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Testing and calibration of coordinate measuring arms
Precision Engineering Journal of the International Societies for Precision Engineering and Nanotechnology 25 (2001) 90 –99
Testing and calibration of coordinate measuring arms Igor Kovacˇa,*, Adolf Frankb a
b
Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia Institute for Production Technology, Graz University of Technology, Kopernikusgasse 24, A-8010 Graz, Austria Received 30 November 1999; accepted 18 May 2000
Abstract Portable coordinate measuring arms with rotational axes have found their place in many industrial areas. To establish and confirm the accuracy of these measuring devices, related test methods and appropriate devices are needed. After an introduction, a new high precision measuring device for testing and calibration of portable coordinate measuring arms is presented. Analysis showed that the best results can be obtained with a device for measuring along a straight line adjusted in various spatial directions. We discuss the design and construction of this measuring system and provide a theoretical calculation of its measurement accuracy, which was confirmed by experiments carried out on a prototype of a high precision measuring device in both unloaded and loaded conditions. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Testing; Calibration; Portable coordinate measuring arms
1. Introduction Portable coordinate measuring arms (CMAs) have been successfully introduced into measuring technology [1]. Their main areas of use are in the automotive, aerospace, heavy engineering, railway and energy industries. A robotlike, manually driven, multi-joint, mechanical arm connected to a computer allows the user to achieve measurement tasks during maintenance, assembly, quality assurance, inspection and replication of complex models into 3-D data, or in measuring surfaces of free form and curved pipe lines. The structures of CMAs also allow measurement of workpieces directly in a machine fastening device. Another application field is in connection with industrial robots [2]. To carry out measurement tasks in the manufacturing industry, the accuracy level of the measuring device is one of its most important requirements. From a brief survey of existing device performances [3] it is evident that the accuracy characteristics of such devices are below those of the common Cartesian coordinate measuring machines (CMMs). Measurement of the repeatability performance of CMAs shows that it is possible to achieve relatively good * Corresponding author. Tel.: ⫹0-61-727-048; fax: ⫹386-62-2207990. E-mail address: [email protected] (I. Kovacˇ).
repeatability of positioning. It was also noticed that the remaining sources of error have a mostly systematic character [4]. In this way the device accuracy characteristics can be improved through calibration and compensation by software. Many authors have considered and tested such calibration and compensation procedures [5– 8]. Experiments in robotics show that it is possible to improve the absolute accuracy nearly up to the repeatability limit. The critical points of these procedures are the effectiveness of the compensation model, the capability of the measuring device to collect all positional data in space, and the accuracy level of the measuring device used for the calibration. Existing coordinate measuring arms are calibrated and tested very differently [9]. As a method for calibration and testing of CMAs a special calibration and testing jig or an adapted ball-bar approach for establishing the degree of volumetric accuracy can be used [10,11]. A horizontal articulated coordinate measuring device [5] can achieve the required accuracy together with calibration and compensation procedures, involving the use of different artifacts [12]. Another possibility for measuring manually driven measuring arms could be a Cartesian CMM. However, the measurement results did not prove to be useful since a high deviation of results appeared, caused by deflection of the CMM system as a consequence of reaction forces caused by pushing [13]. From the above investigations in this area it was clear
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ments contacting the horizontal and vertical beam faces are added. In this way we can make the best approximation to the theoretical supposition of measuring target positions along a straight line by constant orientation. 2.1. Initial stage
Fig. 1. Main components of high precision measuring device.
that only robust mechanical equipment for measuring and guiding along any reference line adjustable in various spatial directions can offer a promising high precision solution. To confirm this supposition, an existing high precision length comparator was used [14]. Using this fixed high precision length comparator in a climatic chamber, repeatability and accuracy measurements of CMAs were successfully carried out along some horizontal straight lines [15]. However, testing and calibration along a limited number of horizontal lines cannot give representative results for assessment of a whole device. Therefore, we decided to design and develop a new high precision measuring device for testing and calibration of CMAs, which can be adjusted in various spatial directions.
2. New high precision measuring device For the design and the development of a new high precision measuring device we made some comparative studies [16]. The main construction problem is to make a light and rigid system of the highest precision, which can be adjusted in various spatial directions. After analyses of different approaches to this problem, we decided to build a system in which the measurement of position is carried out with a measuring system located separately from the line gauge beam. Therefore, the main task of the line gauge beam remains only to guide the sled exactly within the demanded limits with respect to deviations in orientation along a straight line. The main components of the high precision measuring device are presented in Fig. 1. The target positions along the line gauge beam are measured with a laser interferometer. While the construction of the high precision measuring device cannot be rigid enough to keep within the demanded limits in the orthogonal directions to the line gauge beam under various loading conditions of the device to be measured, length indicators mounted on separate supports to control lateral displace-
At the initial stage of the design of the new measuring device we have to set the limit of positional accuracy which the measuring device should achieve. This limit was established through repeatability measurements made on an existing CMA. The experiment, which was made on a high precision length comparator in the stable environment of a climatic chamber, showed that the repeatability in the most advantageous workspace amounts to r ⫽ 2.5 m for a statistical probability of ⫾2 according to ISO 9283 [17]. However, there is no need for the measuring device to be better than this limit. Therefore, the expanded uncertainty of measurement of the measuring device was set to upini ⫽ 2.5 m by the coverage factor k ⫽ 2, which for a normal distribution corresponds to a coverage probability of approximately 95% according to the ISO guide to the expression of uncertainty of measurement. 2.2. Determination of uncertainty of measurement To determine the uncertainty of measurement a knowledge of all possible sources of deviation is needed. The main components contributing to this value are the line gauge beam, the bearing system and the measuring system (Fig. 1). Deviations are mainly associated with changes in the environmental conditions, through internal and external sources of forces and moments and through geometrical deviations. Internal sources are the beam’s own weight, beam straightness, the weight of the moving sled, the influence of connecting cables and pipe lines, the influence of the drive system - especially its connection to the sled - and bearing deviations. These deviations can be either constant, or theoretically foreseen, or so small that they can be neglected. We usually try to solve such problems mechanically with special design solutions. However, for some types of deviations software compensation tools can be introduced. The influence of external sources of forces and moments is even more complex. The main source is the coupling of the device to be measured. All moving forces and moments are transmitted from the device to be measured to the high precision measuring device. These forces and moments are constantly changing and depend on the momentary device configuration. The consequence of this influence is bending and twisting of the whole measuring device construction with its support installation. The next source of possible errors can be located in the physical connection between the device to be measured and the high precision measuring device. We must ensure that during the measurement the distance between the high precision measuring device co-
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ordinate system and the CMA base coordinate system stays constant. Since the experiments were done in a stable environment, the influence of temperature conditions was estimated to be within ⫾0.5 K. The expanded uncertainty of measurement for a simplified but corresponding model of the high precision measuring device under constant environmental conditions was calculated theoretically as a function of input quantities. Y ⫽ f共G, B, M, C, S兲
(1)
G in Eq. (1) expresses the line gauge beam system, B the sled bearing system, M the measuring system, C the control system and S the support arrangement. In this calculation we divided the measuring uncertainty into positional and orientational parts. While the high precision measuring device is designed for test and calibration measurements in space, all three one-dimensional uncertainties of measurement u1 (ux, uy, uz) for the positional part and three angle uncertainties of measurement (uRx, uRy, uRz) as rotations around the X, Y and Z axes for the orientational part should be considered. 2.3. Line gauge beam The line gauge beam was designed with purpose-built software. This software could take account of the external loads, its own beam weight, the support location, material characteristics and the beam shape form. The calculations were made with a moving external load of Fm ⫽ 90 N in the vertical (Z) direction. The moving external load represents the expected sled weight, the estimated influence of connecting cables and pipe-lines and an external force of Fz ⫽ 50 N. The external force represents the force from the CMA side. It was determined through experiments on a real system [18]. A similar calculation, but without a sled weight, was made in the horizontal Y direction. To cover the most interesting CMAs for testing and calibration, a hollow ceramic beam length of L ⫽ 2000 mm supported at Bessel-points was chosen as the straight line gauge. After consideration of all the abovementioned items, the calculation procedure gave a beam with a width w ⫽ 100 mm, height h ⫽ 160 mm and wall thickness t ⫽ 10 mm. In the calculation procedure the changes of angle values in both directions and bending deflections resulting from them were the most important factors in the beam optimization procedure. The theoretical results obtained for beam angle value changes are presented in Fig. 2, while Fig. 3 shows the bending deflections. While the line gauge beam cannot be used at its ends, the deviation Ge associated with the beam’s own weight and the moving external load was calculated along the beam length area from L ⫽ 200 to 1800 mm. The positional difference calculated in the Z direction lay within the interval Gez ⫽ 0 to ⫺0.5 m. Since the external force of Fy ⫽ ⫾50 N always appeared in the plus or minus Y direction, the deviation in the Y direction lay within the interval Gey ⫽ ⫾0.175 m. The orientational changes about the Y axis were within the
Fig. 2. Trajectory of beam angle value changes under different conditions in the Z direction.
