assessing thermally induced errors of machine tools by 3d length measurements

Assessing Thermally Induced Errors of Machine Tools by 3D Length Measu rernents

G.H.J. Florussen. F.L.M. Delbressine (2). P.H.J. Schellekens (1). Precision Engineering sedion. Department of Mechaniml Engineering.

Eindhoven Universltyof Techndqy. Eindhoven. the Netherlands

Abstract A new measurement technique is proposed for the assessmert of thermally induced errors of machhe W s . The basic idea is to measure changes of length by a telesmpic double bdl bar FDBB) at rmltiple bmtions in the machine's wakspace while the machine is thermally excited. In addition thermal machine error models are verified and optimsed by -ring measured and predided TDBB length deviations. Validation measlrements reveal that m e than 60 % of the thermally induced errors can be described by the thermal machine error model proposed at any time and at any posRKxl in the machine's workspace.

Keywords Machine t d . T h e m 1 error. Measuring instrument

1 INTRODUCTION The positioning accuracy of machine t d s is affeded to a large extent by the themmechanical behaviour of the mrrponents Mhin its strudural loop [I .2]. Due to internal and external heat w r c e s . the terrperature distribution of a machine t d changes in time. As a result. the relame position and orientation of the t d Mh resped to the mete table changes in time and with axis positron since the materials mmnonly used (i-e. steel, cast ion etc.) expand andlor bend Mh terrperature (gradient) rise. These thermally induced errors can deteriorate the positMing accuracy of machine t d s signifimnUy. resulting in geometrical deviations of manufadured metes. To measure the t h e d l y induced errors of mchine t d s . most often the thermal drift of a t d Mh resped to the m e c e table is determined Wile the mamine's spindle executes a certain duty cyde [3.4]. The madine's axes however are idle during such a measuremert Relative t d drift measurements performed at different lomtions in the machine's M n g volume are required to assess the position dependency of thermally induced errors of machine t d s . but this however is often neglededkmitted due to time restridions. In response to these &awbacks a new measuring methcd has been developed for assessing thermally induced m i n g errors of machine t d s lomted in Hwkshops without dimate mtrd. The basic idea is to measlre changes of length of a telesmplc double bdl bar FDBB) [5] at rmltiple lomtions in the machine's wrking volume while the machine is excited thermally. For m n t i n g the TDBB to the machine tml with a runring spindle. a near expansion free adapter has been desmed and realised. see Figure 1. These TDBB length measurements. Wich can be executed in a few mnutes due to the high measuing speed of a TDf3B. are subsequently performed at certain time intervals (i-e. each 15 or 30 mnutes). By -ring measured TDBB lengths performed at successive time intervals mrrespnding to a certain lomtion in the machhe's Hwkspace to those measured lengths. detemined h e n

starting a measurement. any machine t d reference terrperature distribution can be msidered. In addtion to the new measuring method. a thermal machine error model is p r o p e d in this paper to describe the thermally induced errors of a machine t d . Based on the measured terrperature distribution of machine parts, the resulting thermal deformations are mrnputed. By m i n i n g these deformations over the machine's s!rudural loop. the machine's t h e m l l y induced positioning errors have been predided. After prqeding the predided positioning error vedor of the machine on the m e s p n d i n g TDBB measurement axis, dired mrrparison with measured TDBB length changes b e m s possible. revealing the performance of the respedive thermal machine error model. Differences in measured and predided values are also used to irrprove!optrmse the thermal machine error model. 2 DESCRIPTION MEASURING METHOD To excite a machine t d thermally d u n g measurements the machine's spindle is adivated for a period of time sinca this affeds the major heat Swrms of a machine t d . The spindle speed duing such a measurement can either be mnstant or varying in time for obtaining realistic terrperature distributions in the respedive machine t d [3.4]. Due to the presence of a running spindle, an adapter is required for m n t i n g a ball of the TDBB to the machine's mlling head in a safe and reliable way. Therefore an adapter has been designed to m n e d a ball of the TDBB at a lomtion representative for the t d position as shown in Figure 1.

