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Modelling and simulation environment for machining of low-rigidity components
Journal of Materials Processing Technology 153–154 (2004) 67–73
Modelling and simulation environment for machining of low-rigidity components S. Ratchev, W. Huang∗ , S. Liu, A.A. Becker School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham NG7 2RD, UK
Abstract Machining of low-rigidity components is a key process in industries such as aerospace, marine engineering and power engineering. The part deflection caused by the cutting force due to the flexible part structure reduces the validity of the CAM output and leads to additional machining errors that are difficult to predict and control. The paper reports a modelling methodology and integration architecture for multi-step simulation of cutting processes of low-rigidity components incorporating a finite element analysis (FEA)-based component model, FE analysis tool, force model and material removal algorithm. The FEA-based data model of low-rigidity component is proposed based on describing key object-oriented classes such as component, element, node and force to create a common integrated decision making environment. Each object has unique decision making methods associated with it that allow seamless integration in simulating the part behaviour during machining. Two iterative algorithms are proposed within the simulation environment for cutting force prediction and material removal simulation. A prototype version of the simulation environment has been developed using C++, and the feasibility of the proposed approach has been illustrated using practical examples backed up by experimental data. © 2004 Elsevier B.V. All rights reserved. Keywords: Integration; Finite element analysis (FEA); Object-oriented modelling; Flexible part
1. Introduction Machining of low-rigidity components is a key process in industries such as aerospace, marine engineering and power engineering. Producing the right profile in such parts increasingly depends on specialised CAM packages for defining appropriate cutting strategies and tool paths. However, the part deflection caused by the cutting force due to the low-rigidity of the part reduces the validity of the CAM output and leads to additional machining errors that are difficult to predict and control. The direct experimental approach to study machining processes is often expensive and time consuming. The alternative approaches are numerical simulations including finite element methods (FEM), force modelling techniques and material removal models [1]. Spence et al. [2] reported a comprehensive physical machining process simulation program based on a solid modelling kernel. Parts were created as solid models first and then meshed by using a cellular topology husk, which was provided by a solid model and adapted for finite element meshing for simulation of machining using only six-node elements to represent the machined
∗ Corresponding author. E-mail address: [email protected] (W. Huang).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.301
surface. Tsai and Liao [3] developed a finite element model along with an end milling cutting force model to analyse the surface dimensional errors in the peripheral milling of a thin-walled workpiece. They used 3D isoparametric 12-node elements taking into account the geometry and thickness variation of the workpiece during peripheral milling making a number of assumptions on the size of the elements and their relationships with the transient cutting surface that restricted its applicability. A simulation model of peripheral milling of very flexible cantilever plates was proposed by Budak and Altintas [4]. The cutting tool was represented as an elastic beam and the partial disengagement of the plate from the cutter due to excessive bending was taken into account. Liu et al. [5] developed deflection and cutting models by considering additional sources of error such as machine set-up error, spindle and axis tilt, vibration and cutter centre offset runout. Another active area of research has been the development of material removal models and force prediction in simulating machining processes. Sagherian and Elbestawi [6] reported a dynamic cutting model that took into account the effect of material removal using an automatic mesh generation program. Jang et al. [7] developed a voxel-based simulator for multi-axis CNC machining. The voxel representation was used to efficiently model the state of the
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in-process workpiece, which was generated by successively subtracting tool swept volumes from the workpiece. Ratchev et al. [8,9] developed a voxel-based material removal by cutting through the voxels at the tool–part contact surface and replacing them with equivalent set of mesh compliant volumetric elements. Tsai and Liao [3] developed an end milling cutting force model to analyse the surface dimensional errors in the milling of thin-walled parts. The authors argued that for a flexible cutting system, the effect of cutting system deflections on the cutting force distribution must be included and this has been done by the modified Newton–Raphson method in their study. Despite the recent developments in machining simulation, there are still significant gaps between the theoretically predicted and the measured surfaces in machining of complex low-rigidity parts. This is mainly due to the relatively small part deflection errors that could not be interpreted by the existing systems. Although FE-based simulation methods have been developed and successfully applied, there is a need for a more holistic approach to the modelling and analysis of the part–tool behaviour during machining including force data, creation and replacement of new elements and nodes, calculation and recalculation of boundary conditions and their iterative update to support a more accurate multi-step cutting process simulation. Moreover, there is a need for establishing a clear integration platform between FE-based simulation methods, material removal approaches and force modelling methods for simulation of flexible part behaviour during machining. There is a particular need to further develop a finite element analysis (FEA)-based data model of components that includes complete mesh and analysis information for predicting part deflection and enables iterative data updating for multi-step simulation of cutting processes of low-rigidity components. The paper reports an integration methodology for multi-step simulation of cutting processes of low-rigidity components. The methodology is based on integrating a common data model representing part instances during machining, with cutting force model and material removal algorithms. The integration approach is illustrated using simplified 2D and 3D examples.