interval GeRy ⫽ 0 to 0.3⬙ (arc seconds) and about the Z axis within the interval GeRz ⫽ 0 to 0.2⬙. Another source of deviation is represented through the surface manufacturing inaccuracies which were given in the manufacturer’s inspection certificate. The flatness over the total length of L ⫽ 2000 mm of vertical surfaces was within Gsy ⫽ 0.0012 mm and the flatness of horizontal surface within Gsz ⫽ 0.0017 mm. These inaccuracies also gave deviations in orientation GsRx ⫽ GsRy ⫽ 1.46⬙ around the X and Y axis and GsRz ⫽ 2.06⬙ around the Z axis. Before measurement, care was taken to ensure the most constant temperature ambient. The remaining difference of temperature was estimated to be within ⫾0.5 K. The difference in the position Gt associated with sled positional deviations as a consequence of linear thermal expansion of the ceramic beam (␣ ⫽ 6.1 ⫻ 10⫺6 K⫺1) and difference of temperature was calculated to be within the limits Gty ⫽ ⫾0.15 m in the Y direction and Gtz ⫽ ⫾0.5 m in the Z direction. Undesired deviations can be caused by temperature gradients in the material structure. The vertical distribution of the temperature can especially contribute to such an effect. So the temperature difference between the upper
Fig. 3. Trajectory of beam deflection deviations under different conditions in the Z direction.
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Fig. 4. Sled section of the high precision measuring device.
and lower surfaces of the ceramic beam is estimated to be within ⌬T ⫽ 0.01 K. From this, the positional difference is assumed to be Gtgz ⫽ 1 m and the orientational difference GtgRy ⫽ 0.2⬙. 2.4. Sled bearing system For the sled bearing system we examined aerostatic and ball bearings [19]. For our needs aerostatic bearings showed the most advantages. They can be designed in lightweight form, with high accuracy and in the case of a preloaded construction they are also rigid enough. Therefore, we decided to use an L-type sled with a preloaded vacuum-air bearing. This is very light, small and convenient for connecting to CMAs. The components of the measuring systems are also located on the sled. This type of sled has another essential advantage over comparable devices. Due to its L-type construction it is possible to support the line gauge beam at the Bessel-points and in spite of the supports, the preloaded sled can move freely along the whole beam length. Most existing CMAs that are used in measuring technology have a minimum of three, but more often, five or more axes. Nevertheless, the last rotation about the touch probe axis can be omitted. This axis is, in the case of the ballshaped touch probe, not necessary for measurement with multiaxial CMAs. However, only mechanisms which can move in six degrees of freedom can be rigidly connected to the high precision measuring device. In the case of a CMA with five axes one degree of freedom is missing. To solve this problem we added an additional high-precision rotational preloaded vacuum-air bearing mounted on one of the two prepared perpendicular mounting surfaces of the sled. The final connection of the CMA with this system was enabled through a connecting pin (Fig. 4). The whole air bearing system was designed and manufactured for the stated range of external loads and moments. The measuring deviations arising from the linear bearing system based on the manufacturer’s data are deviations in position within Bly ⫽ 1 m in the Y direction and within Blz
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⫽ 1 m in the Z direction. Deviations in orientation are assumed to be within BlRx ⫽ 0.2⬙ for rotation about the X-axis and within BlRy ⫽ 0.2⬙ for rotation about the Y axis. Measuring deviations for the stated range of external loads and moments also arise from the rotational bearing. The manufacturer’s data for deviations in position lie within Brx ⫽ Bry ⫽ Brz ⫽ 0.5 m. Deviations in orientation are negligible. Some additional deviations in position arise from bearing run-out errors which are assumed to be within Brry ⫽ Brrz ⫽ 0.4 m. Since the angle of rotation of the rotational bearing never exceeds an angle of ⫾75° the run-out error can be assumed to be only half of this value for deviations in position in the Y and Z direction. All these manufacturer’s data were checked and confirmed by experiments carried out on the sled bearing system of the high precision measuring device under the desired load. The connecting pin represents the weakest and the most sensitive element in the whole measuring device. Its shape and size depends on the connection mode of the device to be measured. In our case the connecting pin was designed the same as the CMA touch-trigger probe with a diameter Dtp ⫽ 9.5 mm and with a length Ltp ⫽ 45 mm. It was manufactured together with the rotational bearing. For the stated range of loads and moments arising from the device to be measured the deviation in position is within Bpby ⫽ 2.5 m due to bending and within Bpry ⫽ 1 m due to run-out error. The direction of positional deviation depends on the momentary CMA configuration. But the most unfavorable situation is expected in the Y direction. Deviation in orientation around the X-axis is then within BpbRx ⫽ 10⬙ on account of bending and within BprRx ⫽ 6.87⬙ on account of run-out error. The difference in position Bt associated with sled positional deviations as a consequence of linear thermal expansion of the bearing system made of Al-alloy (␣ ⫽ 22.5 ⫻ 10⫺6 K⫺1) with the connecting pin made of steel (␣ ⫽ 11.5 ⫻ 10⫺6 K⫺1) and a difference of temperature ⫾0.5 K, is calculated to be within the limits Bty ⫽ ⫾1.1 m in the Y direction and Btz ⫽ ⫾2.1 m in the Z direction. Since CMAs are not equipped with a drive system, the movement of the device to be calibrated or tested into the measuring position has to be carried out by an external drive system. Only in this way it is possible to perform automatic, repeatable positioning along any line adjusted in various spatial directions. For this reason the sled was driven through a steel cable by an AC motor. The motor was equipped with a harmonic drive gear of minimum backlash. This type of construction of the drive system allows very high mechanical rigidity for the smallest system weight. Through a convenient single axis control system, which was located in the personal computer, it was possible to make programmed movements at different velocities and stops in any position along the high precision measuring device. In the case of static measurements very high positioning repeatability is demanded. In the case of dynamic measure-
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Fig. 5. Arrangement of the measuring system in the X direction and control systems in the Y and Z directions.
