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Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine
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Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine Yuta Oba ∗ , Yasuhiro Kakinuma Department of System Design Engineering, Keio University, Japan
a r t i c l e
i n f o
Article history: Received 10 January 2017 Accepted 16 January 2017 Available online xxx Keywords: Polishing Parallel mechanism Unknown curved surface Automation Sensor-less force control Skilled technique
a b s t r a c t In automotive manufacturing, the repair polishing process of an automotive body is still manually performed by skilled polishing workers. This is because skilled workers can appropriately control the polishing motion and force according to the workpiece conditions based on their experience. However, the number of skilled workers has been decreasing. Additionally, the skill development of younger workers has not been satisfactorily conducted. To overcome such problems, in a previous research investigation, we developed a serial-parallel mechanism polishing machine that effectively reproduced the polishing motion and force of skilled workers. This replication system, however, had limited use because the acquired polishing techniques could not adapt to various workpiece conditions, such as shape and size. The present study aimed to expand the polishing method for application to curved surfaces, in other words, adapt the replication system to changes in the workpiece shape. In the past polishing methods for curved surfaces, the workpiece shape was acquired by using CAD data or external sensors that often led to an increase in process time and cost. However, the newly proposed method in this study requires neither CAD data nor external sensors, and was able to effectively achieve simultaneous posture and force control on unknown curved surface. The experimental results showed that the skilled polishing techniques were successfully replicated on an unknown curved surface and the surface roughness was greatly improved by integrating the newly proposed method into the skilled polishing replication system. © 2017 Elsevier Inc. All rights reserved.
1. Introduction The repair polishing process for an automotive body is important for satisfying the high surface quality requirements of automotive manufacturing. The polishing process is still manually carried out by workers with the required polishing technique. This is because the skilled worker is capable of adjusting the polishing motion and force according to the workpiece conditions based on their experience. However, the number of skilled workers has been decreasing because of an aging population, and the skill development of younger workers has not been satisfactorily conducted [1]. Therefore, polishing automation technology has been proposed in many research studies so that ultimately it can replace manual polishing and improve polishing efficiency [2–8]. In our previous research, a replication system of the skilled polishing technique was developed using a serial-parallel mechanism polishing machine [7]. This polishing machine was capable of inde-
∗ Corresponding author at: Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku, Yokohama, Kanagawa 223-8522, Japan. E-mail address: [email protected] (Y. Oba).
pendently controlling the polishing motion and force, namely, the displacement on x-y plane (horizontal plane), angular displacements in yawing and pitching modes, and force in z-axis mode [8]. Therefore, the skilled polishing techniques of these three physical parameters were acquired from skilled workers to replicate the skilled polishing process using the polishing machine. By inputting the acquired data into the developed polishing machine as command values, the skilled polishing process could be successfully replicated. However, the constructed replication system was considered to be incomplete because the skilled polishing techniques did not change according to the workpiece conditions such as shape and size. Therefore, a method for detecting changes in workpiece conditions was required to use the proposed skilled polishing replication system for polishing automation. This study focuses on only the workpiece shape. The previously proposed system of skilled polishing replication could be used only on flat surfaces. However, actual automotive bodies are not flat, but curved. In general, both the tool posture and the direction of the polishing force should be controlled normal to the curved surface. Therefore, an automated polishing method is required to adapt the skilled polishing replication system to the curved surface. In past research investigations, the polishing automation for curved
http://dx.doi.org/10.1016/j.precisioneng.2017.01.006 0141-6359/© 2017 Elsevier Inc. All rights reserved.
Please cite this article in press as: Oba Y, Kakinuma Y. Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine. Precis Eng (2017), http://dx.doi.org/10.1016/j.precisioneng.2017.01.006
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Nomenclature Fdis Freac Ffric Kt Ia M x
Disturbance force [N] Reaction force [N] Friction force [N] Motor thrust force coefficient [N m/A] Motor current [A] Mass [kg] Position [m] v Velocity [m/s] a Acceleration [m/s2 ] Angle [rad] (Subscript)n Nominal value cmd
Command value (Superscript) ref Reference value (Superscript) res Response value (Superscript) Caret Estimated value
Fig. 1. Serial-parallel mechanism polishing machine. Table 1 Specifications of machine.
surfaces was achieved using CAD data [9–11] or external sensors [12–14]. For example, Z. Jianming et al. [11] proposed a polishing method for aspheric surfaces by acquiring the workpiece shape from CAD data prior to the polishing operation. However, the workpiece shape from the CAD data does not always correspond to the real shape because the workpiece shape from the CAD data does not account for installation error. Therefore, the polishing process using CAD data requires an additional step for position adjustment depending on human skill, and thus the entire process duration increases. S. Kamezaki et al. [12] proposed a polishing method for metal molds with force sensors. In their work, the workpiece shape was estimated based on reaction force information by a 6axis force sensor installed in the polishing tool. Z. Yang et al. [14] used a touch trigger probe for surface measurement to achieve edge polishing. However, applying external sensors generally results in increased production costs and frequent maintenance. To eliminate the abovementioned problems, the simultaneous control method of tool posture and polishing force in the normal direction of curved surfaces, which is independent of CAD data and external sensors, is proposed in this study. The purpose of the present study is to adapt the skilled polishing replication system to curved surfaces with the proposed control method. First, a tool posture control method of an unknown curved surface was proposed. The posture angles in yawing and pitching modes were determined based on force information acquired from the parallel mechanism component with a reaction force observer [15–17]. Second, a normal force control method based on tool posture information was proposed. Using these proposed methods simultaneously, the tool posture and polishing force were controlled in the normal direction of unknown curved surfaces. From the experimental results, the skilled polishing techniques were successfully replicated on the unknown curved surface with the newly proposed method. In addition, the surface quality after polishing fully satisfied the surface quality criteria. 2. Serial-parallel mechanism polishing machine 2.1. Composition of mechanism Fig. 1 shows an overview of the serial-parallel mechanism polishing machine [8]. The parallel mechanism is suitable for polishing automation because it enables high precision and high-speed movements compared to the serial mechanism. However, the parallel mechanism machine is often not used in industrial polishing automation owing to its limited workspace. To address this drawback, a two-degree-of-freedom (DOF) serial mechanism (XY stage)
330 mm × 340 mm × 405 mm 8.10 kg 75.4 mm × 50.4 mm × 44.4 mm 15.90◦ × 18.18◦ 16 mm radius 1.0 m 250 s
Size of machine (X × Y × Z) Weight of machine Movement range (X × Y × Z) Angle range (Yawing × Pitching) Size of buff tool Resolution of linear encoder Control sampling time
that provides a larger workspace is assembled in between the base frame and the three DOF parallel mechanism. The XY stage has three linear motors (one in the X stage and two in the Y stage) and the parallel mechanism has three linear motors positioned at 120◦ intervals. At the lower end of the shaft in the parallel mechanism, the rod is connected to the revolute joint of one-DOF linkage. The other end of the rod is attached to the endplate through a spherical joint. This structure allows the parallel mechanism to move in the z-direction, as well as x-axis rotation (pitching) and y-axis rotation (yawing). Each axis has one optical linear encoder. A wool buff is attached to the lower end of the spindle. The polishing force and the tool posture are independently controlled at the 3-DOF parallel mechanism, and the displacement of the tool on x-y plane is controlled at the XY stage. The specifications of the developed polishing machine are listed in Table 1. 2.2. Position and force control theory The motion of the developed machine is controlled based on disturbance observer (DOB) [18] and [19]. DOB is designed to cancel disturbance forces. The estimated disturbance force is obtained ref from the velocity response vres and the current reference Ia as shown in Eq. (1). ref
Fdis = Freac + Ffric + Mg + Kt Ia − Msvres ref
(1)
= Ktn Ia − Mn svres The velocity response vres is calculated by the differential of the position response xres read by the linear encoder, and the current ref reference Ia is applied to the actuator. Fig. 2 shows a block diagram of the position control based on DOB. A first order low pass filter (LPF) is inserted in order to suppress the noise generated from the differential of the velocity. Also, the estimated disturbance is fed back as a current value to actively cancel a bad influence of the disturbance to the control system. A proportional-derivative (PD) controller is suitable because the disturbance cancellation serves as an integrator. The positioning performance and robustness are determined by the position controller and DOB, respectively.
