Machine tools error characterization & compensation by on-line measurement of artifact a
Abdul Wahid Khan*a, Wuyi Chena, Lili Wua, School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, P. R. China.
ABSTRACT Most manufacturing machine tools are utilized for mass production or batch production with high accuracy at a deterministic manufacturing principle. Volumetric accuracy of machine tools depends on the positional accuracy of the cutting tool, probe or end effector related to the workpiece in the workspace volume. In this research paper, a methodology is presented for volumetric calibration of machine tools by on-line measurement of an artifact or an object of a similar type. The machine tool geometric error characterization was carried out through a standard or an artifact, having similar geometry to the mass production or batch production product. The artifact was measured at an arbitrary position in the volumetric workspace with a calibrated Renishaw touch trigger probe system. Positional errors were stored into a computer for compensation purpose, to further run the manufacturing batch through compensated codes. This methodology was found quite effective to manufacture high precision components with more dimensional accuracy and reliability. Calibration by on-line measurement gives the advantage to improve the manufacturing process by use of deterministic manufacturing principle and found efficient and economical but limited to the workspace or envelop surface of the measured artifact’s geometry or the profile. Keywords: Calibration, Machine tools, On-line measurement, Measuring methodology, Error characterization, Compensation, Touch trigger probe.
1. INTRODUCTION Machine tools error characterization and compensation are an inevitable integral part to improve the accuracy of the machine tools due to high accuracy demands of manufacturing precision components. The machine tool’s accuracy is deteriorated because of several factors influencing on it, which are manufacturing joint errors, assembling errors of components, misalignment, gravitational and environmental effects, stiffness, aging, mishandling and misuse of machine tools [1]. On account of these influential factors, the on ground actual accuracy of machine tools is quite different to its designed or manufacturer predicted accuracy. This inaccuracy of machine tools badly affects the manufacturing of high precision components so machine tools need to be characterized periodically and made correct to maintain the accuracy and consistency of ascertained quality level. For error characterization and its compensation, various researchers investigated in different ways whereas limited standard guidelines and measurement methods are available like ASME B.5.54, ISO 10360, ISO 230 series, ISO 10791 series and ISO 13041 series [2-6]. Most of them are useful only for three axis machine tools or covered the 5-axis machine tools partially. Volumetric accuracy of machine tools is dependent on the systematic geometric error of machine tools and is defined as the error of relative position between the tool and the workpiece that vary slowly in time and are related to the kinematics of the machine tool. Experimental evidences show that these errors account for about 70% of the total machine tool errors [7]. The commonly used methodologies for error characterization are direct, indirect and hybrid calibration, which were experimented by the researchers formerly for measuring the systematic geometric errors [8]. In the past for compensation of these errors primarily two approaches were opted to achieve high accuracy, namely, error avoidance and error compensation [9]. Error avoidance approach is a conventional approach in which the major focus is to avoid and reduce the errors at design and manufacturing stages, and is less attractive due to economical constraints. However, the error compensation through software methodology is a quite popular and hot topic in these days due to its cost effective feature [10]. Very few researchers worked on the online calibration of machine tools as Huang and Ni [9] presented an on-line compensation by introducing a parametric measurement method. They used multi-degree-of-freedom measurement system (MDFM) for a three axis machine *
[email protected]; 2009 International Conference on Optical Instruments and Technology: Optoelectronic Measurement Technology and Systems, edited by Shenghua Ye, Guangjun Zhang, Jun Ni, Proc. of SPIE Vol. 7511, 75110K · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.839866 Proc. of SPIE Vol. 7511 75110K-1
tool. Most researchers worked on offline measurement and compensation of machine tools. This current research presented an on-line measurement based calibration methodology to characterize and compensate the machine tool's error. The concept for this research was conceived through the on-line measurement (OMM) of workpieces experimented by the researchers like Kim et al. [11] who researched on the machine measurement system and investigated the form accuracy and surface roughness of the machined workpiece on the machine tools. Cho et al. [12] developed an effective inspection planning strategy for sculptured surfaces in the on-machine measurement. Lee et al. [13, 14] proposed computer-aided inspection planning (CAIP) system for on-machine measurement. Chang et al. [15] presented a system and methodology for on-line free form surface measurement via a scanning contact probe installed on CNC machine tool. Cho et al. [16] presented an integrated machining error compensation method based on polynomial neural network approach and inspection database for on-machine-measurement system. Authors concentrated at on-line measurement notion and developed a methodology for error characterization and compensation by on-line measurement of a standard or an artifact having similar geometry of the component use for mass production. This methodology is for effective, inexpensive calibration and compensation of a machine tool ensuing high precision components with more dimensional accuracy and reliability.
