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Optimization of High Speed Machine Tool Spindle to Minimize Thermal Distortion
Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 58 (2017) 457 – 462
16th CIRP Conference on Modelling of Machining Operations
Optimization of high speed machine tool spindle to minimize thermal distortion Srinivas N. Grama * , Ashvarya Mathur, Ramesh Aralaguppi, Subramanian T. Dr. Kalam center for innovation, Bharat Fritz Werner R&D, Off Tumkur Road, Bengaluru, 560022, India ∗
Corresponding author. Tel.: +91-80-3982-1408; Fax: +91-80-3982-1100; E-mail address: [email protected]
Abstract Thermal errors contribute significantly to the dimensional error on machined components. Various machine design and operating factors are responsible for the thermal error. In the present work, experiments are performed to understand the effect of spindle rotational speed and the chiller unit setting on the temperature distribution in the spindle and consequently the thermal distortion of the Tool Center Point (TCP). A metrology fixture is fabricated and calibrated to measure TCP displacements as a precursor to experimentation. In addition, multiple temperature sensors are affixed at critical points within the spindle. It is seen that the temperature distribution across the outer race of front bearings is nonuniform (> 2.5◦ C) which in turn indicates that the heat extraction is not uniform across the spindle. Concurrently, significant tilt (yaw and pitch angles of the order of 50μ radian) is visible at speeds greater than 5000 rpm. In the second part of the paper, a thermal compensation model is developed in a linear regression framework. To improve robustness of the model and reduce redundancy, only five out of eighteen temperature sensors (two near front bearing, one each near rear bearing and motor coil and an ambient temperature) are chosen through Principal Component Analysis (PCA) and k-means clustering. The predictions of the model agrees well with the measurements taken from a different set of experiments. © Authors. Published by Elsevier B.V. This c 2017 2017The The Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations. Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations Keywords: Motorized spindle, thermal modeling and compensation, machining center, thermal distortion, optimization
1. Introduction Accuracy and precision of machined product along with speed of machining are among the important considerations for a machine tool manufacturer during the design of a general purpose machining center. Although various proving tests are undertaken in the form of leveling test, straightness calibration of axes using laser interferometer, full power tests, etc. during the assembly of a machining center, often significant variability is found in the geometrical accuracy and precision of machined end-products. The reason for such deviation from the ideal situation is the combination of following major error sources: geometric and kinematic error; cutting force induced error; toolwear related error and thermal error. Among these errors, it is well known that about 40 to 70% is due to thermal issues [1]. For instance, geometrical accuracies of products machined in a typical 12-hour shift vary widely (whether the machine was warmed up or not, the change in the ambient temperature) due to the inherent transient behavior of the machine tool till stabilization is attained. Thermo-elastic behavior of machine tool is dependent on a variety of internal and external factors. The major internal factors include the design and assembly of the machine tool and
machining conditions while the variation in ambient temperature and existing temperature gradient in the machine shop are some of the external factors. Various approaches including analytical and/or numerical modeling (finite-element and finite-difference approaches) in conjunction with experimentation have been followed to describe the thermo-mechanical behavior of the machine tool [2]. However accurate thermomechanical modeling of a complete machining center under various operating conditions is quite difficult and complicated [3]. One of the vital machine tool component which is also a major heat source especially in the case of high speed machining is a motorized spindle. It is therefore important to first map the thermo-mechanical characteristics of motorized spindle. Motorized spindle has two main heat sources: the motor and the spindle supporting bearings. Heat generation in the motor is because of the magnetic and electrical losses during the conversion of electrical power to mechanical work while it is due to friction for the case of bearings. Therefore in contrast to the belt-driven or gear-driven spindle, the mode of heat generation and dissipation should be taken into account during the design of motorized spindle. This internal heat generation causes spindle distortion in the form of TCP displacements which in turn results in the degradation of machine tool performance. In order to minimize this effect, machine tool manufacturers employ
2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations doi:10.1016/j.procir.2017.03.253
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forced convection-type heat transfer with the coolant being either air, water or oil. To further minimize TCP displacements in high precision machining centers, two approaches are commonly employed. The first one is to control the heat flow or optimize the mechanical design to reduce the sensitivity to heat flow either through the use of low Coefficient of Expansion (CoE) materials or the use of a novel cooling strategy which directly minimizes TCP displacement itself. The second approach is to allow for spindle distortion which is compensated electronically real-time. In the former case, recent research [4] has shown that differentiated recirculation systems for bearings and motor provide a better dissipation strategy than the traditional cooling system. In addition, further improvement is seen when heat dissipation rate is matched with the heat generation rate through the control of the coolant entry temperature [5]. Nomenclature T i Temperature of ith sensor in ◦ C (i = 1 to 18). ΔT i Temperature change of ith sensor with respect to its initial temperature in ◦ C. ui Spindle displacement at ith location in μm (i = 0◦ , 90◦ , 180◦ , 270◦ position). δ Thermal expansion of spindle in μm. N Spindle speed in rpm. A Augmented temperature matrix with n temperature sensors in columns and m time steps in rows. S i Singular value of A corresponding to ith principal component. Electronic thermal compensation through origin shifting or feedback interception method is the most popular way of reducing thermal errors. Extensive research is conducted to arrive at ’so-called’ robust optimal model which relates the TCP displacements to various internal and external parameters such as temperatures, strains, spindle speed, etc. Various kinds of models using either least squares, regression analysis, transfer function, neural network, support vector machine or hybrid techniques have been developed and their detailed review is provided in [6]. In order to reduce the redundant data input during model fitting, approaches including correlation grouping, group searching have been employed and optimal sensor locations were chosen [7]. In addition to the models which use instantaneous values of internal and external parameters to estimate TCP displacements, some models employ thermo-mechanical history data as well in order to account for the thermal time constant of spindle unit and they show a better predictive capability [8]. The present work is aimed at understanding the thermomechanical behavior of stand-alone motorized spindle in an experimental-modeling framework. The first part of the paper is focused on experimentation wherein the effect of various operating parameters on the temperature distribution in the spindle and resulting TCP displacements are studied. Specifically, Section 2 describes the experimental setup, the design and validation of displacement measurement fixture, the effect of spindle rotational speed and spindle orientation on TCP displacements. The second part is focused on the thermal compensation methodology adopted wherein Section 3 introduces a novel way
to group and select the temperature sensors for compensation model development using PCA and k-means clustering. The predictive capability of the developed model is then checked by performing an experiment very different from the ones used to build the model. Finally, a few concluding remarks are offered in Section 4. 2. Material and Methods The experimental set-up includes a stand-alone motorized spindle which is mounted onto the milling head which in turn is rigidly fixed to the test bed. The bearings in the spindle are arranged in a double ◦-configuration and provision is made to cool the bearings and stator portion of the motor region (Fig. 1) through a recirculation-type chiller unit. Eighteen Pt100 Resistance Temperature Detector (RTD) sensors are affixed at several critical points in the spindle: four each in outer race of front bearings, five in outer race of rear bearings, one each for motor coil, ambient and housing temperature and finally one each at coolant entry and exit points. A custom-built software is used to synchronize the data from FANUC CNC controller (such as spindle speed and motor coil temperature) along with the temperatures from other RTD’s, flow rate and chiller on/off information. Experiments are performed under no-load condition and the resulting thermal displacements are manually measured using high precision Millimess dial gages, which are rigidly clamped in a specially fabricated fixture, whose details are provided in subsection 2.1.
