Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
  • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
  • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
  • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
  • G01B21/042—Calibration or calibration artifacts
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
  • G01S17/66—Tracking systems using electromagnetic waves other than radio waves

Definitions

• Such machines include, for example, coordinate measuring
• Such machines generally have a position transducer for each axis of movement (e.g. a linear encoder scale for linear axes, or an angle encoder for rotational axes).
• the outputs of these transducers are taken to a numerical control or computer, which can thus determine the position in space of an end effector of the machine, such as a tool or probe.
• a position transducer for each axis of movement e.g. a linear encoder scale for linear axes, or an angle encoder for rotational axes.
• the outputs of these transducers are taken to a numerical control or computer, which can thus determine the position in space of an end effector of the machine, such as a tool or probe.
• Various methods and apparatus are already known for determining the accuracy of such machines, e.g. for calibration purposes.
• the artefact may incorporate known or unknown constant lengths, which are measured by the machine at various positions and
• parameters can be determined by direct measurement using a laser interferometer, but this has the disadvantage that a different interferometer set up is required for each parameter, so that the procedure is time consuming. Also, it is difficult or expensive to measure roll using an interferometer.
• One aspect of the present invention provides an apparatus and method using a laser interferometer to measure the accuracy of a number of distances generated on a multi-axis machine, in various orientations.
• a second aspect of the present invention provides a method of determining parametric errors of a multi-axis machine, in which the machine is caused to generate a number of distances in various orientations, and the accuracy of these distances is ascertained.
• the invention then provides a method to determine the required parametric errors from these distances.
• the accuracy measurements can be made by the method of the first aspect of the invention, or they may be obtained from measurements upon artefacts.
• Fig 1 is a schematic diagram of one embodiment of the invention
• Fig 2 is a schematic diagram of a coordinate measuring machine with a second embodiment of the invention.
• Fig 3 is a schematic diagram corresponding to Fig 1 but showing a modification
• Fig 4 is a vector diagram for explaining a method according to the second aspect of the invention.
• Fig 5 is a schematic diagram of a two-dimensional coordinate measuring machine.
• FIG 1 illustrates schematically the apparatus required for making accuracy measurements on a machine having only two axes of movement (or a machine having more than two axes, the remaining axes being held stationary).
• a retroreflector 10 is attached to a portion 12 of the machine which can move within the two axes, for example the end of a ram intended for holding a tool or probe.
• a rotary table 14 is separately mounted on a stationary part of the machine, and can be rotated about an axis as indicated by arrows 16, by means of a motor 18, or manually.
• a mirror 20 is mounted for rotation with the rotary table 14. Light from a laser 24 is passed to the rotatable mirror 20.
• An interferometer 22 includes a retroreflector 23 in a reference arm, and the interferometer is placed between the laser 24 and the mirror 20, so as to measure changes in the path length of the light.
• apparatus is controlled from a computer (not shown in Fig 1).
• the above apparatus is (software) aligned by measuring the position and direction of the reflected beam for several angles of the rotary table 14. Each position and direction is estimated from the scales or other
• position transducers are taken at at least two different, manually tuned, positions where the laser beam is optimally returned to the interferometer 22, as determined by
• a "best fit" straight line is calculated by a "least squares" method.
• a simple CNC program which moves the retroreflector 10 across the laser beam 28 and measures the interferometric signal strength. By obtaining such information for a sufficient number of angles of the rotary table, the position and direction of the reflected beam can be inferred for any other angle of the rotary table. For this, the orientation of the table itself needs to be measurable to a certain minimum accuracy. If this is not possible, the laser beam should be aligned at more angles, or at all angles which are to be used.
• the apparatus is used as follows. In a certain fixed position of the rotary table, the machines ram 12 is automatically moved along the reflected laser beam 28, the position and direction of which are now known. At certain positions, the machine's travel along the line of movement (as determined by the computer from the scales of the machine) is compared with the reading given by the interferometer 22. This gives readings of the accuracy of the machine when making a number of length measurements, e.g. as indicated at 26 between start and finish points 26A,26B. As many such accuracy readings as desired can be made during this movement.
