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Off-line modelling and planning of optimal clamping forces for an intelligent fixturing system
International Journal of Machine Tools & Manufacture 39 (1999) 253–271
Off-line modelling and planning of optimal clamping forces for an intelligent fixturing system Y.F. Wang, Y.S. Wong*, J.Y.H. Fuh Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received 11 December 1997
Abstract An intelligent fixturing system (IFS) for machining aims to adaptively adjust the clamping forces to achieve minimum deformation of the workpiece according to the cutter position and the cutting forces. This paper presents the concept, architecture, control scheme, models and methodologies for an IFS. Using off-line simulations and on-line experimental verifications, the performance of the proposed IFS is evaluated and verified. As adaptive clamping forces appropriate to the dynamic machining environment are employed, the IFS offers higher quality of machined parts and greater robustness to disturbances. This system is suitable for application in high-precision machining environment as well as flexible manufacturing systems (FMS). 1998 Elsevier Science Ltd. All rights reserved.
Nomenclature CR Fc Ff Fn G LB N Pj Ri
Critical value of the clamping force Cutting force Friction force Force applied in the normal direction of the contact surface Weight of the workpiece Lower bound of reaction forces Normal vector at workpiece surface where clamping is applied Clamping force at clamp j Reaction force at locator i
* Corresponding author. Tel.: + 65-8742221; Fax: + 65-779-1459; E-mail: [email protected] 0890-6955/98/$—see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 9 8 ) 0 0 0 2 6 - 1
254
T UB m n rc rf rg rpj rri ⑀
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Cutting torque Upper bound of reaction forces Number of locators Number of clamps Position vector of the cutting force Position vector of the friction force Position vector of the weight of the workpiece Position vector of the clamping force at clamp j Position vector of the reaction force at locator i Safety index The coefficient of friction Weight factor
1. Introduction A fixturing system is used to locate and hold a workpiece in machining, assembly, inspection and other manufacturing operations. Its function is to establish the desired position and orientation of the workpiece for the manufacturing operation. The design and functional requirements of a fixturing system are as varied as the parts to be operated on. The focus of this paper is on a fixturing system for machining. The life-cycle of a fixturing system, from concept to the final dismantling of the system as illustrated in Fig. 1, can be divided into two stages: planning stage and execution stage. During the planning stage, the design is conceptualized, the required fixture elements are designed and fabricated or selected, and the fixturing system is configured. In the execution stage, viz., the fixturing process, the fixturing system is to accomplish its function of locating and holding the workpiece in the desired position during the entire machining process. In the past decades, extensive research on various fixturing issues has primarily focused on the fixture planning stage such
Fig. 1.
Two development stages of a fixturing system.
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as automatic generation of suitable fixture elements and fixture layout [1–5] or the development of advanced hardware to increase the flexibility while accommodating a variety of part types [6– 10]. There has been less attention on the development of strategies, models, and formulations specific to the execution stage to enhance or optimize the performance of the installed fixturing system. Improper or inadequate fixturing process could result in elastic/plastic deformation, and static/elastic displacement that can significantly affect the final part accuracy. This paper examines a fixturing approach that aims to improve the quality of the machined part. It proposes and presents the development of an intelligent fixturing system that can intelligently control the clamping system during machining. The ultimate goal is to fully integrate this Intelligent Fixturing System with CNC machines so as to achieve an optimal fixturing and machining process.
2. Intelligent fixturing system (IFS) Typically, once a part is being fixed and held in the fixturing system, the clamping forces applied to the workpiece are not changed during the entire machining and fixturing process. The application of clamping forces has been largely experience-based, using ‘the sense of proportion’ method. Many machinists arbitrarily apply whatever force they could impart (usually larger than necessary, just to be on the safe side) to the clamps. This often results in over-tightening of parts and may cause serious geometric and dimensional problems in practice as in the aircraft and automotive industry, where precision machining is of particular concern. On the other hand, insufficient clamping may permit the part to slip or detach from the locator during the machining process, causing the fixturing system to lose its effectiveness. More flexible and higher performance fixturing systems are required to improve the accuracy of machined components. Fixturing is process-specific. At some positions along the tool path, small forces may be adequate, but large forces may be required at others. The minimum clamping forces to secure a workpiece are different as the cutter moves along its intended tool path. Hence, our attention is focused on the force distribution. We attempt to design an Intelligent Fixturing System (IFS) such that the fixture elements can be manipulated to provide dynamic clamping forces during the entire machining and fixturing process. For the proposed IFS in this paper, the clamping forces are adaptively adjusted to optimal values according to the cutter position and the cutting forces during machining with the objective of minimizing workpiece distortion while ensuring that it is adequately secured. Since adaptive clamping forces appropriate to the dynamic machining environment are provided, the proposed IFS offers higher quality of machined parts and greater robustness to disturbances. The proposed IFS is characterized by on-line monitoring, dynamic clamping forces, and real-time fixturing process control. 2.1. Design ideas An IFS can be open-loop or closed-loop.
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2.1.1. Open-loop IFS In an open-loop IFS, the desired (optimal) clamping forces with respect to the different cutter positions are pre-computed before machining. A control table is then generated that tabulates the cutter positions and the corresponding predetermined optimal clamping forces. During machining, the control unit of the IFS adjusts the clamping system according to the control table. Since the process of deriving the optimal clamping forces is completed in advance, the response of the controller is therefore not so dependent on the computing power of the controller. However, when sudden or unexpected conditions occur, it will not be able to take appropriate correction. 2.1.2. Closed-loop IFS In a closed-loop IFS, the optimal clamping forces with respect to the different cutter positions are calculated in real-time during machining. Forces acting on the workpiece are obtained from sensors in the system and optimal clamping forces are then deduced and applied. Unlike the mechanism of open-loop IFS, the optimal clamping forces provided by the closed-loop IFS are continually adjusted by monitoring and measuring forces on the workpiece. A closed-loop IFS can intelligently update optimal forces to suit the process conditions. To ensure that the controller has a sufficiently short response time, the models and algorithms should be as simple as possible, and yet effective. The design concept of the proposed Intelligent Fixturing System in this paper is towards a closed-loop IFS. The details are discussed in the following sections. 2.2. Design requirements The general design requirements pertinent to ordinary fixtures also apply to the intelligent fixturing system. The functional requirements of a fixture include total restraint, positive location, repeatability and rigidity. Since the IFS still needs to adjust the clamping forces at different cutter positions and the magnitude of the cutting forces vary during machining, sensor feedback, clamping control and programmability are required to realize its functions. 2.2.1. Sensor feedback Sensor feedback is vital to the design of an intelligent system. Sensors allow real-time information to be transferred between the fixturing system and its controller. In the IFS presented in this paper, piezoelectric single-channel quartz sensors are mounted on the locators to monitor and measure the reaction forces during machining. A cylindrical locator assembly with built-in ringtype force sensor (Kistler Slimline Sensor T9134) is shown in Fig. 2. 2.2.2. Clamping control Clamping devices are designed to apply variable clamping forces to the workpiece during the machining process. Through a remote interface circuit, a personal computer (PC) controls the clamping system to apply the required clamping forces as the cutter moves to different locations on the workpiece. The objective is to minimize the deformation of the workpiece caused by the clamping forces.