Fig. 1: A schematic of the motorized spindle with eighteen temperature sensors and a representative coolant channel.
2.1. Fixture development A steel fixture (Fig. 2) is designed to measure spindle distortion at four designated points (Fig. 2; points ui , i = 0◦ , 90◦ , 180◦ , 270◦ ) on the rotating disk. This precision ground disk (d = 210 mm in diameter1 ) forms an extension of spin1 Larger disk diameter is chosen to magnify the measurements and reduce uncertainty.
Srinivas N. Grama et al. / Procedia CIRP 58 (2017) 457 – 462
dle shaft as it is rigidly clamped onto the spindle. The spindle distortion parameters, i.e., the axial growth, δ = (u0◦ + u90◦ + u180◦ +u270◦ )/4, the pitch angle γ x = tan−1 ((u90◦ − u270◦ )/d) and the yaw angle γy = tan−1 ((u0◦ − u180◦ )/d) are later extrapolated from the four measurements. The measurement procedure is as follows: first the spindle is stopped intermittently from rotation and oriented at a pre-designated position through ’M19’ command; then a slip gage is used to measure the gap and finally the distortion is measured after accounting for the slip gage thickness. This fixture is designed to be different from the commonly used 5-point measurement setup (ISO 230-3 standard [9]) as it overcomes several disadvantages: the use of a precision mandrel is avoided and allows high speed rotation in addition to being a low-cost set-up. Due to high resolution requirement of measurements, the fixture alone is calibrated against a standard granite block and the environmental temperature variation error (ETVE) is found to be systematic across the four points (≈ 4 μm when the ambient temperature change is 6◦ C), thus providing confidence in the experimental measurements. Further, the validity of measurements are reinforced through repetition of experiments and they reveal a similar trend; details of which are provided in further sub-sections.
the only heat source is the friction due to pumping action and in cooling path. The temperature of all RTD’s in addition to the spindle disk distortion are monitored and is plotted in polar axis (Fig. 3) as it showcases the tilt error tacitly. The polar plot illustrates the temperature and distortion of different sensors at their respective position w.r.t. the spindle axis. It is seen that front bearing temperatures are uniform (≈ 38◦ C) across a section while spindle disk distortion is non-uniform (u90◦ >> u270◦ , u0◦ ≈ u180◦ ; refer Fig. 2). On the other hand, when CDT is 10, the chiller trigger frequency is very high (time period ≈ 2.2 minutes) as the heat source is the ambient temperature; the front bearing temperatures are lower (≈ 18◦ C) while spindle disk contracts (u90◦ << u270◦ , u0◦ ≈ u180◦ ) relative to the reference position. As expected, axial growth (δ = 23 μm) is observed for a CDT of +10◦ C while significant contraction (δ = -16 μm) results for CDT of -10◦ C. On the other hand, it is puzzling to find significant tilt error (of the order of 50 μ radian) at these CDT’s even when the spindle is stationary; work is underway to throw light on this aspect and will be reported elsewhere. However, for all practical applications, a CDT of -2◦ C is employed and the same is followed in the further experiments with spindle rotation as described in Section 2.3. 2.3. Effect of spindle speed
Fig. 2: A steel fixture is used to calculate spindle distortion from dial gauge measurements at four designated points (ui , i = 0◦ , 90◦ , 180◦ , 270◦ ).