Please cite this article in press as: Oba Y, Kakinuma Y. Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine. Precis Eng (2017), http://dx.doi.org/10.1016/j.precisioneng.2017.01.006
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·
3
·
where mz ,myaw , and mpitch are accelerations in the z-axis, yawing, ·
·
·
and pitching modes, respectively; z 1 , z 2 , and z 3 are the accelerations of the three links. Fig. 5 shows the block diagram of the motion control system for the parallel mechanism with the quarry matrix at the acceleration dimension. This control system can be divided into two spaces, one is the modal space, and the other is the joint space. At the ref
·
· res
reac
joint space, zi (i = 1∼3), z i (i = 1∼3), and zˆ i (i = 1∼3) denote the acceleration references, the acceleration responses, and the equivalent accelerations of the reaction force, respectively. The subscript shows the actuator number. The acceleration response and the equivalent accelerations of the reaction force are trans-
Fig. 2. Position control system based on DOB.
· res
formed into modal space accelerations mj ·
(j = z, yaw, pitch) and
reac
(j = z, yaw, pitch) through the quarry matrix. The transformed
ˆj m
·
reac
ˆz modes are independent of each other. In this study, m · res mpitch
· res
, myaw ,
and are fed back to independently control the reaction force in the z-axis mode and the tool postures in the yawing and pitching modes, respectively. The mode controllers at the modal space posture force Cmode (s) and Cmode (s) are designed as follows: posture
Cmode (s) =
1 1 Kp + Kv s s2
force
Cmode (s) = Kf
The reaction force observer (RFOB) [15–17] can estimate external forces, e.g. a reaction force, without external sensors that cause an increase in production cost and required maintenance. In the case that the fluctuation of the thrust force coefficient and the mass variation are negligibly small, the reaction force is estimated by subtracting the identified friction force Fˆfric and gravity force Mn g from the disturbance force Fdis . Fig. 3 shows the block diagram of force control based on DOB and RFOB, which can realize the forcesensor-less force control. The identification accuracy of the friction force and gravity force plays an important role in precisely controlling the polishing force. Also, the bandwidth of the estimated reaction force is decided by the cutoff frequency greac . When the polishing process was conducted with the force control system in Fig. 3 in our previous research [8], the monitoring accuracy of the reaction force by RFOB was almost the same as that of force sensor (the estimation error was less than 0.5N) and the effectiveness of RFOB was clarified. 2.3. Parallel mechanism control based on the mode decoupling method The motions of the 3-DOF parallel mechanism component are controlled by using the mode decoupling method based on quarry matrix at an acceleration dimension [20] and [21]. The motions of the parallel mechanism can be transformed into three modal motions with the quarry matrix. Fig. 4 shows the three modal motions. The quarry matrix is represented in Eq. (2). ·
·
Z1
·
( myaw ) = Q3 ( · ) Z2 ·
mpitch
·
Z3
2 1 Q3 = ( 0 6 4
2 2 3
−3 )
−2
−2
(4)
where Kp is the proportional gain, Kv is the differential gain in the posture mode controller, and Kf is the proportional gain in the force mode controller.
Fig. 3. Force control system based on DOB and RFOB.
mz
(3)
(2)
3. Simultaneous posture and force control method on an unknown curved surface 3.1. Tool posture control method on an unknown curved surface To control the tool posture in the normal direction of the surface without CAD data and external sensors, the estimated reaction force by RFOB is used. Fig. 6 shows the relationship between the tool posture and the forces applying to the buff during the polishing process. Fiext (i = x, y) and i (i = x, y) denote the external force in the x-axis or y-axis and the tool posture around the x-axis or y-axis, respectively. In Fig. 6(a), the tool posture is not controlled in the normal direction of the surface, and only a part of the buff is in contact with the surface. Therefore, the external friction force is generated in the opposite direction of the tool rotational direction. On the other hand, in Fig. 6(b), the tool posture is controlled in the normal direction of the surface. In this case, the external force is not generated because the external force couples are cancelled out. To control the tool posture based on this relationship, the tool posture and external force are modeled using a spring-damper model. Transfer function Gi (s) is as follows: Gi (s) =
i 1 = (i = x, y) Ki + Ci s Fiext
(5)
In this study, the external force Fiext (i = x, y) is monitored at the parallel mechanism component. Fig. 7 shows the forces applied to the links of the parallel mechanism component. Fˆjreac (j = 1∼3) denotes the reaction force estimated at the link with RFOB. The subscript shows the link number. In Fig. 7, red and blue lines represent the x-axis and y-axis components of the estimated forces, respectively. By using these estimated x-axis and y-axis forces, the external forces are calculated and represented as the estimated val-
Please cite this article in press as: Oba Y, Kakinuma Y. Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine. Precis Eng (2017), http://dx.doi.org/10.1016/j.precisioneng.2017.01.006
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Fig. 4. Decoupled modes by quarry matrix.
Fig. 5. Motion control system based on mode decoupling method.
