Design of a High-Precision 3D-Coordinate Measuring Machine

Design of a High-Precision 3D-Coordinate Measuring Machine M. M. P.A. Vermeulen, P.C. J.N. Rosielle, P. H.J. Schellekens (2) Eindhoven University of Technology, Precision Engineering Section, Eindhoven, The Netherlands Received on January 8,1998

Abstract In Precision Engineering components are getting smaller and tolerances become tighter, so demands for accuracy are increasing. To improve the precision of Coordinate Measuring Machines (CMMs) we designed an alternative high precision 3D-CMM with measuring uncertainty beneath 0.1 pm in a measuring volume of 1 dm3. The machine design is based on the Abbe and Bryan principle, thus smaller measuring errors are feasible with less effort on software compensation. Application of a light and stiff construction, compensated air bearings and well-positioned linear motors result in high stiffness and favourable dynamic behaviour. A statically determined design, extensive use of aluminium and mechanical thermal length compensation make the machine less sensitive to temperature changes. To prevent mechanical disturbances an active vibration isolation system was designed. This paper focuses on machine design aspects showing analytical- and experimental results and design synthesis. Keywords: Coordinate Measuring Machine, High-precision Design

1. Introduction Coordinate Measuring Machines (CMMs) are often used to measure dimensions and shapes of rather complex products. The tendency of decreasing product sizes and tighter tolerances requires CMMs with higher precision. CMM inaccuracies are primarily determined by geometric errors of the guides and deformations of machine parts due to finite stiffness, inertia and temperature changes. When the measuring systems are on the machine outside -like in conventional CMMs- Abbe errors may occur. These errors can be decreased by reducing the distance between the product and the measuring systems, called the Abbe offset [2][3]. Hence an alternative approach for a high precision CMM was generated [12]. based on the Abbe principle and another basic principle of measurement: the Bryan principle [2]. The main objective was to avoid rotational errors caused by the mechanical design and apply software correction for the remaining translational errors. By minimising the quantities to be corrected a higher measuring accuracy is feasible, because measurement of the interference factor is possible only within limited accuracy [I].

complexity and unfavourable dynamic behaviour. The much simpler design of figure 2 has a vertical slide in the platform, with an internal scale, satisfying the Abbe principle. For measurements outside the mid-plane only small errors appear (Abbe-offset equals the vertical travel (50 mm)). ,This structure also satisfies the Bryan principle in x- and y-direction, making the machine nonsusceptible for straightness errors of the scale support beams.

2. Design Principles Figure 1; Top view of the alternative 3D-CMM In the proposed design much attention is paid to satisfying the Abbe principle to reach higher accuracy. For that purpose separate intermediate bodies in x- and y-direction and crossing beams are used. In figure 1 the x- and yscales (S, and S), used in the measuring systems each are supported on orthogonal beams (x and y), connected to the probe (P) by a moving platform (PL). The beams move through their respective intermediate bodies (A and B), each carrying a measuring head (M, and My). These bodies can move along their respective guiding beams (I and 11) which are mounted on a base. From this base a granite table ( l ) for the products to be measured is suspended. The scales are always aligned with the probe motion, so measuring without any Abbe errors is realised in the horizontal midplane of the machine (i.e. figure 1). This principle could be expanded to a CMM-design satisfying both principles of measurement in the whole measuring volume. However, Figure 2: Schematic drawing of the alternative 3D-CMM that would introduce six intermediate bodies, causing high

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The x- and y-drives (described in section 3.4) are connected between the platform and the intermediate bodies B respectively A (see figure 2: D, and Dy), so their driving forces are directed through the centre of mass of the platform to minimise inertial rotational effects. The zdrive is mounted next to the pinole as close as possible to it's centre of mass. Hence this machine concept is transferable to large size machines. With respect to it's measuring volume (0.1x0.1x0.1m3) the dimensions of the CMM ( 0 . 6 ~ 0 . 6.4m3) ~ 1 are consistent with conventional machines. The machine should act as a platform for a large variety of both contact and non-contact probes, measuring shapes, and scanning surfaces. Especially for scanning, a 20 probing system is being developed [8] with low probing force (mN-range). and an expected accuracy of 10 nm.