2.1 Adapter deslgn As the adapter is mwnted beneath the dling head the adapter will heat up significantly when executing measurements. Therefore the resultmy thermal expansion of the adapter can introduce a measurement error. Wich has to be mnimsed for any duty cyde. By using a rotatiorrsyrrmetrical design. only the adapter expansion in the vertical diredion has to be m s i d e r e d . see Figure 1. This vertical adapter v n s i o n has been mnimsed by balancing out the magnitude and diredion of thermal adapter part expansions mrtually.

Figure 1: Photograph thermal TDBB measurement setup The latter has been realised by using different materials (steel and aluminium), by choosing the geometry of the adapter and by taking into account that adapter parts heat up differently. With these measures, the effect of the thermal behaviour of the adapter on measurement results has been minimised for constant as well as for varying spindle speeds. Validation measurements with a laser interferometer reveal that the adapter is capable of keeping the TDBB ball within 2 pm for any duty cycle of the machine tool, enabling automated execution of length measurements [6].

2.2 Measuring strategy In order to determine the 30 positioning error vector (denoted as 5 ) of a machine tool with length deviations (a scalar), the relationship between these entities is required. The error vector 5 is subsequently defined as the actual relative tool position with respect to the workpiece table minus its nominal value. As a TDBB is a length measuring instrument, it only detects the projection of the machine's positioning error on the TDBB measurement axis (vector n):

NmBB = n T . 5 By varying the orientation of the TDBB in the machine's X-, Y - and Z-direction, including intermediate orientations, the machine's positioning error vector can be reconstructed from TDBB length deviations [7], not necessarily by using trilateration techniques as reported

In order to measure changes of length of a TDBB due to thermally induced errors of a machine tool only, it is important to minimise the effect of other error sources present affecting the machine's positioning accuracy. For machine tools this mainly means that geometrical errors, errors due to the finite stiffness of the structural loop and dynamical errors have to be reduced as much as possible during measurements. The effect of geometrical errors, which do not change in time (disregarding wear), on TDBB length measurements can be eliminated by substracting each measured length corresponding to a spatial position k at timestep j with its value, measured when the machine's spindle was idle. Therefore the measurement procedure, using the developed adapter, is started with an idle spindle. This means that the geometrical errors, present in the first set of length measurements is cancelled by calculating the changes of length of the TDBB at t imej after start as:

by PI.

with k indicating the spatial position of the length measurement in the machine's working volume and ldl) corresponds to the measured TDBB length at that position when starting the measurement procedure (with idle spindle). For reducing the effect of dynamic errors of the machine's axes on the machine's positioning accuracy, these axes are stopped (i.e. a second) before reading the TDBB length in a measuring point. In this way, this kind of error has been eliminated. However, when the spindle is running, vibrations between the milling head and the workpiece table do occur (for instance due to spindle unbalance) and can have a magnitude up to 4 km for the machine considered. The contribution of these vibrations on length measurement errors has been alleviated by using the average of multiple (i.e. 16) TDBB lengths measured quickly after each other at a measuring point k. Finally, the errors due to the finite stiffness of the machine's structural loop under (quasi) static load is reduced by placing no additional loads on the machine's workpiece table during measurements. The mass of the TDBB, adapter and stand is neglectable (c Ikg) compared to the allowed load of 500 kg. The remaining measurement errors to be minimised are those due to the thermal behaviour of the measurement equipment itself: the latter result from the thermal behaviour of the TDBB and the stand, mounted on the workpiece table since these elements can heat up significantly during measurements. The change of length at time j after starting the measurement at time j = l of the TDBB and the stand is computed as:

(3)

with 01 denoting the coefficient of thermal expansion. For correcting the measured change of TDBB length for these 2 effects, the thermal expansion of the stand, stored in a vector dlStmd(/] has to be projected on the TDBB measurement axis n: for each measuring point k:

at time j . These corrected length deviations can subsequently be used for assessing the thermally induced positioning errors of the respective machine tool.