2.2. Effect of chiller setting The heat generated in a motorized spindle is extracted using a recirculation-type oil coolant system (chiller unit). Ambient temperature tracing strategy is employed for triggering the chiller unit. This strategy involves manual setting of chiller differential temperature (CDT), an integral number from +10◦ C to -10◦ C. For instance, the compressor in the chiller unit is triggered when the coolant reservoir temperature reaches ’CDT + 1◦ C’ with respect to ambient temperature, while it is switched off when the reservoir is cooled to ’CDT - 2◦ C’. Although this cooling system allows for the variation in trigger frequency of compressor depending upon the heat generation rate, the dissipation rate will however not match the heat generation rate [5] causing the spindle to distort. The effect of ambient temperature and CDT setting alone (internal heat from motor and bearings are isolated by maintaining the spindle in stationary condition) is studied by choosing two extreme CDT’s. The CDT of +10◦ C reduces the triggering frequency of the chiller unit by a great extent (time period ≈ 180 minutes) as
Speed of the spindle plays an important role in the thermal behavior of the spindle as it dictates the internal heat generation. Experiments are carried out at the following spindle speeds: 2000, 5000 and 8000 rpm. The temperatures are logged once every ten seconds while the spindle distortion is measured intermittently (initially at a higher rate to account for the rapid change in TCP displacements). The spindle is rotated till stabilization is reached [9] after which rotation is stopped until the spindle cools to ambient temperature. The spindle distortion parameters calculated when the spindle is stationary, i.e. approximately during 150 and 300 minutes for 5000 and 8000 rpm experiments (Fig. 4), show a decreasing trend with higher slope just after the spindle is made to stop while it plateaus towards the end of 300 minutes, i.e. when the spindle cools down to ambient temperature. It is interesting to note that δ has not gone back to zero reading mainly because of the increase in ambient temperature from the start of the experiment in addition to the systematic error of the measurement setup. The spindle growth, δ, calculated for all three speeds (Fig. 4) indicates its dependence on the spindle speed and also partly on the change in ambient temperature. In addition, the evolution of critical parameters during 8000 rpm experiment is also illustrated in Fig. 5, wherein the following important points are observed. A non-uniform temperature distribution in front bearings with a positive bias towards the third quadrant (T 3 , T 6 and T 7 are higher compared to rest). Work is underway to reduce this bias through the optimization of coolant circuit and will be reported elsewhere. Further, the chiller triggering frequency is also reflected in T 1 , T 5 and T 8 temperatures in the form of jaggedness in its evolution when compared to other sensors. Motor coil temperature is higher than other RTD’s even when the spindle is not rotating (during 150 and 300 minutes) due to magnetic losses in the powered on condition. The ambient temperature change is about 5◦ C, while housing is influenced by both the ambient and front bearing temperatures. The coolant temperature at the spindle outlet is higher than at inlet and the reser-
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(a)
(b)
Fig. 3: The temperatures of front bearings FB1 and FB2 are almost uniform across a section: (a) when CDT is set at +10◦ C, the FB1 and FB2 temperatures are around 38◦ C and distortion, u is relatively high at 90◦ position; (b) when CDT is -10◦ C, the temperatures are around 20◦ C while u is relatively low at 90◦ position.
voir temperature fluctuation is matching with the chiller triggering frequency. In addition, chiller triggering frequency is much lower during 150 to 300 minutes, i.e., when spindle is stationary. Similar observations are also noted for other spindle speeds and are not plotted here for the sake of brevity. Figure 6 illustrates the temperature variation across front bearing sections in conjunction with the spindle displacements. The δ after stabilization is 32 μm with a pitch angle error of 38 μ radian (u90◦ > u270◦ ; u0◦ ≈ u180◦ ).
3.1. Grouping and selection of temperature sensors Various approaches including engineering judgment, correlation analysis, stepwise regression, sensitivity analysis and fuzzy clustering [7,10] are used to group the temperature sensors and select optimum ones for compensation modeling. In the present work, Principal Component Analysis (PCA), a multi-variate statistical technique, commonly used to reduce the dimensionality and de-noise data, is proposed to cluster the temperature sensors. Uncentred PCA [11,12] is used as we are dealing with ’ratio-scale’ type variables. The first step is to assemble the temperature data obtained from the experiments described in Section 2.3 and build an augmented matrix, A, such that the columns represent different sensors while the rows indicate temporal information of temperatures. Uncentred PCA is performed on A through Singular Value Decomposition (SVD) route: A(m×n) = l(m×m) S(m×n) rT(n×n) ,
Fig. 4: The spindle growth, δ depends on the rotational speed as well as the ambient temperature.
3. Compensation modeling Electronic compensation provides an economic and effective way to minimize thermal errors. A compensation model provides an implicit/explicit relation between the internal/external parameters of the machine tool and the TCP displacement. As described in Section 2, temperature sensors were affixed in the spindle at 18 positions, which were decided on the basis of engineering judgment. However the inclusion of all temperature sensors in the model will increase its redundancy due to the apparent high correlation between temperatures. In order to reduce model redundancy, selection of optimal temperature points is critical and the procedure adopted in this work is detailed in the next sub-section.
(1)
where l = [el1 el2 el3 ... elm ] contains left eigenvectors (i.e. those of AAT ) in the columns and r = [er1 er2 er3 ... ern ] contains right eigenvectors (those of AT A) in the columns. The matrix S contains r = rank(A) non-zero singular values along the diagonal while all other elements are zero. If significant correlation exist within n temperature sensors, then several singular values are much smaller than others. In fact, if only p << r singular values are seen to be dominant, one may reconstruct the original matrix A entirely in terms of the first p right or left eigenvectors, and the reconstruction error is equal to ratio of the sum of the discarded singular values to the sum of all singular values [13]. The Log Singular Value (LSV) spectrum of A (Fig. 7) shows a gradual decrease in singular values and only five singular values (and vectors) contain more than 99% of the information. This fact is used to group the sixteen temperature sensors (the inlet and outlet coolant sensors are excluded) into 5 clusters through the k-means clustering algorithm [14]. The clustered temperature sets shown in Table 1 match the engineering judgment: the first and second clusters consists of sensors in front bearings with typically lower temperatures belonging to the former while T 3 , T 6 and T 7 sensors, with relatively higher temperatures, forming the latter; the third cluster is formed by all the rear bearing temperatures while the fourth is made up
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(a)
(b)
(c)
(d)
Fig. 5: The parameter evolution at various points of the spindle unit when the spindle is rotated at 8000 rpm: (a) front bearing FB1 RTD’s indicate temperature difference >2.5◦ C between sensors T 3 and T 1 , (b) front bearing FB2 RTD’s also indicate a similar variation in temperature across its outer race, (c) The ambient temperature change is around 5◦ C while housing is influenced by both ambient and front bearing temperatures. Motor coil temperature is higher than other RTD’s even when the spindle is not rotating (during 150 and 300 minutes) due to magnetic and other losses in the powered on condition and (d) the coolant exit temperature is higher compared to the entry temperature and the chiller triggering frequency is much lower during 150 to 300 minutes, i.e., when spindle is stationary.
Fig. 6: Temperatures in the front bearings FB1 and FB2 are of a higher magnitude in the region between 150◦ and 290◦ while higher spindle displacement is seen at 90◦ and 180◦ region.
of ambient and housing sensors and finally the motor coil sensor alone forms the fifth cluster. These grouping of temperature sensors into the above five clusters are in line with our observations from Fig. 5 and Section 2.3. 3.2. Regression modeling In order to evaluate the performance of combined PCA and k-means clustering-based technique for temperature sensor selection, a thermal error prediction model is developed based on multi-linear regression (MLR) method. Diverse experiments including 2000, 5000 and 8000 rpm spindle speed are used as training dataset to fit the model. Due to the use of multiple ex-
Fig. 7: The LSV spectrum of A shows a gradual decrease in singular values and 99% of the data is captured in the first 5 principal components.
