A new method for circular testing of machine tools under loaded condition

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1 Available online at Procedia CIRP 1 (2012 ) th CIRP Conference on High Performance Cutting 2012 A new method for circular testing of machine tools under loaded condition Andreas Archenti a *, Mihai Nicolescu a, Guillaume Casterman a, Sven Hjelm b a KTH Royal Institute of Technology, Brinellvägen 68, Stockholm 10044, Sweden b Scania CV AB, TDX Production Development, Södertälje 15187, Sweden * Corresponding author. Tel.: +46 (0) ; fax: +46 (0) address: andreas.archenti@iip.kth.se. Abstract This paper presents a novel test device for the evaluation of the accuracy of machine tools. The design concept is similar to a double ball bar (DBB) with the difference that an adjustable load generated by the device can be applied between spindle nose and machine tool table. The device, called Loaded Double Ball Bar (LDBB), can be used either as an ordinary double ball bar system with no load applied to the structure, or with a predefined load applied to the structure. The load that is generated by the LDBB is generally not equivalent to real cutting forces. However, from the static deflection point of view the effect of the load on the machine tool structure has similar impact on the static behaviour of the system. For instance, the load can in some cases eliminate existing play in ball screws, plays that under normal machining condition will be eliminated by the effect of cutting forces on the structure. With the help of this test device, not only can the identifiable errors by an ordinary DBB be evaluated but also machine tool elastic deflection in different directions. It is also possible to track different error patterns to the applied load The Published Authors. by Published Elsevier BV. by Elsevier Selection B.V. and/or Selection peer-review and/or peer-review under responsibility under responsibility of Prof. Konrad of Professor Wegener Konrad Wegener Open access under CC BY-NC-ND license. Keywords: Loaded Double Ball Bar (LDBB); Machine tool; Testing; Deformation; Static stiffness. 1. Introduction One key issue in the manufacturing of components for new innovative, environmental friendly and safe vehicle products is to meet increasingly higher accuracy requirements in machining of tougher materials. In the component manufacturing industry there is a need for simple, fast and reliable methods to identify and control capability in operational condition for robust machining of complex components with respect to product quality and with competitive productivity. One way of increasing the efficiency of a production system is to continuously improve, and develop new tests and evaluation methods of the machining systems. This is especially important when the goal is to produce a specific part correctly for the first time, in the quickest and most cost effective way. In this regard, new or improved test methods help to gather information about system status and can be stored in digital machine tool models used for analysis and optimization. Machine tool testing methods, developed to aid machine tool manufacturers during fabrication, are now commonly used to qualify new machines at purchase time. These methods, based on international standards define the accuracy during unloaded condition [1]. When the accuracy of a machining system is measured by traditional techniques, effects from neither the static elastic structure s stiffness nor the cutting process are taken into account. This limits the applicability of these techniques for realistic evaluation of a machining system s accuracy [2]. It was early stated that a customer who is buying a machine tool needs an acceptance test, which tests the machine during operation-like conditions, to verify that the machine was design and constructed properly [3]. The first part of the paper emphasizes the importance of new fast machine test methods. In this context the double ball bar (DBB) fast test method for machine tools is reviewed. Methods for the evaluation of a machine tool s elastic deformation are also discussed. Then, the The Authors. Published by Elsevier B.V. Selection and/or peer-review under responsibility of Professor Konrad Wegener Open access under CC BY-NC-ND license /j.procir

2 576 Andreas Archenti et al. / Procedia CIRP 1 ( 2012 ) focus moves on to a novel type of double ball bar device, which has the ability to create a preload on the elastic structure of the machine tool, thus producing realistic conditions for accuracy of measurements. 2. Machine tool test methods The costs of unplanned disturbances are increased when lean and agile production is implemented on the shopfloors. It is becoming more and more important to detect emerging problems at an early stage. There is a need for new machine test methods to be able to perform regular diagnoses of sensitive equipment and to perform preventive maintenance to avoid unplanned disturbances [4]. There are various test methods available for machine tools [5]. Some of them can be used for fast tests (regular testing) but the majority of the tests methods take too long time to be performed (more than an hour) [6]. However, some methods based on circular tests can be considered as fast test methods Circular test methods The basic idea of a circular test is to run a circle path and as the test proceeds, all deviations from the base circle are registered [7]. An error free machine