Fig. 6. Relationship between tool posture and external force.
ues Fˆxext and Fˆyext . A conversion equation for the calculation of the external forces is shown in Equation (7).
Fˆxext Fˆyext
⎛ ˆ reac ⎞ ⎜
F1
⎟
⎛
= M ⎝ Fˆ2reac ⎠ = ⎝ Fˆ3reac
0 1
6 − sin 6
− cos
6 − sin 6 cos
⎞ ⎛ Fˆ reac ⎞ 1 ⎟ ⎠⎜ ⎝ Fˆ2reac ⎠ (7)
where M is the 2 × 3 conversion matrix. Fig. 8 shows the block diagram of the posture control method on an unknown curved surface. The posture command angles around the x-axis xcmd and y-axis ycmd are decided by controlling the estimated external forces Fˆxext and Fˆyext to zero through the transfer functions Gx (s) and Gy (s), respectively.
Fˆ3reac
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Fig. 10. Forces applied to the surface. Fig. 7. Reaction forces measured at parallel mechanism component.
3.3. Polishing force control method on an unknown curved surface The normal direction of the unknown curved surface is determined by using posture information gained by the proposed posture control method. Based on the tool postures around the xaxis and y-axis, x and y , respectively, a rectangular parallelepiped can be drawn (Fig. 10). In Fig. 10, Fx , Fy , and Fz are the forces applied to the workpiece surface. A diagonal direction of the rectangular parallelepiped corresponds to the normal direction of the surface. Therefore, the normal force Fn is calculated as the sum of the diagonal direction components of Fx , Fy , and Fz in Eq. (8), defined as the normal force model. Fig. 8. Posture control method on unknown curved surface.
Fn =
3.2. Tool tip control method With the tool posture control, the displacement of the XY stage needs to be adjusted for controlling the tool tip position. As shown in Fig. 9(a), the tool tip position cannot be located at the desired position with only the tool posture control. l and z denote the length from the tool tip to the endplate and the error in the z-axis, respectively. Additionally, l sin i (i = x, y) represents the error in the x-axis or y-axis. Fig. 9 shows how to correct the errors in the xaxis, y-axis and z-axis. To correct the errors of the tool tip position in the x-axis and y-axis, lsin y and lsin x are added to the displacement command values of the X stage and Y stage, respectively. In addition, the error in z-axis z can be corrected by the z-axis force control. As a result, the errors of the tool tip position are removed, and the tool tip is accurately controlled, as shown in Fig. 9(b).
Fz + Fx tan y + Fy tan x
1 + tan2 x + tan2 y
(8)
In this study, the force control can be done at the z-axis mode of the parallel mechanism component. Therefore, the force in the z-axis mode is controlled to set the normal force to a desired value. The command value of Fz for the normal force control is calculated by solving Eq. (8), as shown in the following equation. Fzcmd = Fncmd
1 + tan2 xcmd + tan2 ycmd − Fˆxext tan ycmd − Fˆyext tan xcmd
(9)
where icmd (i = x, y) and Fˆiext (i = x, y) denote the tool postures around the x-axis and y-axis and the estimated reaction forces in the x-axis and y-axis, respectively. The command value of the polishing force is applied to the command value Fncmd . By using the proposed normal force model, the polishing force is controlled in the normal direction of the workpiece surface.
Fig. 9. Tool tip control method.
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Fig. 11. Simultaneous tool posture and polishing force control system.
3.4. Simultaneous control method of tool posture and polishing force Fig. 11(a) shows the overall block diagram with the tool posture and polishing force control method on an unknown curved surface. The conversion matrix M is newly applied to the joint space in Fig. 11(b). Through the conversion matrix M, the equivalent accelerations of Fˆiext (i = x, y) can be calculated and represented as ·
Table 2 Parameters of experiment. gdis greac (Kp , Kv )
Kf
ext
ˆ i (i = x, y). In addition, the command space based on the prom posed posture and force control method is newly defined in the motion control system. The acceleration posture command values · cmd myaw
· cmd mpitch
in yawing and pitching modes represented as and are calculated through the transfer functions Gy (s) and Gx (s), respectively, and the acceleration force command value in the z-axis mode is decided by using the normal force model. 4. Polishing experiments 4.1. Experimental setup and procedures Fig. 12 shows the experimental setup. A steel plate with a viscoelastic polymer coating was used as the workpiece. The workpiece was bent by warping the cylindrical surface, although the original shape was flat. A gonio stage that can adjust the angle was attached under the cylindrical surface, and the workpiece was titled 4◦ with respect to the bottom face. To compare the estimated force with the actual one, a dynamometer was mounted
(Kx , Cx )
(Ky , Cy )
Cutoff frequency of DOB [rad/s] Cutoff frequency of RFOB [rad/s] Proportional and differential gains of posture mode controller Proportional gain of force mode controller Spring and damping coefficients in posture control method Spring and damping coefficients in posture control method
200.0 30.0 (25.0, 100.0)
0.7 (0.00001, 15.0)
(0.01, 1.2)
between the surface and the base. The polishing compound was alumina abrasive (abrasive size: 10 m) mixed in white-mineral oil. The spindle speed was set to 5000 min−1 . In this experiment, the tool posture was controlled in the normal direction of the surface by the proposed method. On the other hand, the command values of the displacements in the x-axis and y-axis and polishing force in the normal direction were determined using the acquired data of the skilled worker for the flat surface [7]. Fig. 13 shows the acquired data of the displacements in the x-axis and y-axis and polishing force in normal direction. In Fig. 13, the polishing process started 2.9 s after the measurement acquisition began. Therefore, only data from after 2.9 s were used as the command values. The experimental parameters are shown in Table 2.
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Fig. 12. Experimental setup.
Fig. 13. Data of acquired polishing skill.
Fig. 14. Experimental evaluation of posture control.
4.2. Experimental results Fig. 14 shows the result of the tool posture control. The response angles, which represent the posture angles of the endplate, were calculated based on encoder information at the parallel mechanism component. Also, the real angles were calculated using CAD data without the installation error. From this result, the response angles followed the real angles in both modes, although there were errors between these two angles. These errors can be decreased by lowering the damping coefficients Ci (i = x, y) in the proposed transfer functions for posture control Gi (s) (i = x, y). However, if lowering the damping coefficients, the low mechanical stiffness of the parallel mechanism component causes the tool to vibrate. In this research, the vibration of the tool adversely influences not only the tool posture control but also the polishing force control. Therefore, the coefficients in the proposed transfer functions were selected to achieve both accurate posture and stable force control.
Fig. 15. Experimental evaluation of force control.