Table 1: The temperature sensors are classified into 5 different clusters using k-means clustering analysis.
Cluster-1
Cluster-2
Cluster-3
Cluster-4
Cluster-5
T1 T2 T4 T5 T8
T 3 (FB1) T 6 (FB2) T 7 (FB2)
T 9 (RB1) T 10 (RB1) T 11 (RB1) T 13 (RB2) T 14 (RB2)
T 12 (AMB) T 17 (HOUS)
T 18 (COIL)
(FB1) (FB1) (FB1) (FB2) (FB2)
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periments during model development, care is exercised to ensure that no systematic error is carried into the model by adopting relative temperatures ΔT i (one sensor chosen from each cluster, for instance, i = 1, 3, 9, 12, 18, such that only the change in temperature w.r.t its initial temperature is used) as model parameters instead of the absolute temperature values. The model form is chosen as follows: δ p = β0 +
βi ΔT i ,
(2)
i
where βi are the coefficients determined by solving an overdetermined set of linear equations using standard numerical techniques. For the present set of experimental measurements, β = [3.02, -1.99, 4.92, -1.03, -2.41, 0.26] and R2 value is found out to be 0.95. The goodness of fit also reiterates the fact that the assumption in model type as a linear one turns out to be adequate. The predictive capability of the model is then checked by performing a set of experiments different from the ones used to build the model; details of which are provided in Section 3.3. 3.3. Predictive capability of model The linear regression type thermal compensation model developed in Section 3.2 is put to a challenging test by performing a variable spindle speed test. The spindle speeds are varied from 0 rpm to 8000 rpm and for different intervals of time (Fig. 8). It is noted that a higher spindle speed has a dominating effect on the spindle growth δ. For instance, at around 200 minutes when spindle is rotated at 8000 rpm, the slope of δ is quite high and it becomes much lower at lower spindle speeds. The δ p obtained from the developed model fits very well with the measured δ (Fig. 8) and R2 value is 0.94. This confirms that the developed compensation model can be used to predict the axial thermal displacement of the stand-alone motorized spindle.
Fig. 8: The predictions of the developed model agrees quite well with the experimental measurements for a variable spindle speed test.
4. Conclusion The following are the major conclusions from the combined experimental-modeling work to understand the thermomechanical behavior of stand-alone motorized spindle: • Spindle distortion including the tilt and axial thermal error is calculated using dial gages mounted on a custom-built calibrated fixture.
• The cooling strategy employed plays a very important role on TCP displacements. Even when the spindle is stationary, significant pitch angles of 57 μ radian and 38 μ radian are observed at CDT setting of +10◦ C and -10◦ C respectively. Also, axial displacement of 23 μm and -16 μm is observed at +10◦ C and -10◦ C CDT setting respectively. • During spindle rotation, non-uniform temperatures are observed in the outer race of front bearings with a positive bias towards the third quadrant. Concurrently, yaw and pitch angles of 5 and 38 micro radian respectively are observed after stabilization (spindle speed of 8000 rpm). • A compensation model is developed in a linear regression framework using five temperature sensors chosen through combined PCA and fuzzy clustering analysis. • The developed model is able to predict the axial displacement of spindle for a different set of experiment quite well with an R2 value of 0.94. Acknowledgements SNG and AM thank the top management of Bharat Fritz Werner for providing financial support. They also thank Mathworks for providing an evaluation version of Matlab software. Finally, the services extended by Mr. Puneeth M., laboratory technician, during experimentation is duly acknowledged. References [1] Bryan, J.. International status of thermal error research. CIRP AnnalsManufacturing Technology 1990;39(2):645–656. [2] Mayr, J., Jedrzejewski, J., Uhlmann, E., Donmez, M.A., Knapp, W., H¨artig, F., et al. Thermal issues in machine tools. CIRP AnnalsManufacturing Technology 2012;61(2):771–791. [3] Vyroubal, J.. Compensation of machine tool thermal deformation in spindle axis direction based on decomposition method. Precision Engineering 2012;36(1):121–127. [4] Liu, T., Gao, W., Tian, Y., Zhang, H., Chang, W., Mao, K., et al. A differentiated multi-loops bath recirculation system for precision machine tools. Applied Thermal Engineering 2015;76:54–63. [5] Liu, T., Gao, W., Tian, Y., Zhang, D., Zhang, Y., Chang, W.. Power matching based dissipation strategy onto spindle heat generations. Applied Thermal Engineering 2017;113:499–507. [6] Li, Y., Zhao, W., Lan, S., Ni, J., Wu, W., Lu, B.. A review on spindle thermal error compensation in machine tools. International Journal of Machine Tools and Manufacture 2015;95:20–38. [7] Lo, C.H., Yuan, J., Ni, J.. Optimal temperature variable selection by grouping approach for thermal error modeling and compensation. International Journal of Machine Tools and Manufacture 1999;39(9):1383–1396. [8] Brecher, C., Hirsch, P., Weck, M.. Compensation of thermo-elastic machine tool deformation based on control internal data. CIRP AnnalsManufacturing Technology 2004;53(1):299–304. [9] ISO 230-3:2007(E). ISO 230-3:2007(E): Test code for machine tools Part 3: Determination of thermal effects 2007;. [10] Liu, Q., Yan, J., Pham, D.T., Zhou, Z., Xu, W., Wei, Q., et al. Identification and optimal selection of temperature-sensitive measuring points of thermal error compensation on a heavy-duty machine tool. The International Journal of Advanced Manufacturing Technology 2015;:1–9. [11] Noy-Meir, I.. Data Transformations in Ecological Ordination: I. Some Advantages of Non-Centering. Journal of Ecology 1973;61(2):329–341. [12] Grama, S.N., Subramanian, S.J.. Computation of full-field strains using principal component analysis. Experimental Mechanics 2014;54(6):913– 933. [13] Bishop, C.M.. Pattern recognition and machine learning. Springer; 2006. [14] Lloyd, S.. Least squares quantization in pcm. IEEE transactions on information theory 1982;28(2):129–137.