ments, the most important function of the control system is to keep the programmed velocity at a constant level. Since the high precision measuring device was designed for measurements in various spatial directions, including in the extreme case the vertical direction, a counterweight was needed. It was located and guided on separate shafts inside the line gauge beam and connected through a steel cable and a drive system with the sled. These separate shafts allow for completely separate guidance of the counterweight from the line gauge beam and did not cause any deflection of the line gauge beam (Fig. 1). 2.5. Measuring system To achieve the best performance of the whole high precision measuring device we decided to locate the position measuring system separately from and independently of the line gauge beam system. Since the object to be measured causes forces which deflect the whole beam and the supportconstruction, the main advantage of a separately located position measuring system is that deflections do not have any influence on the position measuring results. To obtain all the required positioning data in space, the position measuring system consists of the following elements: a laser interferometer for measuring longitudinal distance (X direction) and a control system to control lateral relative displacements contacting the horizontal and vertical line gauge beam faces in the Y and Z directions (Fig. 5). The absolute inclination value of the line gauge beam in space in accordance with our calibration procedure, is not relevant and is also not measured. For simultaneous triggering of the measuring sequence programmed by the drive control system, which assures the exact reading of measuring data at the same time, the laser interferometer and the system to be measured have to be linked by the controlling computer. In the case of extremely
large displacements in the Y and Z directions a laser liner option was also considered and tested. Since adjustments in various spatial directions are made very often, the position measuring system needs to be readapted every time. Such adjustments are time consuming if a standard laser interferometer device is used. For this reason, we decided to employ a special miniature laser interferometer with an optical glass fiber. In this way only the miniature measuring head with integrated interferometer optics needed to be fixed on a separate support and directed toward the retro-reflector mounted on the sled. To make laser beam adjustments easy and fast, the laser interferometer system was equipped with a special adjustable mounting plate for the laser measuring head, and with a miniature adjustable cross table for the retro-reflector. Such an arrangement allowed easy and rapid laser interferometer adjustment in only a few steps. The distance measuring accuracy of the laser interferometer is given in the manufacturer’s handbook and amounts ⫾0.5 m/m over the range of ⫾20 hPa and ⫾5 K. The accuracy of laser interferometer compensation sensors are valid for temperature changes of ⫾0.3 K, for air pressure changes of ⫾0.5 hPa and for humidity changes of ⫾5.0%. The measuring distance in our case is max. LLI ⫽ 2000 mm. So the distance measuring accuracy over the whole length in the X direction may be assumed to be Mlix ⫽ ⫾1 m. Initially the laser-liner location was planned to be on the same surface as the retro-reflector optics. Therefore, an Abbe offset of Oy ⫽ 70 mm and Oz ⫽ 80 mm between the CMA probe tip and the retro-reflector on the sled occurs as a consequence of this arrangement (Fig. 5). This causes an Abbe error of Max ⫽ 1.2 m since the angular errors from the line gauge beam and sled bearing system are within Ry ⫽ 2.56⬙ about the Y axis and Rz ⫽ 1.85⬙ about the Z axis. A similar situation should appear in option 2 of the rotational air-vacuum bearing arrangement (Fig. 4), if the retroreflector stays at the same place (Max ⫽ 2.1 m). However, further experiments showed that the laser-liner option for measurements of lateral displacement in the X and Z directions can in most cases be omitted and the retro-reflector should be moved into the position Oy ⫽ 0 mm and Oz ⫽ 80 mm. This would bring an Abbe error of Max ⫽ 1.0 m. There is also an offset of Ox ⫽ 130 mm between the retro-reflector and connecting pin in the X direction that brings a positional error as a consequence of temperature deviations. This error can be compensated by software. Since the temperature sensors are accurate within deviations of ⫾0.3 K according to the manufacturer’s data, the remaining error is estimated to be within Mtx ⫽ 1.8 m. The control system consists of length indicators with the accuracy Ci ⫽ ⫾0.5 m, which contact the line gauge beam surfaces in the Y and Z directions. They are located on separate supports (Fig. 5). The only task of this system is to measure displacements, if any occur, caused through loading of the high precision measuring device by the CMA. Besides the influence of positioning deviations in the Y
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have the same length, are evident only in the X and Y direction. The temperature deviation in the concrete foundation was recorded to be within 0.1 K during the whole cycle of measurements. In the X direction a part of this deviation can be compensated by the laser interferometer software. Nevertheless, the deviation in the X direction from the laser interferometer location to the CMA base (lx ⫽ 1300 mm) is assumed to be within Smx ⫽ 1.6 m. In the Y direction the deviation lies within Smy ⫽ 0.8 m. If the measuring device is extremely inclined, the support number 2 is 1200 mm higher then the other supports. This, with a temperature difference of only ⫾0.1 K, brings a positional deviation Stz ⫽ 1.83 m in the Z direction and an orientational deviation StRy ⫽ 0.25⬙ about the Y axis. 2.7. Uncertainty budget Fig. 6. New high precision measuring device with support section in various spatial directions connected to CMA.
direction of Cmfy ⫽ 2.02 m and in the Z direction of Cmfz ⫽ 1.7 m as a consequence of the measuring force from the indicators, more problematical is the influence of temperature in the Z direction, especially if the measuring device is extremely inclined. If the temperature during the measuring period changes only within the limits of ⫾0.1 K, the deviation as a consequence of different thermal expansion coefficients of the supports is assumed to be within Ctz ⫽ 3.4 m. This represents an important contribution to the measuring uncertainty. 2.6. Support arrangement The whole high precision measuring device is supported by solid and rigid elements and fixed to a concrete foundation (Fig. 6). The main sources which contribute to the uncertainty of the high precision measuring device are bending and temperature influences. While the orientational deviations should result in small errors (support torsion deviation about the Z axis is within StRz ⫽ 0.5⬙), the positional deviations are more serious. The most unfavorable results of the calculation were obtained in the Y direction. If the measuring device is extremely inclined, support number 2 should be about 1800 mm high. The connection between support number 2 and the ceramic beam can also represent a problem. Since the external force always appears in the plus or the minus direction (Fy ⫽ ⫾50 N), the calculated deviation in the Y direction, if the support and the connection are not rigid enough, can be about Sby ⫽ ⫾0.024 mm in the extreme case at the top of the beam measuring area. In such a case a separate measuring system to measure this deviation would be indispensable. However, in less unfavorable cases (lower external force, horizontal arrangement) the calculated deviation lies within Sby ⫽ 2.2 m. Temperature deviations in the case, when all supports
The uncertainty budget of measurement presented in Table 1 includes a list of the most important sources of uncertainty together with the associated uncertainties of measurement. Calculations showed that the proposed high-precision measuring device can perform calibration and test space measurements of portable CMAs in the micro millimeter area. In favorable cases, under constant environmental conditions, the expanded uncertainties of measurement are in the X direction Ux ⫽ 0.00218 mm, in the Y direction Uy ⫽ 0.00271 mm, in the Z direction Uz ⫽ 0.00336 mm and for the orientational part URx ⫽ 7.1⬙ around the X-axis, URy ⫽ 1.2⬙ around the Y axis and URz ⫽ 0.9⬙ around the Z axis. The reported expanded uncertainty of measurement is given as the standard uncertainty of measurement multiplied by the coverage factor k ⫽ 2, which for a normal distribution corresponds to a coverage probability of approximately 95%.
3. Experiments To confirm the theoretical suppositions and calculations we carried out experiments on the high precision measuring device which we had developed. We carried out straightness measurements of the preloaded vacuum-air bearing system along the line gauge beam with and without a drive system, as well as measurements of the preloaded vacuum-air bearing system under the desired load. For this purpose we placed the measuring device without supports into a position horizontal on a granite plate. Measurements were carried out with an autocollimator (AC) and with electronic inclinometers (EI) in differential switching. The lateral displacements were checked with length indicators (Fig. 5). During measurement we moved the vacuum-air bearing sled along the line gauge beam. The first position was situated 100 mm from the beginning of the beam. Further test positions were chosen every 100 mm. After more than five repetitions of the same measuring procedure along the
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Table 1 Quantity
Gs y Gs z Gs Rx Gs Ry Gs Rz Ge y Ge z Ge Ry Ge Rz Gtg z Gtg Ry Gt z Gt y Bl y Bl z Bl Rx Bl Ry Br x Br y Br z Brro y Brro z Bpb y Bpro y Bpb Rx Bpro Rx Bt y Bt z Mli x Ma x Mt x Ci y Ci z Cmf y Cmf z Ct z Sb y Sm x Sm y St z St Ry St Rz
Value [m]
Value [⬙]
Contribution to the standard uncertainty ux
1,2 1,7
uy
uz
u Rx
u Ry
u Rz
0,35 0,49 2,063 2,063 1,456
0,6 0,6 0,42
0,35 0,5
0,1 0,14 0,3 0,2
0,09 0,06
1
0,29 0,2
0,06
1 0,3 1 1
0,29 0,09 0,29
Fig. 7. Results of straightness measurements in the Z direction. 0,29
0,2 0,2 0,5 0,5 0,5 0,4 0,4 2,5 1
0,06 0,06 0,14 0,14 0,14 0,12 0,12 0,72 0,29
9,63 2,29 1,1 2,1 2 1,2 2,1 1 1 2,02 1,7 3,4 2,2 1,6 0,8 2,9
2,78 0,66 0,32 0,61 0,58 0,35 0,61 0,29 0,29 0,58 0,49 0,98 0.64 0,46 0,23 0,84
0,25 1
0,07 1,03
1,36
1,71
2,92
0,62
0,29 0.51
whole beam length, the straightness deviations in the horizontal level were statistically processed from the AC or EI angle measurements. The mean values of the straightness deviation in the Z direction are presented in Fig. 7. The results presented in Fig. 7 denoted by AK Man. 1 and AK Man. 2 mean that the movements were made manually, without drive and counterweight influence, firstly with rigid connection of all support parts and secondly with loosened connections of all key supporting parts on the granite table. In this experiment we checked the influence of the constructional elements on beam accuracy deviation. From Fig. 7 no obvious differences were noticed. Only the dispersion of measuring results with loosened connections was a little bit larger. The measurements were also carried
out with a drive and counterweight system in both directions along the beam. The results of straightness measurements in the Z direction are denoted by AK Drive ⫹ for positive and AK Drive ⫺ for negative directions of movement. No hysteresis or other obvious differences from the first measurement results were noticed. To compare the experimental results with the theoretical results, a trajectory calculated with purpose-built software was added and marked as shown by OW ⫹ EL which considers deviations calculated from the beam’s own weight (OW) and from the sum of the external loads (EL). The standard deviation calculated from all measuring data performed in the Z direction was not larger than 2 ⫽ 0.9 m. The results of straightness measurements in the Y direction are presented in Fig. 8. The notation in Fig. 8 has the same meaning as the notation marked in Fig. 7, but in the Y direction. No hysteresis or other obvious differences for different conditions of measurement were apparent. The standard deviation of measuring data in the Y direction was not anywhere larger than 2 ⫽ 1.1 m. The vacuum-air bearing was designed in such a way that it could be adjusted according to momentary changes in the
Fig. 8. Results of straightness measurements in the Y direction.
