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A method for direct evaluation of the dynamic 3D path accuracy of NC machine tools
CIRP Annals - Manufacturing Technology 58 (2009) 343–346
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
A method for direct evaluation of the dynamic 3D path accuracy of NC machine tools B. Bringmann (2)a,*, P. Maglie b a b
StarragHeckert AG, Seebleichestr. 61, 9404 Rorschacherberg, Switzerland Institute of Machine Tools and Manufacturing (IWF), ETH Zurich, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Dynamic Measuring instrument Accuracy
Fast and high-quality machining operations require high dynamic path accuracy of the machine tool in use. Complementary to the work done on NC path planning and mechatronic simulation, in this paper a device is introduced for direct 3D measurements of dynamic path deviations at the tool center point (TCP). With it, linear as well as rotary axes can be tested in one setup, thus dynamic parameters such as jerk and acceleration limits can be set homogeneously for obtaining the required dynamic path accuracy. Relevant Eigenfrequencies of the machine can be identified. Measurement method, uncertainty estimation and result evaluation are explained in this paper. ß 2009 CIRP.
1. Introduction With ever increasing demands for productivity and part quality of metal cutting machine tools, the machines’ dynamic path accuracy is a crucial factor for further improvements. Many different factors have an impact on the dynamic path accuracy. Today’s research topics include tool path planning (see, e.g. [1–3]) as well as the mechatronic simulation of the dynamic machine tool behavior (see, e.g. [4–6]). As a crucial input for path planning as well as for simulation verification, the relative dynamic displacements between tool and workpiece at the tool center point (TCP) must be measured and correlated to dynamic parameters (e.g. jerk and acceleration). In this paper a measurement device based on the ‘R-Test’ [7] is presented for measuring such displacements in the three translatory degrees of freedom. The measurement method including an estimation of the measurement uncertainty is described in Section 2. In Section 3 an application example is described, where the limits for axis acceleration and jerk are determined based on path accuracy. It is shown that together with a modal analysis the measurement allows a very good analysis of critical Eigenfrequencies and Eigenmodes of machines. Finally in Section 4, conclusions are drawn and an outlook on future work is given. 2. Measurement method 2.1. Build-up of the device The R-Test is a device for measuring relative displacements between a precision sphere in the spindle representing the TCP and three or four linear probes (see Fig. 1). The probe travels measured can be transformed into relative displacements in the machine tool
* Corresponding author. 0007-8506/$ – see front matter ß 2009 CIRP. doi:10.1016/j.cirp.2009.03.104
coordinate system. The build-up of the device was introduced in [7], the on-machine calibration of the device (relative orientation of the single transducers with respect to the machine tool coordinate system) has been explained in [8]. So far, the device has been used primarily for identifying geometric errors of machines (e.g. orientation errors of rotary axes), see [7–10]. Here it is used in a new application for evaluating the dynamic behavior of a machine. 2.2. Measurement motion The evaluation starts with the motion of single axes. With the system the dynamic behavior in the nominal direction of motion (positioning) as well as in the two perpendicular directions (crosstalk) can be measured. The motion can be performed with different settings for path velocity, maximum axis acceleration and jerk as well as different settings for, e.g. velocity or acceleration feed-forward, for control gains and frequency filters. Of course the maximum length of motion is limited (to about 3 mm in X, Y, Z with the current setup), but the measurement device allows for a very comprehensive evaluation of the dynamic behavior. A high resolution of 0.5 nm and a sampling rate of up to 10 kHz make it possible to differentiate the incremental position signal and to identify velocity and acceleration at the TCP. Therefore, e.g. effective axis acceleration and crosstalk (dynamic motion square to the nominal direction of motion) can be correlated (see Section 3). Only one setup is necessary to test linear as well as rotary axes. Normally for rotary axes the motion can be set so that tangential, radial and axial directions of the rotary axes coincide with the linear X-, Y- and Z-directions at one angular position of the rotary axes, thus allowing a similar evaluation as for the linear axes. Additionally two linear axes can be used for performing a circular test (with a radius of, e.g. 2 mm). With these tests, the effect of changes in the dynamic parameters can be measured directly (change in positioning and
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B. Bringmann, P. Maglie / CIRP Annals - Manufacturing Technology 58 (2009) 343–346
Since the four probes are used to identify the relative displacements in three directions, this identification is redundant. From any combination of three probes, the nominal sphere center position can be computed. Form errors of sphere and probing planes as well as errors in the relative orientation of the probes lead to a difference in the identified center coordinates. This difference can be given out as a delta value (here as the maximum spatial distance between the four computed sphere centers). The most important contributors to measurement uncertainty have an impact on this delta value. Therefore it is a good estimation for the measurement uncertainty. With a typical machine (with linear scales), the delta value stays below 2 to 3 mm over all dynamic states within the measuring range of, e.g. 2 mm. A relative rotation of the probing system as a whole (no relative shift in the orientation of the probes) as well as a bending of the ball stem has no effect on the delta value. Both are deemed to be considerably smaller than 1 mm under normal conditions. Fig. 1. ‘R-Test’ device on a 5-axes machining center for turbine blade production.