ScienceDirect Procedia CIRP 58 (2017) 457 – 462
16th CIRP Conference on Modelling of Machining Operations
Optimization of high speed machine tool spindle to minimize thermal distortion Srinivas N. Grama * , Ashvarya Mathur, Ramesh Aralaguppi, Subramanian T. Dr. Kalam center for innovation, Bharat Fritz Werner R&D, Off Tumkur Road, Bengaluru, 560022, India ∗
Corresponding author. Tel.: +91-80-3982-1408; Fax: +91-80-3982-1100; E-mail address: [email protected]
Abstract Thermal errors contribute significantly to the dimensional error on machined components. Various machine design and operating factors are responsible for the thermal error. In the present work, experiments are performed to understand the effect of spindle rotational speed and the chiller unit setting on the temperature distribution in the spindle and consequently the thermal distortion of the Tool Center Point (TCP). A metrology fixture is fabricated and calibrated to measure TCP displacements as a precursor to experimentation. In addition, multiple temperature sensors are affixed at critical points within the spindle. It is seen that the temperature distribution across the outer race of front bearings is nonuniform (> 2.5◦ C) which in turn indicates that the heat extraction is not uniform across the spindle. Concurrently, significant tilt (yaw and pitch angles of the order of 50μ radian) is visible at speeds greater than 5000 rpm. In the second part of the paper, a thermal compensation model is developed in a linear regression framework. To improve robustness of the model and reduce redundancy, only five out of eighteen temperature sensors (two near front bearing, one each near rear bearing and motor coil and an ambient temperature) are chosen through Principal Component Analysis (PCA) and k-means clustering. The predictions of the model agrees well with the measurements taken from a different set of experiments. © Authors. Published by Elsevier B.V. This c 2017 2017The The Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations. Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations Keywords: Motorized spindle, thermal modeling and compensation, machining center, thermal distortion, optimization
1. Introduction Accuracy and precision of machined product along with speed of machining are among the important considerations for a machine tool manufacturer during the design of a general purpose machining center. Although various proving tests are undertaken in the form of leveling test, straightness calibration of axes using laser interferometer, full power tests, etc. during the assembly of a machining center, often significant variability is found in the geometrical accuracy and precision of machined end-products. The reason for such deviation from the ideal situation is the combination of following major error sources: geometric and kinematic error; cutting force induced error; toolwear related error and thermal error. Among these errors, it is well known that about 40 to 70% is due to thermal issues [1]. For instance, geometrical accuracies of products machined in a typical 12-hour shift vary widely (whether the machine was warmed up or not, the change in the ambient temperature) due to the inherent transient behavior of the machine tool till stabilization is attained. Thermo-elastic behavior of machine tool is dependent on a variety of internal and external factors. The major internal factors include the design and assembly of the machine tool and
machining conditions while the variation in ambient temperature and existing temperature gradient in the machine shop are some of the external factors. Various approaches including analytical and/or numerical modeling (finite-element and finite-difference approaches) in conjunction with experimentation have been followed to describe the thermo-mechanical behavior of the machine tool [2]. However accurate thermomechanical modeling of a complete machining center under various operating conditions is quite difficult and complicated [3]. One of the vital machine tool component which is also a major heat source especially in the case of high speed machining is a motorized spindle. It is therefore important to first map the thermo-mechanical characteristics of motorized spindle. Motorized spindle has two main heat sources: the motor and the spindle supporting bearings. Heat generation in the motor is because of the magnetic and electrical losses during the conversion of electrical power to mechanical work while it is due to friction for the case of bearings. Therefore in contrast to the belt-driven or gear-driven spindle, the mode of heat generation and dissipation should be taken into account during the design of motorized spindle. This internal heat generation causes spindle distortion in the form of TCP displacements which in turn results in the degradation of machine tool performance. In order to minimize this effect, machine tool manufacturers employ
2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations doi:10.1016/j.procir.2017.03.253
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forced convection-type heat transfer with the coolant being either air, water or oil. To further minimize TCP displacements in high precision machining centers, two approaches are commonly employed. The first one is to control the heat flow or optimize the mechanical design to reduce the sensitivity to heat flow either through the use of low Coefficient of Expansion (CoE) materials or the use of a novel cooling strategy which directly minimizes TCP displacement itself. The second approach is to allow for spindle distortion which is compensated electronically real-time. In the former case, recent research [4] has shown that differentiated recirculation systems for bearings and motor provide a better dissipation strategy than the traditional cooling system. In addition, further improvement is seen when heat dissipation rate is matched with the heat generation rate through the control of the coolant entry temperature [5]. Nomenclature T i Temperature of ith sensor in ◦ C (i = 1 to 18). ΔT i Temperature change of ith sensor with respect to its initial temperature in ◦ C. ui Spindle displacement at ith location in μm (i = 0◦ , 90◦ , 180◦ , 270◦ position). δ Thermal expansion of spindle in μm. N Spindle speed in rpm. A Augmented temperature matrix with n temperature sensors in columns and m time steps in rows. S i Singular value of A corresponding to ith principal component. Electronic thermal compensation through origin shifting or feedback interception method is the most popular way of reducing thermal errors. Extensive research is conducted to arrive at ’so-called’ robust optimal model which relates the TCP displacements to various internal and external parameters such as temperatures, strains, spindle speed, etc. Various kinds of models using either least squares, regression analysis, transfer function, neural network, support vector machine or hybrid techniques have been developed and their detailed review is provided in [6]. In order to reduce the redundant data input during model fitting, approaches including correlation grouping, group searching have been employed and optimal sensor locations were chosen [7]. In addition to the models which use instantaneous values of internal and external parameters to estimate TCP displacements, some models employ thermo-mechanical history data as well in order to account for the thermal time constant of spindle unit and they show a better predictive capability [8]. The present work is aimed at understanding the thermomechanical behavior of stand-alone motorized spindle in an experimental-modeling framework. The first part of the paper is focused on experimentation wherein the effect of various operating parameters on the temperature distribution in the spindle and resulting TCP displacements are studied. Specifically, Section 2 describes the experimental setup, the design and validation of displacement measurement fixture, the effect of spindle rotational speed and spindle orientation on TCP displacements. The second part is focused on the thermal compensation methodology adopted wherein Section 3 introduces a novel way
to group and select the temperature sensors for compensation model development using PCA and k-means clustering. The predictive capability of the developed model is then checked by performing an experiment very different from the ones used to build the model. Finally, a few concluding remarks are offered in Section 4. 2. Material and Methods The experimental set-up includes a stand-alone motorized spindle which is mounted onto the milling head which in turn is rigidly fixed to the test bed. The bearings in the spindle are arranged in a double ◦-configuration and provision is made to cool the bearings and stator portion of the motor region (Fig. 1) through a recirculation-type chiller unit. Eighteen Pt100 Resistance Temperature Detector (RTD) sensors are affixed at several critical points in the spindle: four each in outer race of front bearings, five in outer race of rear bearings, one each for motor coil, ambient and housing temperature and finally one each at coolant entry and exit points. A custom-built software is used to synchronize the data from FANUC CNC controller (such as spindle speed and motor coil temperature) along with the temperatures from other RTD’s, flow rate and chiller on/off information. Experiments are performed under no-load condition and the resulting thermal displacements are manually measured using high precision Millimess dial gages, which are rigidly clamped in a specially fabricated fixture, whose details are provided in subsection 2.1.