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Fig. 9. Results of angular deviation measurements about the X axes.
orthogonality of the beam guiding surfaces. Therefore, only the side beam surface is responsible for the orientational deviations about the X axes. These angular deviations  were measured with EI along the X axes every 100 mm. The standard deviation of these angular measurement data, presented in Fig. 9, was not larger than 2 ⫽ 1.5⬙. From the previous Figs. 8 and 9, some noticeable changes of orientation between 200 and 600 mm were observed. This is a systematic error caused by imperfect beam manufacturing. These imperfections in angular deviations of rx ⫽ 2⬙ are still within the specified limits of the measuring device. Because of their systematic character they can be compensated for by means of the software, should this be necessary. The same measuring setup was also chosen for measurements under loaded conditions. As load a high precision CMA was used. It was placed on the same granite table as the high precision measuring device in order to meet all demands for a constant and stable relationship between the two base coordinate systems. The CMA was positioned in the middle area of the length measurement direction and 622 mm away from the beam center line. The measuring setup for straightness and angle deviation measurements loaded with the CMA in the horizontal level is presented in Fig. 10. Abbreviations in Fig. 10 are as follows: CMACoordinate measuring arm, EI-electronic inclinometer, LLLaser-liner, AK-Autocollimator, LI-laser interferometer. In these measurements we fixed the CMA to the vacuumair bearing sled with a connecting pin from the bearing side. The connecting pin had the same diameter as the touch probe system connected to the CMA. The connecting pin was manufactured very precisely together with the turning part of the rotational vacuum-air bearing. The whole rotational accuracy measured on the connecting pin under the loaded conditions specified for the whole bearing system, was smaller than one micrometer. Therefore, the influence of bearing rotational accuracy can be neglected. The measuring procedure was the same as in the previous measurements under unloaded conditions. Before these measurements we made some small improvements in re-
Fig. 10. Layout of the measuring setup in the horizontal position for straightness and angle deviation measurements when loaded with the CMA.
spect to air quality which resulted in even better measurement results, with smaller deviation of the results. The results for straightness deviation in the Z direction of the high precision measuring device when connected to the CMA as an external load are presented in Fig. 11. The standard deviation of the results obtained by an autocollimator in the Z direction in all positions was not larger for than 2 ⫽ 0.7 m. The situation for the results in the Y direction, presented in Fig. 12 was very similar. For the Y
Fig. 11. Results of straightness measurements in the Z direction.
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Fig. 12. Results of straightness measurements in the Y direction.
direction the standard deviation 2 was not larger than 0.6 m. The results for mean values of angular deviations , measured along the X axes in the horizontal position with EI connected in a differential circuit, are presented in Fig. 13. During the measurement we checked the displacements of the beam gauge at several key locations. Only bending changes at the expected level (in our case negligible) were noted, and no larger displacements in other directions were observed. Finally, we put the whole high precision measuring device on supports and in a position inclined by ␣ ⫽ 50°. In our case this is the most unfavorable configuration since support element number 2 (Fig. 6), representing a possible source of elastic deformation through changeable loading from the device to be measured, is about 1800 mm high. For this reason we measured displacements caused through bending of the support arrangement influenced by the CMA. On both sides of the beam four length indicators were placed on each of the surfaces orthogonal to the line of sled movement to control displacements in the Y and Z direction, as shown in Fig. 14. Because of the solid fixing of the
Fig. 14. Layout of the measuring setup for the whole system extremely inclined and loaded with the CMA.
supports to the concrete base and the rigid connection of the exchangeable support parts, we were successful in keeping these values under the 2 m level for the stated loading conditions.
4. Conclusion A new high precision measuring device for testing and calibration of coordinate measuring arms was designed and developed. Theoretical calculations performed on a simplified but corresponding model suggested the expanded uncertainty of measurement in the X direction Ux ⫽ 0.00218 mm, in the Y direction Uy ⫽ 0.00271 mm, in the Z direction Uz ⫽ 0.00336 mm and for the orientational part URx ⫽ 7.1⬙ around the X-axis, URy ⫽ 1.2⬙ around the Y axis and URz ⫽ 0.9⬙ around the Z axis. Experiments on the real high precision measuring device showed that this level was successfully achieved. Thus the new high precision measuring device can be taken as an appropriate reference measuring system for static or dynamic testing and for calibration of devices with unconventional kinematic structures, such as measuring robots or manually driven coordinate measuring arms. On the other hand, there are no limitations to using the proposed measuring device additionally as a reference gauge system for straightness measurements. And finally, the measuring device (without supports) weighs only about 60 kg and is therefore easily transported.
References
Fig. 13. Results of angular deviation measurements about the X-axis.
[1] Kovacˇ I. Knickarmgera¨te fu¨r die produktionsmetechnik. Int Fachtagung Koordinatenmetechnik - ein Baustein der Qualita¨tssicherung 1994:95–106. [2] Kovacˇ I, Frank A. Automated quality control by a novel anthropoidic measuring device. Third International Symposium on Measurement and Control in Robotics ISMCR’93 1993:164 – 69.
I. Kovacˇ, A. Frank / Precision Engineering 25 (2001) 90 –99 [3] Kovacˇ I, Frank A. High-precision testing and calibration metrology for portable coordinate measuring arms. International Symposium on Laser Metrology for Precision Measurement and Inspection in Industry 1999:1–10. [4] Kovacˇ I, Frank A. Automated geometrical inspection by a new robot guided anthropoidic measuring device. The Third International Conference on Automation Technology 1994;6:107–12. [5] Lotze W. Measuring device with rotation axes - new coordinate measuring device. VDI Berichte 1996;1258:13–24. [6] Whitney DE, Lozinski CA, Rourke JM. Industrial robot forward calibration method and results. ASME Journal of Dynamic Systems, Measurement and Control 1986;108(1):1– 8. [7] Judd RP, Knasinski AB. A technique to calibrate IR with experimental verification. IEEE Transactions on Robotics and Automation 1990;6(1):20 –30. [8] Schroer K, Albright SL, Lisounkin A. Modeling closed-loop mechanisms in robots for purposes of calibration. IEEE Transactions on Robotics and Automation 1996;3:1–32. [9] Kovacˇ I, Frank A. Methods for calibration and testing of flexible arm measuring devices. LAMDAMAP 1999;99:3–12. [10] Raab S. Three dimensional coordinate measuring apparatus. UK patent application GB 2 275 339 A, 1.2.1994.
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[11] Bryan JB. A simple method for testing measuring machines and machine tools. Precision Engineering 1982;1:62–9. [12] Herzog K, Lotze W. Verfahren zur kalibrierung eines koordinatenmegera¨tes mit zwei rotatorischen achsen. EU patent application EP 0 703 430 A2, 7.9.1995. [13] Kovacˇ I, Frank A. High precision measuring equipment for testing and calibration of anthropoidic mechanism devices. 29th International Symposium on Robotics ISR 1998:1– 4. [14] Hirn C. Entwicklung eines klimatisierten pra¨zisionskomparators fu¨r la¨ngen und geradheitsmessungen bis 5 meter. Technik report 1992; 19(6):23– 6. [15] Kovacˇ I, Frank A. Robot-aided coordinate measurement with the anthropoidic measuring device AMG-1. 3rd Asian Conference on Robotics and Its Application 3rd ACRA 1997:197–202. [16] Vorbach S. Construction of a test-place for a measuring device. Thesis at the TU-Graz, Austria, 1994. [17] Kovacˇ I, Frank A. Neues mobiles megera¨t zur fertigungsintegrierten geometriepru¨fung. VDI-Z 1998;140(5):36 – 8. [18] Kovacˇ I, Frank A. AMG-1: a new approach to robot integrated measurement. 27th International Symposium on Industrial Robots ISIR 1996:955– 60. [19] Bartz W. Luftlagerungen, Expert Verlag Band 78, 1992.