3. Mechanical Design 3.1 Machine Frame Deformations in the machine frame directly cause measuring errors. To minimise these deformations several design strategies with respect to dynamic- and thermomechanical behaviour are applied: Dynamic Behaviour: The machine slides are built up as a closed-box plateconstruction to create light and stiff moving parts. The platform has a pyramid-shape for optimal material utilisation (i.e. a uniform mechanical stress distribution). Additional to the geometry of a construction it's dynamic behaviour is determined by the material property Hp, the specific stiffness, given for several materials in table 1. With respect to conventional materials like aluminium and steel a gain factor 3 to 6 can be attained using ceramics. For this reason these materials are used more and more, (e.g. for the pinole in this CMM). However, the machine frame components are made of aluminium because of it's excellent thermal behaviour (see next section) and it's easy obtainability and machinibility, resulting in great design flexibility. These components are CNC milled out of massive blocks, preventing hysteresis and loss of stiffness and conductivity in the plate connections. In plate-constructions both mass and stiffness are directly proportional to the plate thickness. To attain equal stiffness of an aluminium construction with respect to it's steel version, the plate thickness is tripled due to it's smaller density. As a result transversal plate dynamics have improved considerably. Thermomechanical Behaviour: The main reason for choosing an aluminium machine frame above a steel one is it's excellent thermal behaviour, (see table 1): The thermal sensitivity for gradients a/A of aluminium is 2.1 times smaller than steel. Gradients are not likely to occur due to the excellent thermal conductivity A, which is for aluminium 4.6 times better than for steel. The thermal diffusivity .vpC, for aluminium is 5.9 times better than for steel.

for aluminium, the distance between the probe and the measuring systems ('the measuring cirde') is minirnised and mechanically thermal length compensation is integrated for all principal axes. The x- and y-directions have coinciding thermal centres for the machine base and the slide construction in the centre of the measuring volume. For the z-axis different materials are chosen to compensate thermal expansions. Although coefficients of thermal expansion are not better known than within 0.5.106 K [ l ] thermal length compensation can be improved by measuring expansion of machine components due to controlled temperature changes [5] and subsequently creating equal thermal lengths by choosing the proper fixed clamping point of the scales. A granite table plate is chosen despite it's poor thermal behaviour with respect to aluminium [5][7] because of it's availability with high surface flatness. Thermal errors are minimised by several measures: The operators thermal radiation to the machine is shielded by remote motion control. Heat production in the drives (see 3.4) is small due to a high motor constant and a small electrical resistance. Distortions of the granite will be minimised by isolation around the table. Room temperature fluctuations are limited to normal laboratory conditions: &2 K.

3.2 Membrane Air Bearings For all slides air bearings were chosen to attain high guiding accuracy and reproducibility and negligible friction. To optimise the stiffness, passively compensated thrust bearings were developed, based on existing compensation techniques [lo]. In [ll] a comparison is given for five different bearing types, with respect to the static bearing characteristic. In the membrane bearings the compliance of the air film is passively compensated by the deflection of a membrane as a result of a pressure distribution at the front- and backside of the membrane. The membrane thickness and height of the chamber at the membrane backside are used as tuning parameters to experimentally attain infinite static stiffness. For this CMM two bearing diameters (040mm and 060mm) were chosen considering space and load capacity. While slowly decreasing preload, force and axial displacement h (#gap height) were measured. To exclude the influence of tilt, displacement was measured using three sensors. In figure 3 the static bearing characteristic is given for a 060mm bearing pad and for the membrane.

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At a preload-level of Fp= 500 N infinite static stiffness was attained. From the membrane characteristic the actual air gap can be read: h, = 6 pm. For limited-space applications (vertical slide), 040mm bearings were developed. For these bearings infinite static stiffness was reached at a preload level of 250 N and similar gap height.

To minimise the machine sensitivity to temperature changes due to a large coefficient of thermal expansion

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To investigate the dynamic behaviour of the air bearings, vibration tests were performed on the z-slide of the CMM. Figure 4 shows the test set-up with the pinole in a horizontal position. A dynamic radial force (white noise force spectrum) was applied to the nose of the pinole by a shaker (E) and measured by a piezo electric crystal. The radial displacement at the nose of the pinole was measured by eddy current sensors (S) (differential measurement) on aluminium targets. From the force- and displacement signal a dynamic analyser calculated the dynamic stiffness as a function of frequency: Cmse. The preload level per membrane bearing was varied from 150 to 300 N. by changing the pressure of the preload bearings (see section 3.3). The protruding length of the pinole a was varied in three positions: (min.- mid- and max.-position). With respect to the relative bearing distance Ithe dimensionless protruding length ad varies respectively from 0.2. 0.45 to 0.70. Figure 5 shows the dynamic stiffness , c for the mid-position.

a smaller membrane chamber and by enlarging the (number of) channel(s). connecting the chamber to the membrane front side. The resulting stiffness above 5 Hz equals the stiffness of the air film. being proportional to the bearing surface. Hence the dynamic stiffnesses Cmrn and Cmnst could be increased, using larger bearings. Nevertheless, for (quasi)static forces an enormous stiffness-gain is attained with respect to conventional bearings, using bearings of only 40 mm in diameter. For a preload level of 250 N per bearing (optimum static stiffness) the dynamic stiffness values Cmm and Canst are shown in figure 6 as a function of the dimensionless protruding length: an.