As a result, the average error in yawing mode was 0.42◦ and that of the pitching mode was 1.85◦ with minimal vibration. Fig. 15 shows the result of the polishing force control. The force response was the estimated value by RFOB, and the actual force was the measured value by dynamometer. The acquired polishing force in Fig. 13(b) was used as the normal force command value. Therefore, the force command in the z-axis of Fig. 15 was calculated based on the acquired polishing force through Equation (9). The force command value before the process start time was set to 2.0 N to control the tool posture based on the reaction force. From this result, the trend of three forces corresponded, although the monitoring error between the force response and actual force was relatively large. The magnitude of the actual force became large owing to the backlash of the revolute joint part of the parallel mechanism component. However, the force response by RFOB was less subject to the influence of the backlash because the actuators that could estimate the reaction forces were fixed to the base plate in Fig. 1. Consequently, the monitoring error increased especially
Please cite this article in press as: Oba Y, Kakinuma Y. Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine. Precis Eng (2017), http://dx.doi.org/10.1016/j.precisioneng.2017.01.006
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Fig. 16. Surface appearance before and after polishing.
Fig. 17. Analyzed surface after polishing.
Table 3 Surface roughness before and after polishing. Criteria Ra [nm]
Before After
924.6 14.5
941.3 13.3
1015.9 18.2
981.6 18.9
912.3 19.2
30.0
when the posture angle was largely changed. There was a monitoring error resulting from a mechanical problem, but the average error between the force response and actual force was 0.47 N. In addition, both the force response and the actual force could effectively follow the force command. From the evaluation of posture and force control, it was confirmed that tool posture and polishing force were simultaneously controlled in the normal direction of the unknown curved surface by the proposed method, although with errors in both posture and force control. Fig. 16 shows the appearance of the surfaces before and after polishing. The surface before polishing (Fig. 16(a)) was rough, and had a gray color. On the other hand, the color of the surface after polishing (Fig. 16(b)) showed that the workpiece regained its original color black because the polishing process was successfully conducted. To evaluate the surface quality quantitatively, the arithmetic mean roughness Ra of the surface was measured using a 3D optical microscope (New View 6200, Zygo Co., Ltd). The criteria for Ra in the finishing process was defined as 30 nm. The surface roughness measured at five different points before and after polishing is shown in Table 3. In addition, the surfaces after polishing analyzed by the microscope are shown in Fig. 17. The results in Table 3 show all arithmetic mean roughness values after polishing satisfied the criteria, and that those before polishing largely exceeded the criteria. On the other hand, as a result of observing the
analyzed surface in Fig. 17, small scratches partly remained on the surface after polishing. The scratches could not be seen when the tool posture and the polishing force were accurately controlled in our previous research [7]. Therefore, it was possible that the cause of the small scratches were a byproduct of the errors in posture and force control. To remove the scratches, it is essential to solve the mechanical problem of the parallel mechanism component. However, the errors in posture and force control had no influence on the arithmetic mean roughness because both the tool posture and the polishing force could follow their respective target values. In addition, the reproducibility of the results was verified from several tests conducted using the same setup and procedure. 5. Conclusion The simultaneous control method of the tool posture and the polishing force on an unknown curved surface with a serial-parallel mechanism machine was newly proposed to replicate the skilled polishing technique on the unknown curved surface. The proposed theory and the obtained results are as follows: (1) When the tool rotational axis is in the normal direction, the external friction force generated between the tool and the surface is cancelled out. To control the tool posture based on this relationship, the tool posture and the external force estimated based on RFOB were modeled using a spring-damper model. By setting the external force to zero, the tool posture control on the unknown curved surface was achieved without employing CAD data or external sensors. (2) The normal direction of the surface was determined based on the tool posture information gained by the proposed posture
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control method, and the normal force was calculated as the sum of the normal components of the forces in the x-axis, yaxis, and z-axis. In this study, the normal force control on an unknown curved surface was realized by observing these force components with RFOB. (3) An acceleration control system integrating the proposed posture and force control methods was newly proposed. By applying the proposed control system to the developed polishing machine, the tool posture and the polishing force could be simultaneously controlled on an unknown curved surface. (4) The experimental results show that the skilled polishing techniques could successfully be replicated on an unknown curved surface and the surface quality after polishing satisfied the criteria by integrating the proposed posture and force control method into the skilled polishing replication system. In this study, the validity of the newly proposed tool posture and polishing force control method on an unknown curved surface was verified. By increasing the mechanical stiffness or removing the backlash of the revolute joint, the posture and force control accuracy and the surface quality after polishing can be further improved. Acknowledgement This work was partially supported by the Ministry of Education, Science, Sports and Culture, KAKENHI No. 15H03904, 2015. References [1] Unno K. Support and promotion of the skill succession by utilizing expert skilled workers. J Jpn Soc Precis Eng 2015;81(1):30–3. [2] Liao L, Xi F, Liu K. Modeling and control of automated polishing/deburring process using a dual-purpose compliant tool head. Int J Mach Tools Manuf 2008;48:1454–63. [3] Shi Y, Zheng D, Wang L. NC polishing of aspheric surfaces under control of constant pressure using a magnetorheological torque servo. Int J Adv Manuf Technol 2012;58:1061–73.