2. Modelling and simulation methodology 2.1. System integration—an overview A simulation environment for machining of low-rigidity components is illustrated in Fig. 1. The environment incorporates several decision making modules involving cutting force modelling, component deflection modelling and material removal algorithm. There are several iterative loops within the environment. The top loop (1) includes force modelling process and part deflection modelling process, which is used to predict the feasible cutting force for the simulation of each cut. The right loop (2) includes part deflection
Fig. 1. Simulation environment for machining of low-rigidity components—an overview.
modelling process and a material removal algorithm, which is used to simulate the material removal process. The central loop (3) integrates all the modules together within the environment to simulate the multi-step cutting processes. The proposed system integration concept is illustrated in Fig. 2. The FEA-based data model of the component provides a common medium for the simulation environment for integration of FEA tool, force model and material removal algorithm. It includes the complete mesh and analysis information such as nodes, elements, material properties, analysis procedure, boundary conditions, force and output control to predict the deflection of a low-rigidity component during machining. The component model is structured using key object classes such as component, element, node and force to support the common integrated decision making environment. The data in the model are iteratively updated when simulating the multi-step cutting processes. A FEA tool uses the component model as input to predict the part deflection, and then the force model takes the deflected model as input considering the effect of part deflection on force prediction. The material removal algorithm is developed to cut material from the deflected model and return the updated data on nodes and elements. Further details of the material removal simulation and the force model can be found in references [8,9]. The updated data on new nodes, elements and force are then used to modify the component model for next step simulation. The data exchange among different modules within the simulation environment is directed in terms of the component model and the above procedure will be iteratively carried out to simulate the multi-step cutting processes. Two iterative algorithms are developed within the simulation environment to predict cutting force and simulate material removal. One algorithm for force prediction incorporates the component model, FE analysis tool and force model. The other algorithm for material re-
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Fig. 2. System integration within the simulation environment.
moval simulation incorporates the component model, FE analysis tool and material removal algorithm. A prototype version of the simulation environment has been developed in C++. 2.2. FEA-based data model of low-rigidity components A simplified object diagram for the component model is shown in Fig. 3. The component model is developed not only based on FEA principles but also based on object-oriented principles. It includes several key classes: component, node, element and force described with their attributes and associated methods. The attributes are shown in Fig. 3 with their names and types. The methods are not provided due to space limitation, but some methods of class “Component” and “Element” will be described as examples in the following section on system implementation. The class “Component” is the main part of the data model since it holds the complete information for FE analysis. The attribute “Heading” includes the title of the component. “Nodes” and “Elements” hold the mesh in-
Node 1+ Component Heading: string Nodes: Node Elements: Element Material Property: string Analysis Procedure: string Loads: Force Boundary Conditions: string Output Control: string
includes
1+
Number: integer Coordinates: float Displacements: float Element Number: integer Type: string Node number: integer
1+
Force Node number: integer DOF: integer Magnitudes: float
Fig. 3. Simplified object diagram for FEA-based data model of low-rigidity components.
formation for the component. There is no limit on what element types the model can have and also no limit on how many nodes an element can include. After material is removed from a component, the machined surface can be represented accurately by replacing the “old” elements with any type and number of new elements. The attribute “Material Property” indicates the features of part material, e.g. material type, Young’s modulus and Poisson’s ratio. Besides the data for representing the component, the data for controlling the FE analysis procedure are also included. “Analysis Procedure” includes information on analysis type and steps, and “Force” holds the positions (in terms of node numbers and degrees of freedom) and magnitudes of the cutting force. “Boundary Conditions” determines which surface or edge of the component is fixed during machining simulation. “Output Control” determines what FEA results should be output that are useful for the next iteration. For example, the nodal displacements are normally required to indicate the part deflection and will then be used to update the model to be a deflected model. The “Component” class includes objects (at least one object) of other classes such as “Node”, “Element” and “Force”, which have their own methods to update the data during the iterative procedure. 2.3. Decision making algorithms 2.3.1. Iterative algorithm for force prediction The purpose of this iterative algorithm is to find the appropriate cutting force for each cut simulation. Before simulating the cutting process, the force model assumes initial cutting force and depth. Due to the part deflection during machining, the cutting depth changes. Since the force is calculated based on the depth, the predicted cutting force will be different from the initial one. The force difference will be calculated and if it is less than a given tolerance, the feasible cutting force is found. The procedure of the algorithm is described as follows:
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1. A FEA-based component model is created that includes nodes, elements, material property, analysis procedure, cutting force and position, boundary condition and output control, etc. These data are used as input for FE analysis. 2. A FEA tool is run using the input data to predict part deflection caused by the current cutting force. 3. The force model is used to calculate the expected cutting depth and cutting force according to the obtained part deflection. 4. The current cutting force is compared with the expected cutting force predicted by the current iteration. 5. If the force difference is less than a given tolerance, the current force is the appropriate force for the cut to be simulated and the iterative procedure goes to step 6. Otherwise, the expected force is changed to the current force and the force data in the component model are updated. The iterative procedure goes back to step 1. 6. Output the appropriate force for the simulation of the current cut, and the iterative procedure is terminated. 2.3.2. Iterative algorithm for material removal simulation The purpose of this iterative algorithm is to simulate the multi-step material removal process taking into account the deflection of low-rigidity components during machining. The procedure of the iterative algorithm is described as follows: 1. A FEA-based component model is produced that includes nodes, elements, material property, analysis procedure, cutting force and position, boundary conditions and output control, etc. These data are used as input for FE analysis. 2. A FEA tool is run using the input data to predict part deflection. 3. Relevant data such as nodal displacements are searched and extracted from the analysis results. 4. The deflected component model is generated for the material removal algorithm that determines which nodes and elements are removed and which new nodes and elements are created to represent the machined surface. 5. The cutting force for the next step simulation is determined. 6. If some convergence criteria (e.g. the simulation time or the simulated length of the component) are reached, the iterative procedure is terminated. Otherwise, go to step 7. 7. The data in the component model are updated and the iterative procedure goes back to step 1 for the simulation of the next cut.