2. SYSTEMATIC GEOMETRIC ERROR CONCEPT AND ITS MODELING IN WORKSPACE VOLUME Systematic geometric errors are considered as the coincidence error of reference point between the tool and the workpiece or error of relative position between the tool and the workpiece at an arbitrary point in the volumetric workspace of a machine tool. The concept is elaborated through Figure-1. “RCS” is the reference or global coordinate system, “TCS” is the tool coordinate system and “WCS” is the workpiece coordinate system. Initially workpiece coordinate system and tool coordinate system coincide to each other under ideal conditions but due to possible links and joints errors their pose (position and orientation) change and systematic geometric error is introduced.
Fig. 1 Systematic geometric error at arbitrary point of volumetric workspace
Machine tools are basically composed of links and joints and practically most of them are based on prismatic and rotary joints chained in parallel or in serial manners [17]. Erroneous assembly or erroneous movements of these joints developed systematic geometric error at the cutting tool, probe or end effector relative to the workpiece in workspace volume. This systematic geometric error can be calculated through modeling of these links and joints in a systematic
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way. Homogenous transformation matrices (HTMs) can be used for modeling whereas link and joints errors are incorporated into form of HTMs whose rank is 4x4. These matrices represent the pose of any one frame in which top left 3x3 of each matrix represent the directional cosines of the body and top right 3x1 matrix represents the origin position of the body from the reference coordinate system, whereas left 1x3 vector is called perspective vector and at right down placed 1 as a scaling factor. As per rigid body position and movement along with their errors from one joint to its adjacent joint can be described by multiplying the relevant HTMs of the respective joints. For every pair of links and joints there are four HTMs matrices which describe the position, position error, motion and motion errors of the respective pair of link and joint. If multiplied these four matrices a new matrix can be obtained which is denoted as Ai [18].So from these matrices the ideal position and actual position of the tool, probe or end effector in an n-axis machine tool can be denoted as mentioned in equation-1.
ract = [ A1][ A2][ A3].............[ An ][rideal ] = [T ][rideal ]
(1)
In similar way the relationship between the position vector in tool coordinate system and same vector in workpiece coordinate system can be described as equation-2. [rwp ] = [T ][rtl ] (2) The position error vector can be derived from the difference between the actual position vector in the workpiece coordinate system and the ideal positioning vector in the tool coordinate system as explained in equation-3-5.
[ew] = [rwp ] − [rtl ]
(3)
= [T ][rtl ] − [rtl ]
(4)
= [T − I ][rtl ]
(5)
By using this error model, the positioning error vector “ew” within the designated workspace can be obtained. So this model can be used for calibration of volumetric workspace at any arbitrary position.
3. METHODOLOGY FOR ON-LINE MEASUREMENT OF ARTIFACT AND ERROR CHARACTERIZATION & COMPENSATION Machine tool systematic geometric error characterization methodology was carried out with Renishaw probe and a standard artifact whose quantity value or point positions were known or quantified through the coordinate measuring machines (CMM). This artifact has the similar geometric shape and feature as the mass production components to assess the accuracy of the machine tool in the similar envelop volume or geometry which can be used further to enhance the accuracy of machine tool through error compensation, consequently producing high dimensional accuracy and more reliable components. The process is hereby explained through flow diagram as in Figure-2 for error characterization and its compensation in a machine tool. According to the process the artifact geometric values were quantified through a highly accurate CMM and recorded properly and then measured artifact was mounted on the machine tool and again measured with a Renishaw probe which was mounted on the machine spindle and interfaced with controller in a similar way as in on-line measurement. The on-line measurements of geometric values were stored into connected interfaced computer. The data was compared and machine tool errors were characterized. These errors were compensated through a developed algorithm and consequently generating new NC codes by recursive technique until the error difference become smaller than the tolerance limits which was decided before hand for the process tolerance. The main caution in this process is that, environment need to be maintained properly and is similar at each stage of measurement so that random effects and unavoidable errors could be minimized.