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[4] Feng D, Sun Y, Du H. Investigations on the automatic precision polishing of curved surfaces using a five-axis machining centre. Int J Adv Manuf Technol 2014;72:1625–37. [5] Chaves-Jacob J, Linares JM, Sparauel JM. Control of the contact force in a pre-polishing operation of free-form surfaces realised with a 5-axis CNC machine. CIRP Ann −Manuf Technol 2015;64:309–12. [6] Pilny L, Bissacco G. Development of on the machine process monitoring and control strategy in Robot Assisted Polishing. CIRP Ann −Manuf Technol 2015;64(1):313–6. [7] Oba Y, Yamada Y, Kakinuma Y. Replication of skilled polishing technique with serial-parallel mechanism polishing machine. J Inter Soc Precis Eng 2016;45:292–300. [8] Kakinuma Y, Igarashi K, Katsura S, T.Aoyam a. Development of 5-axis polishing machine capable of simultaneous trajectory, posture and force control. CIRP Ann −Manuf Technol 2013;62(1):379–82. [9] Marquez JJ, Perez JM, Rios J, Vizan A. Process modeling for robot polishing. J Mater Proc Tech 2005;159:69–82. [10] Nagata F, Hase T, Watanabe K. CAD/CAM-based position/force controller for a mold polishing robot. Mechatronics 2007;17:207–16. [11] Jianming Z, Sihai Y. A new aspheric surfaces polishing by prallel orthogonality movement/force servomechanism. Trans ASME J Manuf Sci Eng 2011;133(3):1–5, 031011. [12] Kamezaki S, Aoyama T, Inasaki I. Development of a robot-polishing system. Trans Jpn Soc Mech Eng Series C 1991;543:3714–9. [13] Furukawa T, Rye DC, Barratt AJ. Automated polishing of an unknown three-dimensional surface. Robo Comp-Integ Manuf 1996;12(3):261–70. [14] Yang Z, Xi F, Wu B. A shape adaptive motion control system with application to robotic polishing. Robo Comp-Integ Manuf 2005;21:355–67. [15] Murakami T, Yu F, Ohnishi K. Torque sensorless control in multidegree-of-freedom manipulator. IEEE Trans Ind Electron 1993;40(2):259–65. [16] Katsura S, Matsumoto Y, Ohnishi K. Modeling of force sensing and validation of disturbance observer for force control. IEEE Trans Ind Electron 2007;54(1):530–8. [17] Kurihara D, kakinuma Y, Katsura S. Cutting force control applying sensorless cutting force monitoring method. J Adv Mech Des Syst Manuf 2010;34(5):955–65. [18] Ohnishi K, Matsui N, Hori Y. Estimation, identification, and sensorless control in motion control system. Proc IEEE 1994;82(8):1253–65. [19] Ohnishi K, Shibata M, Murakami T. Motion control for advanced mechatronics. IEEE/ASME Trans Mechatron 1996;1(1):56–67. [20] Katsura S, Ohnishi K. Quarry of modal information from environment for advanced motion control. IEEJ Trans Ind Appl 2006;126(4):372–8. [21] Katsura S, Ohishi K. Modal system design of multirobot systems by interaction mode control. IEEE Trans Ind Electron 2007;54(3):1537–46.
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Precision Engineering journal homepage: www.elsevier.com/locate/precision
Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine Yuta Oba ∗ , Yasuhiro Kakinuma Department of System Design Engineering, Keio University, Japan
a r t i c l e
i n f o
Article history: Received 10 January 2017 Accepted 16 January 2017 Available online xxx Keywords: Polishing Parallel mechanism Unknown curved surface Automation Sensor-less force control Skilled technique
a b s t r a c t In automotive manufacturing, the repair polishing process of an automotive body is still manually performed by skilled polishing workers. This is because skilled workers can appropriately control the polishing motion and force according to the workpiece conditions based on their experience. However, the number of skilled workers has been decreasing. Additionally, the skill development of younger workers has not been satisfactorily conducted. To overcome such problems, in a previous research investigation, we developed a serial-parallel mechanism polishing machine that effectively reproduced the polishing motion and force of skilled workers. This replication system, however, had limited use because the acquired polishing techniques could not adapt to various workpiece conditions, such as shape and size. The present study aimed to expand the polishing method for application to curved surfaces, in other words, adapt the replication system to changes in the workpiece shape. In the past polishing methods for curved surfaces, the workpiece shape was acquired by using CAD data or external sensors that often led to an increase in process time and cost. However, the newly proposed method in this study requires neither CAD data nor external sensors, and was able to effectively achieve simultaneous posture and force control on unknown curved surface. The experimental results showed that the skilled polishing techniques were successfully replicated on an unknown curved surface and the surface roughness was greatly improved by integrating the newly proposed method into the skilled polishing replication system. © 2017 Elsevier Inc. All rights reserved.
1. Introduction The repair polishing process for an automotive body is important for satisfying the high surface quality requirements of automotive manufacturing. The polishing process is still manually carried out by workers with the required polishing technique. This is because the skilled worker is capable of adjusting the polishing motion and force according to the workpiece conditions based on their experience. However, the number of skilled workers has been decreasing because of an aging population, and the skill development of younger workers has not been satisfactorily conducted [1]. Therefore, polishing automation technology has been proposed in many research studies so that ultimately it can replace manual polishing and improve polishing efficiency [2–8]. In our previous research, a replication system of the skilled polishing technique was developed using a serial-parallel mechanism polishing machine [7]. This polishing machine was capable of inde-
∗ Corresponding author at: Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku, Yokohama, Kanagawa 223-8522, Japan. E-mail address: [email protected] (Y. Oba).
pendently controlling the polishing motion and force, namely, the displacement on x-y plane (horizontal plane), angular displacements in yawing and pitching modes, and force in z-axis mode [8]. Therefore, the skilled polishing techniques of these three physical parameters were acquired from skilled workers to replicate the skilled polishing process using the polishing machine. By inputting the acquired data into the developed polishing machine as command values, the skilled polishing process could be successfully replicated. However, the constructed replication system was considered to be incomplete because the skilled polishing techniques did not change according to the workpiece conditions such as shape and size. Therefore, a method for detecting changes in workpiece conditions was required to use the proposed skilled polishing replication system for polishing automation. This study focuses on only the workpiece shape. The previously proposed system of skilled polishing replication could be used only on flat surfaces. However, actual automotive bodies are not flat, but curved. In general, both the tool posture and the direction of the polishing force should be controlled normal to the curved surface. Therefore, an automated polishing method is required to adapt the skilled polishing replication system to the curved surface. In past research investigations, the polishing automation for curved
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Nomenclature Fdis Freac Ffric Kt Ia M x
Disturbance force [N] Reaction force [N] Friction force [N] Motor thrust force coefficient [N m/A] Motor current [A] Mass [kg] Position [m] v Velocity [m/s] a Acceleration [m/s2 ] Angle [rad] (Subscript)n Nominal value cmd
Command value (Superscript) ref Reference value (Superscript) res Response value (Superscript) Caret Estimated value
Fig. 1. Serial-parallel mechanism polishing machine. Table 1 Specifications of machine.