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Fig. 2.
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Cylindrical locator assembly with built-in piezo-electric force sensor.
2.2.3. Programmability The sensing and clamping operations of the IFS are controlled by a PC through a remote interface circuit using customized programs for the processing of the input/output signals, monitoring and control of the fixturing process. 2.3. Definitions of IFS terms Some special notions used to describe the operating principles of the IFS are defined in this section. 2.3.1. Fixturing stability A stable fixturing system must hold a workpiece firmly in place during machining. Positive reaction forces at the locators ensure that the workpiece maintains contact with all the locators from the beginning of the cut to the end. A negative reaction force at the locator is physically not possible. If one or more of the reaction forces should go to zero, this indicates that the workpiece is no longer in contact with the corresponding locators and the fixturing system is considered unstable. Hence, a fixturing stability criterion is considered here and it states that all the reaction forces at the locators must be positive during the entire machining process. This approach is also used by other researchers [11,12].
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2.3.2. Optimal clamping force The optimal clamping forces are defined here as the minimum clamping forces necessary to keep the workpiece in static equilibrium throughout the entire machining process. 2.3.3. Control-clamp The control-clamp of a locator refers to the clamp that has the greatest influence on the reaction forces at the locator. All the clamps in a given fixturing system are labeled as the control-clamps of a certain locator. If a reaction force at a locator is near or equal to zero during machining, its control-clamps will be adjusted to increase the clamping forces so that the reaction force will not reach the critical state. 2.3.4. Sampled tool-path points Sampled tool-path points are selected along the tool path where the clamping forces will be adjusted. They are selected according to the geometry of the workpiece and the tool path. These sampled tool-path points include locations of the cutter at the critical areas of the workpiece (where workpiece is likely to deform significantly) and where the cutting forces may change suddenly or significantly. The objective of selecting the sampled tool-path points is to discretize the fixturing process for control by a computer. 2.4. Prototype design The key control function of the IFS is the adjustment of the clamps to adaptively apply optimal clamping forces to the workpiece in real-time during machining. As shown in Fig. 3, the IFS can be categorized into four functional units: intelligent processor (IP), actuating unit, control unit, and sensing unit. The intelligent processor is the brain of the IFS, coordinating the actions of other units and providing optimal clamping forces according to the sensor data, predetermined models and algorithms. The control unit directs and ensures that the actuating unit produces the
Fig. 3. Architecture of the Intelligent Fixturing System.
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desired clamping forces according to the commands issued by the intelligent processor. The sensing unit samples the force signals from force sensors in the fixturing system (that measure reaction and clamping forces) during machining and transmits the force data as feedback to the actuating unit for the clamping force control. The intelligent processor also uses the force data, as well as the cutter location and fixture layout information, to issue appropriate commands to the control unit to ensure that optimal clamping forces are applied to the workpiece.
3. Control scheme of the IFS A model-based control scheme is proposed for the IFS as illustrated in Fig. 4. Two models are employed: fixture–workpiece model and stability monitoring model. At the start of the machining process, the reaction forces are measured through the sensors embedded in the locators. According to the fixture–workpiece model, the cutting forces are estimated, and from the estimated cutting forces and the optimization model, the required optimal clamping forces are predicted. The predicted optimal clamping forces are then applied in real-time to the workpiece using the specially designed clamping system. Once unstable phenomena are detected, the stability monitoring model issues a command to the clamping system to increase the appropriate control-clamp until stability is restored. These processes are repeated until the completion of the machining process. In this way, reaction forces at the locators are monitored and serve as feedback information as the clamping forces are varied automatically throughout the entire machining process. The computation times of the fixture–workpiece and optimization models must be fast enough
Fig. 4. Control scheme of the Intelligent Fixturing System.
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for real-time control. As illustrated in Fig. 5, the optimal clamping forces predicted for the sampled tool-path point i could be applied to the sampled tool-path point j if the computation time is such that the IFS loses its effectiveness. 4. Fixture-workpiece model for IFS A fixture–workpiece model aims to relate the interaction between the fixture and the workpiece during the machining operation. Several kinds of fixture–workpiece models have been developed in the past decades [11–16]. Different forms of fixture–workpiece model have been derived in order to make its application more convenient for the subjects under study. The model proposed for the IFS is based on static equilibrium of the workpiece, mathematically expressed in Eqs. (1) and (2), because of its simplicity for on-line application. This model has also been adopted by other researchers with satisfactory results [17–20].
冘 冘 冘 m
n
Ri +
i=1
冘
Ff + Fc + G = 0
Pj +
(1)
j=1
m
冘 n
(rri × Ri) +
i=1
j=1
(rpj × Pj ) +
冘
(rf × Ff) + rc × Fc + rg × G + T = 0
(2)
4.1. Cutting forces The physical phenomena of cutting are so complex with so many elements involved that even for single-point cutting it is not simple to estimate the cutting forces accurately. To date, a number of validated models have been reported in the literature for milling, drilling, and other machining
Fig. 5.
Apply the predicted optimal clamping forces to the wrong position.