tool results in a perfect, circular path. Circular test methods measure the changes in the distance between the spindle nose, or the end of the tool, and the centre of a circle on the table. The accuracy of the motion is evaluated from the motion error traces, which can be diagnosed by analysing the traces. The measurement offers a high amount of detailed information due to the fact that the most common errors distort the test path in a mathematically definable way [8] Double ball bar The double ball bar (DBB), based on circular test [6], is a device that can be used for quick tests, developed in the early 1980s [9] and it is adopted by ISO230-4 and ANSI B as an instrument for circular test [10], [11]. This ensures unified practice in ball bar measurements and makes it possible to reliably find many machine tool deviation types from this simple measurement. DBB is the most common circular test method for machine tools and can be solely used to analyse unloaded machine tool structures. The device is based on a very accurate linear scale which measures changes in radial direction during a circular motion. The evaluation of the results is well studied and many of the most significant algorithms can be found in literature [8] Machine tools elastic deformation The machining system is represented by the closeloop interaction between the elastic structure (ES) and the cutting process (CP), see Fig 1, which directly affect the manufacturing accuracy. In a quasi-static case, the machining system may be represented by two transfer functions, one in the primary loop, the static compliance, c a (the inverse of the static stiffness k a ), representing the ES, and the other in the feedback loop, the cutting stiffness, r a, representing the CP. The response of ES to a static load corresponds to a relative deflection y, between tool and workpiece. Physically, this means that the cutting tool will be forced in or out of the workpiece. As a result, the real depth of cut describing the position of the tool with respect to the workpiece surface will be a p [mm] instead of the nominal value a p. The resulting cutting force ΔF c q = k h Δa s p (1) where k s [N/mm 2 ] is the specific cutting coefficient, h [mm] is the actual chip thickness, q (0 < q < 1) a small exponent. F c,nom F c,nom + F c F c Elastic structure (ES) c a =1/k a Cutting process (CP) r a =k s h Fig. 1. Closed-loop machining system from static point of view. The machine tool elastic structure forms the primary loop of the machining system, while the cutting process static behaviour is represented as a subsystem in the feedback loop A machine tool s structural characteristics change depending on different factors, such as cutting forces and subsystem configuration. For instance, if a force is acting between the spindle nose and the machine table, the stiffness can be very high. If the same force is acting between a tool holder system and the machine table, the resulting static stiffness can drop as much as 20 to 30 times, and if not compensated for will result in accuracy errors [12]. The most common way to measure the static deflection in a machine tool is by using an external force generator (e.g. hydraulic jerk), a calibrated force sensor and a displacement sensor. The static deformation of a machine structure can then be plotted as a function of the y a p

3 Andreas Archenti et al. / Procedia CIRP 1 ( 2012 ) load. The static stiffness can be calculated from the applied force and resulting deformation [13]. If the machine load is applied in a loading and unloading manner, a deformation diagram can be created and a more complete description of the static behavior for a given direction can be produced Test specimens for deformation test A conventional approach for testing machines under loaded conditions is to produce some specially designed standard specimens, which are designed to generate predefined forces during the machining operation. The parts are then measured and evaluated, in order to draw conclusions of the behaviour of the machine. The disadvantages of this method are that expensive tools and parts are needed and that the results depend on the condition of these. The results from different tests are not comparable if not exactly the same test specimens, tools and process parameters are used. An example of this type of test is the so called BAS machine tool test [14]. The BAS test can be done for different machine tool configurations, e.g. turning and milling machines. In case of a conventional milling machine the test workpiece is milled (climb milling) along the entire long side, the direction of feed is reversed and the cutter is allowed to run out, being withdrawn from the surface half-way along the work piece. The undercut in each direction is taken as a measure of the deflection (measured in radial direction milling in the direction of X, Y and Z). The workpiece is mounted in such a way so that the surface that will be machined coincides at half of table radius (applicable for horizontal machining) and in case of vertical machining, the workpiece should be placed in such a way so that the middle of it coincides at half of the table radius. In case of swivelling milling head, deflection should be measured in both horizontal and vertical planes to get a more complete view of the stability of the system. The test can be done for both positive and negative feed-direction. The results from the BAS-test are used to check if the machine is within the acceptable limits of deflection, and so accurate enough to be used for production. Another concept for analysing the static deformation of a machine tool structure and specially its static stiffness is done by a dynamic approach. The static stiffness of a system can be considered as a special case of dynamic stiffness, when the frequency is zero. For instance, the static stiffness can be determined from an impulse excitation measurement, based on experimental modal analysis (EMA) [15]. 