• the rotary table 14 is rotated by the motor 18, under computer control, so that the laser beam 28 takes up a new orientation.
• the above process is repeated, moving the ram 12 along the new orientation of the laser beam and taking as many comparative readings as desired.
• the process is repeated again for as many different angles of orientation of the laser beam as required.
• the accuracy of a large number of attained distances of the ram 12 in different directions can be measured fully automatically. Since the position and orientation of the mirror is the same at both end points 26A,26B of the measured
• Fig 2 shows in more detail an arrangement for measuring the accuracy of a coordinate measuring machine 30, having three axes x,y,z. A similar arrangement may be used for other machines having three or more axes.
• Fig 2 includes various components which are similar to those of Fig 1, including a retroreflector 10 attached to the ram 12 of the machine, a laser 24 and an interferometer 22.
• a mirror 20 is also provided, as before, except that it is now mounted on a rotary table 14, e.g. in a gimballed arrangement, in such a way that it can be driven about two different axes of rotation (which need not be
• Fig 2 also shows other components of the practical arrangement, including a computer 32 which provides the numerical control of the three axes of movement of the machine 30; and a computer 34 from which the accuracy measurements are controlled and which is linked to the computer 32, e.g. by an RS232 link 36.
• the computer 34 receives readings from the laser interferometer 22,24 via an interface 40, and the readings may be compensated for atmospheric conditions detected by a sensor unit 42 if desired.
• the two axes of rotation of the mirror 20 are preferably motorised and controlled
• the apparatus of Fig 2 is used in exactly the same manner as the apparatus of Fig 1, except of course that the laser beam 28 is directed into a number of orientations in three dimensions, using the two axes of rotation of the mirror
• a machine having three or more axes could also be measured with a mirror 20 having only one axis of rotation, as in Fig 1, by moving the laser 24 and interferometer 22 to obtain the other axis of beam orientation.
• the laser and the mirror 20 must remain fixed relative to each other during each set of measurements at a given
• Fig 3 shows a modification of Fig 1, in which the common components have been given the same reference numerals.
• the modification lies in the provision of a position detector 44, which receives the returning laser beam via a beam splitter 42, after the laser beam has been rereflected by the mirror 20.
• the output signal of the detector 44 controls the position of the mirror 20 via a servo connection 46 to the motor 18. This causes the mirror 20 to track the movements of the retroreflector 10.
• the retroreflector 10 can be moved from the start position 26A to the finish position 26B of the displacement by any convenient route. This is useful in the case of manual or numerically controlled machines which are
• the position detector 44 should be capable of detecting deviations in two dimensions and controlling the two axes of the rotary table 14 accordingly.
• the position detector may be connected to the computer 34 via an
• the position detector 44 is also useful during the initial alignment of the rotary table 14, since it facilitates the detection of the optimal position of the retroreflector 10 during the alignment procedure.
• the retroreflector 10 can be a corner-cube retroreflector, or a cat's-eye retroreflector may be used for its wide angle properties.
• a plane mirror may be used (with a plane mirror interferometer system 22). The plane mirror should be adjustably mounted to the ram 12 so that it can be adjusted to be normal to the beam
• the retroreflector 10 can be mounted on an arm extending laterally from the ram 12. This is particularly desirable if it is desired to measure z-axis roll (in the arrangement depicted in Fig 2).
• the parametric errors of a multi-axis machine can be estimated from the length errors in a large number of such distance measurements.
• the large number of distance measurements may be obtained using the apparatus and method described above, or other interferometer length measurement arrangements. Alternatively, they may be obtained from conventional measurements upon artefacts of the type discussed above.
• the method as discussed below can be applied to machines with prismatic and/or revolute joints in an arbitrary configuration, including large machines, software compensated machines and machines with significant finite stiffness related errors.
• the position errors of the end effector (e.g. a tool or probe) of a multi-axis machine are caused by separate errors introduced in the components of the machine (e.g. squareness, straightness and scale errors, and angular errors of roll, pitch and yaw). These are the so-called parametric errors.