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261
processes [21–24]. However, little has been done to apply them to solve practical problems, such as in fixture design or control. The computation time required is usually too long for realtime applications. In the IFS, the instantaneous cutting forces are derived directly from the sensor data based on the fixture–workpiece model during machining. This method simplifies the determination of the cutting forces and avoids complicated calculation. 4.2. Friction It is well known that the frictional force between two objects is indeterminate until slippage occurs. Due to such uncertainty, the analysis of friction in a fixturing system is difficult. Researchers usually assumed Coulomb friction force between the workpiece surfaces and the fixture elements [15,16,18,25]. This is considered to be the simplest and effective way to deal with friction. In our case, the Coulomb friction law is also adopted. In order to enable a fixturing configuration to embrace a large domain of surface conditions of a workpiece and that of fixturing elements, and various surface contact types, two kinds of coefficients, weight factor and safety index ⑀, are added to the formula as given in Eq. (2). Weight factor is used to indicate whether the contact areas between the workpiece and fixture are frictionless or frictional. For the frictionless contact, the value of is equal to zero; otherwise, it is defined as 1. Since the coefficient of friction is quite unpredictable, the safety index ⑀ whose value ranges from 0 to 1 is attached to ensure fixturing stability. Ff ⱕ ⑀Fn ( = 0 or 1; and 0 ⱕ ⑀ ⱕ 1)
(3)
4.2.1. Frictionless contact For some machining fixtures, unlike the problem of robot grasping, frictional forces are not relied on or necessary to hold the workpiece because the cutting forces can be very large and are inherently dynamic [14]. Friction shows no significant influence on the fixturing system. The weight factor is set to 0 while Eq. (3) is applied. 4.2.2. Frictional contact Other machining fixtures, such as vises, chucks or strap clamps, rely mainly upon friction to maintain the fixturing stability. In this case, ‘ = 1’ is chosen. The value of ⑀ depends on the working environment, such as the use of cutting fluid. Since the objective is to obtain the minimum clamping forces, the critical situation of slippage is assumed. Hence, Eq. (1) can be expressed as Eq. (4). Ff = ⑀Fn (and 0 ⱕ ⑀ ⱕ 1)
(4)
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5. Optimization model for IFS The clamping forces should ideally be just sufficient to constrain and locate the workpiece without causing distortion or damage to the workpiece. If the clamping forces are too large, the machined workpiece may warp significantly when released from the fixture. The objective of the optimization model is to determine optimal clamping forces to be applied in the IFS. The premise of this model is that the fixturing configuration is feasible. 5.1. Objective function A fixture–workpiece system is subject to three main forces: clamping forces, reaction forces and cutting forces. The deformation of the workpiece is directly related to these forces acting on it. The cutting forces are dependent on the machine tool, workpiece material, cutter and cutting conditions, and are considered as external forces to be accommodated by the fixturing system. The controllable applied forces are the clamping forces. The objective function is to minimize all the controllable forces in the fixture–workpiece system. This is expressed as the minimization of the sum of the squares of the clamping and reaction forces: Minimize: ΣP2i and ΣR2j
5.2. Constraints A fixturing system has to satisfy several constraints to effectively perform its functions. The geometric constraint requires that the fixture elements can access desired faces or other features for clamping, and that the proposed fixturing arrangement does not interfere with the expected tool path. The kinematic constraint assures that the fixture arrangement can correctly locate and restrain a part. These two constraints are essential considerations in the design of a suitable fixture configuration. They are not used in the optimization model of the IFS as it is assumed that the fixture configuration of the IFS has been designed to these constraints. The set of constraints used in this model are described as follows: 5.2.1. Stability constraint The necessary and sufficient condition to ensure the stability of the workpiece is obtained when the resultant force and moment are zero. In other words, the stability constraint requires force and moment equilibrium, which can be expressed by the force relationships of Eqs. (1) and (2) for the fixture–workpiece system. 5.2.2. Immovability constraint The stability constraint itself can only keep the fixture–workpiece system balance at a point. It does not check whether the workpiece will move or not. Consider the case illustrated in Fig. 6. The fixture–workpiece system is in a balanced state, but the locator 1 is not in contact with the workpiece due to slippage. Once slippage or detachment occurs at a locator, the reaction force on the locator becomes zero. Hence, all of the reaction forces must be positive in order to keep
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Fig. 6. Slippage occurs while balance.
the workpiece in contact with the locators during the entire machining process. The immovability constraints can be expressed as Ri > 0. 5.2.3. Rigidity constraint In the optimization model, an upper limit on the maximum force acting on the clamps and locators is required. This is to ensure that the deformation of the workpiece is within a tolerance. It aims to prevent over clamping of the fixturing system. Because the fixture elements are much more rigid than the workpiece, the upper-bound force is determined by the given tolerance of the workpiece. 5.2.4. Fixturability constraint To fix the workpiece firmly in its designated position, the clamping forces have to be directed towards the workpiece. Thus, the dot product of the clamping force P and the outer normal vector N of the workpiece boundary face on which the clamp acts should be less than zero: i.e. P·N ⬍ 0. Based on the above objective function and constraint analysis, the optimization model aims to:
冘 冘
Minimize:
n
P2j
j=1 m
R2i
i = 1
冘 冘 冘 冘 冘 m
Subject to:
n
Ri +
i=1
冘 m
i=1
Pj +
Ff + Fc + G = 0
j=1
n
(rri × Ri) +
0 ⬍ Ri ⱕ UB
(rpj × Pj ) +
j=1
(rf × Ff) + rc × Fc + rg × G + T = 0
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Pj ⱕ CR P·N ⬍ 0
6. Experiments and simulation To demonstrate the effectiveness of the proposed Intelligent Fixturing System, a relatively more deformable thin-wall box is designed and simulation experiments are carried out. The workpiece is a 220 mm × 130 mm × 60 mm (6 mm in thickness) pre-machined pocketed block made from 7075 aluminum. The final part is a thin-wall box with a wall thickness of 4 mm as shown in Fig. 7. An end milling operation is used to complete the final pocketing with a 20-mm-diameter, HSScoated 4-flute cutter. The following machining parameters are used: Spindle speed Feed rate Feed per tooth Axial depth of cut Radial depth of cut Cutting fluid
500 rpm 100 mm/min 0.05 mm 20 mm 2 mm None
The information on the tool path is illustrated in Fig. 8, where L1, L2, L3, L4, L5, C1, C2, C3 and C4 are the labels for the different sections of the tool path. Using the cutting force model for end milling described in Ref. [22], the maximum magnitude of the cutting force is F = [Fa Fb Fc] = [297 537 73] (N) corresponding to the aforementioned machining parameters. As shown in Fig. 9, the component force Fa coincides with the feed direc-
Fig. 7. The designed thin-wall box.
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Fig. 8.
265
Cutting path for pocketing.
Fig. 9. Label for the components of cutting force.
tion, Fb is perpendicular to the tool path and is directed toward the workpiece, and Fc is along the axis of the cutter and is directed downward to the workpiece. The fixture configuration is similar to that used in the actual production of similar parts by milling. As shown in Fig. 10, a 3–2–1 locating principle is adopted, where the cones stand for the locators and cylinders for the clamps. The coordinates of the locating points are listed in Table 1. These coordinates are defined relative to the coordinate system illustrated in Fig. 10. In the simulation, sampled tool-path points are selected at intervals of 2 mm along the tool path. Tolerance is assumed to be 0.1 mm. By performing the FEA Module, the upper bound for
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Fig. 10. Fixture configuration for the workpiece.
