 2, 2000, pp. 99-118.doi:10.1016/S0141-6359(99)00034-3
[5] X. Mei, M. Tsutsumi, T. Yamazaki and N. Sun, “Study of the Friction Error for a High-Speed High Precision Table,” International Journal of Machine Tools & Manufacture, Vol. 41, No. 10, 2001, pp. 1405-1415.doi:10.1016/S0890-6955(01)00025-6
[6] X. Mei, M. Tsutsumi, T. Tao and N. Sun, “Study on the Compensation of Error by Stick-Slip for High-Precision Table,” International Journal of Machine Tools & Manu- facture, Vol. 44, No. 6, 2004, pp. 503-510.doi:10.1016/j.ijmachtools.2003.10.027
[7] Y. Suzuki, A. Matsubara and Y. Kakino, “A Study on Improvement of Contouring Accuracy in Small Circular Motion for NC Machine Tools—Improvement of Accu- racy by Altering the Feed Rate Limitation Method,” Journal of the Japan Society for Precision Engineering, Vol. 70, No. 6, 2004, pp. 1266-1270.doi:10.2493/jjspe.70.746
[8] K. Iwasawa, A. Iwama and K. Mitsui, “Development of a Measuring Method for Several Types of Programmed Tool Paths for NC Machine Tools Using a Laser Displacement Interferometer and a Rotary Encoder,” Preci- sion Engineering, Vol. 28, No. 4, 2004, pp. 399-408.doi:10.1016/j.precisioneng.2004.01.004
[9] J. H. Lee, Y. Liu and S.H. Yang, “Accuracy Improve- ment of Miniaturized Machine tool: Geometric Error Modelling and Compensation,” International Journal of Machine Tools & Manufacture, Vol. 46, No. 12-13, 2006, pp. 1508-1516. doi:10.1016/j.ijmachtools.2005.09.004
[10] D. Kono, A. Matsubara, I. Yamaji and T. Fujita, “High- Precision Machining by Measurement and Compensation of Motion Error,” International Journal of Machine Tools & Manufacture, Vol. 48, No. 10, 2008, pp. 1103-1110.doi:10.1016/j.ijmachtools.2008.02.005
[11] S. H. H. Zargarbashi and J. R. R. Mayer, “A Model Based Method for Centring Double Ball Bar Test Results Preventing Fictitious Ovalization Effects,” International Journal of Machine Tools & Manufacture, Vol. 45, No. 10, 2005, pp. 1132-1139.doi:10.1016/j.ijmachtools.2005.01.003
[13] S. Ibaraki, W. Goto, A. Matsubara, T. Ochi and M. Hamamura, “Self-Calibration of a Cross Grid Encoder,” Journal of the Japan Society of Precision Engineering, Vol. 72, No. 8, 2006, pp. 1032-1037.
[14] A. Du, S. Zhang and M. Hong, “Development of a Multi-Step Measuring Method for Motion Accuracy of NC Machine Tools Based on Cross Grid Encoder,” International Journal of Machine Tools & Manufacture, Vol. 50, No. 3, 2010, pp. 270-280.doi:10.1016/j.ijmachtools.2009.11.010
[15] H. Qiu, Y. Li and Y.B. Li, “A New Method and Device for Motion Accuracy Measurement of NC Machine Tools, Part 1: Principle and Equipment,” International Journal of Machine Tools & Manufacture, Vol. 41, No. 4, 2001, pp. 521-534. doi:10.1016/S0890-6955(00)00092-4
[16] H. Qiu, Y.B. Li and Y. Li, “A New Method and Device for Motion Accuracy Measurement of NC Machine Tools, Part 2: Device Error Identification and Trajectory Meas- urement of General Planar Motions,” International Journal of Machine Tools & Manufacture, Vol. 41, No. 4, 2001, pp. 535-554. doi:10.1016/S0890-6955(00)00093-6
[17] ISO 230-1, “Test Code for Machine Tools—Part 1: Geo- metric Accuracy of Machines Operating under No-Load or Finishing Conditions,” 1996.
[18] H. Qiu, “Velocity Measurement for Planar Motions of Machines Using the LM Measuring Device,” Journal of Robotics and Mechatronics, Vol. 10, No. 4, 1998, pp. 358-363.
[19] Y. Kakino, Y. Ihara, N. Y. akatsu, M. Yonetani and T. Teshima, “A Study on the Motion Accuracy of NC Ma- chine Tools (4th Report)—Compensating for Decreasing Error of the Circle Radius during Circular Interpolation Motion,” Journal of the Japan Society for Precision En- gineering, Vol. 54, No. 6, 1988, pp. 1113-1118.doi:10.2493/jjspe.54.1113
[20] Y.T. Shih, C.S. Chen and A.C. Lee, “Path Planning for CNC Contouring around a Corner,” JSME International Journal, Series C, Vol. 47, No. 1, 2004, pp. 412-420.doi:10.1299/jsmec.47.412

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