Compensation of measurement errors due to dynamic deformations in a coordinate measuring machine

TECHNICAL FIELD [0001] The present invention relates to a coordinate measuring machine and a method of compensating measuring errors caused by dynamic deformations.

PREVIOUS BACKGROUND [0002] As is known, coordinate measuring machines generally comprise three carriages that are movable along the coordinate axes of the Ortho-Cartesian reference system and are intended to move the sensor in the measurement volume. The machine is designed to output the coordinates of the element detected by the sensor, calculated as a function of the position of the ambulances along individual axes.

[0003] More specifically, coordinate measuring machines include components such as a base structure provided with guides along the first axis, for example, a table made of granite or other material, or otherwise a pillar structure; a first carriage that is movable on a base structure along a first axis; a second carriage that is supported by the first carriage and is movable along a second axis perpendicular to the first axis; and a third carriage that is supported by the second carriage and is movable with respect to this along a third axis perpendicular to the first two axes. The sensor is supported by a third carriage.

[0004] The first axis is generally horizontal; according to the type of machine, the second axis may be horizontal, and the third axis may be vertical, or vice versa.

[0005] For example, in bridge or gate type machines, the first carriage includes a horizontal cross member

EP 2 167 912 defining the second axis on which the second carriage moves, and the third carriage is formed by a column which is supported by the second carriage and is vertically movable.

[0006] Instead, on horizontal arm type machines, the first carriage includes a vertical column defining a second axis along which the second carriage moves, and the third carriage is formed by a horizontal arm which is supported by the second carriage and is movable horizontally.

[0007] Electric motors are used to move the ambulances that transfer actuating forces to the ambulances using appropriate mechanisms or, alternatively, linear electric motors stationary with respect to the ambulances.

[0008] The accelerations necessary to carry out measuring cycles in increasingly shorter periods of time require high actuating forces to induce elastic deformations of the moving parts of the machine due to the dynamic (inertial) effect. These deformations, which are also caused by the lightweight construction of moving parts, can be significant for the accuracy of the measurement.

[0009] In order to guarantee the accuracy class of the measuring machine, the measurement error caused by the elastic deformation must be estimated and then compensated.

[0010] In US Patent No. Ser. US 2005/0102118 discloses the use of a laser in determining and compensating errors due to elastic deformations in coordinate measuring machines. The laser emitter and sensor are located on the movable member of the coordinate measuring machine, with the reflector on the reference plane. The error determination and compensation is based on the relative movement of the headlight on the one hand and the emitter and sensor on the other hand.

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OBJECT OF THE INVENTION [0011] The object of the present invention is to provide a measuring machine that will be able to accurately estimate measurement errors caused by dynamic deformations as well as a method of compensating for the above mentioned errors.

[0012] The above-mentioned objectives are achieved by the measuring machine according to claim 1 and by the method according to claim 9.

BRIEF DESCRIPTION OF THE FIGURES [0013] In order to better understand the invention, certain preferred embodiments are described below, by way of non-limiting examples, and with reference to the accompanying drawings, in which:

Fig. 1 shows a bridge type measuring machine according to the present invention;

Fig. 2 is a front view in partial cross section of the machine of Fig. 1;

Fig. 3 is a schematic perspective view of the carriage of the machine of Fig. 1 in a first dynamic deformation mode;

Fig. 4 is a schematic front view of the carriage of Fig. 3 in a second dynamic deformation mode;

Fig. 5 is a block diagram of a method of compensating for dynamic deformations that can be used in the measuring machine of the present invention;

Fig. 6 is a block diagram of a model for carrying out the method according to the invention;

Fig. 7 is a graph showing time graphs of physical quantities correlated with the cycle of the carriage of Fig. 3;

Figure 8 is a schematic perspective view of a carriage of the measuring machine of Figure 1, according to another embodiment of the present invention;

Figure 9 is a schematic perspective view of a column of the machine of Figure 1 in accordance with an embodiment of the present invention;

Fig. 10 is a schematic perspective view of a horizontal arm of a measuring machine manufactured according to the present invention;

Fig. 11 is a schematic and partial perspective view of a gantry machine manufactured according to the present invention.