clamps is conservatively set to be 1800 N and 2700 N for locators. The lower bound for the clamps is defined as 10 N. The frictional factor is assumed to be 0.3. In actual machining, the optimal clamping forces of the IFS will be calculated on-line with regard to the cutter position and the cutting forces derived from the reaction forces measured in real-time. In the simulation, only constant cutting forces are simulated and these are derived from the cutting force model presented in Ref. [22]. 6.1. Optimal clamping forces Using the optimization model, the optimal clamping forces for all the sampled tool-path points are obtained and shown in Fig. 11. Labels L1, L2, L3, L4, L5, C1, C2, C3 and C4 are used to indicate the different sections of the tool path as indicated in Fig. 8. The corresponding reaction forces (all greater than zero) obtained under the control of the IFS are given in Fig. 12 which shows that the workpiece will not slip or detach from the six locators and hence accuracy is ensured. 6.2. Comparison with constant clamping scheme For comparison, the workpiece machined under a fixed clamping scheme is simulated, i.e., the clamping forces are kept constant during the entire machining process. One set of the optimal clamping forces (P1 = 10 N, P2 = 100 N and P3 = 820 N) predicted through the optimization Table 1 Coordinates of the locating and clamping points R1 X (mm) Y (mm) Z (mm)
65 115 0
R2 10 15 0
R3 210 15 0
R4 60 0 50
R5
R6
160 0 50
220 65 50
P1 0 65 50
P2
P3
60 130 50
160 130 50
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Fig. 11. Predicted optimal clamping forces.
Fig. 12. The reaction forces obtained under the control of IFS.
model is selected as the fixed clamping forces. The reaction forces for this condition are shown in Fig. 13. It can be seen that the calculated reaction forces R4 and R6 at some machining instances (or cutter locations) are less than zero to maintain the workpiece in equilibrium condition. Since the reaction forces cannot be zero in actual situations, this indicates that the fixturing system is not stable under this set of constant clamping forces. The clamping forces are then increased until all the reaction forces become positive. Only when P1 > 600 N, P2 > 850 N, and P3 > 850 N, all of the reaction forces are positive during the entire machining process as given in Fig. 14 and the fixturing system is stable under the fixed clamping
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Fig. 13. Reaction forces under the fixed clamping forces: unstable fixturing.
Fig. 14. Reaction forces under the fixed clamping scheme: stable fixturing.
scheme. It can be concluded that the clamping forces can be very small by applying varied clamping forces during machining. It also proves the feasibility of the IFS. The measured reaction forces are shown in Fig. 15. With P1 = 600 N, P2 = 850 N, and P3 = 850 N, the designed workpiece was pocketed in a Makino vertical machining center FNC 74-A (Fig. 16). The theoretical calculations and the experiment results match well in terms of the overall trend.
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Fig. 15. The reaction forces measured during machining.
Fig. 16.
The pocketing process on the thin-wall box.
6.3. Deformation analysis Deformation information of the workpiece is analyzed using FE analysis. The workpiece is treated as an isotropic deformable body with an elastic modulus E = 69 GPa and Poisson’s ratio = 0.3. The fixture elements are assumed to be rigid. The workpiece is modeled and meshed using an eight-node HEX8 as shown in Fig. 16. Linear static finite element analysis is used to find the workpiece deformation. The residual stress and work-hardening of the thin-wall metal are not considered. The workpiece deformations under the fixed and the adaptive clamping
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schemes are analyzed using ABAQUS. Fig. 17 shows the corresponding dimensional errors in X-axis direction along the tool path L3 (shown in Fig. 8). The dimensional error for the fixed clamping scheme is 40 m while that for the intelligent clamping scheme is 32 m. The accuracy of the part is improved by 20% when adaptive clamping is used.
7. Conclusions Relevant methodologies and techniques developed for a proposed intelligent fixturing system (IFS) have been presented. The main feature of the IFS is its ability to manipulate fixture elements by software means to arrive at optimal fixturing during machining. The accuracy of the machined workpiece is improved due to adaptive control of the clamping forces and the robustness of the system to disturbances is also greater. Currently, variable clamping force control is not implemented in the IFS. It is envisaged that future implementation will not only incorporate variable and adaptive clamping force control, but also re-positioning of the clamping elements such that workpiece distortion can be greatly reduced. The IFS can be used in an advanced machining environment such as in flexible manufacturing systems (FMS). This system can be beneficial to many industrial users, in particular to the precision engineering industry. In machining precision components, scrap parts due to improper fixturing during machining can be minimized, thereby resulting in substantial saving of production costs.
Acknowledgements The National University of Singapore (NUS) under the Academic Research Project RP950634 funds this project. Prof. A.Y.C. Nee, Dr. M.A. Mannan, Dr. A.S. Kumar and Mr. Z.J. Tao in this fixturing research group have provided invaluable suggestions and comments to this work.
Fig. 17. FEM model.
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References [1] P.M. Ferreira, B. Kochar, C.R. Liu, V. Chandru, AIFIX: An expert system approach to fixture design, ASME Computer Aided/Intelligent Process Planning 19 (1986) 73–82. [2] A.Y.C. Nee, N. Bhattacharyya, A.N. Poo, Applying AI in jigs and fixtures design, Robotics and ComputerIntegrated Manufacturing 3 (2) (1987) 195–201. [3] D.T. Pham, A.D.S. Lazaro, Autofix: An expert CAD system for jigs and fixtures, International Journal of Machine Tools and Manufacturing 30 (3) (1990) 403–411. [4] A. Senthil kumar, A knowledge-based generative modular fixture design methodology for prismatic workpieces, Ph.D. Thesis, National University of Singapore, 1992. [5] Y.C. Chou, Geometric reasoning for layout design of machining fixtures, International Journal of Computer Integrated Manufacturing 7 (3) (1994) 175–185. [6] M.R. Cutkosky, E. Kurokawa, P.K. Wright, Programmable conformable clamping, AUTOFACT 4 Conference Proceedings, SME, vol. 11, 1982, pp. 51–58. [7] M.V. Gandhi, B.S. Thompson, Phase-change fixturing for flexible manufacturing systems, Journal of Manfacturing Systems 4 (1) (1985) 29–39. [8] F.B. Hazen, P.K. Wright, Autonomous fixture loading by a machine tool, Proceedings of Manufacturing International’88, ASME, vol. 3, 1988, pp. 105–111. [9] K.C. Chan, A reconfigurable fixturing system for robotic assembly, Journal of Manufacturing Systems 9 (3) (1990) 206–221. [10] K.C. Chan, C.S. Lin, Development of a computer numerical control modular fixture-machine design of a standard multifinger module, International Journal of Advanced Manufacturing Technology 11 (1996) 18–26. [11] R.O. Mittal, P.H. Cohen, B.J. Gilmore, Dynamic modeling of the fixture–workpiece system, Robotics and Computer-Integrated Manufacturing 8 (4) (1991) 201–217. [12] J.Y.H. Fuh, A.Y.C. Nee, Verification and optimization of workholding schemes for fixture design, Journal of Design and Manufacturing 4 (1994) 307–318. [13] G.S.A. Shawki, M.M. Abdel-Aal, Effect of fixture rigidity and wear on dimensional accuracy, International Journal of Machine Tool Design and Research 5 (1965) 183–202. [14] Y.C. Chou, V. Chandru, M.M. Barash, A mathematical approach to automatic configuration for machining fixtures: analysis and synthesis, Journal of Engineering for Industry, Transaction of the ASME 103 (1981) 725–735. [15] E.C. DeMeter, Min–max load model for optimizing machining fixture