Testing and calibration of coordinate measuring arms Igor Kovacˇa,*, Adolf Frankb a
b
Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia Institute for Production Technology, Graz University of Technology, Kopernikusgasse 24, A-8010 Graz, Austria Received 30 November 1999; accepted 18 May 2000
Abstract Portable coordinate measuring arms with rotational axes have found their place in many industrial areas. To establish and confirm the accuracy of these measuring devices, related test methods and appropriate devices are needed. After an introduction, a new high precision measuring device for testing and calibration of portable coordinate measuring arms is presented. Analysis showed that the best results can be obtained with a device for measuring along a straight line adjusted in various spatial directions. We discuss the design and construction of this measuring system and provide a theoretical calculation of its measurement accuracy, which was confirmed by experiments carried out on a prototype of a high precision measuring device in both unloaded and loaded conditions. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Testing; Calibration; Portable coordinate measuring arms
1. Introduction Portable coordinate measuring arms (CMAs) have been successfully introduced into measuring technology [1]. Their main areas of use are in the automotive, aerospace, heavy engineering, railway and energy industries. A robotlike, manually driven, multi-joint, mechanical arm connected to a computer allows the user to achieve measurement tasks during maintenance, assembly, quality assurance, inspection and replication of complex models into 3-D data, or in measuring surfaces of free form and curved pipe lines. The structures of CMAs also allow measurement of workpieces directly in a machine fastening device. Another application field is in connection with industrial robots [2]. To carry out measurement tasks in the manufacturing industry, the accuracy level of the measuring device is one of its most important requirements. From a brief survey of existing device performances [3] it is evident that the accuracy characteristics of such devices are below those of the common Cartesian coordinate measuring machines (CMMs). Measurement of the repeatability performance of CMAs shows that it is possible to achieve relatively good * Corresponding author. Tel.: ⫹0-61-727-048; fax: ⫹386-62-2207990. E-mail address: [email protected] (I. Kovacˇ).
repeatability of positioning. It was also noticed that the remaining sources of error have a mostly systematic character [4]. In this way the device accuracy characteristics can be improved through calibration and compensation by software. Many authors have considered and tested such calibration and compensation procedures [5– 8]. Experiments in robotics show that it is possible to improve the absolute accuracy nearly up to the repeatability limit. The critical points of these procedures are the effectiveness of the compensation model, the capability of the measuring device to collect all positional data in space, and the accuracy level of the measuring device used for the calibration. Existing coordinate measuring arms are calibrated and tested very differently [9]. As a method for calibration and testing of CMAs a special calibration and testing jig or an adapted ball-bar approach for establishing the degree of volumetric accuracy can be used [10,11]. A horizontal articulated coordinate measuring device [5] can achieve the required accuracy together with calibration and compensation procedures, involving the use of different artifacts [12]. Another possibility for measuring manually driven measuring arms could be a Cartesian CMM. However, the measurement results did not prove to be useful since a high deviation of results appeared, caused by deflection of the CMM system as a consequence of reaction forces caused by pushing [13]. From the above investigations in this area it was clear
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ments contacting the horizontal and vertical beam faces are added. In this way we can make the best approximation to the theoretical supposition of measuring target positions along a straight line by constant orientation. 2.1. Initial stage
Fig. 1. Main components of high precision measuring device.
that only robust mechanical equipment for measuring and guiding along any reference line adjustable in various spatial directions can offer a promising high precision solution. To confirm this supposition, an existing high precision length comparator was used [14]. Using this fixed high precision length comparator in a climatic chamber, repeatability and accuracy measurements of CMAs were successfully carried out along some horizontal straight lines [15]. However, testing and calibration along a limited number of horizontal lines cannot give representative results for assessment of a whole device. Therefore, we decided to design and develop a new high precision measuring device for testing and calibration of CMAs, which can be adjusted in various spatial directions.
2. New high precision measuring device For the design and the development of a new high precision measuring device we made some comparative studies [16]. The main construction problem is to make a light and rigid system of the highest precision, which can be adjusted in various spatial directions. After analyses of different approaches to this problem, we decided to build a system in which the measurement of position is carried out with a measuring system located separately from the line gauge beam. Therefore, the main task of the line gauge beam remains only to guide the sled exactly within the demanded limits with respect to deviations in orientation along a straight line. The main components of the high precision measuring device are presented in Fig. 1. The target positions along the line gauge beam are measured with a laser interferometer. While the construction of the high precision measuring device cannot be rigid enough to keep within the demanded limits in the orthogonal directions to the line gauge beam under various loading conditions of the device to be measured, length indicators mounted on separate supports to control lateral displace-
At the initial stage of the design of the new measuring device we have to set the limit of positional accuracy which the measuring device should achieve. This limit was established through repeatability measurements made on an existing CMA. The experiment, which was made on a high precision length comparator in the stable environment of a climatic chamber, showed that the repeatability in the most advantageous workspace amounts to r ⫽ 2.5 m for a statistical probability of ⫾2 according to ISO 9283 [17]. However, there is no need for the measuring device to be better than this limit. Therefore, the expanded uncertainty of measurement of the measuring device was set to upini ⫽ 2.5 m by the coverage factor k ⫽ 2, which for a normal distribution corresponds to a coverage probability of approximately 95% according to the ISO guide to the expression of uncertainty of measurement. 2.2. Determination of uncertainty of measurement To determine the uncertainty of measurement a knowledge of all possible sources of deviation is needed. The main components contributing to this value are the line gauge beam, the bearing system and the measuring system (Fig. 1). Deviations are mainly associated with changes in the environmental conditions, through internal and external sources of forces and moments and through geometrical deviations. Internal sources are the beam’s own weight, beam straightness, the weight of the moving sled, the influence of connecting cables and pipe lines, the influence of the drive system - especially its connection to the sled - and bearing deviations. These deviations can be either constant, or theoretically foreseen, or so small that they can be neglected. We usually try to solve such problems mechanically with special design solutions. However, for some types of deviations software compensation tools can be introduced. The influence of external sources of forces and moments is even more complex. The main source is the coupling of the device to be measured. All moving forces and moments are transmitted from the device to be measured to the high precision measuring device. These forces and moments are constantly changing and depend on the momentary device configuration. The consequence of this influence is bending and twisting of the whole measuring device construction with its support installation. The next source of possible errors can be located in the physical connection between the device to be measured and the high precision measuring device. We must ensure that during the measurement the distance between the high precision measuring device co-
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ordinate system and the CMA base coordinate system stays constant. Since the experiments were done in a stable environment, the influence of temperature conditions was estimated to be within ⫾0.5 K. The expanded uncertainty of measurement for a simplified but corresponding model of the high precision measuring device under constant environmental conditions was calculated theoretically as a function of input quantities. Y ⫽ f共G, B, M, C, S兲
(1)
G in Eq. (1) expresses the line gauge beam system, B the sled bearing system, M the measuring system, C the control system and S the support arrangement. In this calculation we divided the measuring uncertainty into positional and orientational parts. While the high precision measuring device is designed for test and calibration measurements in space, all three one-dimensional uncertainties of measurement u1 (ux, uy, uz) for the positional part and three angle uncertainties of measurement (uRx, uRy, uRz) as rotations around the X, Y and Z axes for the orientational part should be considered. 2.3. Line gauge beam The line gauge beam was designed with purpose-built software. This software could take account of the external loads, its own beam weight, the support location, material characteristics and the beam shape form. The calculations were made with a moving external load of Fm ⫽ 90 N in the vertical (Z) direction. The moving external load represents the expected sled weight, the estimated influence of connecting cables and pipe-lines and an external force of Fz ⫽ 50 N. The external force represents the force from the CMA side. It was determined through experiments on a real system [18]. A similar calculation, but without a sled weight, was made in the horizontal Y direction. To cover the most interesting CMAs for testing and calibration, a hollow ceramic beam length of L ⫽ 2000 mm supported at Bessel-points was chosen as the straight line gauge. After consideration of all the abovementioned items, the calculation procedure gave a beam with a width w ⫽ 100 mm, height h ⫽ 160 mm and wall thickness t ⫽ 10 mm. In the calculation procedure the changes of angle values in both directions and bending deflections resulting from them were the most important factors in the beam optimization procedure. The theoretical results obtained for beam angle value changes are presented in Fig. 2, while Fig. 3 shows the bending deflections. While the line gauge beam cannot be used at its ends, the deviation Ge associated with the beam’s own weight and the moving external load was calculated along the beam length area from L ⫽ 200 to 1800 mm. The positional difference calculated in the Z direction lay within the interval Gez ⫽ 0 to ⫺0.5 m. Since the external force of Fy ⫽ ⫾50 N always appeared in the plus or minus Y direction, the deviation in the Y direction lay within the interval Gey ⫽ ⫾0.175 m. The orientational changes about the Y axis were within the
Fig. 2. Trajectory of beam angle value changes under different conditions in the Z direction.