3. Loaded double ball bar (LDBB) During machining, from a static behaviour point of view, the cutting tool and the workpiece are connected together by a variable stiffness link. The static stiffness of the link depends on the magnitude and direction of the cutting force. Traditionally, the accuracy of machine tools is measured under unloaded conditions by laser interferometry or more practically by the DBB method. By combining the traditional DBB test and the capability to generate a load on the machine tool structure, a more realistic condition for accuracy measurements is created. A device that combines these two capabilities is named Loaded Double Ball Bar (LDBB) [2]. The device can be used as an ordinary DBB system when no load is applied to the structure, or to apply a predefined load to the structure (the link closing the force loop in the structure). The load that is generated by the LDBB is not equivalent to real cutting forces but from a static deflection point of view the effect of the load on the machine tool structure has similar impact on both static and dynamic behaviours of the system. The load can in some cases eliminate existing play in ball screws, plays that under normal machining condition will be eliminated due to the effect of cutting forces on the structure [2]. The basic design of the system, Fig 2, looks similar to the traditional DBB system. The main difference is that a pneumatic actuator is built inside the detecting probe. Fig. 2. The Loaded Double Ball Bar (LDBB) system

4 578 Andreas Archenti et al. / Procedia CIRP 1 ( 2012 ) LDBB measuring procedure 4.2. Deflection in X-Y plane The LDBB measurement can be done in any cross section of a sphere within the machine tool operation space. The test is divided into five stages; an on-trigger movement, an overshoot movement, a data capture movement, an overshoot movement, and an off-trigger movement. The on and off trigger movements trigger the software to start and stop collecting the data. The overshoot is needed to assure stable measuring conditions (stable feed rate). By running tests at different pressures it is possible to calculate the static stiffness using a mean square method. The strength of the force can be set by increasing pressure on the LDBB between the table joint and the tool joint. The machine tool structure deflects in the force direction with a certain amount that depends on its static stiffness. The resulting deflection in the direction of the applied force on the machine tool structure can be seen in Fig 4. Z X Y Fig. 4. Deflection diagrams in X-Y plane for machine M3 (CCW feed = 1000 mm/min): deflection as function of applied load Pforce (1-8) = {36; 112; 238; 364; 490; 616; 742; 868} N, (scale: 10μm/div) Fig. 3. CAD model of the LDBB clamped in a machine tool. Measurements can be done in the X-Y, Y-Z and Z-X planes with a radius of 150 mm and a sweep of up to 390 degrees 4. Testing machine tools under loaded condition In order to demonstrate LDBB s ability to test machines under load and to determine the deformation and static stiffness of machine tools, a case study in which five five-axis milling machine tools (called M1 to M5) were studied is presented. However, in this paper only some results from the case study are presented Static stiffness in X-Y plane The static stiffness is calculated by using acquisitioned data from the deflection measurement and the force value for each run. As can be seen in Fig 5 the static stiffness varies non-uniform in the investigated plane Experimental setup and data Test parameters were varied within a wide range, but the results presented in the paper refer to feed rate 1000 mm/min (counter-clockwise CCW rotation in the X-Y plane) and eight pressures {0.4; 1; 2; 3; 4; 5; 6; 7} bar. The maximal force in this study is 868 N and it is reached with 7 bar air pressure. The table joint was clamped on the machine tool table by two screws and the tool joint was clamped in the spindle by use of a CoroGrip Capto C8 tool holder (see Fig 2). Fig. 5. Static stiffness diagram in polar coordinates for machine M3 (0.5 N/div). The inner circle of the grid is representing the minimum stiffness, in this case 10.3 N/μm