PREFERRED IMPLEMENTATION ACCORDING TO THE INVENTION [0014] In the first embodiment described, the measuring machine 1 is of the bridge type and comprises a table 5 equipped with a horizontal flat upper surface 6 or a reference surface and a movable unit 7.

[0015] The mobile unit 7 comprises an electrically-driven carriage 8 which slides on the table 5 along the first horizontal axis (Y axis) of the Cartesian reference system X, Y, Z of the measuring volume.

[0016] The carriage 8 has a bridge structure and comprises two vertical columns 8a and 8b and an upper horizontal cross member 8c that extends between the upper ends of the vertical columns 8a and 8b.

[0017] Column 8a comprises at its lower end a motorized slide 9 which can slide on guides 11 parallel to the Y axis and is maintained, in known manner, adjacent the longitudinal edge of the table 5.

[0018] The cross member 8c supports the slide 10, which slides on the guides (not illustrated) along an axis parallel to the second axis (X axis) of the reference system.

[0019] A vertical column 12 is mounted on the slide 10, which is movable along the third axis (Z axis) of the reference system. The vertical column 12 supports at its lower end a measuring sensor 3 (of a known type).

[0020] The carriage 8, slide 10 and column 12 are equipped with suitable electric motors 13, for example linear electric motors (of which only one is visible in Fig. 2), which control their offset along individual coordinate axes.

[0021] The measuring machine 1 is controlled by a control unit 14 equipped with a supply section 14a, which supplies the supply currents I_Y, And_X, And_FROM for electric motors of individual ambulances 8, 10, 12 to move the sensor 3 along the Y, X and Z axes and thereby determine its position in the measurement volume.

[0022] The measuring machine 1 outputs via software based on algorithms of the known type location xa, ya, behind the measuring sensor 3 in the measuring volume as a result of detecting the position of the slides along individual axes X, Y and Z.

[0023] In the operating conditions of the device described above, the position of the measuring sensor 3 is affected by the position error ex, ey, from a dynamic type with respect to the measured values ​​xa, ya, za, caused by the fact that the mechanical construction of the mobile unit 7 that supports the sensor measuring 3 (mainly vertical column 8a, cross member 8c, and the connection area between the upper end of the column 8a and the cross member 8c) is elastically deformed due to the forces exerted by the electric motors driving the slides 8 and 10.

[0024] The deformation of the mobile unit 7 of the measuring machine 1 is for example illustrated with reference to Figures 3 and 4.

[0025] Fig. 3 shows the deformations caused by the carriage 8 moving along the Y axis. The deformations mentioned mainly include:

• bending column 8a;

• bending the cross member 8c;

• twisting the column 8a around the Z axis; and • twisting the cross member 8c around the X axis.

[0026] Instead, Fig. 4 illustrates deformations caused by the displacement of the slide 10 along the X axis.

[0027] The deformations listed mainly include:

• deforming the connection between column 8a and cross member 8c;

• bending the cross member 8c;

• rotational movement of column 8a around the Y axis; and • parallel shift of the cross member 8c along the X axis.

[0028] In the calibration step (dynamic model identification), the ex, ey position error along the Y and X axes is measured directly as a result of mounting on the reference surface 6 a two-dimensional position transducer 15 (of known type), which is not subjected to deformations of the moving parts of the machine, and by measuring the difference (i.e., position error ex, ey) between position xg, yg of the sensor head 3 obtained on the two-dimensional position transducer 15 and the position (xa and ya) detected by the machine, i.e., ex = xg-xa, ey = yg-ya. The ez position error is negligible.

[0029] For example, the functions of the two-dimensional position transducer 15 can be provided by the comparative system VM 182 manufactured by HEIDENHAIN, used for calibrating machines.