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Fig. 2 Flow diagram of error characterization and compensation process
4. SYSTEM CONFIGURATION AND METHODOLOGY IMPLIMENTATION Methodology implementation needs some prerequisites like mounting and interfacing the probe with machine tool and calibration process of probe etc. which are explained in detail for better understanding. As an artifact a turbine blade having a free form sculptured surface was considered and its features were measured and quantified on a CMM. The artifact was then placed on a 5-axis grinding machine and a Renishaw probe LP2DD was mounted on machine tool by changing the cutting tool. The configuration of the system is explained below. 4.1 Probe interfacing Renishaw probe LP2DD was mounted on the machine tool and was interfaced with NC system as well as the interfacing between the CNC controller and an auxiliary computer was made for recording the on-line measurement data concurrently, properly and efficiently through recursive compensation algorithm. Compensated NC codes were generated and fed to the machine for compensation, and resultant output was validated through measurement and repeated the process further for on-line compensation of a machine tool. LP2DD probe connection and interfacing is explained herby is shown in Figure-3. The connection contains two parts, the connection between the probe and CNC system and the connection between the computer and CNC system. Probe connection with the CNC system is very simple which just connects the blue, green output signal cable and its screened cable to the A2, A3 and A1 terminal of MI8-4 interfacing box respectively, which is further connected to the siemens controller 840D NCU X121.
Fig. 3 Probe interfacing with machine tool
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The X121 during interfacing also provides power supply to the MI8-4. Siemens controller 840D CNC X 122 panels has an output auxiliary RS232 port for computer communication through a PC adopter. This PC records the measurement which results to deal with further communication, processing and generating new NC codes for compensation process etc. 4.2 Probe calibration Before executing the on-line calibration the probing errors and the diameter of probe were investigated. The probe calibration was carried out as per standard method and procedures. Calibrated diameter of probe was observed 5.942mm with stylus length of 35mm. For calibration of probe a standard certified sphere make Renishaw whose certified diameter is 29.9938mm was engaged. Pre-travel variation error was calculated which is basically dependent on the tilt and roll angle of the probe approach direction and results were found within limits. In all possible tilt and roll angle ranges the pre-travel deviations were measured to fortify the reliability of measuring process and to minimize the uncertainty of measurement. Along with probing errors the repeatability of probe was also investigated which was observed within 1 micron. The calibration process is shown in Figure-4.
Fig. 4 Probe calibration by using standard sphere
4.3 Measurement of artifact As per methodology, measurement procedure of an artifact has two stages. At first stage the profile and geometric features need to be measured and quantified on CMM whereas point position and results need to be recorded properly. In the second stage the measurement of artifact need to be carried out on machine tool through Renishaw probe, whose system configuration has already been explained in this paper. The turbine blade was selected as an artifact which has a sculptured free form surface. The measurement of marked section as mentioned in Figure-5 & 6 for single and multi section was carried out on CMM and through Renishaw probe for on–line measurement as per the curvature adaptive distribution of measuring points. The difference of measurement (actual and nominal) was carried out through the feature extracted measurement on various sections as mentioned at Table-1 and the difference can be calculated by the below mentioned formulae whereas results are shown through Figure-8.
Error = ( Xm − Xn) 2 + (Ym − Yn) 2 + ( Zm − Zn) 2
(6)
As per the equation-6 the “m” denotes the measured results through on-line measurement on machine tool whereas “n” denotes the nominal value measured/quantified through CMM or some other reliable measuring method. The difference is the error of a machine tool at that specific point. The measurement difference is clearly shown in the Figure-7. Measurement procedure of turbine blade sections is shown in Figures-9.
