D DAVID PUBLISHING. Performance Calibration of Articulated Arm Coordinate Measuring Machine. 1. Introduction
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1 Journal of Mechanics Engineering and Automation 3 (2013) D DAVID PUBLISHING Performance Calibration of Articulated Arm Coordinate Measuring Machine Unai Mutilba, Gorka Kortaberria, Aitor Olarra and Antonio Gutiérrez Mechanical Engineering Unit, IK4 Tekniker Research Centre, Eibar 20600, Spain Received: July 13, 2013 / Accepted: August 30, 2013 / Published: October 25, Abstract: This paper presents the method for the performance calibration of AACMM (articulated arm coordinate measuring machines) according to ASME B Standard. The growing use of this class of measurement equipment has been accompanied by an absence of authorized laboratories to provide calibration certificates for its performance. Due to ASME B and VDI are nowadays the unique standards in the field of AACMM verification, IK4 Tekniker has compared both of them in order to develop internal test procedures to yield reliable performance calibration results. As a result, IK4 Tekniker has been recognized by the Spanish Accreditation Body (ENAC) in the field of AACMM calibration. Internal test procedures and uncertainty evaluation analysis have been developed as well as ENAC certificated reference test equipments have been acquired to ensure a suitable AACMM calibration process. Key words: AACMM, performance calibration, ASME B , ENAC, uncertainty. 1. Introduction 3D (three dimensional) CMM (coordinate measuring machines) are widely used to take measurements directly in the manufacturing environment. For some applications, AACMM offers some advantages compared with orthogonal CMMs, some as measuring of larger measuring volume, ease of use, more measurement freedom and to be less expensive. However, the measurement error of AACMM (articulated arm coordinate measuring machines) exceeds that of orthogonal CMMs because its configuration brings to easy error accumulation. If the measuring equipment is installed in a measuring laboratory where measuring conditions are controlled and measurement equipments are suitably fixed and properly treated, performance characteristics keep under its requirements. Nevertheless, the common use of AACMM is at shop floor level conditions where it is Corresponding author: Unai Mutilba, M.Sc., mechanical engineer, research fields: metrology equipments, mechanical precision engineering and quality assurance. unai.mutilba@tekniker.es. usually manipulated by different operators. Under these conditions, AACMM s performance characteristics get worse and it is hard to determine when it fails to fulfill with its performance specific requirements. The growing use of articulated arm coordinate measuring machines at Spanish industry has been accompanied by an absence of authorized laboratories to provide calibration certificates for AACMM s performance. In this scenario, IK4 Tekniker has set up a performance calibration service of this measuring equipment filling this metrological gap at Spanish industry [1-3]. IK4 Tekniker offers ENAC accredited performance calibration service for different types and volumes of AACMM. Firstly, a search about standards applicable to these machines has been carried out. As a result, two standards have been found, ASME B Standard [4] and VDI Standard [5]. IK4 Tekniker has compared both of them in order to develop internal test procedures to yield reliable performance calibration results. Moreover, ENAC certificated reference test
2 Performance Calibration of Articulated Arm Coordinate Measuring Machine 603 equipments have been acquired and uncertainty evaluation analysis has been developed in order to achieve accreditation by the Spanish Accreditation Body. The paper is organized as follows: Section 2 describes the measurement equipment needed for the whole calibration process; Section 3 discusses the calibration procedure; Section 4 explains uncertainty assignment and evaluation of the measuring process; Section 5 presents results and Section 6 gives conclusions. 2. Test Equipment According to ASME B Standard, the whole calibration performance test of an AACMM is subdivided into three different tests: effective diameter test, SPAT (single-point articulation test) and volumetric test. For this reason, multiple reference test equipments are needed to carry out the whole calibration test. As general rule, reference test equipments must be ENAC certificated and its uncertainty must be within one tenth of the working tolerance for each of the three performance tests. Precision reference ball is used for effective diameter test and single-point articulation test for switching probes. The sphere is made up of ceramic and the combined surface finish and sphericity does not exceed one fifth