Actively Controlled Compliance Device for Machining Error Reduction

Actively Controlled Compliance Device for Machining Error Reduction K. Matsumoto, Y. Hatamura (I), M. Nakao Department of Engineering Synthesis, Faculty of Engineering, The University of Tokyo, Tokyo, Japan Received on January 3,2000

Abstract Deformation of the tool itself, due to cutting forces, is one of the major causes of machining error in precision machining. The authors propose a new solution to the problem that employs an actively controlled compliance device. By applying 'negative' compliance of the device, deformation of the machining tool can be compensated, and the machining error can be reduced to zero. This paper reports our analysis of the machining process to compensate machining error using negative compliance. It also evaluates our method through experiments of grinding silicon wafers and turbine blades.

Keywords: Machining error reduction, Compliance control, Grinding

1 INTRODUCTION Deformation of the tool itself, due to cutting forces, is one of the major causes of machining error in precision machining. Such conventional methods of adding rigidity to the machine frame, chuck, and tool for higher precision make the machines larger, heavier and more complex. The authors propose a different solution to the problem that measures the machining force, and actively compensates the machine deformation. Figure l(a) shows general configuration of a machining system. Machining force is expressed by a curve. The force flow curve forms a 'C'loop starting at the machining tool and ending at the work. The machining system deforms along the C loop, and dislocation of the start and end points causes machining error. Figure l(b) sketches how we compensate the machining error. The dislocation is corrected by detecting the machining force and estimating the machine deformation. The authors previously proposed a force sensor with actively This sensor provides negative controlled compliance [l]. compliance. The sensor deforms in the direction opposite to the force applied. This paper reports our analysis of the machining process to compensate machining error using negative compliance. To verify our method, it shows a 3-axis active compliance surface grinding system using the ring-shaped active force sensor we developed. It also shows a 2-axis active compliance grinding system using a normal force sensor and servo motors. It evaluates our method of machining error compensation from tests using these systems. 2 MACHINING PROCESS ANALYSIS Figure 2(a) sketches the conventional machining process. Even if the system controls the tool to follow a predetermined trajectory, the resulting surface differs from the desired shape. The machining force deforms the tool, the workpiece and the structural frame to produce machining error (spring-back). Figure 2(b) shows the machining process with negative compliance. To compensate the spring-back, the negative compliance device increases the cutting depth. Figure 3 shows a model to analyze the machining process with negative compliance. The following equations describe machining force F, spring-back S and machining error E

Annals of the ClRP Vol. 49/1/2000

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Figure 2: Analysis of machining process. when the initial cutting depth is Z. The suffix 0 indicates initial state. Cm is machining compliance defined as the ratio (cutting depth)/(machining force). CS is the machining system compliance. The initial machining force Fo and the springback So are: Z FO=(1) C m i-Cs

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Figure 3: Model of machining process with negative compliance. negative compliance generates. When CZ is the negative compliance to generate additional cutting depth Zc, the additional cutting depth ZCI responding to f o , the total machining force f i to cut Z and Zcr, and the spring-back S I to f I are: -Cz FO (3) Z - E I - Z-SI+ZcI FI=(4) Cm Cin S!=CSFI (5) From these equations, the machining force f I is described as:

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Z Cm + Cs iCz Equation (11) shows we can set the machining error to zero regardless of the cutting depth Z if CZis set to -CS.This means a precise measurement of the machining system compliance CS enables constructing an error free machining system whose machining error automatically converges to zero regardless of the cutting depth Z and cutting force f .

3 SURFACE GRINDING SYSTEM FOR SILICON WAFER 3.1 System configuration Figure 4 shows a surface grinding machine equipped with an active force sensor to generate 3-axis active compliance. The machine is developed to obtain wide and flat surface which is required in silicon wafer or optical-flat by grinding. The cutter is a diameter 30 mm straight cup wheel driven by a 3 MPa water pressure turbine motor running at 10,000 rpm. A dynamic water pressure bearing supports the rotation shaft that couples the turbine and the grinding tool. The active force sensor is mounted between the turbine and the z-

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Figure 5: Ring-shaped active force sensor. direction feeding mechanism. We glued the work, an 8-inch silicon wafer, to the x-direction table using hot wax.

3.2 Active compliance system We developed a 3-axis compliance system with the ringshaped active force sensor. Figure 5 shows the structure of the sensor. Four sets of active sensing units are placed, one at every 90 degrees, between the upper and lower rings. Each unit can detect force and displacement, and actuate as well. The four outputs from the units allow computing force in the z-direction (Fz),and moment values around the x and y-axes (Mx,My). Actuating the piezo elements in the 4 units generates displacement in z-direction (Dfz) and rotation around the x and y-axes (Dmx, Dmy). By controlling the displacement and rotations respondingto the applied force and moment, a variety of compliance in zdirection, and around x- and y- axes are generated. Figure 6 shows an example how the working surface moved. The figure shows negative compliance was achieved as well as positive Compliance. There are bounds to the working range, indicated by dotted lines, due to limitations of the piezo device range of stroke. 3.3 Grinding experiment The cup wheel diameter is 30 mm, with grain #2000.We set the x-direction feed rate to 100 mmlmin., and the active force sensor control system bandwidth to around 10 Hz, with DC gain of about 60 dB. We prepared a base surface with a trapezoid step. The remaining height of the step after feeding