surfaces was achieved using CAD data [9–11] or external sensors [12–14]. For example, Z. Jianming et al. [11] proposed a polishing method for aspheric surfaces by acquiring the workpiece shape from CAD data prior to the polishing operation. However, the workpiece shape from the CAD data does not always correspond to the real shape because the workpiece shape from the CAD data does not account for installation error. Therefore, the polishing process using CAD data requires an additional step for position adjustment depending on human skill, and thus the entire process duration increases. S. Kamezaki et al. [12] proposed a polishing method for metal molds with force sensors. In their work, the workpiece shape was estimated based on reaction force information by a 6axis force sensor installed in the polishing tool. Z. Yang et al. [14] used a touch trigger probe for surface measurement to achieve edge polishing. However, applying external sensors generally results in increased production costs and frequent maintenance. To eliminate the abovementioned problems, the simultaneous control method of tool posture and polishing force in the normal direction of curved surfaces, which is independent of CAD data and external sensors, is proposed in this study. The purpose of the present study is to adapt the skilled polishing replication system to curved surfaces with the proposed control method. First, a tool posture control method of an unknown curved surface was proposed. The posture angles in yawing and pitching modes were determined based on force information acquired from the parallel mechanism component with a reaction force observer [15–17]. Second, a normal force control method based on tool posture information was proposed. Using these proposed methods simultaneously, the tool posture and polishing force were controlled in the normal direction of unknown curved surfaces. From the experimental results, the skilled polishing techniques were successfully replicated on the unknown curved surface with the newly proposed method. In addition, the surface quality after polishing fully satisfied the surface quality criteria. 2. Serial-parallel mechanism polishing machine 2.1. Composition of mechanism Fig. 1 shows an overview of the serial-parallel mechanism polishing machine [8]. The parallel mechanism is suitable for polishing automation because it enables high precision and high-speed movements compared to the serial mechanism. However, the parallel mechanism machine is often not used in industrial polishing automation owing to its limited workspace. To address this drawback, a two-degree-of-freedom (DOF) serial mechanism (XY stage)
330 mm × 340 mm × 405 mm 8.10 kg 75.4 mm × 50.4 mm × 44.4 mm 15.90◦ × 18.18◦ 16 mm radius 1.0 m 250 s
Size of machine (X × Y × Z) Weight of machine Movement range (X × Y × Z) Angle range (Yawing × Pitching) Size of buff tool Resolution of linear encoder Control sampling time
that provides a larger workspace is assembled in between the base frame and the three DOF parallel mechanism. The XY stage has three linear motors (one in the X stage and two in the Y stage) and the parallel mechanism has three linear motors positioned at 120◦ intervals. At the lower end of the shaft in the parallel mechanism, the rod is connected to the revolute joint of one-DOF linkage. The other end of the rod is attached to the endplate through a spherical joint. This structure allows the parallel mechanism to move in the z-direction, as well as x-axis rotation (pitching) and y-axis rotation (yawing). Each axis has one optical linear encoder. A wool buff is attached to the lower end of the spindle. The polishing force and the tool posture are independently controlled at the 3-DOF parallel mechanism, and the displacement of the tool on x-y plane is controlled at the XY stage. The specifications of the developed polishing machine are listed in Table 1. 2.2. Position and force control theory The motion of the developed machine is controlled based on disturbance observer (DOB) [18] and [19]. DOB is designed to cancel disturbance forces. The estimated disturbance force is obtained ref from the velocity response vres and the current reference Ia as shown in Eq. (1). ref
Fdis = Freac + Ffric + Mg + Kt Ia − Msvres ref
(1)
= Ktn Ia − Mn svres The velocity response vres is calculated by the differential of the position response xres read by the linear encoder, and the current ref reference Ia is applied to the actuator. Fig. 2 shows a block diagram of the position control based on DOB. A first order low pass filter (LPF) is inserted in order to suppress the noise generated from the differential of the velocity. Also, the estimated disturbance is fed back as a current value to actively cancel a bad influence of the disturbance to the control system. A proportional-derivative (PD) controller is suitable because the disturbance cancellation serves as an integrator. The positioning performance and robustness are determined by the position controller and DOB, respectively.
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·
3
·
where mz ,myaw , and mpitch are accelerations in the z-axis, yawing, ·
·
·
and pitching modes, respectively; z 1 , z 2 , and z 3 are the accelerations of the three links. Fig. 5 shows the block diagram of the motion control system for the parallel mechanism with the quarry matrix at the acceleration dimension. This control system can be divided into two spaces, one is the modal space, and the other is the joint space. At the ref
·
· res
reac
joint space, zi (i = 1∼3), z i (i = 1∼3), and zˆ i (i = 1∼3) denote the acceleration references, the acceleration responses, and the equivalent accelerations of the reaction force, respectively. The subscript shows the actuator number. The acceleration response and the equivalent accelerations of the reaction force are trans-
Fig. 2. Position control system based on DOB.
· res
formed into modal space accelerations mj ·
(j = z, yaw, pitch) and
reac
(j = z, yaw, pitch) through the quarry matrix. The transformed
ˆj m
·
reac
ˆz modes are independent of each other. In this study, m · res mpitch
· res
, myaw ,
and are fed back to independently control the reaction force in the z-axis mode and the tool postures in the yawing and pitching modes, respectively. The mode controllers at the modal space posture force Cmode (s) and Cmode (s) are designed as follows: posture
Cmode (s) =
1 1 Kp + Kv s s2
force
Cmode (s) = Kf
The reaction force observer (RFOB) [15–17] can estimate external forces, e.g. a reaction force, without external sensors that cause an increase in production cost and required maintenance. In the case that the fluctuation of the thrust force coefficient and the mass variation are negligibly small, the reaction force is estimated by subtracting the identified friction force Fˆfric and gravity force Mn g from the disturbance force Fdis . Fig. 3 shows the block diagram of force control based on DOB and RFOB, which can realize the forcesensor-less force control. The identification accuracy of the friction force and gravity force plays an important role in precisely controlling the polishing force. Also, the bandwidth of the estimated reaction force is decided by the cutoff frequency greac . When the polishing process was conducted with the force control system in Fig. 3 in our previous research [8], the monitoring accuracy of the reaction force by RFOB was almost the same as that of force sensor (the estimation error was less than 0.5N) and the effectiveness of RFOB was clarified. 2.3. Parallel mechanism control based on the mode decoupling method The motions of the 3-DOF parallel mechanism component are controlled by using the mode decoupling method based on quarry matrix at an acceleration dimension [20] and [21]. The motions of the parallel mechanism can be transformed into three modal motions with the quarry matrix. Fig. 4 shows the three modal motions. The quarry matrix is represented in Eq. (2). ·
·
Z1
·
( myaw ) = Q3 ( · ) Z2 ·
mpitch
·
Z3
2 1 Q3 = ( 0 6 4
2 2 3
−3 )
−2
−2
(4)
where Kp is the proportional gain, Kv is the differential gain in the posture mode controller, and Kf is the proportional gain in the force mode controller.