3. System implementation A prototype version of the simulation environment has been developed in C++ to implement the proposed methodology. A control program, MASTER, is produced in C++ to manage the data exchanges among different modules to form
Class: Component Attributes: Heading Nodes Elements Loads Constants OutputControl Methods: Input Data for FEA InputIniData GetDisplacments CreateInputData Nodes & Elements OutputDeflectedMesh InputNewMesh Force OutputDeflections InputNewLoads
Fig. 4. The object class of component.
a common integrated decision making environment. A number of object classes are developed within the environment and each object has unique decision making methods associated with it that allow seamless integration in simulating the part deflection during machining. Object classes of component and element are illustrated in Fig. 4 and Fig. 5 as examples. The attributes and methods of class “Component” and “Element” are given. For the object class of component, “Constants” represents some unchanged data during the iterative procedure, e.g. the material property of component. The methods under “Input Data for FEA” create the input data for FE analysis and manage the data exchanges with the FEA package in each iteration. The methods under “Nodes and Elements” manage the data exchanges with the material removal algorithm and update the mesh information of the component in each iteration. The methods under “Force” control the data exchanges with the force model. For the object class of “Element”, the methods are mainly used to update data on element type, element number and element nodes. The developed system allows the integration of mainstream FEA packages and specialist programs. The in-
Class: Element Attributes: ElementNumber ElementType ElementNodes Methods: SetElementNumber SetElementType SetElementNodes GetElementNumber GetElementType GetElementNodes
Fig. 5. The object class of element.
S. Ratchev et al. / Journal of Materials Processing Technology 153–154 (2004) 67–73
corporation of ABAQUS, a mainstream FEA commercial package, within the developed simulation environment has been achieved as a proof of concept. However, the proposed methodology and the developed programs are generic by nature and can be easily integrated with other FEA packages due to the object-oriented implementation environment that allows easy and quick change. The system is scalable and it can be extended to incorporate mainstream CAD and CAM packages in the future.
Table 1 Data input sheet for a 2D example Title
Cantilever cutting example
Geometry
4. Examples Two examples are provided to demonstrate the feasibility of the proposed approach. A 2D example is used to show how the iterative algorithm works out the feasible cutting force for one cut, where the input data for FE analysis to predict the part deflection are illustrated in Table 1. The applied loads provided in this table are the assumed initial forces (Fx and Fy ) for a cut and it will be iteratively updated using the proposed algorithm for force prediction until an appropriate cutting force is obtained. Table 2 shows the predicted forces and deflections used to calculate the predicted cutting depth. Ux and Uy represent the predicted deflection (i.e. the displacements of the cutting point) in the X and Y directions, respectively, and Fx and Fy represent the predicted cutting forces in the X and Y directions, respectively, at the cutting point. The tolerance for force difference is 0.1% in the Y direction since the deflection of the workpiece in the Y direction contributes the most error in machining. After four iterations, the system converges to a feasible cutting force. A practical 3D example of milling of a thin-wall part is illustrated in Fig. 6. The eight vertices of the part are labelled A, B, C, D, E, F, G and H. The original centre of the global coordinate system is at point A. When the milling tool starts cutting, it contacts the part in the edge of FB and causes the part to deflect. The axial cutting depth is 24 mm represented by the contact line FN in FB and the radial cutting depth is 2 mm. The input data used for FE analysis to predict the part deflection are shown in Table 3. To simplify the FE analysis, the cutting force is assumed to be applied at point P, which is the middle point of FN. Two sensors are used to measure the part deflection of points M and N, where the length of FM is 6 mm. The predicted cutting forces at point P and the predicted displacements of points P, M and N in the Y direction in each iteration are shown in Table 4. The force tolerance is 0.1% in the Y direction. It takes 10 iterative loops
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Material properties Analysis type Boundary conditions Applied loads Element type
2D plane stress; overall dimensions of the component: 100 mm × 20 mm Young’s modulus: E = 200 × 103 MPa (N/mm2 ); Poisson’s ratio: v = 0.3 Static elastic analysis The left boundary of the workpiece is fixed Initial concentrated load, Fx = −6.3191 × 106 N and Fy = −2.5211 × 106 N, applied at point A Eight-node isoparametric quadratic plane stress with reduced-integration
Fig. 6. A thin-wall part under milling.