interval GeRy ⫽ 0 to 0.3⬙ (arc seconds) and about the Z axis within the interval GeRz ⫽ 0 to 0.2⬙. Another source of deviation is represented through the surface manufacturing inaccuracies which were given in the manufacturer’s inspection certificate. The flatness over the total length of L ⫽ 2000 mm of vertical surfaces was within Gsy ⫽ 0.0012 mm and the flatness of horizontal surface within Gsz ⫽ 0.0017 mm. These inaccuracies also gave deviations in orientation GsRx ⫽ GsRy ⫽ 1.46⬙ around the X and Y axis and GsRz ⫽ 2.06⬙ around the Z axis. Before measurement, care was taken to ensure the most constant temperature ambient. The remaining difference of temperature was estimated to be within ⫾0.5 K. The difference in the position Gt associated with sled positional deviations as a consequence of linear thermal expansion of the ceramic beam (␣ ⫽ 6.1 ⫻ 10⫺6 K⫺1) and difference of temperature was calculated to be within the limits Gty ⫽ ⫾0.15 m in the Y direction and Gtz ⫽ ⫾0.5 m in the Z direction. Undesired deviations can be caused by temperature gradients in the material structure. The vertical distribution of the temperature can especially contribute to such an effect. So the temperature difference between the upper
Fig. 3. Trajectory of beam deflection deviations under different conditions in the Z direction.
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Fig. 4. Sled section of the high precision measuring device.
and lower surfaces of the ceramic beam is estimated to be within ⌬T ⫽ 0.01 K. From this, the positional difference is assumed to be Gtgz ⫽ 1 m and the orientational difference GtgRy ⫽ 0.2⬙. 2.4. Sled bearing system For the sled bearing system we examined aerostatic and ball bearings [19]. For our needs aerostatic bearings showed the most advantages. They can be designed in lightweight form, with high accuracy and in the case of a preloaded construction they are also rigid enough. Therefore, we decided to use an L-type sled with a preloaded vacuum-air bearing. This is very light, small and convenient for connecting to CMAs. The components of the measuring systems are also located on the sled. This type of sled has another essential advantage over comparable devices. Due to its L-type construction it is possible to support the line gauge beam at the Bessel-points and in spite of the supports, the preloaded sled can move freely along the whole beam length. Most existing CMAs that are used in measuring technology have a minimum of three, but more often, five or more axes. Nevertheless, the last rotation about the touch probe axis can be omitted. This axis is, in the case of the ballshaped touch probe, not necessary for measurement with multiaxial CMAs. However, only mechanisms which can move in six degrees of freedom can be rigidly connected to the high precision measuring device. In the case of a CMA with five axes one degree of freedom is missing. To solve this problem we added an additional high-precision rotational preloaded vacuum-air bearing mounted on one of the two prepared perpendicular mounting surfaces of the sled. The final connection of the CMA with this system was enabled through a connecting pin (Fig. 4). The whole air bearing system was designed and manufactured for the stated range of external loads and moments. The measuring deviations arising from the linear bearing system based on the manufacturer’s data are deviations in position within Bly ⫽ 1 m in the Y direction and within Blz
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⫽ 1 m in the Z direction. Deviations in orientation are assumed to be within BlRx ⫽ 0.2⬙ for rotation about the X-axis and within BlRy ⫽ 0.2⬙ for rotation about the Y axis. Measuring deviations for the stated range of external loads and moments also arise from the rotational bearing. The manufacturer’s data for deviations in position lie within Brx ⫽ Bry ⫽ Brz ⫽ 0.5 m. Deviations in orientation are negligible. Some additional deviations in position arise from bearing run-out errors which are assumed to be within Brry ⫽ Brrz ⫽ 0.4 m. Since the angle of rotation of the rotational bearing never exceeds an angle of ⫾75° the run-out error can be assumed to be only half of this value for deviations in position in the Y and Z direction. All these manufacturer’s data were checked and confirmed by experiments carried out on the sled bearing system of the high precision measuring device under the desired load. The connecting pin represents the weakest and the most sensitive element in the whole measuring device. Its shape and size depends on the connection mode of the device to be measured. In our case the connecting pin was designed the same as the CMA touch-trigger probe with a diameter Dtp ⫽ 9.5 mm and with a length Ltp ⫽ 45 mm. It was manufactured together with the rotational bearing. For the stated range of loads and moments arising from the device to be measured the deviation in position is within Bpby ⫽ 2.5 m due to bending and within Bpry ⫽ 1 m due to run-out error. The direction of positional deviation depends on the momentary CMA configuration. But the most unfavorable situation is expected in the Y direction. Deviation in orientation around the X-axis is then within BpbRx ⫽ 10⬙ on account of bending and within BprRx ⫽ 6.87⬙ on account of run-out error. The difference in position Bt associated with sled positional deviations as a consequence of linear thermal expansion of the bearing system made of Al-alloy (␣ ⫽ 22.5 ⫻ 10⫺6 K⫺1) with the connecting pin made of steel (␣ ⫽ 11.5 ⫻ 10⫺6 K⫺1) and a difference of temperature ⫾0.5 K, is calculated to be within the limits Bty ⫽ ⫾1.1 m in the Y direction and Btz ⫽ ⫾2.1 m in the Z direction. Since CMAs are not equipped with a drive system, the movement of the device to be calibrated or tested into the measuring position has to be carried out by an external drive system. Only in this way it is possible to perform automatic, repeatable positioning along any line adjusted in various spatial directions. For this reason the sled was driven through a steel cable by an AC motor. The motor was equipped with a harmonic drive gear of minimum backlash. This type of construction of the drive system allows very high mechanical rigidity for the smallest system weight. Through a convenient single axis control system, which was located in the personal computer, it was possible to make programmed movements at different velocities and stops in any position along the high precision measuring device. In the case of static measurements very high positioning repeatability is demanded. In the case of dynamic measure-
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Fig. 5. Arrangement of the measuring system in the X direction and control systems in the Y and Z directions.