performance, Journal of Engineering for Industry, Transaction of the ASME 117 (1995) 186–193. [16] N.H. Wu, K.C. Chan, S.S. Leong, Fixturing verification based on the analysis of multi-discipline frictional contacts, Manufacturing Science and Engineering, ASME MH3–1 (1995) 735–745. [17] M.V. Gandhi, B.S. Thompson, Automated design of modular fixtures for flexible manufacturing systems, Journal of Manufacturing Systems 5 (4) (1986) 243–252. [18] A.J.C. Trappey, C.R. Liu, An automatic workholding verification system, Robotics and Computer-Integrated Manufacturing 9 (4/5) (1992) 321–326. [19] D.A. King, A. Lazaro, Process and tolerance considerations in the automated design of fixtures, Journal of Mechanical Design, Transaction of the ASME 116 (1994) 480–486. [20] Y. Rong, S.H. Wu, T. Chu, Automated verification of clamping stability in computer-aided fixture design, Computers in Engineering, ASME 1 (1994) 421–426. [21] W.A. Kline, R.E. DeVor, R. Lindberg, The prediction of cutting forces in end milling with application to cornering cuts, International Journal of Machine Tool Design and Research 22 (1) (1982) 7–22. [22] Y. Altintas, A. Spence, End milling force algorithms for CAD systems, Annals of the CIRP 40 (1991) 31–34. [23] E.J.A. Armarego, N.P. Deshpande, Force prediction models and CAD/CAM software for helical tooth milling processes, International Journal of Production Research 32 (7) (1994) 1715–1783. [24] A.E. Bayoumi, G. Yucesan, L.A. Kendall, An analytic mechanistic cutting force model for milling operations: a theory and methodology, Journal of Engineering for Industry, Transaction of the ASME 116 (1995) 324–339. [25] S.H. Lee, M.R. Cutkosky, Fixture planning with friction, Journal of Engineering for Industry, Transaction of the ASME 113 (1991) 320–327.
Off-line modelling and planning of optimal clamping forces for an intelligent fixturing system Y.F. Wang, Y.S. Wong*, J.Y.H. Fuh Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received 11 December 1997
Abstract An intelligent fixturing system (IFS) for machining aims to adaptively adjust the clamping forces to achieve minimum deformation of the workpiece according to the cutter position and the cutting forces. This paper presents the concept, architecture, control scheme, models and methodologies for an IFS. Using off-line simulations and on-line experimental verifications, the performance of the proposed IFS is evaluated and verified. As adaptive clamping forces appropriate to the dynamic machining environment are employed, the IFS offers higher quality of machined parts and greater robustness to disturbances. This system is suitable for application in high-precision machining environment as well as flexible manufacturing systems (FMS). 1998 Elsevier Science Ltd. All rights reserved.
Nomenclature CR Fc Ff Fn G LB N Pj Ri
Critical value of the clamping force Cutting force Friction force Force applied in the normal direction of the contact surface Weight of the workpiece Lower bound of reaction forces Normal vector at workpiece surface where clamping is applied Clamping force at clamp j Reaction force at locator i
* Corresponding author. Tel.: + 65-8742221; Fax: + 65-779-1459; E-mail: [email protected] 0890-6955/98/$—see front matter 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 9 8 ) 0 0 0 2 6 - 1
254
T UB m n rc rf rg rpj rri ⑀
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Cutting torque Upper bound of reaction forces Number of locators Number of clamps Position vector of the cutting force Position vector of the friction force Position vector of the weight of the workpiece Position vector of the clamping force at clamp j Position vector of the reaction force at locator i Safety index The coefficient of friction Weight factor
1. Introduction A fixturing system is used to locate and hold a workpiece in machining, assembly, inspection and other manufacturing operations. Its function is to establish the desired position and orientation of the workpiece for the manufacturing operation. The design and functional requirements of a fixturing system are as varied as the parts to be operated on. The focus of this paper is on a fixturing system for machining. The life-cycle of a fixturing system, from concept to the final dismantling of the system as illustrated in Fig. 1, can be divided into two stages: planning stage and execution stage. During the planning stage, the design is conceptualized, the required fixture elements are designed and fabricated or selected, and the fixturing system is configured. In the execution stage, viz., the fixturing process, the fixturing system is to accomplish its function of locating and holding the workpiece in the desired position during the entire machining process. In the past decades, extensive research on various fixturing issues has primarily focused on the fixture planning stage such
Fig. 1.
Two development stages of a fixturing system.
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as automatic generation of suitable fixture elements and fixture layout [1–5] or the development of advanced hardware to increase the flexibility while accommodating a variety of part types [6– 10]. There has been less attention on the development of strategies, models, and formulations specific to the execution stage to enhance or optimize the performance of the installed fixturing system. Improper or inadequate fixturing process could result in elastic/plastic deformation, and static/elastic displacement that can significantly affect the final part accuracy. This paper examines a fixturing approach that aims to improve the quality of the machined part. It proposes and presents the development of an intelligent fixturing system that can intelligently control the clamping system during machining. The ultimate goal is to fully integrate this Intelligent Fixturing System with CNC machines so as to achieve an optimal fixturing and machining process.
2. Intelligent fixturing system (IFS) Typically, once a part is being fixed and held in the fixturing system, the clamping forces applied to the workpiece are not changed during the entire machining and fixturing process. The application of clamping forces has been largely experience-based, using ‘the sense of proportion’ method. Many machinists arbitrarily apply whatever force they could impart (usually larger than necessary, just to be on the safe side) to the clamps. This often results in over-tightening of parts and may cause serious geometric and dimensional problems in practice as in the aircraft and automotive industry, where precision machining is of particular concern. On the other hand, insufficient clamping may permit the part to slip or detach from the locator during the machining process, causing the fixturing system to lose its effectiveness. More flexible and higher performance fixturing systems are required to improve the accuracy of machined components. Fixturing is process-specific. At some positions along the tool path, small forces may be adequate, but large forces may be required at others. The minimum clamping forces to secure a workpiece are different as the cutter moves along its intended tool path. Hence, our attention is focused on the force distribution. We attempt to design an Intelligent Fixturing System (IFS) such that the fixture elements can be manipulated to provide dynamic clamping forces during the entire machining and fixturing process. For the proposed IFS in this paper, the clamping forces are adaptively adjusted to optimal values according to the cutter position and the cutting forces during machining with the objective of minimizing workpiece distortion while ensuring that it is adequately secured. Since adaptive clamping forces appropriate to the dynamic machining environment are provided, the proposed IFS offers higher quality of machined parts and greater robustness to disturbances. The proposed IFS is characterized by on-line monitoring, dynamic clamping forces, and real-time fixturing process control. 2.1. Design ideas An IFS can be open-loop or closed-loop.