to converge to a feasible cutting force. The converged forces and displacements are compared with the measured forces and displacement (see Table 5). It can be observed that the predicted force at point P and displacements at point N are
Table 2 The predicted force and displacements in each iteration for the 2D example Iteration number
Fx (N)
1 2 3 4
−6.3191 −3.1596 −3.0607 −3.0637
Fy (N) × × 106 × 106 × 106 106
−2.5211 −1.2606 −1.2212 −1.2224
Ux (mm) × × 106 × 106 × 106 106
1.5646 7.8238 7.5800 7.5652
Uy (mm) 10−4
× × 10−5 × 10−5 × 10−5
−5.3125 −2.6564 −2.5734 −2.5761
× × × ×
10−3 10−3 10−3 10−3
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Table 3 Data input sheet for a practical 3D example Title
Thin-wall part cutting example
Geometry Material properties Analysis type Boundary conditions Applied loads Element type
Overall dimensions of the part: 150 mm × 80 mm × 5 mm Young’s modulus: E = 69 × 103 MPa (N/mm2 ); Poisson’s ratio: v = 0.33 Static elastic analysis The bottom surface (ABCD) of the part is fixed Initial concentrated load, Fx = −362.40 N; Fy = −401.40 N; and Fz = 118.40 N that are applied at point P. Eight-node isoparametric brick elements with full-integration
Table 4 The predicted force and displacements in each iteration for the 3D example Iteration number
Point P
1 2 3 4 5 6 7 8 9 10
Fy (N)
Fz (N)
Uy (mm)
Uy (mm)
Uy (mm)
−362.400 −294.144 −244.329 −276.151 −280.694 −272.330 −274.840 −276.296 −275.340 −275.450
−401.400 −301.628 −225.318 −276.205 −273.334 −261.622 −265.070 −267.074 −265.760 −265.900
118.400 92.200 72.464 83.855 85.506 82.391 83.310 83.850 83.500 83.900
−0.9833 −0.7412 −0.5565 −0.6794 −0.6733 −0.6449 −0.6532 −0.6581 −0.6549 −0.6553
−1.0500 −0.7911 −0.5934 −0.7249 −0.7183 −0.6879 −0.6968 −0.7020 −0.6986 −0.6990
−0.7200 −0.5425 −0.4069 −0.4971 −0.4925 −0.4717 −0.4778 −0.4814 −0.4791 −0.4793
Point P
Point M
Point N
Fx (N)
Fy (N)
Fz (N)
Uy (mm)
Uy (mm)
−262.20 −275.45
−248.80 −265.90
78.850 83.900
−0.8493 −0.6990
−0.4868 −0.4793
5.05
6.87
Difference (%)
Point N
Fx (N)
Table 5 The comparison between measured and predicted force and displacements
Measured value Predicted value
Point M
6.40
−17.70
−1.54
reasonably close to the measured values, with a large deviation of displacement at point M. There are two possible reasons for the large deviation. One reason is that for simplification, a concentrated cutting force was assumed to be applied at point A. It is expected that a better approximation can be achieved if a distributed force is applied along FN and this can be implemented in the future. Another possible reason for the large deviation is that point M is relatively far from the fixed bottom surface and there is a larger deflection that leads to increased errors.
5. Conclusions A modelling methodology and integration architecture for multi-step simulation of cutting processes of low-rigidity components incorporating a FEA-based component model, FE analysis tool, force model and material removal algorithm have been proposed. One of the key outcomes is that it provides a practical approach to the integration of complete FE mesh and analysis information using mainstream
FEA software tools to predict part deflection during machining. The proposed component model provides convenient object-oriented methods that enable iterative data updating for multi-step machining simulation. A prototype version of the simulation environment has been developed using C++ and the feasibility of the proposed approach has been illustrated using practical examples backed up by experimental data.
Acknowledgements The reported research is part of the project “Adaptive Planning for Machining of Complex Low-Rigidity Components” funded by British EPSRC (GR/R13098/01), the support of which is gratefully acknowledged.
References [1] J. Mackerle, Finite-element analysis and simulation of machining: a bibliography (1976-1996), J. Mater. Process. Technol. 86 (1999) 17– 44. [2] A.D. Spence, F. Abrari, M.A. Elbestawi, Integrated solid modeller based solutions for machining, Comput. Aided Des. 32 (2000) 553– 568. [3] J. Tsai, C. Liao, Finite-element modelling of static surface errors in the peripheral milling of thin-walled workpieces, J. Mater. Process. Technol. 94 (1999) 235–246. [4] E. Budak, Y. Altintas, Modeling and avoidance of static form errors in peripheral milling of plates, Int. J. Mach. Tools Manuf. 35 (3) (1995) 459–476.