[0030] In addition, a laser sensor 16 is installed on the measuring machine 1, which provides information regarding the dynamic deformations to which the mobile unit 7 is subjected during the movements of the carriage 8 and the slide 10 (for deformations, see the description of Figures 3 and 4).

[0031] Particularly referring to Figure 2, the laser sensor 16 is disposed in the longitudinal recess 24 of the cross member 8c and includes a laser emitter 22 positioned at one end of the recess 24 and a disc 28 positioned at the opposite end of the recess 24. Emitter 22 emits a laser beam 26 which passes through the recess 24 parallel to the X axis and hits the disc 28.

[0032] Conveniently, the emitter 22 is supported by a vertical rod 20 which is as stiff as possible and which extends inside the vertical recess 19 of the column 8a and includes the first lower end 20a rigidly attached to the shoe 9 (and hence not is affected by the deformation of the vertical column 8a) and the second upper end which extends from the column 8a into the recess 24 of the cross member 8c, and on which the laser beam emitting device 22 is attached.

[0033] The disk 28 is formed by a PSD (positioning sensitive device of known type) that detects the incidence of the laser beam 26 along two axes parallel to the Y and Z axes of the reference system as a function of the deformation of the mechanical structure with respect to the reference position which corresponds to the undeformed state.

[0034] We and m displacements from the laser beam detected on target 28 along the Y and Z axes, along with other information, allow tracking (for example, using the techniques described later in this section

EP 2 167 912 description) dynamic deformations to which the mechanical structure undergoes as a result of movement along the Y and X axes.

[0035] In the initial calibration step (block 100, in Fig. 5), an input-output M model is defined that describes the dynamic behavior of the measuring machine 1 (said step is also defined as the model identification step).

[0036] In particular, the M input / output model (Fig. 6) is multidimensional and receives at the input (u) the supply currents of two electric motors to control individual offsets along the X and Y axes (it has been initially verified that the dynamics caused by the displacement of the slide along the Z axis leads to negligible errors), and gives the output ( y) many quantities including the position ya and xa of the measuring sensor 3 obtained in relation to the machine axis, ey and ex position errors introduced due to the elasticity of the machine 1 along the X and Y axes, and measured using a two-dimensional position transducer 14, and the we and m deformations from the machine, measured using a laser sensor 16.

[0037] Due to the linearity of this phenomenon for small disorders, the whole model is split into two models:

- the first model M1, which receives the input Iy of the Y-axis electric motor at the input and gives the output ya along the Y axis, as well as the ey and ex position errors and the deformation measurements my and m along the Y and Z axes; and

- the second model M2, completely equivalent to the model M1, which receives the current Ix of the X-axis electric motor at the input, and produces xa along the X-axis as well as ey and ex position errors and we and mz deformation measurements along the Y and Z axes .

[0038] In fact, the stress along one of the axes corresponds to the main error component along the same axis and the secondary component (resulting from couplings

EP 2 167 912) along a perpendicular axis. The total machine error is the result of overlapping influences of error components provided by these two models (this part will be explained in more detail later in this description).

[0039] The following describes the definition of the first M1 model with respect to one of the axes (Y axis) to the extent that the definition of the second M2 model with respect to the other axis (X axis) is completely equivalent.

[0040] Model M1 has as input quantity u current Iy. Output y values ​​include:

• position ya along the Y axis provided by the machine

1;

• deformations we and mz along the Y and Z axes measured using a laser sensor 16; and • ey and ex position error along the Y and X axes measured using a two-dimensional position transducer 15.

