- Email: [email protected]
Modeling and simulative analysis of the micro-finishing process
CIRP Annals - Manufacturing Technology 64 (2015) 321–324
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Modeling and simulative analysis of the micro-finishing process Petra Kersting a,b,*, Raffael Joliet a, Michael Kansteiner a a
Institute of Machining Technology, TU Dortmund University, Baroper Straße 303, 44227 Dortmund, Germany Institute of Manufacturing Technology and Quality Management, Universita¨tsplatz 2, 39106 Magdeburg, Germany Submitted by Klaus Weinert (1), Dortmund, Germany. b
A R T I C L E I N F O
A B S T R A C T
Keywords: Honing Modeling Surface
Honing operations are primarily applied to enhance tribologically loaded surfaces. In order to reduce the experimental effort during process design and optimization, a prediction of the specific surface topography resulting from a particular honing operation is necessary. Therefore, a high-resolution geometric process model for force-controlled honing operations was developed, which utilizes numerical data of tools and workpieces from topographic scans. In this paper, the modeling approach is presented and applied to a micro-finishing process with different process parameter values. The simulation results are also compared to surface topographies generated in experiments in order to validate the simulation model. ß 2015 CIRP.
1. Introduction Honing operations are used to reduce form and dimensional errors and to influence frictional properties of tribologically loaded surfaces. A typical application of short-stroke honing processes, so called micro-finishing, is the manufacturing of crankshaft bearings [1]. Due to the complexity of the material removal mechanisms [2] and the strong effects and interactions of the process parameter values on the topography of the resulting workpieces, the manufacturing of surfaces with the desired characteristics is a great challenge. Often a great deal of process expertise and many experiments are necessary to achieve the required properties [3]. In order to gain deeper process knowledge and to reduce the number of experiments, simulation systems can be used, which allow a virtual analysis and optimization of processes. An extensive overview of recent developments in the simulation of machining and grinding processes [4,5] is given by Brinksmeier et al. [6] and Altintas et al. [7]. For the simulation of honing operations, different models focusing on specific aspects of the process are known in literature [8–14]. Voronov et al. [9,10] used numerical models to simulate the dynamic tool behavior of a bore-honing process on the macroscopic level. Reizer and Pawlus [11] developed a method for computer-generated topographies of plateau-honed cylinder surfaces based on measured data. A macroscopic simulation of the honing process was developed by Goeldel et al. [12], which takes the cylinder and tool geometry as well as the initial roughness values into account. Covington et al. [13] presented a macroscopic simulation using FEM, while statistical models were investigated by Buj-Corral et al. [14]. In contrast to these approaches which are based on characteristic values (e.g., roughness), the system proposed in this paper
* Corresponding author. E-mail address: [email protected] (P. Kersting). http://dx.doi.org/10.1016/j.cirp.2015.04.014 0007-8506/ß 2015 CIRP.
allows the prediction of the resulting surface characteristics based on original topographic data. A high resolution geometrical representation combined with a force-control model allows for an accurate prediction of the resulting surface characteristics. This simulation system, the experimental setup for the validation experiments, and a comparison of simulated and machined results will be presented in this paper. 2. Modeling of the micro-finishing process The simulation of honing processes requires a geometric modeling of the tool and the workpiece and of their engagement situation [7]. In this article, a simulation system is presented which represents the workpiece and the finishing belt by height fields [15]. By geometrically intersecting the tool and the workpiece model, the uncut chip shape can be described and analyzed in order to predict the cutting forces. These forces are used in an additional control model in order to simulate force-controlled operations. 2.1. Geometric models of the tool and the workpiece For a detailed modeling of the resulting surfaces which are free of undercuts, both the workpiece and the tool are geometrically represented by height fields (Fig. 1a). The basic idea of this efficient modeling technique is to discretize an object by parallel line segments of variable length which are arranged on a grid-like structure over a defined domain (Fig. 1b) [7]. In order to analyze the micro-finishing process, this domain is curved so as to model the finishing belt and the geometry of the workpiece. In order to be able to analyze the resulting honing structures on the workpiece surface, a high resolution of the grid is necessary. The values of the height fields are initialized utilizing measured data of the tool and the workpiece. For this purpose, topography
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Fig. 3. Calculation of the uncut chip thickness h for each row of the removed material in order to calculate the normal force on the tool. In the cutting direction, the uncut chip thickness is determined by using the maximum and the minimum values. All force values are summed up perpendicular to the cutting direction.
Fig. 1. (a) Experimental setup and simulated workpiece surface. For the simulation of the process, only a very small area of 0.4 mm 0.4 mm is taken into account. (b) The height values are defined with respect to a two-dimensional reference area.
scans had to be made using, e.g., a confocal white light microscope. The model of the finishing belt is limited to the contact area and is assumed to be representative for the whole belt. Since the model does not take tool wear into account, the belt feed is neglected in the simulation model. 2.2. Modeling of the material removal process The approach developed here is based on a time-domain simulation system [15]. For each discrete time step, the relative position of the tool and the workpiece is updated and the intersection between the two models has to be computed in order to calculate the current material removal. Since the finishing belt, which is pressed against the workpiece by an elastic roller, adapts to the shape of the workpiece in the contact area and, thus, the radii of the finishing belt and the outer shaft are equal, the engagement can be limited to this twodimensional region (Fig. 2a). For each height value of the workpiece model, the nearest height value of the tool model in surface normal direction is determined and this value is used to clip the height value of the workpiece (Fig. 2b). As a result, the intersected and removed parts define a model of the uncut chip, which is used for the force calculation.