S. Ratchev et al. / Journal of Materials Processing Technology 153–154 (2004) 67–73 [5] O. Liu, C. Zhang, H.P.B. Wang, Form-accuracy analysis and prediction in computer-integrated manufacturing, Int. J. Mach. Tools Manuf. 37 (3) (1997) 237–248. [6] R. Sagherian, M. Elbestawi, A simulation system for improving machining accuracy in milling, Comput. Ind. 14 (1990) 293– 305. [7] D. Jang, K. Kim, J. Jung, Voxel-based virtual multi-axis machining, Int. J. Adv. Manuf. Technol. 16 (2000) 709–713.
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[8] S. Ratchev, E. Govender, S. Nikov, Analysis and prediction of the accuracy of machining of thin wall components, in: Proceedings of the 33rd CIRP International Seminar on Manufacturing System, Stockholm, Sweden, 5–7 June, 2000, pp. 220–225. [9] S. Ratchev, S. Nikov, I. Moualek, Material removal simulation of peripheral milling of thin wall low-rigidity structure using FEA, in: Proceedings of the 35th CIRP International Seminar on Manufacturing Systems, Seoul, Korea, 13–15 May, 2002, pp. 371–377.
Modelling and simulation environment for machining of low-rigidity components S. Ratchev, W. Huang∗ , S. Liu, A.A. Becker School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham NG7 2RD, UK
Abstract Machining of low-rigidity components is a key process in industries such as aerospace, marine engineering and power engineering. The part deflection caused by the cutting force due to the flexible part structure reduces the validity of the CAM output and leads to additional machining errors that are difficult to predict and control. The paper reports a modelling methodology and integration architecture for multi-step simulation of cutting processes of low-rigidity components incorporating a finite element analysis (FEA)-based component model, FE analysis tool, force model and material removal algorithm. The FEA-based data model of low-rigidity component is proposed based on describing key object-oriented classes such as component, element, node and force to create a common integrated decision making environment. Each object has unique decision making methods associated with it that allow seamless integration in simulating the part behaviour during machining. Two iterative algorithms are proposed within the simulation environment for cutting force prediction and material removal simulation. A prototype version of the simulation environment has been developed using C++, and the feasibility of the proposed approach has been illustrated using practical examples backed up by experimental data. © 2004 Elsevier B.V. All rights reserved. Keywords: Integration; Finite element analysis (FEA); Object-oriented modelling; Flexible part
1. Introduction Machining of low-rigidity components is a key process in industries such as aerospace, marine engineering and power engineering. Producing the right profile in such parts increasingly depends on specialised CAM packages for defining appropriate cutting strategies and tool paths. However, the part deflection caused by the cutting force due to the low-rigidity of the part reduces the validity of the CAM output and leads to additional machining errors that are difficult to predict and control. The direct experimental approach to study machining processes is often expensive and time consuming. The alternative approaches are numerical simulations including finite element methods (FEM), force modelling techniques and material removal models [1]. Spence et al. [2] reported a comprehensive physical machining process simulation program based on a solid modelling kernel. Parts were created as solid models first and then meshed by using a cellular topology husk, which was provided by a solid model and adapted for finite element meshing for simulation of machining using only six-node elements to represent the machined
∗ Corresponding author. E-mail address: [email protected] (W. Huang).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.301
surface. Tsai and Liao [3] developed a finite element model along with an end milling cutting force model to analyse the surface dimensional errors in the peripheral milling of a thin-walled workpiece. They used 3D isoparametric 12-node elements taking into account the geometry and thickness variation of the workpiece during peripheral milling making a number of assumptions on the size of the elements and their relationships with the transient cutting surface that restricted its applicability. A simulation model of peripheral milling of very flexible cantilever plates was proposed by Budak and Altintas [4]. The cutting tool was represented as an elastic beam and the partial disengagement of the plate from the cutter due to excessive bending was taken into account. Liu et al. [5] developed deflection and cutting models by considering additional sources of error such as machine set-up error, spindle and axis tilt, vibration and cutter centre offset runout. Another active area of research has been the development of material removal models and force prediction in simulating machining processes. Sagherian and Elbestawi [6] reported a dynamic cutting model that took into account the effect of material removal using an automatic mesh generation program. Jang et al. [7] developed a voxel-based simulator for multi-axis CNC machining. The voxel representation was used to efficiently model the state of the
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in-process workpiece, which was generated by successively subtracting tool swept volumes from the workpiece. Ratchev et al. [8,9] developed a voxel-based material removal by cutting through the voxels at the tool–part contact surface and replacing them with equivalent set of mesh compliant volumetric elements. Tsai and Liao [3] developed an end milling cutting force model to analyse the surface dimensional errors in the milling of thin-walled parts. The authors argued that for a flexible cutting system, the effect of cutting system deflections on the cutting force distribution must be included and this has been done by the modified Newton–Raphson method in their study. Despite the recent developments in machining simulation, there are still significant gaps between the theoretically predicted and the measured surfaces in machining of complex low-rigidity parts. This is mainly due to the relatively small part deflection errors that could not be interpreted by the existing systems. Although FE-based simulation methods have been developed and successfully applied, there is a need for a more holistic approach to the modelling and analysis of the part–tool behaviour during machining including force data, creation and replacement of new elements and nodes, calculation and recalculation of boundary conditions and their iterative update to support a more accurate multi-step cutting process simulation. Moreover, there is a need for establishing a clear integration platform between FE-based simulation methods, material removal approaches and force modelling methods for simulation of flexible part behaviour during machining. There is a particular need to further develop a finite element analysis (FEA)-based data model of components that includes complete mesh and analysis information for predicting part deflection and enables iterative data updating for multi-step simulation of cutting processes of low-rigidity components. The paper reports an integration methodology for multi-step simulation of cutting processes of low-rigidity components. The methodology is based on integrating a common data model representing part instances during machining, with cutting force model and material removal algorithms. The integration approach is illustrated using simplified 2D and 3D examples.