Fig. 1: A schematic of the motorized spindle with eighteen temperature sensors and a representative coolant channel.
2.1. Fixture development A steel fixture (Fig. 2) is designed to measure spindle distortion at four designated points (Fig. 2; points ui , i = 0◦ , 90◦ , 180◦ , 270◦ ) on the rotating disk. This precision ground disk (d = 210 mm in diameter1 ) forms an extension of spin1 Larger disk diameter is chosen to magnify the measurements and reduce uncertainty.
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dle shaft as it is rigidly clamped onto the spindle. The spindle distortion parameters, i.e., the axial growth, δ = (u0◦ + u90◦ + u180◦ +u270◦ )/4, the pitch angle γ x = tan−1 ((u90◦ − u270◦ )/d) and the yaw angle γy = tan−1 ((u0◦ − u180◦ )/d) are later extrapolated from the four measurements. The measurement procedure is as follows: first the spindle is stopped intermittently from rotation and oriented at a pre-designated position through ’M19’ command; then a slip gage is used to measure the gap and finally the distortion is measured after accounting for the slip gage thickness. This fixture is designed to be different from the commonly used 5-point measurement setup (ISO 230-3 standard [9]) as it overcomes several disadvantages: the use of a precision mandrel is avoided and allows high speed rotation in addition to being a low-cost set-up. Due to high resolution requirement of measurements, the fixture alone is calibrated against a standard granite block and the environmental temperature variation error (ETVE) is found to be systematic across the four points (≈ 4 μm when the ambient temperature change is 6◦ C), thus providing confidence in the experimental measurements. Further, the validity of measurements are reinforced through repetition of experiments and they reveal a similar trend; details of which are provided in further sub-sections.
the only heat source is the friction due to pumping action and in cooling path. The temperature of all RTD’s in addition to the spindle disk distortion are monitored and is plotted in polar axis (Fig. 3) as it showcases the tilt error tacitly. The polar plot illustrates the temperature and distortion of different sensors at their respective position w.r.t. the spindle axis. It is seen that front bearing temperatures are uniform (≈ 38◦ C) across a section while spindle disk distortion is non-uniform (u90◦ >> u270◦ , u0◦ ≈ u180◦ ; refer Fig. 2). On the other hand, when CDT is 10, the chiller trigger frequency is very high (time period ≈ 2.2 minutes) as the heat source is the ambient temperature; the front bearing temperatures are lower (≈ 18◦ C) while spindle disk contracts (u90◦ << u270◦ , u0◦ ≈ u180◦ ) relative to the reference position. As expected, axial growth (δ = 23 μm) is observed for a CDT of +10◦ C while significant contraction (δ = -16 μm) results for CDT of -10◦ C. On the other hand, it is puzzling to find significant tilt error (of the order of 50 μ radian) at these CDT’s even when the spindle is stationary; work is underway to throw light on this aspect and will be reported elsewhere. However, for all practical applications, a CDT of -2◦ C is employed and the same is followed in the further experiments with spindle rotation as described in Section 2.3. 2.3. Effect of spindle speed
Fig. 2: A steel fixture is used to calculate spindle distortion from dial gauge measurements at four designated points (ui , i = 0◦ , 90◦ , 180◦ , 270◦ ).
2.2. Effect of chiller setting The heat generated in a motorized spindle is extracted using a recirculation-type oil coolant system (chiller unit). Ambient temperature tracing strategy is employed for triggering the chiller unit. This strategy involves manual setting of chiller differential temperature (CDT), an integral number from +10◦ C to -10◦ C. For instance, the compressor in the chiller unit is triggered when the coolant reservoir temperature reaches ’CDT + 1◦ C’ with respect to ambient temperature, while it is switched off when the reservoir is cooled to ’CDT - 2◦ C’. Although this cooling system allows for the variation in trigger frequency of compressor depending upon the heat generation rate, the dissipation rate will however not match the heat generation rate [5] causing the spindle to distort. The effect of ambient temperature and CDT setting alone (internal heat from motor and bearings are isolated by maintaining the spindle in stationary condition) is studied by choosing two extreme CDT’s. The CDT of +10◦ C reduces the triggering frequency of the chiller unit by a great extent (time period ≈ 180 minutes) as
Speed of the spindle plays an important role in the thermal behavior of the spindle as it dictates the internal heat generation. Experiments are carried out at the following spindle speeds: 2000, 5000 and 8000 rpm. The temperatures are logged once every ten seconds while the spindle distortion is measured intermittently (initially at a higher rate to account for the rapid change in TCP displacements). The spindle is rotated till stabilization is reached [9] after which rotation is stopped until the spindle cools to ambient temperature. The spindle distortion parameters calculated when the spindle is stationary, i.e. approximately during 150 and 300 minutes for 5000 and 8000 rpm experiments (Fig. 4), show a decreasing trend with higher slope just after the spindle is made to stop while it plateaus towards the end of 300 minutes, i.e. when the spindle cools down to ambient temperature. It is interesting to note that δ has not gone back to zero reading mainly because of the increase in ambient temperature from the start of the experiment in addition to the systematic error of the measurement setup. The spindle growth, δ, calculated for all three speeds (Fig. 4) indicates its dependence on the spindle speed and also partly on the change in ambient temperature. In addition, the evolution of critical parameters during 8000 rpm experiment is also illustrated in Fig. 5, wherein the following important points are observed. A non-uniform temperature distribution in front bearings with a positive bias towards the third quadrant (T 3 , T 6 and T 7 are higher compared to rest). Work is underway to reduce this bias through the optimization of coolant circuit and will be reported elsewhere. Further, the chiller triggering frequency is also reflected in T 1 , T 5 and T 8 temperatures in the form of jaggedness in its evolution when compared to other sensors. Motor coil temperature is higher than other RTD’s even when the spindle is not rotating (during 150 and 300 minutes) due to magnetic losses in the powered on condition. The ambient temperature change is about 5◦ C, while housing is influenced by both the ambient and front bearing temperatures. The coolant temperature at the spindle outlet is higher than at inlet and the reser-
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(a)
(b)
Fig. 3: The temperatures of front bearings FB1 and FB2 are almost uniform across a section: (a) when CDT is set at +10◦ C, the FB1 and FB2 temperatures are around 38◦ C and distortion, u is relatively high at 90◦ position; (b) when CDT is -10◦ C, the temperatures are around 20◦ C while u is relatively low at 90◦ position.
