NanoCMM : a 3D coordinate measuring machine with low moving mass for measuring small products in array with nanometer uncertainty

To measure dimensions and shape of complex three dimensional products (e.g. engines, mouldings, etc) with low uncertainty, Coordinate Measuring Machines (CMMs) are adequate instruments due to their universal applicability, easy measurement set-up and measuring flexibility. Motion software is generated in teaching by doing manual mode, allowing automated repetition in series produced products. To keep on track with the trend towards miniaturization and looking forward to the upcoming market for Micro-Electro-Mechanical Systems (MEMS), the industry requires a fast 3D CMM for measuring small products in array with nanometer uncertainty for an acceptable price. Although there are commercial CMMs available with sub micrometer and even claimed nanometer measurement uncertainty, none of them allows measuring with high speed in 3D as a result of their huge moving mass in the horizontal plane and/or vertical direction. To meet the above industry requirements, it was decided to develop a 3D CMM with a low moving mass in x-, y- and z-direction and a volumetric uncertainty of 25 nm in a 50 × 50 × 4 mm measuring volume. The design, realization and calibration of this CMM are described in this thesis. Business related information is included in a Marketing Plan by the same author in a MBA final project at TIAS Business School. After comparing the guides of the CMM concepts, which emerged in the last ten years and components such as air bearings, actuators and encoders, the design was formulated as a completely aluminum CMM, based on a horizontal air bearing system without Abbe errors, an elastically guided vertical axis, measurement by 1 nm resolution optical linear encoders (optical measuring head and reflective scale) and single phase Lorentz actuator drives. The horizontal air bearing system consists of two scale beams (each carrying a reflective scale) and two intermediate bodies (each carrying an optical measuring head), all equipped with separate stress frames which prevent distortion of the optical linear encoders by preload forces. The optical linear encoders are in line with the lengths being measured in x- and ydirection, which eliminates Abbe errors in the horizontal plane. Further, it eliminates straightness errors of the scale beams according to the Bryan principle. The straightness errors of the machine base surfaces which guide the intermediate bodies and the angle between these guiding surfaces affect the measuring uncertainty of the CMM so they have to be calibrated. To ease external calibration, a removable angle standard, which can be fixed and detached without internal deformation, is incorporated in the machine base. The air supply to the horizontal air bearing system is provided by patented frictionless air supply systems. Such frictionless air supply system avoids a robot that carries hoses and the with friction associated hysteresis. The vertical stroke of the CMM is provided by an elastically straight-guiding mechanism. It is stiffness- (by stiffness compensation spring) and weight (by weight compensation spring) compensated. The stiffness compensation spring reduces the stiffness in drive direction with a factor of around 50, i.e. 50 times less force (F) for the same stroke. This reduction also occurs in the motor coil current (I) which will reduce the required power (P) 2500 times as it is proportional to the square of current. Measurements showed that 80 mW was required to keep the probe, which is connected to the vertical axis, at the maximum displacement from its mid position. The weight compensation spring has a stiffness of 715 N/m and is connected to a lever with a ratio of 1 : 10 from the vertical drive system. This means that this drive system has to apply an extra force of 715/102 × 0.002 ˜ 15 mN to keep the probe at the maximum displacement from its mid position. This is negligible compared to the 0.08 N needed to overcome residual stiffness. The CMM has a size of 450 × 450 × 200 mm, a moving mass of 8.5 kg in the horizontal plane and a moving mass of 100 g in vertical direction. Compared to today’s high accuracy CMMs, this CMM has a 4.5 to 7 times lower moving mass in the horizontal plane and an up to 300 times lower moving mass in vertical direction, which reduces power required for measuring with high speed in 3D and thereby avoids thermo-mechanical effects. Taking Lproduct as the product length in x- respectively y-direction, Hproduct as the product height in z-direction and DT the temperature change during a measurement, the sensitivity for temperature variations during a measurement can be described by (7E-3 + Lproduct) × 23E-6 × DT for the x- and ydirection and by (20E-3 + Hproduct) × 23E-6 × DT for the z-direction. After tuning the PID-controller the positioning error in z-direction was ± 2 nm and a bandwidth of 200 Hz was realized for the elastically guided vertical axis. The positioning errors in x- and y-direction were ± 4 nm respectively ± 3 nm. The open-loop frequency response functions of the horizontal air bearing system showed a bandwidth of 35 Hz in xdirection and of 50 Hz in y-direction. This difference can be explained by the asymmetric configuration of the horizontal air bearing system for reasons of kinematic design. The total error vector of the CMM results from the sum of the individual error vectors of the moving bodies of this CMM and the squareness errors between the guide systems for x, y and z. The errors in this vector (13 error sources) were calibrated to be able to estimate the volumetric uncertainty of the CMM. To ensure traceability of the uncertainty claimed, the calibrations were performed by the Dutch National Metrology Institute (NMi VSL). The temperature stability of the calibration set-ups was increased by active cooling of the measuring systems and laboratory temperature variations (typically 70 mK over a 150 min time period) were reduced by enclosing the set-ups by a box of polystyrene foam. Furthermore zero-point drift-correction was implemented to eliminate thermal expansion differences of the various materials in the thermal loop of the calibration set-ups. The standard uncertainty of a volumetric length measurement, due to geometric errors, was estimated to be about 13 nm (2 × 13 = 26 nm expanded uncertainty (k = 2)) in best case and 38 nm (2 × 38 = 76 nm expanded uncertainty (k = 2)) in worst case. These values apply to 3D objects with dimensions of the measuring volume. For the intended small products, the expanded uncertainty (k = 2) in nanometers is about 11 + 0.3×L in best case and 19 + 1.2×L in worst case, with L the measured length in mm.