2. Modelling and simulation methodology 2.1. System integration—an overview A simulation environment for machining of low-rigidity components is illustrated in Fig. 1. The environment incorporates several decision making modules involving cutting force modelling, component deflection modelling and material removal algorithm. There are several iterative loops within the environment. The top loop (1) includes force modelling process and part deflection modelling process, which is used to predict the feasible cutting force for the simulation of each cut. The right loop (2) includes part deflection
Fig. 1. Simulation environment for machining of low-rigidity components—an overview.
modelling process and a material removal algorithm, which is used to simulate the material removal process. The central loop (3) integrates all the modules together within the environment to simulate the multi-step cutting processes. The proposed system integration concept is illustrated in Fig. 2. The FEA-based data model of the component provides a common medium for the simulation environment for integration of FEA tool, force model and material removal algorithm. It includes the complete mesh and analysis information such as nodes, elements, material properties, analysis procedure, boundary conditions, force and output control to predict the deflection of a low-rigidity component during machining. The component model is structured using key object classes such as component, element, node and force to support the common integrated decision making environment. The data in the model are iteratively updated when simulating the multi-step cutting processes. A FEA tool uses the component model as input to predict the part deflection, and then the force model takes the deflected model as input considering the effect of part deflection on force prediction. The material removal algorithm is developed to cut material from the deflected model and return the updated data on nodes and elements. Further details of the material removal simulation and the force model can be found in references [8,9]. The updated data on new nodes, elements and force are then used to modify the component model for next step simulation. The data exchange among different modules within the simulation environment is directed in terms of the component model and the above procedure will be iteratively carried out to simulate the multi-step cutting processes. Two iterative algorithms are developed within the simulation environment to predict cutting force and simulate material removal. One algorithm for force prediction incorporates the component model, FE analysis tool and force model. The other algorithm for material re-
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Fig. 2. System integration within the simulation environment.
moval simulation incorporates the component model, FE analysis tool and material removal algorithm. A prototype version of the simulation environment has been developed in C++. 2.2. FEA-based data model of low-rigidity components A simplified object diagram for the component model is shown in Fig. 3. The component model is developed not only based on FEA principles but also based on object-oriented principles. It includes several key classes: component, node, element and force described with their attributes and associated methods. The attributes are shown in Fig. 3 with their names and types. The methods are not provided due to space limitation, but some methods of class “Component” and “Element” will be described as examples in the following section on system implementation. The class “Component” is the main part of the data model since it holds the complete information for FE analysis. The attribute “Heading” includes the title of the component. “Nodes” and “Elements” hold the mesh in-
Node 1+ Component Heading: string Nodes: Node Elements: Element Material Property: string Analysis Procedure: string Loads: Force Boundary Conditions: string Output Control: string
includes
1+
Number: integer Coordinates: float Displacements: float Element Number: integer Type: string Node number: integer
1+
Force Node number: integer DOF: integer Magnitudes: float
Fig. 3. Simplified object diagram for FEA-based data model of low-rigidity components.