[0041] The differential equations that characterize the M1 model are:

<img file="PL2167912T3_D0001.tif" />

v = Cx + Du + ε in which u is the measured input (current Iy for the electric motor), y is the output, x is the dynamic state variables, and al is the innovation process resulting from identification. Finally, A, B, C, D and K are model matrices. In particular,

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<img file="PL2167912T3_D0002.tif" />

<td></td><td>k</td><td>k</td><td>k</td><td>k</td>

<td>Ί1</td><td>"Ί2</td><td>^λΙ3</td><td>Λ | 4</td><td>Λ-, ₅</td>

<td></td><td>· l</td><td>k</td><td>k</td><td>L ·</td>

<td> 21</td><td>Λ. &gt;?</td><td></td><td>Λ 24</td><td>^Λ25</td>

<td></td><td>k</td><td>k</td><td>k</td><td>k</td>

<td> 31</td><td>Λι-ϊ</td><td>^λ33</td><td>^λ34</td><td>^Λ35</td>

<td></td><td>b</td><td>k</td><td>k</td><td>b</td>

<td> '41</td><td>^λ42</td><td>^λ43</td><td>Λ. 44</td><td>^α45</td>

<td></td><td></td><td>k</td><td> !</td><td>b</td>

<td> 51</td><td>^Α52</td><td>^λ53</td><td> *54</td><td>^κ55</td>

<td> 61</td><td>Κζ</td><td>k^Λ63</td><td></td><td> *65</td>

In the process of innovation, Lennart Ljung "System [0042] Regarding the definition, refer to the publication:

Identification - Theory for the user ”, Prentice-Hall; Upper Saddle River, NJ, 1999.

[0043] Input quantities u and output quantities y are measured and recorded during a series of operating cycles (block 110) in which the carriage 8 is forced to move along the Y axis as a result of subjecting the machine 1 to start-up, which causes deformation of the machine itself due to the effect dynamic. Then, the M1 dynamic input / output model is identified, which describes the elastic behavior of the machine by determining the relationship between input quantities and output quantities y.

[0044] A typical example of a duty cycle used for identification is shown in Figure 3b.

[0 045] The Y-axis carriage 8 is forced to perform, with closed-loop control, shifts, starting from steady state, according to the principle of dynamics, which provides (Fig. 7) the first acceleration stage, which corresponds to a steady increase in speed T1, the second constant speed stage, third stage to reduce speed T3 until it stops again. This dynamic principle corresponds to a current cycle characterized by a positive stage during acceleration, a reduced value during constant speed motion and a negative stage during deceleration.

[0046] During the calibration step, input quantities u and output values ​​y are tested randomly using a sampling period of 500 ms and stored.

[0047] Samples of the input and output quantities are provided to an identification algorithm that, using the maximum probability approach applied to the linear innovation model characterized by the five matrices A, B, C, D, K, identifies the model M1 input output as described by the system of equations differentials given above (for the definition of the maximum probability algorithm you can refer to

EP 2 167 912 publications: Lennart Ljung "System Identification - Theory for user", Prentice-Hall; Upper Saddle River, NJ, 1999).

[0048] More specifically, the model is not constant across the entire measuring volume of the machine, thereby carrying out various calibration steps similar to those described above to cover the entire measuring volume.

[0049] The variability of the model relates to the X and Z axes, as a result of which the measuring volume is divided into many parts (for example, into nine parts: bottom-left, bottom-center, bottom-right, center-left, ...), in which individual models M1a, M1b, M1c, ..., M1n are defined.

[0050] Next, the overall model M1compl is defined, which approximates the various models M1a, M1b, M1c, ..., M1n in the measurement volume.

[0051] In particular, it has been noticed that matrices A, B, D and K according to various models are essentially constant throughout the entire measuring volume, while only part of the matrix C changes in the measuring volume.

[0052] The overall M1compl model consequently includes matrices A, B, D and K that do not change in the measurement volume and a matrix C containing a part (lines corresponding to ex and ey error signals) with variable parameters, which is a function of the coordinates of the X and With and thus it changes in the measuring volume:

<img file="PL2167912T3_D0003.tif" />

[0053] The said function C = C (xa, za) is non-linear with respect to the X and Z axes, and is obtained by interpolation of the C matrix according to various models M1a, M1b, M1c, ..., M1n in different parts of the measurement volume , using b-fold functions (for the definition of fold functions, see M. Broen, C. Harris, "NeuroFuzzy Adaptive Modeling and Control," Prentice-Hall International (UK) Limited, 1994).