Fig. 3. Force control system based on DOB and RFOB.
mz
(3)
(2)
3. Simultaneous posture and force control method on an unknown curved surface 3.1. Tool posture control method on an unknown curved surface To control the tool posture in the normal direction of the surface without CAD data and external sensors, the estimated reaction force by RFOB is used. Fig. 6 shows the relationship between the tool posture and the forces applying to the buff during the polishing process. Fiext (i = x, y) and i (i = x, y) denote the external force in the x-axis or y-axis and the tool posture around the x-axis or y-axis, respectively. In Fig. 6(a), the tool posture is not controlled in the normal direction of the surface, and only a part of the buff is in contact with the surface. Therefore, the external friction force is generated in the opposite direction of the tool rotational direction. On the other hand, in Fig. 6(b), the tool posture is controlled in the normal direction of the surface. In this case, the external force is not generated because the external force couples are cancelled out. To control the tool posture based on this relationship, the tool posture and external force are modeled using a spring-damper model. Transfer function Gi (s) is as follows: Gi (s) =
i 1 = (i = x, y) Ki + Ci s Fiext
(5)
In this study, the external force Fiext (i = x, y) is monitored at the parallel mechanism component. Fig. 7 shows the forces applied to the links of the parallel mechanism component. Fˆjreac (j = 1∼3) denotes the reaction force estimated at the link with RFOB. The subscript shows the link number. In Fig. 7, red and blue lines represent the x-axis and y-axis components of the estimated forces, respectively. By using these estimated x-axis and y-axis forces, the external forces are calculated and represented as the estimated val-
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Fig. 4. Decoupled modes by quarry matrix.
Fig. 5. Motion control system based on mode decoupling method.
Fig. 6. Relationship between tool posture and external force.
ues Fˆxext and Fˆyext . A conversion equation for the calculation of the external forces is shown in Equation (7).
Fˆxext Fˆyext
⎛ ˆ reac ⎞ ⎜
F1
⎟
⎛
= M ⎝ Fˆ2reac ⎠ = ⎝ Fˆ3reac
0 1
6 − sin 6
− cos
6 − sin 6 cos
⎞ ⎛ Fˆ reac ⎞ 1 ⎟ ⎠⎜ ⎝ Fˆ2reac ⎠ (7)
where M is the 2 × 3 conversion matrix. Fig. 8 shows the block diagram of the posture control method on an unknown curved surface. The posture command angles around the x-axis xcmd and y-axis ycmd are decided by controlling the estimated external forces Fˆxext and Fˆyext to zero through the transfer functions Gx (s) and Gy (s), respectively.
Fˆ3reac
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Fig. 10. Forces applied to the surface. Fig. 7. Reaction forces measured at parallel mechanism component.
3.3. Polishing force control method on an unknown curved surface The normal direction of the unknown curved surface is determined by using posture information gained by the proposed posture control method. Based on the tool postures around the xaxis and y-axis, x and y , respectively, a rectangular parallelepiped can be drawn (Fig. 10). In Fig. 10, Fx , Fy , and Fz are the forces applied to the workpiece surface. A diagonal direction of the rectangular parallelepiped corresponds to the normal direction of the surface. Therefore, the normal force Fn is calculated as the sum of the diagonal direction components of Fx , Fy , and Fz in Eq. (8), defined as the normal force model. Fig. 8. Posture control method on unknown curved surface.
Fn =
3.2. Tool tip control method With the tool posture control, the displacement of the XY stage needs to be adjusted for controlling the tool tip position. As shown in Fig. 9(a), the tool tip position cannot be located at the desired position with only the tool posture control. l and z denote the length from the tool tip to the endplate and the error in the z-axis, respectively. Additionally, l sin i (i = x, y) represents the error in the x-axis or y-axis. Fig. 9 shows how to correct the errors in the xaxis, y-axis and z-axis. To correct the errors of the tool tip position in the x-axis and y-axis, lsin y and lsin x are added to the displacement command values of the X stage and Y stage, respectively. In addition, the error in z-axis z can be corrected by the z-axis force control. As a result, the errors of the tool tip position are removed, and the tool tip is accurately controlled, as shown in Fig. 9(b).
Fz + Fx tan y + Fy tan x
1 + tan2 x + tan2 y
(8)
In this study, the force control can be done at the z-axis mode of the parallel mechanism component. Therefore, the force in the z-axis mode is controlled to set the normal force to a desired value. The command value of Fz for the normal force control is calculated by solving Eq. (8), as shown in the following equation. Fzcmd = Fncmd
1 + tan2 xcmd + tan2 ycmd − Fˆxext tan ycmd − Fˆyext tan xcmd
(9)
where icmd (i = x, y) and Fˆiext (i = x, y) denote the tool postures around the x-axis and y-axis and the estimated reaction forces in the x-axis and y-axis, respectively. The command value of the polishing force is applied to the command value Fncmd . By using the proposed normal force model, the polishing force is controlled in the normal direction of the workpiece surface.
Fig. 9. Tool tip control method.
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Fig. 11. Simultaneous tool posture and polishing force control system.
3.4. Simultaneous control method of tool posture and polishing force Fig. 11(a) shows the overall block diagram with the tool posture and polishing force control method on an unknown curved surface. The conversion matrix M is newly applied to the joint space in Fig. 11(b). Through the conversion matrix M, the equivalent accelerations of Fˆiext (i = x, y) can be calculated and represented as ·
Table 2 Parameters of experiment. gdis greac (Kp , Kv )
Kf
ext
ˆ i (i = x, y). In addition, the command space based on the prom posed posture and force control method is newly defined in the motion control system. The acceleration posture command values · cmd myaw
· cmd mpitch
in yawing and pitching modes represented as and are calculated through the transfer functions Gy (s) and Gx (s), respectively, and the acceleration force command value in the z-axis mode is decided by using the normal force model. 4. Polishing experiments 4.1. Experimental setup and procedures Fig. 12 shows the experimental setup. A steel plate with a viscoelastic polymer coating was used as the workpiece. The workpiece was bent by warping the cylindrical surface, although the original shape was flat. A gonio stage that can adjust the angle was attached under the cylindrical surface, and the workpiece was titled 4◦ with respect to the bottom face. To compare the estimated force with the actual one, a dynamometer was mounted
(Kx , Cx )
(Ky , Cy )
Cutoff frequency of DOB [rad/s] Cutoff frequency of RFOB [rad/s] Proportional and differential gains of posture mode controller Proportional gain of force mode controller Spring and damping coefficients in posture control method Spring and damping coefficients in posture control method
200.0 30.0 (25.0, 100.0)
0.7 (0.00001, 15.0)
(0.01, 1.2)
between the surface and the base. The polishing compound was alumina abrasive (abrasive size: 10 m) mixed in white-mineral oil. The spindle speed was set to 5000 min−1 . In this experiment, the tool posture was controlled in the normal direction of the surface by the proposed method. On the other hand, the command values of the displacements in the x-axis and y-axis and polishing force in the normal direction were determined using the acquired data of the skilled worker for the flat surface [7]. Fig. 13 shows the acquired data of the displacements in the x-axis and y-axis and polishing force in normal direction. In Fig. 13, the polishing process started 2.9 s after the measurement acquisition began. Therefore, only data from after 2.9 s were used as the command values. The experimental parameters are shown in Table 2.