voir temperature fluctuation is matching with the chiller triggering frequency. In addition, chiller triggering frequency is much lower during 150 to 300 minutes, i.e., when spindle is stationary. Similar observations are also noted for other spindle speeds and are not plotted here for the sake of brevity. Figure 6 illustrates the temperature variation across front bearing sections in conjunction with the spindle displacements. The δ after stabilization is 32 μm with a pitch angle error of 38 μ radian (u90◦ > u270◦ ; u0◦ ≈ u180◦ ).
3.1. Grouping and selection of temperature sensors Various approaches including engineering judgment, correlation analysis, stepwise regression, sensitivity analysis and fuzzy clustering [7,10] are used to group the temperature sensors and select optimum ones for compensation modeling. In the present work, Principal Component Analysis (PCA), a multi-variate statistical technique, commonly used to reduce the dimensionality and de-noise data, is proposed to cluster the temperature sensors. Uncentred PCA [11,12] is used as we are dealing with ’ratio-scale’ type variables. The first step is to assemble the temperature data obtained from the experiments described in Section 2.3 and build an augmented matrix, A, such that the columns represent different sensors while the rows indicate temporal information of temperatures. Uncentred PCA is performed on A through Singular Value Decomposition (SVD) route: A(m×n) = l(m×m) S(m×n) rT(n×n) ,
Fig. 4: The spindle growth, δ depends on the rotational speed as well as the ambient temperature.
3. Compensation modeling Electronic compensation provides an economic and effective way to minimize thermal errors. A compensation model provides an implicit/explicit relation between the internal/external parameters of the machine tool and the TCP displacement. As described in Section 2, temperature sensors were affixed in the spindle at 18 positions, which were decided on the basis of engineering judgment. However the inclusion of all temperature sensors in the model will increase its redundancy due to the apparent high correlation between temperatures. In order to reduce model redundancy, selection of optimal temperature points is critical and the procedure adopted in this work is detailed in the next sub-section.
(1)
where l = [el1 el2 el3 ... elm ] contains left eigenvectors (i.e. those of AAT ) in the columns and r = [er1 er2 er3 ... ern ] contains right eigenvectors (those of AT A) in the columns. The matrix S contains r = rank(A) non-zero singular values along the diagonal while all other elements are zero. If significant correlation exist within n temperature sensors, then several singular values are much smaller than others. In fact, if only p << r singular values are seen to be dominant, one may reconstruct the original matrix A entirely in terms of the first p right or left eigenvectors, and the reconstruction error is equal to ratio of the sum of the discarded singular values to the sum of all singular values [13]. The Log Singular Value (LSV) spectrum of A (Fig. 7) shows a gradual decrease in singular values and only five singular values (and vectors) contain more than 99% of the information. This fact is used to group the sixteen temperature sensors (the inlet and outlet coolant sensors are excluded) into 5 clusters through the k-means clustering algorithm [14]. The clustered temperature sets shown in Table 1 match the engineering judgment: the first and second clusters consists of sensors in front bearings with typically lower temperatures belonging to the former while T 3 , T 6 and T 7 sensors, with relatively higher temperatures, forming the latter; the third cluster is formed by all the rear bearing temperatures while the fourth is made up
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(a)
(b)
(c)
(d)
Fig. 5: The parameter evolution at various points of the spindle unit when the spindle is rotated at 8000 rpm: (a) front bearing FB1 RTD’s indicate temperature difference >2.5◦ C between sensors T 3 and T 1 , (b) front bearing FB2 RTD’s also indicate a similar variation in temperature across its outer race, (c) The ambient temperature change is around 5◦ C while housing is influenced by both ambient and front bearing temperatures. Motor coil temperature is higher than other RTD’s even when the spindle is not rotating (during 150 and 300 minutes) due to magnetic and other losses in the powered on condition and (d) the coolant exit temperature is higher compared to the entry temperature and the chiller triggering frequency is much lower during 150 to 300 minutes, i.e., when spindle is stationary.
Fig. 6: Temperatures in the front bearings FB1 and FB2 are of a higher magnitude in the region between 150◦ and 290◦ while higher spindle displacement is seen at 90◦ and 180◦ region.
of ambient and housing sensors and finally the motor coil sensor alone forms the fifth cluster. These grouping of temperature sensors into the above five clusters are in line with our observations from Fig. 5 and Section 2.3. 3.2. Regression modeling In order to evaluate the performance of combined PCA and k-means clustering-based technique for temperature sensor selection, a thermal error prediction model is developed based on multi-linear regression (MLR) method. Diverse experiments including 2000, 5000 and 8000 rpm spindle speed are used as training dataset to fit the model. Due to the use of multiple ex-
Fig. 7: The LSV spectrum of A shows a gradual decrease in singular values and 99% of the data is captured in the first 5 principal components.