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Applied force Fz N Figure 6: Compliance control operation in z-axis. the grinding tool along the base surface is the machining error that we measured. The Initial height and length of a trapezoid step is 10 u m and 30mm. The z-direction compliance of the grinding system CSwas measured 0.257 u mlN at the table center. The z-direction machining compliance Cm was 2.80 u mlN, which is over 10 times that of the grinding system CS.The system remains stable while changing the z-direction compliance Cfz as long as its absolute value is smaller than Cm. Figure 7 relates machining error, measured along the center, the left and right line of the cup wheel trajectory, to compliance Crz when compliance Cmx and Cmy are set to zero. Where Crz is 0 u m/N, is when the sensor rigidity is high, providing compliance equivalent to grinding without the active force sensor. The machining error in the center is 0.9 m and this is the machining error upon grinding without compensation. Left of the 0 u mlN line is the positive compliance region, and right is the negative. Setting Cfz to the negative side reduces machining error. The machining error minimized when Crz was set to -0.3 u m/N. From the analysis in Section 2, machining error should be zero when the compliance Crz is set to -CS.The value is close to -0.257 u mlN as the analysis predicted. Setting the compliance further to the negative side (to the right), caused under-cut. The error on the left side is 0.2 u m higher, while that at the right is 0.2 cc m lower. The machining force holds a moment component MXaround the center line because the grinding force distribution combines to FZthat works on points deviated from the cup wheel trajectory center. We then kept the zdirection compliance to -0.3 u mlN and altered the x-axis rotational compliance. Figure 8 shows the results and when Cmx is set to -0.3 mradlNm, the error was 0.1 u m or under including the left and right sides. Figure 9 shows the resulting surface profile along the cup wheel trajectory center line after the above experiment. When the z-direction compliance Cfz is -0.1, -0.3, and -0.5 u mlN, the machining error is 0.6, 0, and -0.6 u m, respectively. Machining error increases where the feed exceeds 100 mm. This larger error is due, we assume, to change in the condition for machining error reduction. When the grinding point approaching the table end, the compliance CSdeviates from that at the table center. 4 GRINDING SYSTEM FOR TURBINE BLADE 4.1 System configuration Figure 10 shows a grinding machine for turbine blade with 2axis active compliance. The machine is developed to grind edge of turbine blade automatically. The cutter is a grinding wheel of 120mm diameter driven by a spindle motor running at 1,500rpm. The grinding wheel is moved in z-direction by a table driven by an AC servo motor. A turbine blade in a holder attached to an x-y table is also

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4.2 Active compliance system In the active compliance system described in section 3.2, an active force sensor with force sensing and actuating capabilities was employed to generate active compliance. In the grinding system for turbine blade here, a normal force sensor without actuation capability and servo motors which

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Figure 11: 2-axis force sensor with parallel plate structures. drive tables are used to generate compliance. We developed a 2-axis force sensor with parallel plate structures[2][3]. Figure 11 shows the structure of the sensor. Four sets of parallel plates are placed at each side of the sensor. Forces in x and z directions ( f x , Fz)are detected by the strain gauges on the parallel plates. By controlling the motions of the x-y table and the z table, a variety of compliance in x- and z- axes is generated. Figure 12 shows an example of table movement responding to applied force. As shown in Figure 6, the compliance by the active force sensor has bounds of the working range due to the piezo elements. This system uses servo motors as actuators, so it has no bounds of working range. 4.3 Grinding experiment In this grinding system, the compliance in x- and z-directions has to be controlled, as machining force that affects machining error has these components. The system compliance in x-direction CSXwas measured 5.07 u mlN, while that in z-direction CSZwas 3.47 u m/N. We set the y-direction feed rate to 150 mmlmin, and the bandwidth of the compliance control system to around 5 Hz. We employed an A2017 sample instead of a real titanium blade. Direction of cutting feed was 45 degrees in x-z plane, so as to grind the edge of the sample. The cutting depth was 100 u m. Figure 13 shows machining error to compliance Cfx and Ctr normalized by the system compliance CSXand CSZ respectively. In this experiment, these compliances were changed together. Where CfxlCsx and Cfz/Csz are 0, the machining error is 30 u m. This is when the system provides compliance equivalent to natural compliance of the grinding system without control. The machining error is minimized when they are set to -1. This result meets the analysis in Section 2.

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Compliance C&/CSX ,CtzlCsz Figure 13: Compliance Cfx/Csx,Cfz/Cszvs. grinding error. 5 CONCLUSION We suggested an active method for compensating machining error to enhance precision during machining processes. The method is based on negative compliance system that measures the machining force and accordingly cancels the machining system deformation. We analyzed the machining process to derive a stable condition for a negative compliance system and showed that it can compensate for machining error. To verify the method with face grinding, we developed a surface grinding system for silicon wafer with a ring-shaped active force sensor. We further developed a grinding system for turbine blade with an active compliance system using a normal force sensor. Through experiments, machining error reduction by negative compliance has been confirmed. REFERENCES [I]Matsumoto, K., Hatamura, Y., Nakao, M., 1994, ATrial of Force Sensor with Actively Controlled Compliance, Proceedings of ASPE Spring Topical Meeting on Mechanisms and Controls for UltraprecisionMotion, ASPE,Tucson, 116-121 [2] Nagao, T., Hatamura, Y., Sato, H., 1987, Development of a Flexible Grinding System with Six-Axis Force Sensor for Curved Surfaces, Annuals of the CIRP, Vol. 36/1:215218 [3] Hatamura, Y., Matsumoto, K., Morishita, H., 1988, A Miniature 6-axis Force Sensor of Multilayer Parallel Plate Structure, Proceedingsof IMEKO, Houston, 621-636