crosstalk, change in effective velocity and acceleration). For the evaluation of the measurement, a lot of possible correlations can be drawn (e.g. positioning over time, velocity over position and crosstalk over position). Two parameters are especially in the focus of the measurements so far: Axis acceleration: the acceleration of any component causes a momentum as long as the driving force has an offset from the components center of gravity. This momentum is causing a tilt motion of the device (crosstalk) with a magnitude which is – assuming linear stiffness – linearly dependent on the acceleration and the offset of the point of measurement (see [11]). That means that by measuring crosstalk and correlating it to effective acceleration, a sensible limit for the maximum allowable acceleration values for each axis can be set depending on the anticipated path accuracy. Axis jerk: the axis jerk is a dynamic excitation of the machine, which will – as a result – oscillate in its Eigenmodes. With the measurement sensible axis jerk limits can be identified (by looking mainly at positioning). The exact behavior here is dependent on the drive torque or force and the transfer behavior. This means there is no simple correlation as for acceleration and crosstalk. But from the measured positioning behavior the relevant Eigenfrequencies can be identified with a fast Fourier transformation (FFT). This gives clear information which frequencies are relevant, meaning that they are causing relative displacements between tool and workpiece. With an additional experimental modal analysis, the corresponding Eigenmodes can be determined. With this information, a systematic improvement of the machine design can be made (see Section 3). 2.3. Measurement uncertainty 2.3.1. Static measurement uncertainty The measurement uncertainty estimation for the static case has basically been described in [9]. The orientation of each one of the linear probes is identified by making a reference motion of the machine to 2 mm in X, Y and Z. From the relative probe travels between these measurement points the orientation of each probe is computed with a best fit. Besides the form deviation of sphere and probing planes the errors of the machine tool itself are a main source of error. The reference motion for the calibration should be perfect, but this is not the case due to geometric motion errors (e.g. positioning, straightness and squareness errors). Therefore the static measurement uncertainty of the system depends mainly on the quality of the machine tool itself. For the measurement system with four linear probes, a very good experimental crosscheck of the measurement uncertainty does exist.
2.3.2. Dynamic measurement uncertainty For the dynamic measurement uncertainty, other additional contributors do exist which have an impact on the measurement uncertainty. Of course a loss of contact must be avoided. The maximum allowable acceleration must be higher than the expected acceleration (for the example in Section 3 the probe acceleration has been measured to be bigger than 1 g). Due to the different load directions (compression or expansion of the probe springs) there will be a change in the load of probing planes and connection shaft. Its stiffness is assumed to be sufficiently high to be of no concern. Another issue is the synchronization of the measurement signals of the single transducers. For all these points, with an ‘R-Test’ with four probes, these contributors would affect the delta value. For the measurements presented, e.g. in Section 3 such effects could not be measured. Additionally there will definitely be certain damping due to the direct contact with the transducers. No estimation has been done so far, but it is assumed to be smaller than the process damping under normal cutting conditions. From the positioning signal the velocity and the acceleration are derived by differentiation. With a maximum velocity during measurement of, e.g. 12 m/min, the motion would be over 100 signal periods of the transducers per sample (with a signal period of 2 mm and a sample rate of 1000 ms). On this 200 mm the error range RPos is estimated to be 0.2 mm (maximum error within one signal period plus length depending error mainly caused by sphere and plane form errors; for probe manufacturer’s specification see [12]). With an assumed rectangular distribution of this error the standard uncertainty for the average velocity over one sample can be computed according to [13]: RPos 0:4 mm ¼ 0:12 mm=s uy ¼ pffiffiffiffiffiffi ¼ pffiffiffiffiffiffi 12 1000 ms 12 t sampling ¼ 6:9 mm=min With the same approach the uncertainty of the acceleration can be estimated. The difference in velocity between two samples is used. Each sample has the standard uncertainty as shown above which can be added, assuming that the two uncertainties are not independent (see [13]): 2uy 2 0:12 mm=s ua ¼ ¼ 240 mm=s2 ¼ 1000 ms t sampling The sample time is assumed to have no relevant error (relative frequency error for such systems is usually in the order of 105). 3. Application example The 5-axes machining center under test is built for machining parts with complex geometries, especially turbine blades. Machining such parts requires high axis accelerations. The total finishing time is depending heavily on the maximum allowable axis jerk values.