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2.1.1. Open-loop IFS In an open-loop IFS, the desired (optimal) clamping forces with respect to the different cutter positions are pre-computed before machining. A control table is then generated that tabulates the cutter positions and the corresponding predetermined optimal clamping forces. During machining, the control unit of the IFS adjusts the clamping system according to the control table. Since the process of deriving the optimal clamping forces is completed in advance, the response of the controller is therefore not so dependent on the computing power of the controller. However, when sudden or unexpected conditions occur, it will not be able to take appropriate correction. 2.1.2. Closed-loop IFS In a closed-loop IFS, the optimal clamping forces with respect to the different cutter positions are calculated in real-time during machining. Forces acting on the workpiece are obtained from sensors in the system and optimal clamping forces are then deduced and applied. Unlike the mechanism of open-loop IFS, the optimal clamping forces provided by the closed-loop IFS are continually adjusted by monitoring and measuring forces on the workpiece. A closed-loop IFS can intelligently update optimal forces to suit the process conditions. To ensure that the controller has a sufficiently short response time, the models and algorithms should be as simple as possible, and yet effective. The design concept of the proposed Intelligent Fixturing System in this paper is towards a closed-loop IFS. The details are discussed in the following sections. 2.2. Design requirements The general design requirements pertinent to ordinary fixtures also apply to the intelligent fixturing system. The functional requirements of a fixture include total restraint, positive location, repeatability and rigidity. Since the IFS still needs to adjust the clamping forces at different cutter positions and the magnitude of the cutting forces vary during machining, sensor feedback, clamping control and programmability are required to realize its functions. 2.2.1. Sensor feedback Sensor feedback is vital to the design of an intelligent system. Sensors allow real-time information to be transferred between the fixturing system and its controller. In the IFS presented in this paper, piezoelectric single-channel quartz sensors are mounted on the locators to monitor and measure the reaction forces during machining. A cylindrical locator assembly with built-in ringtype force sensor (Kistler Slimline Sensor T9134) is shown in Fig. 2. 2.2.2. Clamping control Clamping devices are designed to apply variable clamping forces to the workpiece during the machining process. Through a remote interface circuit, a personal computer (PC) controls the clamping system to apply the required clamping forces as the cutter moves to different locations on the workpiece. The objective is to minimize the deformation of the workpiece caused by the clamping forces.
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Fig. 2.
257
Cylindrical locator assembly with built-in piezo-electric force sensor.
2.2.3. Programmability The sensing and clamping operations of the IFS are controlled by a PC through a remote interface circuit using customized programs for the processing of the input/output signals, monitoring and control of the fixturing process. 2.3. Definitions of IFS terms Some special notions used to describe the operating principles of the IFS are defined in this section. 2.3.1. Fixturing stability A stable fixturing system must hold a workpiece firmly in place during machining. Positive reaction forces at the locators ensure that the workpiece maintains contact with all the locators from the beginning of the cut to the end. A negative reaction force at the locator is physically not possible. If one or more of the reaction forces should go to zero, this indicates that the workpiece is no longer in contact with the corresponding locators and the fixturing system is considered unstable. Hence, a fixturing stability criterion is considered here and it states that all the reaction forces at the locators must be positive during the entire machining process. This approach is also used by other researchers [11,12].
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2.3.2. Optimal clamping force The optimal clamping forces are defined here as the minimum clamping forces necessary to keep the workpiece in static equilibrium throughout the entire machining process. 2.3.3. Control-clamp The control-clamp of a locator refers to the clamp that has the greatest influence on the reaction forces at the locator. All the clamps in a given fixturing system are labeled as the control-clamps of a certain locator. If a reaction force at a locator is near or equal to zero during machining, its control-clamps will be adjusted to increase the clamping forces so that the reaction force will not reach the critical state. 2.3.4. Sampled tool-path points Sampled tool-path points are selected along the tool path where the clamping forces will be adjusted. They are selected according to the geometry of the workpiece and the tool path. These sampled tool-path points include locations of the cutter at the critical areas of the workpiece (where workpiece is likely to deform significantly) and where the cutting forces may change suddenly or significantly. The objective of selecting the sampled tool-path points is to discretize the fixturing process for control by a computer. 2.4. Prototype design The key control function of the IFS is the adjustment of the clamps to adaptively apply optimal clamping forces to the workpiece in real-time during machining. As shown in Fig. 3, the IFS can be categorized into four functional units: intelligent processor (IP), actuating unit, control unit, and sensing unit. The intelligent processor is the brain of the IFS, coordinating the actions of other units and providing optimal clamping forces according to the sensor data, predetermined models and algorithms. The control unit directs and ensures that the actuating unit produces the
Fig. 3. Architecture of the Intelligent Fixturing System.
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desired clamping forces according to the commands issued by the intelligent processor. The sensing unit samples the force signals from force sensors in the fixturing system (that measure reaction and clamping forces) during machining and transmits the force data as feedback to the actuating unit for the clamping force control. The intelligent processor also uses the force data, as well as the cutter location and fixture layout information, to issue appropriate commands to the control unit to ensure that optimal clamping forces are applied to the workpiece.
3. Control scheme of the IFS A model-based control scheme is proposed for the IFS as illustrated in Fig. 4. Two models are employed: fixture–workpiece model and stability monitoring model. At the start of the machining process, the reaction forces are measured through the sensors embedded in the locators. According to the fixture–workpiece model, the cutting forces are estimated, and from the estimated cutting forces and the optimization model, the required optimal clamping forces are predicted. The predicted optimal clamping forces are then applied in real-time to the workpiece using the specially designed clamping system. Once unstable phenomena are detected, the stability monitoring model issues a command to the clamping system to increase the appropriate control-clamp until stability is restored. These processes are repeated until the completion of the machining process. In this way, reaction forces at the locators are monitored and serve as feedback information as the clamping forces are varied automatically throughout the entire machining process. The computation times of the fixture–workpiece and optimization models must be fast enough
Fig. 4. Control scheme of the Intelligent Fixturing System.