ments, the most important function of the control system is to keep the programmed velocity at a constant level. Since the high precision measuring device was designed for measurements in various spatial directions, including in the extreme case the vertical direction, a counterweight was needed. It was located and guided on separate shafts inside the line gauge beam and connected through a steel cable and a drive system with the sled. These separate shafts allow for completely separate guidance of the counterweight from the line gauge beam and did not cause any deflection of the line gauge beam (Fig. 1). 2.5. Measuring system To achieve the best performance of the whole high precision measuring device we decided to locate the position measuring system separately from and independently of the line gauge beam system. Since the object to be measured causes forces which deflect the whole beam and the supportconstruction, the main advantage of a separately located position measuring system is that deflections do not have any influence on the position measuring results. To obtain all the required positioning data in space, the position measuring system consists of the following elements: a laser interferometer for measuring longitudinal distance (X direction) and a control system to control lateral relative displacements contacting the horizontal and vertical line gauge beam faces in the Y and Z directions (Fig. 5). The absolute inclination value of the line gauge beam in space in accordance with our calibration procedure, is not relevant and is also not measured. For simultaneous triggering of the measuring sequence programmed by the drive control system, which assures the exact reading of measuring data at the same time, the laser interferometer and the system to be measured have to be linked by the controlling computer. In the case of extremely
large displacements in the Y and Z directions a laser liner option was also considered and tested. Since adjustments in various spatial directions are made very often, the position measuring system needs to be readapted every time. Such adjustments are time consuming if a standard laser interferometer device is used. For this reason, we decided to employ a special miniature laser interferometer with an optical glass fiber. In this way only the miniature measuring head with integrated interferometer optics needed to be fixed on a separate support and directed toward the retro-reflector mounted on the sled. To make laser beam adjustments easy and fast, the laser interferometer system was equipped with a special adjustable mounting plate for the laser measuring head, and with a miniature adjustable cross table for the retro-reflector. Such an arrangement allowed easy and rapid laser interferometer adjustment in only a few steps. The distance measuring accuracy of the laser interferometer is given in the manufacturer’s handbook and amounts ⫾0.5 m/m over the range of ⫾20 hPa and ⫾5 K. The accuracy of laser interferometer compensation sensors are valid for temperature changes of ⫾0.3 K, for air pressure changes of ⫾0.5 hPa and for humidity changes of ⫾5.0%. The measuring distance in our case is max. LLI ⫽ 2000 mm. So the distance measuring accuracy over the whole length in the X direction may be assumed to be Mlix ⫽ ⫾1 m. Initially the laser-liner location was planned to be on the same surface as the retro-reflector optics. Therefore, an Abbe offset of Oy ⫽ 70 mm and Oz ⫽ 80 mm between the CMA probe tip and the retro-reflector on the sled occurs as a consequence of this arrangement (Fig. 5). This causes an Abbe error of Max ⫽ 1.2 m since the angular errors from the line gauge beam and sled bearing system are within Ry ⫽ 2.56⬙ about the Y axis and Rz ⫽ 1.85⬙ about the Z axis. A similar situation should appear in option 2 of the rotational air-vacuum bearing arrangement (Fig. 4), if the retroreflector stays at the same place (Max ⫽ 2.1 m). However, further experiments showed that the laser-liner option for measurements of lateral displacement in the X and Z directions can in most cases be omitted and the retro-reflector should be moved into the position Oy ⫽ 0 mm and Oz ⫽ 80 mm. This would bring an Abbe error of Max ⫽ 1.0 m. There is also an offset of Ox ⫽ 130 mm between the retro-reflector and connecting pin in the X direction that brings a positional error as a consequence of temperature deviations. This error can be compensated by software. Since the temperature sensors are accurate within deviations of ⫾0.3 K according to the manufacturer’s data, the remaining error is estimated to be within Mtx ⫽ 1.8 m. The control system consists of length indicators with the accuracy Ci ⫽ ⫾0.5 m, which contact the line gauge beam surfaces in the Y and Z directions. They are located on separate supports (Fig. 5). The only task of this system is to measure displacements, if any occur, caused through loading of the high precision measuring device by the CMA. Besides the influence of positioning deviations in the Y
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have the same length, are evident only in the X and Y direction. The temperature deviation in the concrete foundation was recorded to be within 0.1 K during the whole cycle of measurements. In the X direction a part of this deviation can be compensated by the laser interferometer software. Nevertheless, the deviation in the X direction from the laser interferometer location to the CMA base (lx ⫽ 1300 mm) is assumed to be within Smx ⫽ 1.6 m. In the Y direction the deviation lies within Smy ⫽ 0.8 m. If the measuring device is extremely inclined, the support number 2 is 1200 mm higher then the other supports. This, with a temperature difference of only ⫾0.1 K, brings a positional deviation Stz ⫽ 1.83 m in the Z direction and an orientational deviation StRy ⫽ 0.25⬙ about the Y axis. 2.7. Uncertainty budget Fig. 6. New high precision measuring device with support section in various spatial directions connected to CMA.
direction of Cmfy ⫽ 2.02 m and in the Z direction of Cmfz ⫽ 1.7 m as a consequence of the measuring force from the indicators, more problematical is the influence of temperature in the Z direction, especially if the measuring device is extremely inclined. If the temperature during the measuring period changes only within the limits of ⫾0.1 K, the deviation as a consequence of different thermal expansion coefficients of the supports is assumed to be within Ctz ⫽ 3.4 m. This represents an important contribution to the measuring uncertainty. 2.6. Support arrangement The whole high precision measuring device is supported by solid and rigid elements and fixed to a concrete foundation (Fig. 6). The main sources which contribute to the uncertainty of the high precision measuring device are bending and temperature influences. While the orientational deviations should result in small errors (support torsion deviation about the Z axis is within StRz ⫽ 0.5⬙), the positional deviations are more serious. The most unfavorable results of the calculation were obtained in the Y direction. If the measuring device is extremely inclined, support number 2 should be about 1800 mm high. The connection between support number 2 and the ceramic beam can also represent a problem. Since the external force always appears in the plus or the minus direction (Fy ⫽ ⫾50 N), the calculated deviation in the Y direction, if the support and the connection are not rigid enough, can be about Sby ⫽ ⫾0.024 mm in the extreme case at the top of the beam measuring area. In such a case a separate measuring system to measure this deviation would be indispensable. However, in less unfavorable cases (lower external force, horizontal arrangement) the calculated deviation lies within Sby ⫽ 2.2 m. Temperature deviations in the case, when all supports
The uncertainty budget of measurement presented in Table 1 includes a list of the most important sources of uncertainty together with the associated uncertainties of measurement. Calculations showed that the proposed high-precision measuring device can perform calibration and test space measurements of portable CMAs in the micro millimeter area. In favorable cases, under constant environmental conditions, the expanded uncertainties of measurement are in the X direction Ux ⫽ 0.00218 mm, in the Y direction Uy ⫽ 0.00271 mm, in the Z direction Uz ⫽ 0.00336 mm and for the orientational part URx ⫽ 7.1⬙ around the X-axis, URy ⫽ 1.2⬙ around the Y axis and URz ⫽ 0.9⬙ around the Z axis. The reported expanded uncertainty of measurement is given as the standard uncertainty of measurement multiplied by the coverage factor k ⫽ 2, which for a normal distribution corresponds to a coverage probability of approximately 95%.
3. Experiments To confirm the theoretical suppositions and calculations we carried out experiments on the high precision measuring device which we had developed. We carried out straightness measurements of the preloaded vacuum-air bearing system along the line gauge beam with and without a drive system, as well as measurements of the preloaded vacuum-air bearing system under the desired load. For this purpose we placed the measuring device without supports into a position horizontal on a granite plate. Measurements were carried out with an autocollimator (AC) and with electronic inclinometers (EI) in differential switching. The lateral displacements were checked with length indicators (Fig. 5). During measurement we moved the vacuum-air bearing sled along the line gauge beam. The first position was situated 100 mm from the beginning of the beam. Further test positions were chosen every 100 mm. After more than five repetitions of the same measuring procedure along the
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Table 1 Quantity
Gs y Gs z Gs Rx Gs Ry Gs Rz Ge y Ge z Ge Ry Ge Rz Gtg z Gtg Ry Gt z Gt y Bl y Bl z Bl Rx Bl Ry Br x Br y Br z Brro y Brro z Bpb y Bpro y Bpb Rx Bpro Rx Bt y Bt z Mli x Ma x Mt x Ci y Ci z Cmf y Cmf z Ct z Sb y Sm x Sm y St z St Ry St Rz
Value [m]
Value [⬙]
Contribution to the standard uncertainty ux
1,2 1,7
uy
uz
u Rx
u Ry
u Rz
0,35 0,49 2,063 2,063 1,456
0,6 0,6 0,42
0,35 0,5
0,1 0,14 0,3 0,2
0,09 0,06
1
0,29 0,2
0,06
1 0,3 1 1
0,29 0,09 0,29
Fig. 7. Results of straightness measurements in the Z direction. 0,29
0,2 0,2 0,5 0,5 0,5 0,4 0,4 2,5 1
0,06 0,06 0,14 0,14 0,14 0,12 0,12 0,72 0,29
9,63 2,29 1,1 2,1 2 1,2 2,1 1 1 2,02 1,7 3,4 2,2 1,6 0,8 2,9
2,78 0,66 0,32 0,61 0,58 0,35 0,61 0,29 0,29 0,58 0,49 0,98 0.64 0,46 0,23 0,84
0,25 1
0,07 1,03
1,36
1,71
2,92
0,62
0,29 0.51
whole beam length, the straightness deviations in the horizontal level were statistically processed from the AC or EI angle measurements. The mean values of the straightness deviation in the Z direction are presented in Fig. 7. The results presented in Fig. 7 denoted by AK Man. 1 and AK Man. 2 mean that the movements were made manually, without drive and counterweight influence, firstly with rigid connection of all support parts and secondly with loosened connections of all key supporting parts on the granite table. In this experiment we checked the influence of the constructional elements on beam accuracy deviation. From Fig. 7 no obvious differences were noticed. Only the dispersion of measuring results with loosened connections was a little bit larger. The measurements were also carried
out with a drive and counterweight system in both directions along the beam. The results of straightness measurements in the Z direction are denoted by AK Drive ⫹ for positive and AK Drive ⫺ for negative directions of movement. No hysteresis or other obvious differences from the first measurement results were noticed. To compare the experimental results with the theoretical results, a trajectory calculated with purpose-built software was added and marked as shown by OW ⫹ EL which considers deviations calculated from the beam’s own weight (OW) and from the sum of the external loads (EL). The standard deviation calculated from all measuring data performed in the Z direction was not larger than 2 ⫽ 0.9 m. The results of straightness measurements in the Y direction are presented in Fig. 8. The notation in Fig. 8 has the same meaning as the notation marked in Fig. 7, but in the Y direction. No hysteresis or other obvious differences for different conditions of measurement were apparent. The standard deviation of measuring data in the Y direction was not anywhere larger than 2 ⫽ 1.1 m. The vacuum-air bearing was designed in such a way that it could be adjusted according to momentary changes in the
Fig. 8. Results of straightness measurements in the Y direction.