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Fig. 5 Turbine blade on which a single section measurement through CMM and on-machine measurement
Fig. 6 Turbine blade on which multi-section measurement through CMM and on-machine measurement
Fig. 7 Error characterization by comparison of CMM and on-line measurement
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Table-1 Error characterization by through on-line measurement
Error in X-direction at various measured sections 145 130 119.6 94.1 80
175
68.7
0.0015
-0.1453
-0.1166
0.0548
-0.0213
-0.0547
0.0367
-0.0535
-0.1473
-0.1019
-0.0782
-0.0928
-0.0803
0.01
-0.1378
-0.1502
-0.1247
-0.1142
-0.1374
-0.0979
-0.0169
-0.1729
-0.1528
-0.1344
-0.1257
-0.1632
-0.1007
-0.0373
-0.2004
-0.1621
-0.1551
-0.1392
-0.167
-0.0976
-0.0532
-0.2386
-0.1772
-0.1915
-0.1545
-0.146
-0.0933
-0.0645
-0.3098
-0.208
-0.2322
-0.184
-0.1245
-0.095
-0.0905
-0.4059
-0.2611
-0.2762
-0.2098
-0.1223
-0.1202
-0.1346
-0.5065
-0.3437
-0.3376
-0.2469
-0.1661
-0.1444
-0.1575
-0.4322
-0.4085
-0.306
-0.2188
-0.1642
-0.2019
-0.5073
-0.4852
-0.3879
-0.2882
-0.2231
-0.2757
-0.4883
-0.3766
-0.3141
-0.3396
-0.382
-0.4343
-0.4456
-0.4869
-0.4693
Machine tool workspace error 0. 1 0
Error (mm)
- 0. 1
1
2
3
4
5
6
7
8
9 10 11 12 13 14
- 0. 2 - 0. 3 - 0. 4 - 0. 5 - 0. 6 Displacement as per adoptive distribution method
Fig. 8 Error observed during measurement at different section of artifact
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175 145 130 119. 6 94. 1 80 68. 7
Fig. 9 Error Measurement process by on-line machine measurement
4.4 Error compensation Error compensation is based on error correction through software way and generation of new NC codes. The difference of measurement between actual and nominal values indicates the error characterization of machine tool. This error was compensated by removing the characterized machine tool error. For this purpose new CNC codes were generated through an algorithm in which the machine tool error was removed by recursive iteration technique and difference of the tool paths brings into allowed tolerance limits. The procedure is explained through a flow diagram as mentioned in Figure-10 and its validation is exhibited through Figure-11.
Fig.10 Error compensation methodology
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Fig. 11 Validation of compensation by software way
5. MEASUREMENT RESUTLS AND DISCUSSION Turbine blade artifact’s quantified/known feature values were used for on-machine measurement for error characterization and for further compensation of machine tool. It was observed that workspace volumetric measured error was significantly large which indicates the state of machine and need to be adjusted physically by hardware way. This machine is in its design validation process whose main elemental parametric accuracy is within limits but volumetric accuracy is beyond the limits due to spindle and axis misalignment whose adjustment is underway. In addition there is small impact of measurement and machining errors too, which will be eliminated by the refinement of methodology and removing the shortcomings which are under considerations. However the accuracy of the measuring results depends on various functions in which the main function is the number of measuring points, environmental effect, probe calibration and the point position for measurement. Adaptive measuring point method was used against a general case in which number of measuring point decreases the information about the measurement of surfaces becomes insufficient, whereas in adaptive distribution of measuring points technique in which the selected points were divided according to the nature of the curvature and eliminate that drawback of a general case. Measurement was carried out in controlled environmental conditions whereas probe was properly calibrated to avoid unnecessary errors of measurements. Results exhibit that this calibration methodology is viable, inexpensive and efficient especially for enhancing the accuracy and reliability for mass production components.
6. SUMMARY AND CONCLUSION In this paper an on-line calibration methodology was presented, which is capable to characterize and compensate the machine tool error by using a standard/artifact. The geometric features of artifact were quantified at different sections and by using adoptive point’s method compared through on-line measurements; hence the machine tool error is separated by taking the difference of both measurements (actual and nominal measurement) at the specific points. This error was attached to the NC path and compared with the actual NC path. Difference was compensated through an algorithm by recursive compensation technique and new NC codes were generated to feed directly to the controller for efficient compensation. By compensation of a machine tool errors can be removed easily and hence the accuracy of machine tool be improved. The calibration methodology is quite useful and efficient for mass production of products but limited up to the artifact geometry or envelops volume.
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