B. Bringmann, P. Maglie / CIRP Annals - Manufacturing Technology 58 (2009) 343–346
345
Fig. 2. ‘R-Test’ measurement of Z-axis positioning (jerk limit 70 m/s3). Fig. 4. ‘R-Test’ measurement of X-crosstalk during Z-motion (jerk limit 70 m/s3).
Here the goal is to identify acceleration and jerk limits of the machine axes that are as high as possible while still guaranteeing certain dynamic path accuracy. The user can then select a set of parameters for, e.g. roughing, pre-finishing or finishing where the effective limits for acceleration and jerk change. The user is then able to use the full dynamic capabilities of the machine tool and without having to reduce the productivity more than necessary. 3.1. Positioning of axes
structure. Through the collection of enough measurement points at selected locations with help of 3D-acceleration sensors, the vibration modes of the machine tool can be identified. Fig. 3 shows the lowest non rigid-body mode found by this method. It depicts a relative displacement between the tool center point and the workpiece in Z-direction at a frequency of approximately 55 Hz. These results match the transient response of the Z-axis positioning shown in Fig. 2: the oscillation observed in the decaying phase corresponds indeed to a frequency of circa 57 Hz. With overshoot, the effective damping of the positioning can be measured. Of course this is not the damping of the mechanical system, but the mechatronic system response, which depends, e.g. on the gain in the velocity control loop.
The dynamic positioning of axes can be tested, e.g. for overshoot. Different jerk values can be tested at different velocities. The system’s transient response can be measured (see Fig. 2). The measurement results can be used to define, e.g. jerk limits, but also to test the settings for, e.g. the velocity feed forward control. Due to the dynamic excitation the machine will oscillate in its Eigenfrequencies. That means, the relevant Eigenfrequencies for finishing operations can be identified directly by making a FFT analysis of the time signal. For finishing operations the damping and stiffening due to the process will be very small, so that the measured values are expected to be very close to the ones during machining. The dynamic behavior derived from this method can be compared to the vibrational properties deduced from the experimental modal analysis of the machine. An excitation of the machine with an impulse hammer produces an approximated Dirac delta, which excites the whole frequency range of the
As described the displacements square to the nominal direction of motion can also be measured with the device. This crosstalk can be measured in parallel to the positioning measurements during the same machine motion (forward/backward motion of one axis). It can be compared to the acceleration in the nominal direction of motion. Measured crosstalk in X-direction and acceleration in Z for a Z-axis motion are shown in Figs. 4–7 (several forward and backward paths). A very good repeatability can be seen for both crosstalk and acceleration measurements. The same evaluation is also possible for rotary axes (not shown).
Fig. 3. Vibration mode at 55 Hz (relative displacement between TCP and workpiece).
Fig. 5. Acceleration in Z-direction derived from ‘R-Test’ measurement during Zmotion (jerk limit 70 m/s3).
3.2. Crosstalk measurement
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B. Bringmann, P. Maglie / CIRP Annals - Manufacturing Technology 58 (2009) 343–346
Fig. 9. Circular test XZ-plane, magnification 100 (contouring feed 1000 mm/min, nominal diameter 2 mm). Fig. 6. ‘R-Test’ measurement of X-crosstalk during Z-motion (jerk limit 150 m/s3).
to the limited circle diameter R, geometric errors like squareness or straightness cannot be evaluated. With small circles and increasing path feeds f, the required axis jerk values become very high (maximum values f3/R2). Therefore dynamically these tests are mainly useful to verify the response to jerk excitation. Examples can be seen in Figs. 8 and 9. The magnification factor is 100. That means a path error of 10 mm is shown as 1 mm in the axis scales. 4. Conclusion and outlook
Fig. 7. Acceleration in Z-direction derived from ‘R-Test’ measurement during Zmotion (jerk limit 150 m/s3).