I. Kovacˇ, A. Frank / Precision Engineering 25 (2001) 90 –99
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Fig. 9. Results of angular deviation measurements about the X axes.
orthogonality of the beam guiding surfaces. Therefore, only the side beam surface is responsible for the orientational deviations about the X axes. These angular deviations  were measured with EI along the X axes every 100 mm. The standard deviation of these angular measurement data, presented in Fig. 9, was not larger than 2 ⫽ 1.5⬙. From the previous Figs. 8 and 9, some noticeable changes of orientation between 200 and 600 mm were observed. This is a systematic error caused by imperfect beam manufacturing. These imperfections in angular deviations of rx ⫽ 2⬙ are still within the specified limits of the measuring device. Because of their systematic character they can be compensated for by means of the software, should this be necessary. The same measuring setup was also chosen for measurements under loaded conditions. As load a high precision CMA was used. It was placed on the same granite table as the high precision measuring device in order to meet all demands for a constant and stable relationship between the two base coordinate systems. The CMA was positioned in the middle area of the length measurement direction and 622 mm away from the beam center line. The measuring setup for straightness and angle deviation measurements loaded with the CMA in the horizontal level is presented in Fig. 10. Abbreviations in Fig. 10 are as follows: CMACoordinate measuring arm, EI-electronic inclinometer, LLLaser-liner, AK-Autocollimator, LI-laser interferometer. In these measurements we fixed the CMA to the vacuumair bearing sled with a connecting pin from the bearing side. The connecting pin had the same diameter as the touch probe system connected to the CMA. The connecting pin was manufactured very precisely together with the turning part of the rotational vacuum-air bearing. The whole rotational accuracy measured on the connecting pin under the loaded conditions specified for the whole bearing system, was smaller than one micrometer. Therefore, the influence of bearing rotational accuracy can be neglected. The measuring procedure was the same as in the previous measurements under unloaded conditions. Before these measurements we made some small improvements in re-
Fig. 10. Layout of the measuring setup in the horizontal position for straightness and angle deviation measurements when loaded with the CMA.
spect to air quality which resulted in even better measurement results, with smaller deviation of the results. The results for straightness deviation in the Z direction of the high precision measuring device when connected to the CMA as an external load are presented in Fig. 11. The standard deviation of the results obtained by an autocollimator in the Z direction in all positions was not larger for than 2 ⫽ 0.7 m. The situation for the results in the Y direction, presented in Fig. 12 was very similar. For the Y
Fig. 11. Results of straightness measurements in the Z direction.
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I. Kovacˇ, A. Frank / Precision Engineering 25 (2001) 90 –99
Fig. 12. Results of straightness measurements in the Y direction.
direction the standard deviation 2 was not larger than 0.6 m. The results for mean values of angular deviations , measured along the X axes in the horizontal position with EI connected in a differential circuit, are presented in Fig. 13. During the measurement we checked the displacements of the beam gauge at several key locations. Only bending changes at the expected level (in our case negligible) were noted, and no larger displacements in other directions were observed. Finally, we put the whole high precision measuring device on supports and in a position inclined by ␣ ⫽ 50°. In our case this is the most unfavorable configuration since support element number 2 (Fig. 6), representing a possible source of elastic deformation through changeable loading from the device to be measured, is about 1800 mm high. For this reason we measured displacements caused through bending of the support arrangement influenced by the CMA. On both sides of the beam four length indicators were placed on each of the surfaces orthogonal to the line of sled movement to control displacements in the Y and Z direction, as shown in Fig. 14. Because of the solid fixing of the
Fig. 14. Layout of the measuring setup for the whole system extremely inclined and loaded with the CMA.
supports to the concrete base and the rigid connection of the exchangeable support parts, we were successful in keeping these values under the 2 m level for the stated loading conditions.
4. Conclusion A new high precision measuring device for testing and calibration of coordinate measuring arms was designed and developed. Theoretical calculations performed on a simplified but corresponding model suggested the expanded uncertainty of measurement in the X direction Ux ⫽ 0.00218 mm, in the Y direction Uy ⫽ 0.00271 mm, in the Z direction Uz ⫽ 0.00336 mm and for the orientational part URx ⫽ 7.1⬙ around the X-axis, URy ⫽ 1.2⬙ around the Y axis and URz ⫽ 0.9⬙ around the Z axis. Experiments on the real high precision measuring device showed that this level was successfully achieved. Thus the new high precision measuring device can be taken as an appropriate reference measuring system for static or dynamic testing and for calibration of devices with unconventional kinematic structures, such as measuring robots or manually driven coordinate measuring arms. On the other hand, there are no limitations to using the proposed measuring device additionally as a reference gauge system for straightness measurements. And finally, the measuring device (without supports) weighs only about 60 kg and is therefore easily transported.
References
Fig. 13. Results of angular deviation measurements about the X-axis.
[1] Kovacˇ I. Knickarmgera¨te fu¨r die produktionsmetechnik. Int Fachtagung Koordinatenmetechnik - ein Baustein der Qualita¨tssicherung 1994:95–106. [2] Kovacˇ I, Frank A. Automated quality control by a novel anthropoidic measuring device. Third International Symposium on Measurement and Control in Robotics ISMCR’93 1993:164 – 69.
I. Kovacˇ, A. Frank / Precision Engineering 25 (2001) 90 –99 [3] Kovacˇ I, Frank A. High-precision testing and calibration metrology for portable coordinate measuring arms. International Symposium on Laser Metrology for Precision Measurement and Inspection in Industry 1999:1–10. [4] Kovacˇ I, Frank A. Automated geometrical inspection by a new robot guided anthropoidic measuring device. The Third International Conference on Automation Technology 1994;6:107–12. [5] Lotze W. Measuring device with rotation axes - new coordinate measuring device. VDI Berichte 1996;1258:13–24. [6] Whitney DE, Lozinski CA, Rourke JM. Industrial robot forward calibration method and results. ASME Journal of Dynamic Systems, Measurement and Control 1986;108(1):1– 8. [7] Judd RP, Knasinski AB. A technique to calibrate IR with experimental verification. IEEE Transactions on Robotics and Automation 1990;6(1):20 –30. [8] Schroer K, Albright SL, Lisounkin A. Modeling closed-loop mechanisms in robots for purposes of calibration. IEEE Transactions on Robotics and Automation 1996;3:1–32. [9] Kovacˇ I, Frank A. Methods for calibration and testing of flexible arm measuring devices. LAMDAMAP 1999;99:3–12. [10] Raab S. Three dimensional coordinate measuring apparatus. UK patent application GB 2 275 339 A, 1.2.1994.
99
[11] Bryan JB. A simple method for testing measuring machines and machine tools. Precision Engineering 1982;1:62–9. [12] Herzog K, Lotze W. Verfahren zur kalibrierung eines koordinatenmegera¨tes mit zwei rotatorischen achsen. EU patent application EP 0 703 430 A2, 7.9.1995. [13] Kovacˇ I, Frank A. High precision measuring equipment for testing and calibration of anthropoidic mechanism devices. 29th International Symposium on Robotics ISR 1998:1– 4. [14] Hirn C. Entwicklung eines klimatisierten pra¨zisionskomparators fu¨r la¨ngen und geradheitsmessungen bis 5 meter. Technik report 1992; 19(6):23– 6. [15] Kovacˇ I, Frank A. Robot-aided coordinate measurement with the anthropoidic measuring device AMG-1. 3rd Asian Conference on Robotics and Its Application 3rd ACRA 1997:197–202. [16] Vorbach S. Construction of a test-place for a measuring device. Thesis at the TU-Graz, Austria, 1994. [17] Kovacˇ I, Frank A. Neues mobiles megera¨t zur fertigungsintegrierten geometriepru¨fung. VDI-Z 1998;140(5):36 – 8. [18] Kovacˇ I, Frank A. AMG-1: a new approach to robot integrated measurement. 27th International Symposium on Industrial Robots ISIR 1996:955– 60. [19] Bartz W. Luftlagerungen, Expert Verlag Band 78, 1992.