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for real-time control. As illustrated in Fig. 5, the optimal clamping forces predicted for the sampled tool-path point i could be applied to the sampled tool-path point j if the computation time is such that the IFS loses its effectiveness. 4. Fixture-workpiece model for IFS A fixture–workpiece model aims to relate the interaction between the fixture and the workpiece during the machining operation. Several kinds of fixture–workpiece models have been developed in the past decades [11–16]. Different forms of fixture–workpiece model have been derived in order to make its application more convenient for the subjects under study. The model proposed for the IFS is based on static equilibrium of the workpiece, mathematically expressed in Eqs. (1) and (2), because of its simplicity for on-line application. This model has also been adopted by other researchers with satisfactory results [17–20].
冘 冘 冘 m
n
Ri +
i=1
冘
Ff + Fc + G = 0
Pj +
(1)
j=1
m
冘 n
(rri × Ri) +
i=1
j=1
(rpj × Pj ) +
冘
(rf × Ff) + rc × Fc + rg × G + T = 0
(2)
4.1. Cutting forces The physical phenomena of cutting are so complex with so many elements involved that even for single-point cutting it is not simple to estimate the cutting forces accurately. To date, a number of validated models have been reported in the literature for milling, drilling, and other machining
Fig. 5.
Apply the predicted optimal clamping forces to the wrong position.
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261
processes [21–24]. However, little has been done to apply them to solve practical problems, such as in fixture design or control. The computation time required is usually too long for realtime applications. In the IFS, the instantaneous cutting forces are derived directly from the sensor data based on the fixture–workpiece model during machining. This method simplifies the determination of the cutting forces and avoids complicated calculation. 4.2. Friction It is well known that the frictional force between two objects is indeterminate until slippage occurs. Due to such uncertainty, the analysis of friction in a fixturing system is difficult. Researchers usually assumed Coulomb friction force between the workpiece surfaces and the fixture elements [15,16,18,25]. This is considered to be the simplest and effective way to deal with friction. In our case, the Coulomb friction law is also adopted. In order to enable a fixturing configuration to embrace a large domain of surface conditions of a workpiece and that of fixturing elements, and various surface contact types, two kinds of coefficients, weight factor and safety index ⑀, are added to the formula as given in Eq. (2). Weight factor is used to indicate whether the contact areas between the workpiece and fixture are frictionless or frictional. For the frictionless contact, the value of is equal to zero; otherwise, it is defined as 1. Since the coefficient of friction is quite unpredictable, the safety index ⑀ whose value ranges from 0 to 1 is attached to ensure fixturing stability. Ff ⱕ ⑀Fn ( = 0 or 1; and 0 ⱕ ⑀ ⱕ 1)
(3)
4.2.1. Frictionless contact For some machining fixtures, unlike the problem of robot grasping, frictional forces are not relied on or necessary to hold the workpiece because the cutting forces can be very large and are inherently dynamic [14]. Friction shows no significant influence on the fixturing system. The weight factor is set to 0 while Eq. (3) is applied. 4.2.2. Frictional contact Other machining fixtures, such as vises, chucks or strap clamps, rely mainly upon friction to maintain the fixturing stability. In this case, ‘ = 1’ is chosen. The value of ⑀ depends on the working environment, such as the use of cutting fluid. Since the objective is to obtain the minimum clamping forces, the critical situation of slippage is assumed. Hence, Eq. (1) can be expressed as Eq. (4). Ff = ⑀Fn (and 0 ⱕ ⑀ ⱕ 1)
(4)
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5. Optimization model for IFS The clamping forces should ideally be just sufficient to constrain and locate the workpiece without causing distortion or damage to the workpiece. If the clamping forces are too large, the machined workpiece may warp significantly when released from the fixture. The objective of the optimization model is to determine optimal clamping forces to be applied in the IFS. The premise of this model is that the fixturing configuration is feasible. 5.1. Objective function A fixture–workpiece system is subject to three main forces: clamping forces, reaction forces and cutting forces. The deformation of the workpiece is directly related to these forces acting on it. The cutting forces are dependent on the machine tool, workpiece material, cutter and cutting conditions, and are considered as external forces to be accommodated by the fixturing system. The controllable applied forces are the clamping forces. The objective function is to minimize all the controllable forces in the fixture–workpiece system. This is expressed as the minimization of the sum of the squares of the clamping and reaction forces: Minimize: ΣP2i and ΣR2j
5.2. Constraints A fixturing system has to satisfy several constraints to effectively perform its functions. The geometric constraint requires that the fixture elements can access desired faces or other features for clamping, and that the proposed fixturing arrangement does not interfere with the expected tool path. The kinematic constraint assures that the fixture arrangement can correctly locate and restrain a part. These two constraints are essential considerations in the design of a suitable fixture configuration. They are not used in the optimization model of the IFS as it is assumed that the fixture configuration of the IFS has been designed to these constraints. The set of constraints used in this model are described as follows: 5.2.1. Stability constraint The necessary and sufficient condition to ensure the stability of the workpiece is obtained when the resultant force and moment are zero. In other words, the stability constraint requires force and moment equilibrium, which can be expressed by the force relationships of Eqs. (1) and (2) for the fixture–workpiece system. 5.2.2. Immovability constraint The stability constraint itself can only keep the fixture–workpiece system balance at a point. It does not check whether the workpiece will move or not. Consider the case illustrated in Fig. 6. The fixture–workpiece system is in a balanced state, but the locator 1 is not in contact with the workpiece due to slippage. Once slippage or detachment occurs at a locator, the reaction force on the locator becomes zero. Hence, all of the reaction forces must be positive in order to keep
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Fig. 6. Slippage occurs while balance.
the workpiece in contact with the locators during the entire machining process. The immovability constraints can be expressed as Ri > 0. 5.2.3. Rigidity constraint In the optimization model, an upper limit on the maximum force acting on the clamps and locators is required. This is to ensure that the deformation of the workpiece is within a tolerance. It aims to prevent over clamping of the fixturing system. Because the fixture elements are much more rigid than the workpiece, the upper-bound force is determined by the given tolerance of the workpiece. 5.2.4. Fixturability constraint To fix the workpiece firmly in its designated position, the clamping forces have to be directed towards the workpiece. Thus, the dot product of the clamping force P and the outer normal vector N of the workpiece boundary face on which the clamp acts should be less than zero: i.e. P·N ⬍ 0. Based on the above objective function and constraint analysis, the optimization model aims to:
冘 冘
Minimize:
n
P2j
j=1 m
R2i
i = 1
冘 冘 冘 冘 冘 m
Subject to:
n
Ri +
i=1
冘 m
i=1
Pj +
Ff + Fc + G = 0
j=1
n
(rri × Ri) +
0 ⬍ Ri ⱕ UB
(rpj × Pj ) +
j=1
(rf × Ff) + rc × Fc + rg × G + T = 0
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Pj ⱕ CR P·N ⬍ 0
6. Experiments and simulation To demonstrate the effectiveness of the proposed Intelligent Fixturing System, a relatively more deformable thin-wall box is designed and simulation experiments are carried out. The workpiece is a 220 mm × 130 mm × 60 mm (6 mm in thickness) pre-machined pocketed block made from 7075 aluminum. The final part is a thin-wall box with a wall thickness of 4 mm as shown in Fig. 7. An end milling operation is used to complete the final pocketing with a 20-mm-diameter, HSScoated 4-flute cutter. The following machining parameters are used: Spindle speed Feed rate Feed per tooth Axial depth of cut Radial depth of cut Cutting fluid
500 rpm 100 mm/min 0.05 mm 20 mm 2 mm None
The information on the tool path is illustrated in Fig. 8, where L1, L2, L3, L4, L5, C1, C2, C3 and C4 are the labels for the different sections of the tool path. Using the cutting force model for end milling described in Ref. [22], the maximum magnitude of the cutting force is F = [Fa Fb Fc] = [297 537 73] (N) corresponding to the aforementioned machining parameters. As shown in Fig. 9, the component force Fa coincides with the feed direc-
Fig. 7. The designed thin-wall box.