2.3 Measuring point distribution Due to the limited measuring range of the TDBB of 10 mm, the measuring points have to be distributed on a semi-sphere with respect to the stand. In this paper, these points are divided by step angles of 45' in the horizontal as well as in the vertical plane (regarding

Saml-rphadcal mamuranant with 088

Figure 2: Applied measuring point distribution. The tool's relative path is indicated by a solid line and the

stand position is indicated by b

Figure 1). resulting in a total of 17 measuring p in ts . see Figure 2. These 17 measuring points p W d e enough information to remnstrud the machine's 3D position@ error vector since the orientation of the TDBB measurement axis is varied sufficiently along the machine's axes v.91. Such a semspheriml TDBB measurement can be executed in typmlly 2 mnutes and this is repeated at successive time intervals j . The thermal drift withh such a semspheriml TDBB measurement can be negleded.

2.4 Experlmental resulb In Figure 3 the results of a thermal TDBB measurement on a mlling machine, loaded with a spindle speed of 6000 rpm for 6 hours followed by a d i n g down period of 7 hours are plotted.

machine tools is divided into the folloclring modeling steps: 1. Segment a machine tool into (relatively simple)

geometrical elements; 2. Desaibe the (instatimary) terrperature distribution

of such a geometrical element; 3. Compute the acmrrpanying thermal de-tions of

that element due to its terrperature distribution; 4 Calculate the thermal relative drift of the tool with

respect to the mete table by mmbining the element d e f m t i o n s present in the machine's strudual loop.

Ad 1) When mnsidering the strudure of a machine tool. often a plate framework mnstrudion can be r e q n i s e d . Such strudures are often used since this m i n e s a

Figure 3: Measured changes of TDBB lengths of 17 measuring p n t s during a 6000 rpm duty cyde

In this figure, the measured change of TDBB lengths is displayed for the 17 measuring p i n t s (see Figure 2) versus the time of measurement. The stand was positioned near the front side of the mete table. The measured change of length due to t h e m mechmiml madine behaviour is positi3n dependent. since thermally induced posRKxling errors vary t h r m the machine's m n g volume. Len@ deviations exceeding 100 pm have been observed for the machine mnsidered and the largest errors a d in the machhe's Z- and YdiedKxl. Regard@ Figure 3, the orientation of the TDBB has a large ef fed on the measwed l e y t h deviations since the mamine's structural loop is differed for different measuring p i n t s k and the sensitrvlty of TDBB length deviations for the mrrponents of the error vedor is different. F u r t h e m e . the position of the stand in the mamine's Hwkspace has a large ef fed on the measured length deviations. Corrparison of these values with those obtained using a mnventional tool drift measurement setup reveal smlar results [8.10]. Note that for a zero TDBB length. both methods are simlar when mitting the relative orientation error of the tool. 3 THERMAL MACHINE ERROR MODEL Besides measuring the thermally induced drift of a machhe tool. the measurirq method developed can also be used for evaluating andlor optrmsing the performance of a thermal machine error model. intended for software error mqmnsa t ion purposes. In t t i s sedion. a mamine type dependent machine error model is presented. realised by using physical relationships desaibing the themmechan ica l behaviwr of a machine tool. In order to mnstruct such a machine error model. the problem of describing thermally induced posibning errors of

high stiffness with a relative low mass. i rqmtant properties for the machine's dynamcal behaviwr. Therefore. a machine tool is subsequently regarded as a mnstrudion of flat plates. whose thickness is rmch smaller than its other dimensions. Ad 2) As a first approach. the terrperature distribution of a plate is obtained by using terrperature sensors attached to the machine in mmbination Mth a linear interpolation scheme. In order to limit the errors in terrperature. mainly due to assumed linear dependency with position. a relatively large number of wnsors has been applied, resulting in a mnsiderable spatid sensor densw (52 sensors in total). In this way, loml terrperature gradients and average plate temperatures have been mrnpRed. For reducing the number of terrperature sensors required for obtaining a mrrparable accuracy. therrmdynamcal models desmibing heat flows have been used. Ad 3) When the terrperature distribution has been mlculated. the acmrrpanying thermal deformation has to be mrnputed. Since a machine part is modeled with Rat plate elements. only deformations in the plate's plane have to be mnsidered: deformations ading perpendicular to the plate's plane can be neglected since no sgnificant thermal gradients are to be expoded over the plate thickness due to the good heat mndudive properties of metals. F u r t h e m e . the ef fed of thermally induced stresses and strains, relevant for -ex terrperature distributions other than m e n e a s andlor Ihear. is gnored due to the assumed linear dependency of terrperature with pition. Finite elements techniques have been used to estimate these effeds. bllt this is a subject of current research. For desaibing the relative thermal deformations a d n g in the plate's plane between two p i n t s (say A and B)