of the working tolerance. A reference ball of 30 mm diameter has been fixed to a table to carry out performance tests. Trihedral seat comprises three hardened spheres placed in a flat bottom or cup. In this way, a very stable and high repeatable mount is obtained for locating AACMM s tip through three point contacts. It is used for the single-point articulation test with hard probes. It has been ENAC calibrated using a CMM machine available at IK4 Tekniker. A ball bar of 2,400 mm maximum calibrated length has been purchased for the volumetric performance test. It is made up of carbon fiber composite and it comprises 13 balls, the distance between two consecutive balls is 200 mm and every distance is ENAC calibrated. Therefore, the ball bar has a minimum calibrated length of 200 mm and a maximum calibrated length of 2,400 mm, which allows IK4 Tekniker to carry out performance calibration of AACMM as long as 4 m of sphere diameter. The ball bar has been mounted in precise rotatory table to position it in horizontal, vertical and 45 orientations. It is shown in Fig. 1. RA 7320SE romer absolute arm has been used to check the reliability of the calibration process prepared at IK4 Tekniker, as can be seen in Section 5. Its measuring range is 2 m (sphere diameter) and it is made up of carbon fiber. Probing is done manually by the operator since it includes a hard contact probe of 6 mm (diameter). It has been mounted in a portable plate to be located in each of the 20 positions of the volumetric performance test. 3. Calibration Procedure As mentioned above, the whole calibration performance test of an AACMM is subdivided into three different tests: effective diameter test, SPAT and volumetric performance test [4]. The intent of the calibration process is to evaluate the performance of an AACMM, enabling to the final users to determine if it is appropriate for their specific requirements or not. Prior to conducting performance calibration test, the machine must be mounted in accordance with final user specifications and ensuring suitable mounting stiffness and orientation. Moreover, appropriate environmental, electrical and vibration conditions must be provided during the entire process. Effective diameter test: Rigidly mounted precision reference ball is measured using nine probing points, with this information a sphere is determined through Fig. 1 Calibrated ball bar for the volumetric performance test.
3 604 Performance Calibration of Articulated Arm Coordinate Measuring Machine the AACMM software and its diameter is calculated. The measuring process must be carried out minimizing the articulation of the AACMM. The difference between the measured and calibrated diameters of the sphere is reported as diameter deviation. The effective diameter performance test value is reported as the maximum deviation regardless of sign. Obtained results may reveal different problems as machine or probe hysteresis or improper probe calibration [4]. SPAT: It seeks to assess the ability of the AACMM to provide similar values of a point coordinate when the equipment is articulated through the maximum possible range of motion for that single point. This test incorporates aspects of both repeatability and reproducibility. If the AACMM incorporates a hard probe, trihedral seat is used as reference equipment. Nevertheless, when using switching probe precision reference ball is mounted as reference equipment. The single-point performance articulation test is performed placing the trihedral seat or precision reference ball at three different locations within the working volume. For each of three positions, 10 points are taken by the AACMM. The statistics used to represent the single point articulation performance are the maximum deviation of the points from a mean value and twice standard deviation of the point location [4]. Volumetric performance test: It will assess aspects of the linear displacement accuracy and volumetric performance of the AACMM. The measuring process takes into account five measuring variables to define 20 measuring positions for the ball bar: ball bar length, working octants, ball bar inclination, distance from AACMM to reference ball bar and measuring direction. The general approach is to position the ball bar in two vertical orientations, 10 horizontal orientations and eight 45 orientations with respect to the AACMM to a given distance (near/far) and measure five points per sphere, working out center-to-center calibrated value. Since ball bar is fixed in a rotatory plate to get performance orientation, AACMM is placed around the ball bar to carry out each length measurement. As a result, 20 distance values are obtained according to the 20 measuring positions defined in Table 1. The results of this test will be reported as three Table 1 Volumetric performance