In this paper a measuring system for direct evaluation of the dynamic 3D path accuracy has been introduced. It is suitable for linear as well as rotary axes and its setup is very easy. With it, the control parameters affecting the dynamic behavior of the machine can be set purposefully, thus allowing an improved use of the dynamic capabilities of the machine. A first evaluation method has been proposed. In future steps the loop to mechatronic simulation of the machine can be closed. The measurement system allows a direct verification of the simulation. The simulation can provide an in-depth understanding of the system behavior—thus allowing a systematic improvement of the test procedure as well as further improvements in the control parameter settings.
References
Fig. 8. Circular test YZ-plane, magnification 100 (contouring feed 100 mm/min, nominal diameter 2 mm).
3.3. Circular testing With the system circular tests according to [14] can be made. Of course, e.g. reversal errors of axes can be seen with the system. Due
[1] Koninckx B, Van Brussel H (2002) Real-Time NURBS Interpolator for Distributed Motion Control. Annals of the CIRP 51(1):315–318. [2] Altintas Y, Erkorkmaz K (2003) Feedrate Optimization for Spline Interpolation in High Speed Machine Tools. Annals of the CIRP 52:297–302. [3] Erkorkmaz K, Heng M (2008) A Heuristic Feedrate Optimization Strategy for NURBS Toolpaths. Annals of the CIRP 57(1):407–410. [4] Zaeh M, Siedl D (2007) A New Method for Simulation of Machining Performance by Integrating Finite Element and Multi-body Simulation for Machine Tools. Annals of the CIRP 56(1):383–386. [5] Altintas Y, Brecher C, Weck M, Witt S (2005) Virtual Machine Tool. Annals of the CIRP 54:651–673. [6] Neugebauer R, Denkena B, Wegener K (2007) Mechatronic Systems for Machine Tools. Annals of the CIRP 56(2):657–686. [7] Weikert S, Knapp W (2004) R-Test, A New Device for Accuracy Measurements on Five Axis Machine Tools. Annals of the CIRP 53(1):429–432. [8] Bringmann B, Ku¨ng A, Knapp W (2005) A Measuring Artefact for True 3D Machine Testing and Calibration. Annals of the CIRP 54:471–474. [9] Bringmann B, Knapp W (2006) Model-based ‘Chase-the-Ball’ Calibration of a 5Axes Machining Center. Annals of the CIRP 55:531–534. [10] Florussen GHJ, Spaan HAM (2007) Static R-Test: Allocating the Centreline of Rotary Axes of Machine Tools. Proceedings of the 8th Lamdamap Conference, 196–202. [11] Knapp W, Weikert S (1999) Testing the Contouring Performance in 6 Degrees of Freedom. Annals of the CIRP 48:433–436. [12] Heidenhain, 2008, Catalogue ‘‘Length Gauges’’. [13] ISO/IEC, 1995, Guide to the Expression of Uncertainty in Measurement, International Organization of Standardization, 2nd ed. [14] ISO, 230-4:2005, Test Code for Machine Tools. Part 4. Circular Tests for Numerically Controlled Machine Tools.
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
A method for direct evaluation of the dynamic 3D path accuracy of NC machine tools B. Bringmann (2)a,*, P. Maglie b a b
StarragHeckert AG, Seebleichestr. 61, 9404 Rorschacherberg, Switzerland Institute of Machine Tools and Manufacturing (IWF), ETH Zurich, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Dynamic Measuring instrument Accuracy
Fast and high-quality machining operations require high dynamic path accuracy of the machine tool in use. Complementary to the work done on NC path planning and mechatronic simulation, in this paper a device is introduced for direct 3D measurements of dynamic path deviations at the tool center point (TCP). With it, linear as well as rotary axes can be tested in one setup, thus dynamic parameters such as jerk and acceleration limits can be set homogeneously for obtaining the required dynamic path accuracy. Relevant Eigenfrequencies of the machine can be identified. Measurement method, uncertainty estimation and result evaluation are explained in this paper. ß 2009 CIRP.