formation for the component. There is no limit on what element types the model can have and also no limit on how many nodes an element can include. After material is removed from a component, the machined surface can be represented accurately by replacing the “old” elements with any type and number of new elements. The attribute “Material Property” indicates the features of part material, e.g. material type, Young’s modulus and Poisson’s ratio. Besides the data for representing the component, the data for controlling the FE analysis procedure are also included. “Analysis Procedure” includes information on analysis type and steps, and “Force” holds the positions (in terms of node numbers and degrees of freedom) and magnitudes of the cutting force. “Boundary Conditions” determines which surface or edge of the component is fixed during machining simulation. “Output Control” determines what FEA results should be output that are useful for the next iteration. For example, the nodal displacements are normally required to indicate the part deflection and will then be used to update the model to be a deflected model. The “Component” class includes objects (at least one object) of other classes such as “Node”, “Element” and “Force”, which have their own methods to update the data during the iterative procedure. 2.3. Decision making algorithms 2.3.1. Iterative algorithm for force prediction The purpose of this iterative algorithm is to find the appropriate cutting force for each cut simulation. Before simulating the cutting process, the force model assumes initial cutting force and depth. Due to the part deflection during machining, the cutting depth changes. Since the force is calculated based on the depth, the predicted cutting force will be different from the initial one. The force difference will be calculated and if it is less than a given tolerance, the feasible cutting force is found. The procedure of the algorithm is described as follows:
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1. A FEA-based component model is created that includes nodes, elements, material property, analysis procedure, cutting force and position, boundary condition and output control, etc. These data are used as input for FE analysis. 2. A FEA tool is run using the input data to predict part deflection caused by the current cutting force. 3. The force model is used to calculate the expected cutting depth and cutting force according to the obtained part deflection. 4. The current cutting force is compared with the expected cutting force predicted by the current iteration. 5. If the force difference is less than a given tolerance, the current force is the appropriate force for the cut to be simulated and the iterative procedure goes to step 6. Otherwise, the expected force is changed to the current force and the force data in the component model are updated. The iterative procedure goes back to step 1. 6. Output the appropriate force for the simulation of the current cut, and the iterative procedure is terminated. 2.3.2. Iterative algorithm for material removal simulation The purpose of this iterative algorithm is to simulate the multi-step material removal process taking into account the deflection of low-rigidity components during machining. The procedure of the iterative algorithm is described as follows: 1. A FEA-based component model is produced that includes nodes, elements, material property, analysis procedure, cutting force and position, boundary conditions and output control, etc. These data are used as input for FE analysis. 2. A FEA tool is run using the input data to predict part deflection. 3. Relevant data such as nodal displacements are searched and extracted from the analysis results. 4. The deflected component model is generated for the material removal algorithm that determines which nodes and elements are removed and which new nodes and elements are created to represent the machined surface. 5. The cutting force for the next step simulation is determined. 6. If some convergence criteria (e.g. the simulation time or the simulated length of the component) are reached, the iterative procedure is terminated. Otherwise, go to step 7. 7. The data in the component model are updated and the iterative procedure goes back to step 1 for the simulation of the next cut.
3. System implementation A prototype version of the simulation environment has been developed in C++ to implement the proposed methodology. A control program, MASTER, is produced in C++ to manage the data exchanges among different modules to form
Class: Component Attributes: Heading Nodes Elements Loads Constants OutputControl Methods: Input Data for FEA InputIniData GetDisplacments CreateInputData Nodes & Elements OutputDeflectedMesh InputNewMesh Force OutputDeflections InputNewLoads
Fig. 4. The object class of component.
a common integrated decision making environment. A number of object classes are developed within the environment and each object has unique decision making methods associated with it that allow seamless integration in simulating the part deflection during machining. Object classes of component and element are illustrated in Fig. 4 and Fig. 5 as examples. The attributes and methods of class “Component” and “Element” are given. For the object class of component, “Constants” represents some unchanged data during the iterative procedure, e.g. the material property of component. The methods under “Input Data for FEA” create the input data for FE analysis and manage the data exchanges with the FEA package in each iteration. The methods under “Nodes and Elements” manage the data exchanges with the material removal algorithm and update the mesh information of the component in each iteration. The methods under “Force” control the data exchanges with the force model. For the object class of “Element”, the methods are mainly used to update data on element type, element number and element nodes. The developed system allows the integration of mainstream FEA packages and specialist programs. The in-
Class: Element Attributes: ElementNumber ElementType ElementNodes Methods: SetElementNumber SetElementType SetElementNodes GetElementNumber GetElementType GetElementNodes
Fig. 5. The object class of element.
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corporation of ABAQUS, a mainstream FEA commercial package, within the developed simulation environment has been achieved as a proof of concept. However, the proposed methodology and the developed programs are generic by nature and can be easily integrated with other FEA packages due to the object-oriented implementation environment that allows easy and quick change. The system is scalable and it can be extended to incorporate mainstream CAD and CAM packages in the future.
Table 1 Data input sheet for a 2D example Title
Cantilever cutting example
Geometry
4. Examples Two examples are provided to demonstrate the feasibility of the proposed approach. A 2D example is used to show how the iterative algorithm works out the feasible cutting force for one cut, where the input data for FE analysis to predict the part deflection are illustrated in Table 1. The applied loads provided in this table are the assumed initial forces (Fx and Fy ) for a cut and it will be iteratively updated using the proposed algorithm for force prediction until an appropriate cutting force is obtained. Table 2 shows the predicted forces and deflections used to calculate the predicted cutting depth. Ux and Uy represent the predicted deflection (i.e. the displacements of the cutting point) in the X and Y directions, respectively, and Fx and Fy represent the predicted cutting forces in the X and Y directions, respectively, at the cutting point. The tolerance for force difference is 0.1% in the Y direction since the deflection of the workpiece in the Y direction contributes the most error in machining. After four iterations, the system converges to a feasible cutting force. A practical 3D example of milling of a thin-wall part is illustrated in Fig. 6. The eight vertices of the part are labelled A, B, C, D, E, F, G and H. The original centre of the global coordinate system is at point A. When the milling tool starts cutting, it contacts the part in the edge of FB and causes the part to deflect. The axial cutting depth is 24 mm represented by the contact line FN in FB and the radial cutting depth is 2 mm. The input data used for FE analysis to predict the part deflection are shown in Table 3. To simplify the FE analysis, the cutting force is assumed to be applied at point P, which is the middle point of FN. Two sensors are used to measure the part deflection of points M and N, where the length of FM is 6 mm. The predicted cutting forces at point P and the predicted displacements of points P, M and N in the Y direction in each iteration are shown in Table 4. The force tolerance is 0.1% in the Y direction. It takes 10 iterative loops
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Material properties Analysis type Boundary conditions Applied loads Element type
2D plane stress; overall dimensions of the component: 100 mm × 20 mm Young’s modulus: E = 200 × 103 MPa (N/mm2 ); Poisson’s ratio: v = 0.3 Static elastic analysis The left boundary of the workpiece is fixed Initial concentrated load, Fx = −6.3191 × 106 N and Fy = −2.5211 × 106 N, applied at point A Eight-node isoparametric quadratic plane stress with reduced-integration
Fig. 6. A thin-wall part under milling.