test based on 20 measuring positions. Position No. Artifact length Octants Inclination Distance Direction 1 Short 8 Horizontal Near Radial 2 Short 5 Horizontal Near Radial 3 Short 1 & 2 Horizontal Far Tangential 4 Short 4 & 7 45 deg Far Tangential 5 Short 7 & 3 Vertical Far Tangential 6 Short 1 & 5 Vertical Far Tangential 7 Short 2 Horizontal Near Radial 8 Long 2 & 8 45 deg Near Tangential 9 Short 3 45 deg Near Radial 10 Long 1 & 7 45 deg Near Tangential 11 Short 1 & 6 45 deg Far Tangential 12 Short 6 & 3 45 deg Far Tangential 13 Short 5 & 4 45 deg Far Tangential 14 Short 3 & 8 45 deg Far Tangential 15 Short 5 & 2 45 deg Far Tangential 16 Short 1 & 8 45 deg Far Tangential 17 Short 2 & 7 45 deg Far Tangential 18 Long 3 & 4 Horizontal Near Tangential 19 Long 2 & 6 Vertical Far Tangential 20 Long 4 & 8 Vertical Near Tangential
4 Performance Calibration of Articulated Arm Coordinate Measuring Machine 605 quantities: the maximum deviation from the calibrated ball bar value, the range of the deviations and two times the root-mean-square of the deviations [4]. 4. Uncertainty Evaluation Uncertainty evaluation analysis has been developed to evaluate all error sources associated with the testing equipment under the conditions that prevail at the time of testing. Since the whole calibration process involves three different test measurements, an individual uncertainty is addressed to each of three individual calibration tests. Effective diameter test: Uncertainty sources that contribute to this test uncertainty are calibrated diameter of the precision reference ball, temperature at the time of testing and the uncertainty associated with the lack of rigidity of the reference ball mount. In this case, mount does seem to be rigid enough to disregard this error source. SPAT: Uncertainty sources to be considered are the rigidity of the trihedral seat and its geometrical perfection. The contribution of the trihedral seat has been analyzed and calibrated in CMM and uncertainty associated with the rigidity of the seat has also been considered to be zero. Volumetric performance test: Uncertainty sources include ball bar s uncertainty stated on the calibration certificate, uncertainty due to dimensional drift of the ball bar, uncertainty contribution of the temperature at the time of testing and uncertainty because of the fixturing. For the ball bar, expanded uncertainty is explained in Eq. (1): U STANDARD = L STANDARD (1) Due to the lack of information to calculate the dimensional drift of the ball bar based on different observations, it has been considered that dimensional drift is equal to the calibration uncertainty of the ball bar and it follows a rectangular distribution. Eq. (2) shows expanded uncertainty for the dimensional drift of the ball bar. U DRIFT = 2 ( L STANDARD )/ 6 (2) In temperature contribution case, law of propagation of uncertainty has been applied in order to analyze the effect of the variables uncertainties on the uncertainty of the temperature function based on this variables [6-8]. These variables are ball bar calibrated length, thermal expansion coefficient and temperature variation from 20 ºC. Eq. (3) explains length correction to be done. ΔL = L a T (3) In this case, variables are uncorrelated between them, so the combined standard uncertainty is give by law of propagation of uncertainty given by Eq. (4) [6-8]. N f c( y) i1xi 2 2 x i (4) In Eqs. (5) and (6), law of propagation of uncertainty is applied to the length correction to be done L 2 L 2 L 2 AL L T u u u u (5) L T And 2 u T u L T u L u (6) L L T Considering that calibration is done at laboratory conditions, length difference between AACMM and measuring equipment is considered to be zero. Therefore, length variation uncertainty (µl) is disregarded as shown in Eq. (7): u T u L T u L u (7) L L T Eq. (7) is numerically developed as shown in Eq. (8). Since length variable is different for AACMM and ball bar, both lengths are introduced in Eq. (8): u TEMP u L L T S AACMM T u LS LAACMM (8) where, L S = standard s length used in the calibration, which depends on AACCM length; L AACMM = AACMM s length to be calibrated; (Sent by the client); ΔT = temperature variation. Laboratory conditions are 20 ± 0.5 C at IK4 Tekniker; α = coefficient of thermal expansion. Both AACMM and ball bar standard are made up of the same material