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Fig. 12. Experimental setup.
Fig. 13. Data of acquired polishing skill.
Fig. 14. Experimental evaluation of posture control.
4.2. Experimental results Fig. 14 shows the result of the tool posture control. The response angles, which represent the posture angles of the endplate, were calculated based on encoder information at the parallel mechanism component. Also, the real angles were calculated using CAD data without the installation error. From this result, the response angles followed the real angles in both modes, although there were errors between these two angles. These errors can be decreased by lowering the damping coefficients Ci (i = x, y) in the proposed transfer functions for posture control Gi (s) (i = x, y). However, if lowering the damping coefficients, the low mechanical stiffness of the parallel mechanism component causes the tool to vibrate. In this research, the vibration of the tool adversely influences not only the tool posture control but also the polishing force control. Therefore, the coefficients in the proposed transfer functions were selected to achieve both accurate posture and stable force control.
Fig. 15. Experimental evaluation of force control.
As a result, the average error in yawing mode was 0.42◦ and that of the pitching mode was 1.85◦ with minimal vibration. Fig. 15 shows the result of the polishing force control. The force response was the estimated value by RFOB, and the actual force was the measured value by dynamometer. The acquired polishing force in Fig. 13(b) was used as the normal force command value. Therefore, the force command in the z-axis of Fig. 15 was calculated based on the acquired polishing force through Equation (9). The force command value before the process start time was set to 2.0 N to control the tool posture based on the reaction force. From this result, the trend of three forces corresponded, although the monitoring error between the force response and actual force was relatively large. The magnitude of the actual force became large owing to the backlash of the revolute joint part of the parallel mechanism component. However, the force response by RFOB was less subject to the influence of the backlash because the actuators that could estimate the reaction forces were fixed to the base plate in Fig. 1. Consequently, the monitoring error increased especially
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Fig. 16. Surface appearance before and after polishing.
Fig. 17. Analyzed surface after polishing.
Table 3 Surface roughness before and after polishing. Criteria Ra [nm]
Before After
924.6 14.5
941.3 13.3
1015.9 18.2
981.6 18.9
912.3 19.2
30.0
when the posture angle was largely changed. There was a monitoring error resulting from a mechanical problem, but the average error between the force response and actual force was 0.47 N. In addition, both the force response and the actual force could effectively follow the force command. From the evaluation of posture and force control, it was confirmed that tool posture and polishing force were simultaneously controlled in the normal direction of the unknown curved surface by the proposed method, although with errors in both posture and force control. Fig. 16 shows the appearance of the surfaces before and after polishing. The surface before polishing (Fig. 16(a)) was rough, and had a gray color. On the other hand, the color of the surface after polishing (Fig. 16(b)) showed that the workpiece regained its original color black because the polishing process was successfully conducted. To evaluate the surface quality quantitatively, the arithmetic mean roughness Ra of the surface was measured using a 3D optical microscope (New View 6200, Zygo Co., Ltd). The criteria for Ra in the finishing process was defined as 30 nm. The surface roughness measured at five different points before and after polishing is shown in Table 3. In addition, the surfaces after polishing analyzed by the microscope are shown in Fig. 17. The results in Table 3 show all arithmetic mean roughness values after polishing satisfied the criteria, and that those before polishing largely exceeded the criteria. On the other hand, as a result of observing the
analyzed surface in Fig. 17, small scratches partly remained on the surface after polishing. The scratches could not be seen when the tool posture and the polishing force were accurately controlled in our previous research [7]. Therefore, it was possible that the cause of the small scratches were a byproduct of the errors in posture and force control. To remove the scratches, it is essential to solve the mechanical problem of the parallel mechanism component. However, the errors in posture and force control had no influence on the arithmetic mean roughness because both the tool posture and the polishing force could follow their respective target values. In addition, the reproducibility of the results was verified from several tests conducted using the same setup and procedure. 5. Conclusion The simultaneous control method of the tool posture and the polishing force on an unknown curved surface with a serial-parallel mechanism machine was newly proposed to replicate the skilled polishing technique on the unknown curved surface. The proposed theory and the obtained results are as follows: (1) When the tool rotational axis is in the normal direction, the external friction force generated between the tool and the surface is cancelled out. To control the tool posture based on this relationship, the tool posture and the external force estimated based on RFOB were modeled using a spring-damper model. By setting the external force to zero, the tool posture control on the unknown curved surface was achieved without employing CAD data or external sensors. (2) The normal direction of the surface was determined based on the tool posture information gained by the proposed posture
Please cite this article in press as: Oba Y, Kakinuma Y. Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine. Precis Eng (2017), http://dx.doi.org/10.1016/j.precisioneng.2017.01.006
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ARTICLE IN PRESS Y. Oba, Y. Kakinuma / Precision Engineering xxx (2017) xxx–xxx
control method, and the normal force was calculated as the sum of the normal components of the forces in the x-axis, yaxis, and z-axis. In this study, the normal force control on an unknown curved surface was realized by observing these force components with RFOB. (3) An acceleration control system integrating the proposed posture and force control methods was newly proposed. By applying the proposed control system to the developed polishing machine, the tool posture and the polishing force could be simultaneously controlled on an unknown curved surface. (4) The experimental results show that the skilled polishing techniques could successfully be replicated on an unknown curved surface and the surface quality after polishing satisfied the criteria by integrating the proposed posture and force control method into the skilled polishing replication system. In this study, the validity of the newly proposed tool posture and polishing force control method on an unknown curved surface was verified. By increasing the mechanical stiffness or removing the backlash of the revolute joint, the posture and force control accuracy and the surface quality after polishing can be further improved. Acknowledgement This work was partially supported by the Ministry of Education, Science, Sports and Culture, KAKENHI No. 15H03904, 2015. References [1] Unno K. Support and promotion of the skill succession by utilizing expert skilled workers. J Jpn Soc Precis Eng 2015;81(1):30–3. [2] Liao L, Xi F, Liu K. Modeling and control of automated polishing/deburring process using a dual-purpose compliant tool head. Int J Mach Tools Manuf 2008;48:1454–63. [3] Shi Y, Zheng D, Wang L. NC polishing of aspheric surfaces under control of constant pressure using a magnetorheological torque servo. Int J Adv Manuf Technol 2012;58:1061–73.
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Please cite this article in press as: Oba Y, Kakinuma Y. Simultaneous tool posture and polishing force control of unknown curved surface using serial-parallel mechanism polishing machine. Precis Eng (2017), http://dx.doi.org/10.1016/j.precisioneng.2017.01.006