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The following can be concluded: The bandwidth of the pinole for the mid-position is 160 Hz. (For minimum and maximum protruding length the bandwidth is 165 and 110 Hz respectively). The minimum stiffness Cmin at the nose for the mid position arises at 217 Hz, being the first natural frequency of the system. (For the min. and max. protruding length the first natural frequency appears at 196 respectively 166 Hz). The minimum stiffness value does not vary much with preload. In the frequency range from 5 to 100 Hz the stiffness is approximately constant, described by Canst. Below 5 Hz the stiffness increases tremendously to infinite stiffness for static situations. The dependence of Canst on the preload level is small. Obviously the compensation mechanism in the air bearings can not follow well vibrations above 5 Hz. The air-flow rate to the chamber at the membrane backside is too small to bend the membrane fast enough, so compensation for air gap change does not occur above this frequency. The drop frequency could be increased by

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At large protruding length the stiffness at the nose of the pinole Cmse is reduced considerably with respect to the bearing stiffness c. For this effect three causes are responsible. In table 2 the compliance contribution of each cause is given for the three protruding positions. The first effect is the compliance of the pinole. having a third power relation to aA. Using a ceramic pinole o50x50mm this effect is negligible for the resulting compliance. The second effect is the translation of the pinole caused by the compliance of the bearings. The third and determinative effect is the rotation of the pinole due to the cantilevereffect: the ratio the dimensionless stiffness Cnose /c is proportional to the square of a/l.

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Compliance-contribution["h] min mid rnax Dinole comdiance I 0 1 1 1 3 14 34 21 translation-effect rotation-effect (cantilever effect) 66 78 83 100 100 100 total Table 2: Compliance-contributions for min.- mid- and max.- protruding positions

3.3 Preload Bearings To attain a constant gap height the membrane bearings are preloaded in a force closed way by adjusting the preload level with a spring and an additional preload bearing (in contrast to form closed preload where the optimum gap between two bearings and a guide has to be adjusted). The spring absorbs geometric errors of the guideway and thermal expansions between the slide and the guide. In common metal springs a relatively large spring volume and adjustment-mechanism is needed, affecting both it's size and it's price. To provide a safe and simple assembly a very compact preload bearing was designed with integrated pneumatic spring. The pneumatic spring is an air chamber in the air supply behind the bearing disk. For a given preload level of a membrane bearing, pressure and chamber diameter are chosen. The membrane bearing and it's preload bearing are placed as an opposite pair to prevent bending of the guide. In case of pressure drop the bearing becomes forceless, protecting the guideway from contact damage.

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3.4 Drives To enable accurate positioning in high precision machines the application of linear motor drives is increasing due to their favourable properties with respect to conventional feed drives: high dynamic characteristics, high servo bandwidth due to a direct and linear relation between motor current and feed force, simple design and neither friction nor backlash. These drives are used in the CMM in a closed loop servo system with 5 nm resolution interference scales for position feed back. Tests have shown [13][11] that practical positioning accuracies are restricted by the controller and the measuring systems: position errors of 10 nm (a few counts) are feasible. The effect of disturbing motor forces is very low due to a nonferro coil-carrier causing neither cogging nor attraction forces between magnets and coils perpendicular to the axial direction. For driving at very low speed additional damping should be added (e.g. in the controller software) due to the absence of friction. Proper tuning between the servo controller and the motor is important. For high feed forces motor cooling might be required [13]. In our case power dissipation is limited to 1 W because of a high force constant, a small electrical resistance and small (inertial) feed forces.