EP 2 167 912 [0054] At the end of the calibration step, the two-dimensional position transducer 15 is removed.

[0055] According to the definition of the overall M1compl model, which represents the "signature" of the individual machine being calibrated, step 100 is followed by step 200, in which, starting from the overall model M1compl, an estimator filter 1 is constructed.

[0056] For this stage of construction, the M1compl model is represented (in time domain, similar discontinuous representation is possible) in the following form:

χ = Ax + Bu + Ke v = Cb + D \ uz = C2.v + D2u where:

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<img file="PL2167912T3_D0004.tif" />

C2 =

<td>^C41</td><td>C42</td><td>^Æ45</td><td>^C44</td><td>^Æ?45</td><td>4P</td><td>D2 =</td><td> ¢/41</td>

<td> _^C51</td><td> ^52</td><td>^C53</td><td>^C54</td><td>^C55</td><td>^C56_</td><td></td><td>C /₅and_</td>

[0057] Among the initial quantities, the most important are the measured values ​​(distinguished by the y symbol in the arrangement illustrated above) and the unmeasured quantities that must be estimated (distinguished by the z symbol in the arrangement illustrated above).

[0058] The matrix C1 contains the first three rows of matrix C and the matrix C2 contains the last two rows of matrix C

In a similar manner, matrix D1 contains the first three rows of matrix D, and matrix D2 contains the last two rows of matrix

D.

[0059] Regarding the variations in the measurement volume, according to this new model representation, only the C2 matrix is ​​indeed a function of the position of the X and Z axes, while all other matrices are constant:

<img file="PL2167912T3_D0005.tif" />

[0060] Estimator filter 1 is constructed as a result of the use of robust filtration analytical techniques (in this context, see publication: P. Colaneri, A. Locatelli, JC Jeromel "Control theory and design, RH2-RH-inf viewpoint", Academic Press, 1997) based on the total M1compl model previously identified.

[0061] An effective technique that allows an estimator to be improved is that said filter will provide a time delayed estimate. This technique is described, for example, in Bolzer, P. Colaneri, and G. De Nicolao "Discrete-Time H- Infinity fixed lag smoothing ”IEEE Trans. On Signal Processing, volume 52, n. 1, pp. 132-141, 2004.

[0062] In other words, it provides an estimate of the strain corresponding to the moment (t-Delta) at the time of time. Delta is a time delay that is short enough not to compromise the machine's efficiency when performing immediately available measurements, but is long enough to improve estimation accuracy. Practically, it has been found that a convenient Delta size is several hundredths of a second.

[0063] Estimator filter ^ΛΜ1 provides an estimate of the error in response to the measured input quantities u and output quantities y (measurements ya along the Y axis and strain sizes my and mz).

(article interpolation: P.

t) dynamic estimator

EP 2 167 912 [0064] Estimator filter ^ANDM1 is represented by the equations:

i = Ax + Bu + Ky i - C2 (xa, za) x + D2u in which y is the vector of output quantities measured using the machine, and u is the vector of input quantities, and in which matrices ^ΛΑ, ^ΛΚ are the result of constructing an estimator starting from matrices A, B, K, C1, D1, according to the techniques of robust filtering, which were referred to above.

[0065] In this way, the estimator filter ^ANDM1 gives an output of the dynamic type error.

[0066] Estimator filter matrices ^ANDM1 linear types, as defined, are stored and integrated in the machine measurement software to estimate the unknown error (block 400).

[0067] The operations illustrated above are repeated for the X axis current to define the estimator filter ^ANDM2. Inbound results from filters^ANDM1 and ^ANDM2 are added due to overlapping effects.

[0068] The method described above is a non-limiting example of how we and mz measurements can be used analytically to estimate the dynamic behavior of a machine. Of course, it is possible to use any other analytical method suitable for this purpose.

[0069] Figures 8 to 11 illustrate various implementations of measuring machines, or parts thereof, in which laser sensors are used to estimate dynamic type deformations.