1. Introduction With ever increasing demands for productivity and part quality of metal cutting machine tools, the machines’ dynamic path accuracy is a crucial factor for further improvements. Many different factors have an impact on the dynamic path accuracy. Today’s research topics include tool path planning (see, e.g. [1–3]) as well as the mechatronic simulation of the dynamic machine tool behavior (see, e.g. [4–6]). As a crucial input for path planning as well as for simulation verification, the relative dynamic displacements between tool and workpiece at the tool center point (TCP) must be measured and correlated to dynamic parameters (e.g. jerk and acceleration). In this paper a measurement device based on the ‘R-Test’ [7] is presented for measuring such displacements in the three translatory degrees of freedom. The measurement method including an estimation of the measurement uncertainty is described in Section 2. In Section 3 an application example is described, where the limits for axis acceleration and jerk are determined based on path accuracy. It is shown that together with a modal analysis the measurement allows a very good analysis of critical Eigenfrequencies and Eigenmodes of machines. Finally in Section 4, conclusions are drawn and an outlook on future work is given. 2. Measurement method 2.1. Build-up of the device The R-Test is a device for measuring relative displacements between a precision sphere in the spindle representing the TCP and three or four linear probes (see Fig. 1). The probe travels measured can be transformed into relative displacements in the machine tool
* Corresponding author. 0007-8506/$ – see front matter ß 2009 CIRP. doi:10.1016/j.cirp.2009.03.104
coordinate system. The build-up of the device was introduced in [7], the on-machine calibration of the device (relative orientation of the single transducers with respect to the machine tool coordinate system) has been explained in [8]. So far, the device has been used primarily for identifying geometric errors of machines (e.g. orientation errors of rotary axes), see [7–10]. Here it is used in a new application for evaluating the dynamic behavior of a machine. 2.2. Measurement motion The evaluation starts with the motion of single axes. With the system the dynamic behavior in the nominal direction of motion (positioning) as well as in the two perpendicular directions (crosstalk) can be measured. The motion can be performed with different settings for path velocity, maximum axis acceleration and jerk as well as different settings for, e.g. velocity or acceleration feed-forward, for control gains and frequency filters. Of course the maximum length of motion is limited (to about 3 mm in X, Y, Z with the current setup), but the measurement device allows for a very comprehensive evaluation of the dynamic behavior. A high resolution of 0.5 nm and a sampling rate of up to 10 kHz make it possible to differentiate the incremental position signal and to identify velocity and acceleration at the TCP. Therefore, e.g. effective axis acceleration and crosstalk (dynamic motion square to the nominal direction of motion) can be correlated (see Section 3). Only one setup is necessary to test linear as well as rotary axes. Normally for rotary axes the motion can be set so that tangential, radial and axial directions of the rotary axes coincide with the linear X-, Y- and Z-directions at one angular position of the rotary axes, thus allowing a similar evaluation as for the linear axes. Additionally two linear axes can be used for performing a circular test (with a radius of, e.g. 2 mm). With these tests, the effect of changes in the dynamic parameters can be measured directly (change in positioning and
344
B. Bringmann, P. Maglie / CIRP Annals - Manufacturing Technology 58 (2009) 343–346
Since the four probes are used to identify the relative displacements in three directions, this identification is redundant. From any combination of three probes, the nominal sphere center position can be computed. Form errors of sphere and probing planes as well as errors in the relative orientation of the probes lead to a difference in the identified center coordinates. This difference can be given out as a delta value (here as the maximum spatial distance between the four computed sphere centers). The most important contributors to measurement uncertainty have an impact on this delta value. Therefore it is a good estimation for the measurement uncertainty. With a typical machine (with linear scales), the delta value stays below 2 to 3 mm over all dynamic states within the measuring range of, e.g. 2 mm. A relative rotation of the probing system as a whole (no relative shift in the orientation of the probes) as well as a bending of the ball stem has no effect on the delta value. Both are deemed to be considerably smaller than 1 mm under normal conditions. Fig. 1. ‘R-Test’ device on a 5-axes machining center for turbine blade production.