5 Andreas Archenti et al. / Procedia CIRP 1 ( 2012 ) By plotting the stiffness in polar coordinates this behaviour can clearly be seen, see Fig. 5. The average static stiffness in the plane is 11.8 N/μm and the maximum stiffness is 13.4 N/μm, represented by the green vector (13.4 N/μm at 120.2º). The minimum static stiffness can be found at the inner circle of the diagram, represented by the purple vector (10.3 N/μm at 207º) in the figure Circular deviation G The circular deviation G of the measured circles is defined by ISO standard to be the minimum radial separation of two concentrically circles enveloping the actual path. The circular deviation has been calculated for all machines and the trend is that the value increases with increased load applied onto the machine tool structure. In Fig 6 the results from M3 and M5 show the results from measuring with 1000 mm/min feed. This feed has been chosen because it is the closest to the actual milling feed used on investigated machine tools. As can be seen in the figure when the applied load increases, the circular deviation of the measured path also increases (i.e. the difference between the maximum and the minimum radius is increasing with the load on the machine tool structure). Increasing the pressure inside the LDBB will result in enlarging the circular error. From circular deviation point of view this means that the machine is more accurate under low loads on the structure, e.g. in finishing operations, which corresponds to the general knowledge of machining systems. Circular deviation G (mm) 0,025 0,020 0,015 0,010 0,005 0,000 Load (N) Fig. 6. Circular deviation G, in CW and CCW feed rotation, for M3 and M Hysteresis in the machine tool structure M3 CW M3 CCW M5 CW M5 CCW To investigate the hysteresis characteristics during loaded and unloaded conditions, the hysteresis were measured at four fixed angular positions (separated by 90 ). The loads were increased and decreased accordingly, following steps P force {36; 112; 238; 364; 490; 616; 742; 868} N. The absolute displacements were measured at each step. As can be seen in Fig 7 hysteresis after one load and unload cycle is small, between 3 μm and 6 μm, depending on the angular position. Deflection (μm) Fig. 7. Hysteresis diagram. The hysteresis in four direction after a load and unload cycle displayed for machine tool M3 The stiffness varies between 10.1 N/μm and 12.4 N/μm for the test done with continuous feed and between 10.0 N/μm and 11.7 N/μm for the test done during zero feed (Table 1). Table 1. Comparison between the calculated stiffness based on deflection obtained during continuous feed and stiffness calculated when feed is zero (M5) Angle in X-Y plane [ ] Continuous feed k [N/μm] Feed=0 k [N/μm] Conclusions Load (N) The following major conclusions concerning the introduced method for testing a machine tool s deformation and static stiffness can be drawn: load errors at the tool workpiece position depend on the total static stiffness of the machine tool and can be determined from process independent indirect measurements using LDBB tests; the static deformation analysed with LDBB showed no uniformly distributed deformation in X-Y plane;

6 580 Andreas Archenti et al. / Procedia CIRP 1 ( 2012 ) the load generated by the LDBB has a great impact on the deformation of the machine tool structure. For instance, it has been observed that the circular deviation increases as the load increase; the LDBB enables, in contrast to the traditional method (e.g. BAS machine tool test), deflection and static stiffness in all directions in the measured plane (see Fig 8). Fig. 8. Projecting the measured deflection and calculated static stiffness onto a schematic picture of the test specimen used by the industry (BAS machine tool test) [6] Archenti A, Österlind T, Nicolescu CM, Evaluation and representation of machine tool deformations, Journal of Machine Engineering, vol 12/1, 2012 [7] Knapp W, Circular test for three-coordinate measuring machines and machine tools, Precision Engineering, Butterworth & Co; 1983, Vol. 5/3, pp [8] Kakino Y, Ihara Y, Shinohara A, Accuracy Inspection of NC Machine Tools by Double Ball Bar Method, Carl Hansen Verlag, Munich, Germany; [9] Bryan JB, Method for testing measuring machines and machine tools, Part 1 and 2, Precision Engineering; [10] ISO 230-4, Test code for machine tools Part 4: Circular tests for numerically controlled machine tools, ISO; [11] ANSI/ASME B , Methods for performance, evaluation of computer numerically controlled machining centres; [12] Stephenson DA, John S. Agapiou, Metal Cutting Theory and Practice, CRC Press; 2 edition; ISBN-13: ; 2005 [13] Weck M, Brecher C, Werkzeugmaschinen 5 Messtechnische Untersuchung und Beurteilung, dynamische Stabilität, CRC Press; 2 edition; ISBN-13: ; 2005 [14] Asea, Bofors, Scania Alfa Laval, Bearbeitungstests zur Untersuchung des dynamischen Maschinenverhaltens der Firmen AB Bofors, Alfa-Laval AB, ASEA and SAAB-Scania (BASnorm). Sweden; 1970 [15] Ewins DJ, Modal testing: theory and practice, in: J.B. Roberts (Ed.), Research Studies Press Ltd., Bruel & Kjær, 1986 Acknowledgements The authors are grateful for support and contribution from Sverker Johansson (CE Johansson/Hexagon). This work is funded by VINNOVA (The Swedish Governmental Agency for Innovation Systems) and KTH DMMS (centre of Design and Management of Manufacturing Systems) and has been supported by XPRES (Initiative for excellence in production research). References [1] Schwenke H, Knapp W, Haitjerna H, Weckenmann A, Geometric error measurement and compensation of machines - An update, CIRP Annals Manufacturing Technology, vol. 57, pp ; 2008 [2] Archenti A, A Computational Framework for Control of Machining systems Capability From Formulation to Implementation, PhD thesis, KTH Royal Institute of Technology, Stockholm, Sweden, ISBN ; [3] Tobias SA, Dynamic acceptance tests for machine tools, International Journal of Machine Tool Design and Research, vol. 2, no. 3, pp ; [4] Hjelm S, New test method for Industrial Robots and Numerical Controlled equipment, in ISR, vol. 33; 2002 [5] ISO 230-1, Test code for machine tools - Part 1:Geometric accuracy of machines operating under no-load or quasi-static conditions, ISO (ISO 230-1:2012(E)); 2012.