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Fig. 8.
265
Cutting path for pocketing.
Fig. 9. Label for the components of cutting force.
tion, Fb is perpendicular to the tool path and is directed toward the workpiece, and Fc is along the axis of the cutter and is directed downward to the workpiece. The fixture configuration is similar to that used in the actual production of similar parts by milling. As shown in Fig. 10, a 3–2–1 locating principle is adopted, where the cones stand for the locators and cylinders for the clamps. The coordinates of the locating points are listed in Table 1. These coordinates are defined relative to the coordinate system illustrated in Fig. 10. In the simulation, sampled tool-path points are selected at intervals of 2 mm along the tool path. Tolerance is assumed to be 0.1 mm. By performing the FEA Module, the upper bound for
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Fig. 10. Fixture configuration for the workpiece.
clamps is conservatively set to be 1800 N and 2700 N for locators. The lower bound for the clamps is defined as 10 N. The frictional factor is assumed to be 0.3. In actual machining, the optimal clamping forces of the IFS will be calculated on-line with regard to the cutter position and the cutting forces derived from the reaction forces measured in real-time. In the simulation, only constant cutting forces are simulated and these are derived from the cutting force model presented in Ref. [22]. 6.1. Optimal clamping forces Using the optimization model, the optimal clamping forces for all the sampled tool-path points are obtained and shown in Fig. 11. Labels L1, L2, L3, L4, L5, C1, C2, C3 and C4 are used to indicate the different sections of the tool path as indicated in Fig. 8. The corresponding reaction forces (all greater than zero) obtained under the control of the IFS are given in Fig. 12 which shows that the workpiece will not slip or detach from the six locators and hence accuracy is ensured. 6.2. Comparison with constant clamping scheme For comparison, the workpiece machined under a fixed clamping scheme is simulated, i.e., the clamping forces are kept constant during the entire machining process. One set of the optimal clamping forces (P1 = 10 N, P2 = 100 N and P3 = 820 N) predicted through the optimization Table 1 Coordinates of the locating and clamping points R1 X (mm) Y (mm) Z (mm)
65 115 0
R2 10 15 0
R3 210 15 0
R4 60 0 50
R5
R6
160 0 50
220 65 50
P1 0 65 50
P2
P3
60 130 50
160 130 50
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267
Fig. 11. Predicted optimal clamping forces.
Fig. 12. The reaction forces obtained under the control of IFS.
model is selected as the fixed clamping forces. The reaction forces for this condition are shown in Fig. 13. It can be seen that the calculated reaction forces R4 and R6 at some machining instances (or cutter locations) are less than zero to maintain the workpiece in equilibrium condition. Since the reaction forces cannot be zero in actual situations, this indicates that the fixturing system is not stable under this set of constant clamping forces. The clamping forces are then increased until all the reaction forces become positive. Only when P1 > 600 N, P2 > 850 N, and P3 > 850 N, all of the reaction forces are positive during the entire machining process as given in Fig. 14 and the fixturing system is stable under the fixed clamping
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Fig. 13. Reaction forces under the fixed clamping forces: unstable fixturing.
Fig. 14. Reaction forces under the fixed clamping scheme: stable fixturing.
scheme. It can be concluded that the clamping forces can be very small by applying varied clamping forces during machining. It also proves the feasibility of the IFS. The measured reaction forces are shown in Fig. 15. With P1 = 600 N, P2 = 850 N, and P3 = 850 N, the designed workpiece was pocketed in a Makino vertical machining center FNC 74-A (Fig. 16). The theoretical calculations and the experiment results match well in terms of the overall trend.
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Fig. 15. The reaction forces measured during machining.
Fig. 16.
The pocketing process on the thin-wall box.
6.3. Deformation analysis Deformation information of the workpiece is analyzed using FE analysis. The workpiece is treated as an isotropic deformable body with an elastic modulus E = 69 GPa and Poisson’s ratio = 0.3. The fixture elements are assumed to be rigid. The workpiece is modeled and meshed using an eight-node HEX8 as shown in Fig. 16. Linear static finite element analysis is used to find the workpiece deformation. The residual stress and work-hardening of the thin-wall metal are not considered. The workpiece deformations under the fixed and the adaptive clamping
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schemes are analyzed using ABAQUS. Fig. 17 shows the corresponding dimensional errors in X-axis direction along the tool path L3 (shown in Fig. 8). The dimensional error for the fixed clamping scheme is 40 m while that for the intelligent clamping scheme is 32 m. The accuracy of the part is improved by 20% when adaptive clamping is used.
7. Conclusions Relevant methodologies and techniques developed for a proposed intelligent fixturing system (IFS) have been presented. The main feature of the IFS is its ability to manipulate fixture elements by software means to arrive at optimal fixturing during machining. The accuracy of the machined workpiece is improved due to adaptive control of the clamping forces and the robustness of the system to disturbances is also greater. Currently, variable clamping force control is not implemented in the IFS. It is envisaged that future implementation will not only incorporate variable and adaptive clamping force control, but also re-positioning of the clamping elements such that workpiece distortion can be greatly reduced. The IFS can be used in an advanced machining environment such as in flexible manufacturing systems (FMS). This system can be beneficial to many industrial users, in particular to the precision engineering industry. In machining precision components, scrap parts due to improper fixturing during machining can be minimized, thereby resulting in substantial saving of production costs.
Acknowledgements The National University of Singapore (NUS) under the Academic Research Project RP950634 funds this project. Prof. A.Y.C. Nee, Dr. M.A. Mannan, Dr. A.S. Kumar and Mr. Z.J. Tao in this fixturing research group have provided invaluable suggestions and comments to this work.
Fig. 17. FEM model.
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