crosstalk, change in effective velocity and acceleration). For the evaluation of the measurement, a lot of possible correlations can be drawn (e.g. positioning over time, velocity over position and crosstalk over position). Two parameters are especially in the focus of the measurements so far: Axis acceleration: the acceleration of any component causes a momentum as long as the driving force has an offset from the components center of gravity. This momentum is causing a tilt motion of the device (crosstalk) with a magnitude which is – assuming linear stiffness – linearly dependent on the acceleration and the offset of the point of measurement (see [11]). That means that by measuring crosstalk and correlating it to effective acceleration, a sensible limit for the maximum allowable acceleration values for each axis can be set depending on the anticipated path accuracy. Axis jerk: the axis jerk is a dynamic excitation of the machine, which will – as a result – oscillate in its Eigenmodes. With the measurement sensible axis jerk limits can be identified (by looking mainly at positioning). The exact behavior here is dependent on the drive torque or force and the transfer behavior. This means there is no simple correlation as for acceleration and crosstalk. But from the measured positioning behavior the relevant Eigenfrequencies can be identified with a fast Fourier transformation (FFT). This gives clear information which frequencies are relevant, meaning that they are causing relative displacements between tool and workpiece. With an additional experimental modal analysis, the corresponding Eigenmodes can be determined. With this information, a systematic improvement of the machine design can be made (see Section 3). 2.3. Measurement uncertainty 2.3.1. Static measurement uncertainty The measurement uncertainty estimation for the static case has basically been described in [9]. The orientation of each one of the linear probes is identified by making a reference motion of the machine to 2 mm in X, Y and Z. From the relative probe travels between these measurement points the orientation of each probe is computed with a best fit. Besides the form deviation of sphere and probing planes the errors of the machine tool itself are a main source of error. The reference motion for the calibration should be perfect, but this is not the case due to geometric motion errors (e.g. positioning, straightness and squareness errors). Therefore the static measurement uncertainty of the system depends mainly on the quality of the machine tool itself. For the measurement system with four linear probes, a very good experimental crosscheck of the measurement uncertainty does exist.
2.3.2. Dynamic measurement uncertainty For the dynamic measurement uncertainty, other additional contributors do exist which have an impact on the measurement uncertainty. Of course a loss of contact must be avoided. The maximum allowable acceleration must be higher than the expected acceleration (for the example in Section 3 the probe acceleration has been measured to be bigger than 1 g). Due to the different load directions (compression or expansion of the probe springs) there will be a change in the load of probing planes and connection shaft. Its stiffness is assumed to be sufficiently high to be of no concern. Another issue is the synchronization of the measurement signals of the single transducers. For all these points, with an ‘R-Test’ with four probes, these contributors would affect the delta value. For the measurements presented, e.g. in Section 3 such effects could not be measured. Additionally there will definitely be certain damping due to the direct contact with the transducers. No estimation has been done so far, but it is assumed to be smaller than the process damping under normal cutting conditions. From the positioning signal the velocity and the acceleration are derived by differentiation. With a maximum velocity during measurement of, e.g. 12 m/min, the motion would be over 100 signal periods of the transducers per sample (with a signal period of 2 mm and a sample rate of 1000 ms). On this 200 mm the error range RPos is estimated to be 0.2 mm (maximum error within one signal period plus length depending error mainly caused by sphere and plane form errors; for probe manufacturer’s specification see [12]). With an assumed rectangular distribution of this error the standard uncertainty for the average velocity over one sample can be computed according to [13]: RPos 0:4 mm ¼ 0:12 mm=s uy ¼ pffiffiffiffiffiffi ¼ pffiffiffiffiffiffi 12 1000 ms 12 t sampling ¼ 6:9 mm=min With the same approach the uncertainty of the acceleration can be estimated. The difference in velocity between two samples is used. Each sample has the standard uncertainty as shown above which can be added, assuming that the two uncertainties are not independent (see [13]): 2uy 2 0:12 mm=s ua ¼ ¼ 240 mm=s2 ¼ 1000 ms t sampling The sample time is assumed to have no relevant error (relative frequency error for such systems is usually in the order of 105). 3. Application example The 5-axes machining center under test is built for machining parts with complex geometries, especially turbine blades. Machining such parts requires high axis accelerations. The total finishing time is depending heavily on the maximum allowable axis jerk values.
B. Bringmann, P. Maglie / CIRP Annals - Manufacturing Technology 58 (2009) 343–346
345
Fig. 2. ‘R-Test’ measurement of Z-axis positioning (jerk limit 70 m/s3). Fig. 4. ‘R-Test’ measurement of X-crosstalk during Z-motion (jerk limit 70 m/s3).