Table 1: The temperature sensors are classified into 5 different clusters using k-means clustering analysis.
Cluster-1
Cluster-2
Cluster-3
Cluster-4
Cluster-5
T1 T2 T4 T5 T8
T 3 (FB1) T 6 (FB2) T 7 (FB2)
T 9 (RB1) T 10 (RB1) T 11 (RB1) T 13 (RB2) T 14 (RB2)
T 12 (AMB) T 17 (HOUS)
T 18 (COIL)
(FB1) (FB1) (FB1) (FB2) (FB2)
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periments during model development, care is exercised to ensure that no systematic error is carried into the model by adopting relative temperatures ΔT i (one sensor chosen from each cluster, for instance, i = 1, 3, 9, 12, 18, such that only the change in temperature w.r.t its initial temperature is used) as model parameters instead of the absolute temperature values. The model form is chosen as follows: δ p = β0 +
βi ΔT i ,
(2)
i
where βi are the coefficients determined by solving an overdetermined set of linear equations using standard numerical techniques. For the present set of experimental measurements, β = [3.02, -1.99, 4.92, -1.03, -2.41, 0.26] and R2 value is found out to be 0.95. The goodness of fit also reiterates the fact that the assumption in model type as a linear one turns out to be adequate. The predictive capability of the model is then checked by performing a set of experiments different from the ones used to build the model; details of which are provided in Section 3.3. 3.3. Predictive capability of model The linear regression type thermal compensation model developed in Section 3.2 is put to a challenging test by performing a variable spindle speed test. The spindle speeds are varied from 0 rpm to 8000 rpm and for different intervals of time (Fig. 8). It is noted that a higher spindle speed has a dominating effect on the spindle growth δ. For instance, at around 200 minutes when spindle is rotated at 8000 rpm, the slope of δ is quite high and it becomes much lower at lower spindle speeds. The δ p obtained from the developed model fits very well with the measured δ (Fig. 8) and R2 value is 0.94. This confirms that the developed compensation model can be used to predict the axial thermal displacement of the stand-alone motorized spindle.
Fig. 8: The predictions of the developed model agrees quite well with the experimental measurements for a variable spindle speed test.
4. Conclusion The following are the major conclusions from the combined experimental-modeling work to understand the thermomechanical behavior of stand-alone motorized spindle: • Spindle distortion including the tilt and axial thermal error is calculated using dial gages mounted on a custom-built calibrated fixture.
• The cooling strategy employed plays a very important role on TCP displacements. Even when the spindle is stationary, significant pitch angles of 57 μ radian and 38 μ radian are observed at CDT setting of +10◦ C and -10◦ C respectively. Also, axial displacement of 23 μm and -16 μm is observed at +10◦ C and -10◦ C CDT setting respectively. • During spindle rotation, non-uniform temperatures are observed in the outer race of front bearings with a positive bias towards the third quadrant. Concurrently, yaw and pitch angles of 5 and 38 micro radian respectively are observed after stabilization (spindle speed of 8000 rpm). • A compensation model is developed in a linear regression framework using five temperature sensors chosen through combined PCA and fuzzy clustering analysis. • The developed model is able to predict the axial displacement of spindle for a different set of experiment quite well with an R2 value of 0.94. Acknowledgements SNG and AM thank the top management of Bharat Fritz Werner for providing financial support. They also thank Mathworks for providing an evaluation version of Matlab software. Finally, the services extended by Mr. Puneeth M., laboratory technician, during experimentation is duly acknowledged. References [1] Bryan, J.. International status of thermal error research. CIRP AnnalsManufacturing Technology 1990;39(2):645–656. [2] Mayr, J., Jedrzejewski, J., Uhlmann, E., Donmez, M.A., Knapp, W., H¨artig, F., et al. Thermal issues in machine tools. CIRP AnnalsManufacturing Technology 2012;61(2):771–791. [3] Vyroubal, J.. Compensation of machine tool thermal deformation in spindle axis direction based on decomposition method. Precision Engineering 2012;36(1):121–127. [4] Liu, T., Gao, W., Tian, Y., Zhang, H., Chang, W., Mao, K., et al. A differentiated multi-loops bath recirculation system for precision machine tools. Applied Thermal Engineering 2015;76:54–63. [5] Liu, T., Gao, W., Tian, Y., Zhang, D., Zhang, Y., Chang, W.. Power matching based dissipation strategy onto spindle heat generations. Applied Thermal Engineering 2017;113:499–507. [6] Li, Y., Zhao, W., Lan, S., Ni, J., Wu, W., Lu, B.. A review on spindle thermal error compensation in machine tools. International Journal of Machine Tools and Manufacture 2015;95:20–38. [7] Lo, C.H., Yuan, J., Ni, J.. Optimal temperature variable selection by grouping approach for thermal error modeling and compensation. International Journal of Machine Tools and Manufacture 1999;39(9):1383–1396. [8] Brecher, C., Hirsch, P., Weck, M.. Compensation of thermo-elastic machine tool deformation based on control internal data. CIRP AnnalsManufacturing Technology 2004;53(1):299–304. [9] ISO 230-3:2007(E). ISO 230-3:2007(E): Test code for machine tools Part 3: Determination of thermal effects 2007;. [10] Liu, Q., Yan, J., Pham, D.T., Zhou, Z., Xu, W., Wei, Q., et al. Identification and optimal selection of temperature-sensitive measuring points of thermal error compensation on a heavy-duty machine tool. The International Journal of Advanced Manufacturing Technology 2015;:1–9. [11] Noy-Meir, I.. Data Transformations in Ecological Ordination: I. Some Advantages of Non-Centering. Journal of Ecology 1973;61(2):329–341. [12] Grama, S.N., Subramanian, S.J.. Computation of full-field strains using principal component analysis. Experimental Mechanics 2014;54(6):913– 933. [13] Bishop, C.M.. Pattern recognition and machine learning. Springer; 2006. [14] Lloyd, S.. Least squares quantization in pcm. IEEE transactions on information theory 1982;28(2):129–137.