3.5 Vibration Isolation and Machine Levelling To separate the machine from mechanical disturbances, passive vibration isolation is applied [4].Pneumatic isolators are used instead of metal springs because preload and additional damping are easily feasible and slinky modes present in metal springs- are absent. Furthermore automatic pneumatic levelling of the machine is easily performed: by changing the pressure of each pneumatic spring, the machine can be levelled in 20s. During operation the load on the isolators changes due to machine movements. To avoid machine tilt an additional levelling system is required, fast enough to keep up with machine movements (bandwidth 10 Hz). A mechatronic design is chosen, using differential inductive sensors, voice coil actuators and cantilevers. The dynamic behaviour of the levelling system is investigated by modelling and simulation, using bond graph techniques. The maximum tilt angle during set-up is limited to 2.102mrad. 4. Error Analysis and Calibration

An extensive error analysis was made to predict the machine error budget. The following can be concluded: Application of the right design principles to geometry and assembly of -machine components leads to high static stiffness 10' Nlm, (resulting in a finite-stiffness error of 5 nm) and favourable dynamic behaviour (lowest natural frequency: 90 Hz. and resulting dynamic error of positioning: 4 nm). rn The machine susceptibility to temperature changes and gradients is minimised by extensive use of aluminium and mechanical thermal length compensation. The resulting thermomechanical errors -mainly caused by distortions of the granite table [7]- are about 10 nm. For the 20-probe. that is being developed [8], the estimated probing errors are 10 nm. The inaccuracy of the measuring systems is 100 nm for 100 mm measuring length. This error will be reduced by software correction to 20 nm. This machine concept with intermediate bodies satisfying the Abbe and Bryan principle reduces rotational errors to 12 nm. For the remaining translational errors (straightness errors of the guiding beams (I and II), the granite table and the ceramic pinole): about 3 pm, error correction will be applied. Using a laser interferometer 30 nm straightness error can be reached.

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A relatively easy and accurate calibration can be executed using the PTB-method of measuring 2D reference objects in different optimally selected positions [6]. This method allows a direct traceability of the CMM via one pre-calibrated reference artefact, that has to be developed for this CMM. Using this calibration method a total measuring uncertainty of 0.1 pm is expected.

5. Realisation To construct, test and calibrate a prototype of this machine, a Ph.D. project was started in 1994. The project is executed in the Precision Engineering section and the Design and Engineering Facilities, both of EUT. CMM manufacturer Zeiss contributes motion control and measuring sofiware. Calibration procedures and error compensation are prepared to precede the envisaged use as from the end of 1998 in the Precision Engineering section of EUT and in the Dutch Metrology Institute (NMI), which financially supports the project.

6.Conclusion The design of the high precision 3D-CMM, described in this paper, with a measuring volume of 1 dm3 is quite alternative with respect to conventional CMMs. The machine design -transferable to large size machines- is based on the Abbe and Bryan principle, thus a higher measuring accuracy is feasible with less effort on software compensation. The main objective was to avoid rotational errors caused by the mechanical design and apply software correction for the remaining translational errors. The resulting estimated volumetric measuring uncertainty is 0.1 pm. References Breyer, K.H., Pressel, H.G., 1991, Paving the way to thermally stable Coordinate Measuring Machines, Progress in Precision Engineering, 56-75 Bryan, J.B., Carter, D.L., 1979, Design of a new error-corrected co-ordinate measuring machine, Precision Engineering, 1 (3): 125-128 Bryan, J.B., 1979, The Abbe Principle revisited, Precision Engineering, 1 (3): 129-132 De Bra, D.B., 1991, Vibration isolation, Stanford University CA, ASP€ Annual Meeting Kunzmann, H..Waldele. F., 1988, Performance of CMMs, Annals of the CIRP, 3712: 633-640 Kunzmann, H., Trapet, E., Waldele. F.. 1990,A Uniform Concept for Calibration, Acceptance Test, and Periodic Inspection of CMMs Using Reference Objects, Annals of the CIRP. 39/11561-564 Meijer,J., 1989, From straightness to flatness, thesis, University of Twente. ISBN 90-9003117-0 Pril. W.O.. Struik, K.G., Schellekens, P.H.J., 1997, Development of a 20 probing system with nanometer resolution, Proc. of 16IhASPE, 438-442 Smith, S.T., Chetwynd. D.G., 1992, Foundations of Ultraprecision Mechanism Design, Gordon and Breach Science Publishers Snoeys, R.. Al-Bender, F., 1987, Development of improved externally pressurised gas bearings, KSME Journal, Vol. 1, 81-88 Vermeulen, J.P.M.B., Rosielle, P.C.J.N., Schellekens. P.H.J., 1996, Innovations in the Design and Development of Ultraprecision Machines, Proc. of 14IhASPE, 631-636 Vermeulen. M.M.P.A., Rosielle, P.C.J.N., Schellekens, P.H.J., 1994, A small CMM design, not just scaling down, Proc. of lothASPE, 133-136 Weck, M., Day, M., 1997, Linear Motors in Ultra Precision Machines, Proc. of 9Ih IPES, 429-432