Here the goal is to identify acceleration and jerk limits of the machine axes that are as high as possible while still guaranteeing certain dynamic path accuracy. The user can then select a set of parameters for, e.g. roughing, pre-finishing or finishing where the effective limits for acceleration and jerk change. The user is then able to use the full dynamic capabilities of the machine tool and without having to reduce the productivity more than necessary. 3.1. Positioning of axes
structure. Through the collection of enough measurement points at selected locations with help of 3D-acceleration sensors, the vibration modes of the machine tool can be identified. Fig. 3 shows the lowest non rigid-body mode found by this method. It depicts a relative displacement between the tool center point and the workpiece in Z-direction at a frequency of approximately 55 Hz. These results match the transient response of the Z-axis positioning shown in Fig. 2: the oscillation observed in the decaying phase corresponds indeed to a frequency of circa 57 Hz. With overshoot, the effective damping of the positioning can be measured. Of course this is not the damping of the mechanical system, but the mechatronic system response, which depends, e.g. on the gain in the velocity control loop.
The dynamic positioning of axes can be tested, e.g. for overshoot. Different jerk values can be tested at different velocities. The system’s transient response can be measured (see Fig. 2). The measurement results can be used to define, e.g. jerk limits, but also to test the settings for, e.g. the velocity feed forward control. Due to the dynamic excitation the machine will oscillate in its Eigenfrequencies. That means, the relevant Eigenfrequencies for finishing operations can be identified directly by making a FFT analysis of the time signal. For finishing operations the damping and stiffening due to the process will be very small, so that the measured values are expected to be very close to the ones during machining. The dynamic behavior derived from this method can be compared to the vibrational properties deduced from the experimental modal analysis of the machine. An excitation of the machine with an impulse hammer produces an approximated Dirac delta, which excites the whole frequency range of the
As described the displacements square to the nominal direction of motion can also be measured with the device. This crosstalk can be measured in parallel to the positioning measurements during the same machine motion (forward/backward motion of one axis). It can be compared to the acceleration in the nominal direction of motion. Measured crosstalk in X-direction and acceleration in Z for a Z-axis motion are shown in Figs. 4–7 (several forward and backward paths). A very good repeatability can be seen for both crosstalk and acceleration measurements. The same evaluation is also possible for rotary axes (not shown).
Fig. 3. Vibration mode at 55 Hz (relative displacement between TCP and workpiece).
Fig. 5. Acceleration in Z-direction derived from ‘R-Test’ measurement during Zmotion (jerk limit 70 m/s3).
3.2. Crosstalk measurement
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B. Bringmann, P. Maglie / CIRP Annals - Manufacturing Technology 58 (2009) 343–346
Fig. 9. Circular test XZ-plane, magnification 100 (contouring feed 1000 mm/min, nominal diameter 2 mm). Fig. 6. ‘R-Test’ measurement of X-crosstalk during Z-motion (jerk limit 150 m/s3).
to the limited circle diameter R, geometric errors like squareness or straightness cannot be evaluated. With small circles and increasing path feeds f, the required axis jerk values become very high (maximum values f3/R2). Therefore dynamically these tests are mainly useful to verify the response to jerk excitation. Examples can be seen in Figs. 8 and 9. The magnification factor is 100. That means a path error of 10 mm is shown as 1 mm in the axis scales. 4. Conclusion and outlook
Fig. 7. Acceleration in Z-direction derived from ‘R-Test’ measurement during Zmotion (jerk limit 150 m/s3).
In this paper a measuring system for direct evaluation of the dynamic 3D path accuracy has been introduced. It is suitable for linear as well as rotary axes and its setup is very easy. With it, the control parameters affecting the dynamic behavior of the machine can be set purposefully, thus allowing an improved use of the dynamic capabilities of the machine. A first evaluation method has been proposed. In future steps the loop to mechatronic simulation of the machine can be closed. The measurement system allows a direct verification of the simulation. The simulation can provide an in-depth understanding of the system behavior—thus allowing a systematic improvement of the test procedure as well as further improvements in the control parameter settings.
References
Fig. 8. Circular test YZ-plane, magnification 100 (contouring feed 100 mm/min, nominal diameter 2 mm).
3.3. Circular testing With the system circular tests according to [14] can be made. Of course, e.g. reversal errors of axes can be seen with the system. Due
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