• a mathematical model is built of the machine's error structure, including a
• squareness error can be considered as a steady gradient in the parametric equations describing straightness errors, or it can be considered as a static rotation error. It should be modelled as one of these alternatives, but not both. In the description below, it is modelled as a static rotation.
• this least squares method is used to allocate the errors between the parameters, as opposed to simply allocating a given error to a given parameter.
• this linear regression may be performed using off-the-shelf software, either in the computer 34 (Fig 2) or in another computer using the data recorded by the computer 34.
• Each parametric error is described as a linear combination of known functions.
• the known functions are defined on the position of the machine's axes and other relevant variables (e.g., the output of a certain temperature sensor).
• pk(x) is a known function defined on the relevant independent variables contained in the vector x.
• Bk is the unknown parameter describing the contributions of this function to the parametric error Ei,j , and has to be estimated.
• variable knot positions carries the practical danger of overfitting the data, and makes testing of the hypothesis concerning areas of structural change virtually impossible. Unless prior information is available, we use a basic model which contains enough polynomial pieces with a fixed length and a specified maximum degree, to accommodate the most complex error expected.
• the relative position error of the end-effector of the machine is related to the parametric errors using an error model [3].
• error model [3].
• a large variety of such models have been described, these models are linear in the parametric errors, since the difference between the nominal and the actual machine geometry usually does not significant change the active arm of angular errors and the direction in which the various errors acts.
• the model can be summarized as:
• Equation 2 the vector Ei contains the three angular and three
• the 3 ⁇ 6 matrix uFi describes how these parametric errors affect the errors ⁇ P in the relative position of the end-effector. This matrix is completely defined by the nominal geometry of the machine, the length of the
• Vector eu contains the
• ⁇ we use the observed errors in a large number of distance measurements. These measurements can be realized by artifacts, or by using a distance measuring instrument with a high relative accuracy (e.g., laser interferometer), for instance as described above .
• a distance measuring instrument with a high relative accuracy (e.g., laser interferometer), for instance as described above .
• the difference between the measured (by the machine) and actual position and orientation of the reference distance has a negligible effect on the measurement error of this distance.
• ⁇ i represents the measurement error due to non-repeatable and non-modelled machine errors.
• Vector xi contains the variables which describe the status of the machine and its environment during the measurement (e.g., the position of the machines axes for each measured point).
• the known function igk(Xi) describes the effect of parameter ⁇ k on the feature's measurement error.
• pk(x) in relation 1. that describes the effect of the of parameter ⁇ k on the respective parametric error, are calculated for the status of the machine when measuring the end points of the considered distance. These values are then inserted in relation 2 to obtain the effect of ⁇ k on the displacement error of the end-effector for various measured points.
• igk(xi) is computed as the dot product of the difference between both displacement errors with the direction vector along the measured distance.
• the vector ⁇ has to be expanded to include these dimensions.
• at least one measurement of known dimensions has to be made, in order to obtain absolute accuracy.
• Equation (1) above is a simplification, because it ignores cross-talk between different axes, that is, the way in which the position in one axis affects the errors in another.
• the vector x can be generalised to include the effects seen in the x axis when y and z are varied:
• equation (1A) will have further terms
• a two-dimensional coordinate measuring machine depicted schematically in Fig 5.
• the machine has an x slide 50 connected to a y slide 52.
• a probe P is connected to the y slide 52, offset by a distance a.
• the position of the probe P is measured by the machine as having coordinates (X,Y).
• the discussion below also refers to a direction z, normal to the plane of Fig 5.
• the parametric errors of the machine are:
• Equations E2 and E3 constitute a formal statement of the properties of the machine. Substituting E1 into E3 gives:
• ⁇ i is a term relating to the difference between the real error and the modelled error
• the actual length of the artefact is defined as:
• Equation E10 can now be described as:

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• 1992
  • 1992-10-12 EP EP92921141A patent/EP0607240A1/de not_active Withdrawn
  • 1992-10-12 WO PCT/GB1992/001871 patent/WO1993008449A1/en not_active Application Discontinuation

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