[0070] Fig. 8 is a bridge type machine 30 similar to that of Fig. 1, however, in which

EP 2 167 912 laser sensor 16 is used to obtain mx and we measurements correlated with other components of machine deformation.

[0071] More specifically, the laser emitter 22 is supported by a horizontal rod 31, which is located inside the recess 24 of the cross member 8c and has one end rigidly attached to the upper end of the column 8a of the carriage 8 and the opposite end carrying the laser emitter 22. The emitter 22 emits laser beam 26 downwards. The beam 26 passes through the vertical recess of the carriage column 8b and strikes the PSD device 28 located in the foot of the column 8b.

[0072] This type of configuration allows specific detection of the twist of the transverse member around the X axis and the bending of the transverse member 8c in the XY plane, according to which the PSD device 28 measures the non-alignment of the mx and my sizes of the laser beam 26 with respect to the undeformed position.

[0073] Fig. 9 is another embodiment in which the laser sensor 16 is installed inside the column 12, with the stationary emitter 22 relative to the rigid support 32 which is attached to the upper end of the column itself, and with the PSD 28 device attached to the lower end 33. Consequently, this configuration allows detection of dynamic bending of column 12 in the X and Y directions.

[0074] The systems shown in Figs. 8 and 9 can be combined with each other and / or with the system illustrated in Fig. 2 in such a way as to have a larger number of measurable output quantities of the model available and, consequently, to allow more accurate estimation of deformations type of dynamic mobile unit

7.

[0075] Figures 10 and 11 illustrate similar solutions used for other types of machines.

[0076] For example, Fig. 10 shows a horizontal arm of a machine 40 comprising: a vertical column 42 that is

Moveable on the table 43 along the first X axis; a movable carriage 44 that is supported by a column 42 and is movable along a second vertical Z axis; and a horizontal arm 45, which is supported by a carriage 44 and can move longitudinally along a third horizontal axis Y.

[0077] In this case, the laser sensor 16 comprises an emitter 22 located on a rigid support 32 relative to the column foot 46, and the PSD device 28 is located adjacent the upper free end 47 of the column itself. In this way, any bending of the column in the X and Y directions is detected.

[0078] A similar system may also be installed in the horizontal arm 45 to detect any bending of the arm itself in the X and Z directions.

[0079] Fig. 11 shows a carriage 50 of a gate machine 51. The carriage 50 is movable along the Y axis on a pair of guides 52 and 53 supported by posts (not shown).

[0080] The carriage 50 is formed by an electric motor slide 54 that is movable along the guide 52, the auxiliary slide 55 is movable along the guide 53, and a girder 56 transverse to the guides 52 and 53, which has ends individually attached to the guides 52 and 53. Girder 56 defines guides (not illustrated) for moving in the X direction of the next carriage (also not shown), intended to carry a column that is movable in the vertical direction (Z).

[0081] The laser sensor in this case comprises an emitter 22 stationary with respect to slide 54 and a PSD 28 stationary with respect to slide 55. This configuration is suitable for detecting any bending of the spar 56 in the Y direction.

[0082] As a result of testing the characteristics of the machines 1, 30, 40 and 51, the advantages enabled by the present invention become apparent.

[0083] In particular, the use of laser sensors 16 makes it possible to detect in a simple and inexpensive manner measurable quantities correlated with deformations of moving machine parts resulting from the dynamic effect.

[0084] Said quantities can be used in real time to calculate and compensate for measurement errors caused by structural deformation of the machine using appropriate mathematical methods.

In particular, it is possible to define a machine input / output model that is more or less complex, according to the machine type and to a larger or smaller range of certain error components, where the input quantities (which can be measured) are supply currents electric motors, and the input quantities are measurable (in particular, quantities supplied by the laser sensor) and non-measurable quantities (measurement errors). Consequently, it is possible to define an estimator filter that provides, in response to input and output quantities suitable for measuring quantities, estimated values ​​of unmeasurable quantities.

[0086] Finally, it is clear that the machines and method described can be subjected to modifications and changes, without thereby departing from the scope of protection defined by the claims.

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