located at the plate's boundary 2 translational and 1 rotational error mrrponent have to be evaluated: 0 Longitudinal translation of line segment A-B;

0 Rotation due to terrperature gradient ading perpendicular to line segment A-• (bending);

0 Transversal translation of p i n t q relative to p M t A due to rotation.

Note that due to axis movements. these p i n t s A andlor q can move along the plate's boundary. Based on the average line segment terrperature and terrperature gradients perpendicular to the line segment these 3 relative errors have been mrnputed for each machine part. For describing the thermal deformation of the machine's (linear enmder) scales however. only the longitudinal translation has to be taken into acmunt. Ad 4) When the three aforementioned relative errors have been mrnputed for each machine part. these thermally induced deformations are m i n e d by mnsidering the machine's strudural loop. In this way the W e l e d 3D positioning error vedor of the mlling head. with resped to the wwkpiece table, which varies Mh axis position. is &tamed [6.9]. Subsequenb. these calculated positioning errors can be used to mrred the machine's axis positions to enhance the machine's posltroning behaviour. 4 VALIDATION MACHINE ERROR MODEL In this sedion the thermal machine error model presented will be validated. using the TDBB measuring method introduced. This impCes that the predided positioning erru vedor. generated with this model. has to be prqeded on the TDBB measurement axis for each measuring p n t k. Therefme. the predided length deviation at time j is calculated as:

which is subsequently to be -red with measured values for measurements charaderised by: 0 Constant spindle speeds (0.3000 and 6000 rpm for

6 hours) induding a d i n g dow period; 0 Varying spindle speeds (DIN8602) [4]; 0 Various stand positions on the wodqnece table

Generally. the mrrponents of error vedor ek(l) , evaluated A e n starting the experiment h e n the machine's spindle is idle. are not equal to 0 bemuse the machine's initial terrperature distribubn is not homqeneousty at 20 OC (i.e. heat transfer due to hydraulic pumps. servo system. varying air terrperature etc.)m. In Figure 4 the absolute values of the measured and residual (measured mnus predided) length deviations are plotted for the 17 measuring points. see

Figure 4: Measured and residual length deviations for a 6000 rpm duty cyde on a mlling mchine.

Figure 2. The machine's spindle was running at 6000 rpm and the displayed results mrrespond to a semspheriml TDBB measurement performed 2 hours after starting the experiment.

When mnsidering all measurements performed as listed, m e than 60 % of the measured lerqth deviations can be predided. The performance of this model to describe thermally induced positioning errors is somehow mstrained by the assumptions made: linear terrperature gradients. negleding thermal stresses and strains and using a simplified machine tool deformation model [based on flat plates). 5 CONCLUSION A new measuring method has been presented for assessing thermally induced pitioning errors of machine tools. TDBB length measurements have been used for this purpose since it enables fast and automated execution of l e w measurements at rmltiple locations in the machine's wwkspaoe at relatively low msts. For mned ing a TDBB ball to the machine's mlling head. a near expansion free adapter has been realised. F u r t h e m e . a thermal machine error model has been presented. intended for W a r e error mrrpensation purposes. Validation measurements show that m e than 60% of all the thermally induced positioning errors can be predided by this model. Research efforts are made to optrmse the performance of this model and to reduce the number of terrperature sensors required sgnifimntly (from 52 to approximately 20 sensors). 6 ACKNOWLEDGEMENTS The authors gratefully adolowledge the financial support of the STW foundation and the technical support from IBS Precision Engineering B.V. F u r t h e m e the authors would Ike to thank i. K.F. Bustraan for his msiderable mntribution to the research presented in this paper. 7 REFERENCES

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