to converge to a feasible cutting force. The converged forces and displacements are compared with the measured forces and displacement (see Table 5). It can be observed that the predicted force at point P and displacements at point N are
Table 2 The predicted force and displacements in each iteration for the 2D example Iteration number
Fx (N)
1 2 3 4
−6.3191 −3.1596 −3.0607 −3.0637
Fy (N) × × 106 × 106 × 106 106
−2.5211 −1.2606 −1.2212 −1.2224
Ux (mm) × × 106 × 106 × 106 106
1.5646 7.8238 7.5800 7.5652
Uy (mm) 10−4
× × 10−5 × 10−5 × 10−5
−5.3125 −2.6564 −2.5734 −2.5761
× × × ×
10−3 10−3 10−3 10−3
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Table 3 Data input sheet for a practical 3D example Title
Thin-wall part cutting example
Geometry Material properties Analysis type Boundary conditions Applied loads Element type
Overall dimensions of the part: 150 mm × 80 mm × 5 mm Young’s modulus: E = 69 × 103 MPa (N/mm2 ); Poisson’s ratio: v = 0.33 Static elastic analysis The bottom surface (ABCD) of the part is fixed Initial concentrated load, Fx = −362.40 N; Fy = −401.40 N; and Fz = 118.40 N that are applied at point P. Eight-node isoparametric brick elements with full-integration
Table 4 The predicted force and displacements in each iteration for the 3D example Iteration number
Point P
1 2 3 4 5 6 7 8 9 10
Fy (N)
Fz (N)
Uy (mm)
Uy (mm)
Uy (mm)
−362.400 −294.144 −244.329 −276.151 −280.694 −272.330 −274.840 −276.296 −275.340 −275.450
−401.400 −301.628 −225.318 −276.205 −273.334 −261.622 −265.070 −267.074 −265.760 −265.900
118.400 92.200 72.464 83.855 85.506 82.391 83.310 83.850 83.500 83.900
−0.9833 −0.7412 −0.5565 −0.6794 −0.6733 −0.6449 −0.6532 −0.6581 −0.6549 −0.6553
−1.0500 −0.7911 −0.5934 −0.7249 −0.7183 −0.6879 −0.6968 −0.7020 −0.6986 −0.6990
−0.7200 −0.5425 −0.4069 −0.4971 −0.4925 −0.4717 −0.4778 −0.4814 −0.4791 −0.4793
Point P
Point M
Point N
Fx (N)
Fy (N)
Fz (N)
Uy (mm)
Uy (mm)
−262.20 −275.45
−248.80 −265.90
78.850 83.900
−0.8493 −0.6990
−0.4868 −0.4793
5.05
6.87
Difference (%)
Point N
Fx (N)
Table 5 The comparison between measured and predicted force and displacements
Measured value Predicted value
Point M
6.40
−17.70
−1.54
reasonably close to the measured values, with a large deviation of displacement at point M. There are two possible reasons for the large deviation. One reason is that for simplification, a concentrated cutting force was assumed to be applied at point A. It is expected that a better approximation can be achieved if a distributed force is applied along FN and this can be implemented in the future. Another possible reason for the large deviation is that point M is relatively far from the fixed bottom surface and there is a larger deflection that leads to increased errors.
5. Conclusions A modelling methodology and integration architecture for multi-step simulation of cutting processes of low-rigidity components incorporating a FEA-based component model, FE analysis tool, force model and material removal algorithm have been proposed. One of the key outcomes is that it provides a practical approach to the integration of complete FE mesh and analysis information using mainstream
FEA software tools to predict part deflection during machining. The proposed component model provides convenient object-oriented methods that enable iterative data updating for multi-step machining simulation. A prototype version of the simulation environment has been developed using C++ and the feasibility of the proposed approach has been illustrated using practical examples backed up by experimental data.
Acknowledgements The reported research is part of the project “Adaptive Planning for Machining of Complex Low-Rigidity Components” funded by British EPSRC (GR/R13098/01), the support of which is gratefully acknowledged.
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