5 606 Performance Calibration of Articulated Arm Coordinate Measuring Machine (carbon fiber); µ α = 10% of the thermal expansion coefficient; µ T = thermometer s uncertainty stated on its calibration certificate. Expanded uncertainty for the temperature contribution is shown in Eq. (9), it is obtained by multiplying the combined standard uncertainty achieved in Eq. (8) by a coverage factor k, which can be assumed that taking k = 2 produces an interval having a level of confidence of approximately 95% [6-8]. U (9) TEMP. 2 TEMP Uncertainty associated with the fixture has been considered to be zero. Therefore, expanded uncertainty for the volumetric performance test is as Eq. (10). Introducing information related to the standard s length, AACMM s length, temperature variation, expanded uncertainty for the volumetric performance test is achieved. U U U U (10) STANDARD DRIFT TEMP. In order to set up a calibration service of AACMM at IK4 Tekniker, a CMC (calibration and measurement capability) available to customers has been defined [9]. Eq. (11) describes the realizable measurement capability of IK4 Tekniker at AACMM performance calibration. CMC L (11) AACMM Eq. (11) is expressed in microns (µm) and L AACMM is the diameter length of AACCM introduced in millimeters (mm). 5. Results According to ASME B Standard each of three individual calibration tests has its own data analysis and its own uncertainty evaluation. After developing calibration procedure and uncertainty evaluation, RA 7320SE romer absolute arm has been used to check the reliability of both developments prepared at IK4 Tekniker and to design the format for reporting performance evaluation results. Effective diameter test: As mentioned above, the effective diameter performance test value is reported as the maximum deviation regardless of sign. Table 2 shows these results in millimeters (mm). SPAT: The statistics used to represent the single point articulation performance are the maximum deviation of the points from a mean value and twice standard deviation of the point location. Table 3 and Table 2 Effective diameter (mm) test results. Calibrated Measured diameter Mean Max. Expanded diameter M1 M2 M3 diameter deviation uncertainty μm Table 3 SPAT results. Measuring X i Y i Z i δ i δ i Mean Max. deviation (δ max ) S SPAT Exp. uncertainty 0 μm
6 Performance Calibration of Articulated Arm Coordinate Measuring Machine 607 X i = X measured coordinate touch by the AACMM; Y i = Y measured coordinate touch by the AACMM; Z i = Z measured coordinate touch by the AACMM; δ i = Three dimensional deviation from the average coordinates to each of the corresponding 10 points. Error (um) 2S SPAT Max. deviation Fig. 2 SPAT results depicted. Fig. 2 show results obtained at SPAT. Volumetric performance test: For each of the 20 measuring positions defined in Table 1, center-to-center length is calculated as depicted in Table 4. The results of this test are reported as three quantities: the maximum deviation from the calibrated ball bar value, the range of the deviations and two times the root-mean-square of the deviations. Fig. 3 shows test results depicted. 6. Conclusions A reliable calibration test procedure has been developed to describe and break down AACMM s performance. Furthermore, uncertainty evaluation of all error sources involved in the calibration process has also been analyzed; results in Section 5 show that uncertainty values achieved are small enough to ensure a reasonable performance evaluation of an AACMM. As a result of the job presented, a calibration service for this class of measurement equipment has been created at metrology unit of IK4 Tekniker research centre and it has been certified by achieving ENAC accreditation by the Spanish Accreditation Body. By the way, the lack of this service at the Spanish industry is satisfied successfully. Table 4 Volumetric performance test results. Measuring L i L c δ i δ i δ i Max. deviation (δ max ) Range RMS Exp. uncertainty μm L i = Measured length by the AACMM; L c = Calibrated length of the ball bar standard; δ i = Length deviation from the ball bar value. Error (um) Fig. 3 Max. deviation Volumetric performance test results depicted.
7 608 Performance Calibration of Articulated Arm Coordinate Measuring Machine References [1] ENAC Home Page, [2] H. Hamana, M. Tominaga, M. Ozaki, R. Furutani, Calibration of articulated arm coordinate measuring machine considering measuring posture, Int. J. of Automation Technology 5 (2) (2011) [3] J.J. Aguilar, J. Santolaria, J.A. Yagüe, A. Majarena, Multi-posture kinematic calibration technique and parameter identification algorithm for articulated arm coordinate measuring machines, in: Proceedings IMETI 2008, Orlando, Florida, USA, [4] Methods for Performance Evaluation of Articulated Arm Coordinate Measuring Machines, American Society of Mechanical Engineers, USA, [5] VDI/VDE 2617 Part 9: Acceptance and Reverification Test for Articulated Arm Measuring Machines, Verein Deutscher Ingenieure, Germany, [6] Guide to the Expression of Uncertainty in Measurement, International Organization of Standardization, Switzerland, [7] Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST, USA, [8] Uncertainty Evaluation, NPL, UK, [9] BIPM Home Page,
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