an empirical model according to [15]. For this purpose, the uncut chip thickness h is necessary, which can be determined using the model of the removed material (Section 2.2). For each row of the height values the uncut chip thickness h is determined (Fig. 3). These values are used to calculate local force values, which are then combined to compute the normal force. By dividing this value by the contact area, the surface pressure is obtained [15]. The calculated pressure value is used in the control model to adapt the radial infeed rinf of the tool. For each time step t, the radial infeed rinf,t is updated, based on the smoothed pressure difference Dpsmooth,t, which is a weighted sum of currently and previously calculated pressure values: r inf;t ¼ r inf;t1 þ f correction ðD psmooth;t Þ;
f correction > 0
D psmooth;t ¼ D psmooth;t1 ð1 aÞ þ ð psim;t ptarget Þ a; a 1:
(1) 0 (2)
The parameters fcorrection and a characterize the behavior of the control mechanism, and ptarget defines the pressure value used in the real experiments. This value was calculated by assuming a constant contact area. If the simulated pressure value psim,t is too high, the radius of the tool model is increased, which leads to a lower engagement of the grains. By applying this approach, the simulation of the force-controlled process becomes possible. The influence of the parameter a is presented in Fig. 4. Using both parameter values, a = 0.25 and a = 0.5, the simulation is able to match the predefined force of 400 N. With a = 0.25, the control tends to overshoot the predefined force value. Higher values for a resulted in an unstable control behavior.
Fig. 2. (a) The outer shell of a cylinder was used to model both the shaft perimeter and the finishing belt during the contact situation. (b) For each time step, the relative position of the tool and the workpiece is calculated by intersecting each height value with the nearest value of the tool model.
Fig. 4. Parameterization of the infeed control model and its effect on the process kinematics. The model corrects the radial infeed of the tool model in order to reach a predefined contact force.
2.3. Force calculation and control feedback
3. Experimental setup
In order to model the force-controlled operation, the normal forces and the pressure on the workpiece surface have to be calculated. The forces are determined in each simulation step using
To validate the simulation model, experiments with different values for the parameters process time, tangential velocity, feed of the finishing belt, and contact force were conducted. The
P. Kersting et al. / CIRP Annals - Manufacturing Technology 64 (2015) 321–324
323
Table 1 Process parameters varied in the experiments.
Process time t Tangential velocity vt Feed velocity (belt) vfb Contact force F
Unit
Minimum
Maximum
s m/min mm/min N
10 5 6 60
60 125 64 540
Fig. 6. Simulated transient maximum height of profile Rz for the central point of the experimental design plan. The lines correspond to different parameter values m of the force model and a constant value for kc of 10,000 N/mm2.
Fig. 5. Setup for the validation experiments. A Supfina finishing device is mounted onto a turning machine. The finishing belt is pressed against the rotating workpiece with a predefined force. The belt and the elastic roller used oscillate in the axial direction.
0.3 mm and a tool model of size 1.4 mm 5.5 mm with a resolution of 0.6 mm were chosen. The time step has to be adapted to the resolution of the workpiece [15]. For this purpose, the tool movement is limited to 0.5 mm in each time step in the experiments. In addition to the parameter values of the general simulation setup, those of the empirical force model based on the Kienzle equation [17] F ¼ b kc
experimental investigations are based on a central composite design with 29 experiments. As the axial distance was set to aCCD = 2, the five levels of the design equidistantly cover the experimental region (Table 1). The grounded workpieces made of unhardened 100Cr6 with a diameter of 50 mm were finished using a finishing belt with electrostatically directed Al2O3 grains of size 30 mm. The experiments were conducted under dry conditions utilizing a Supfina finishing device, mounted onto a MAG Boehringer M 670 turning machine (Fig. 5). The oscillation frequency was 21 Hz for all experiments. The experiments were evaluated by fitting a second order multiple regression model to the resulting roughness values. In order to determine the coefficients b integrated into the regression model, the t-statistic was considered [16]. This statistic transforms the effect magnitude, its uncertainty, and the number of experiments used for its estimation, into a p-value which reflects the probability of seeing the results in case of no actual effect of the parameter. The lower the p-value the higher is the evidence for the corresponding parameter effect. The statistic model indicated a significant effect of the force (b = 0.17, p < 0.01) and the process time (b = 0.13, p < 0.01), whereas the tangential velocity seemed to slightly effect the results (b = 0.09, p = 0.09), and the feed of the finishing belt likely has no influence on the roughness values (b = 0.02, p = 0.38). This latter result supported the assumption made in the simulation model presented that the feed of the finishing belt can be neglected for the finishing of ductile materials. 4. Simulation results For the initialization and validation of the developed simulation model, the corresponding simulations were conducted and compared to the real experiments. In order to achieve accurate simulation results, appropriate values for the model resolution and the time step are necessary. 4.1. Simulation setup While the resolution of the workpiece model mainly defines the computational speed, the accuracy of the tool model only affects the memory requirements. For the following results, a workpiece model of size 0.4 mm 0.4 mm (Fig. 1a) with a resolution of
h h0
1m
(3)
have to be determined (Fig. 6). For all simulation runs described in this paper, the process parameter values were set to m = 0.65 and kc = 10,000 N/mm2. These values were determined in calibration experiments by minimizing the mean deviation between the measured and simulated roughness values for a subset of the experimental design. In this subset, only the process time t 2 {10 s, 35 s, 60 s} was varied and the other parameters were fixed to the center of their domain (Table 1). The obtained parameter values also resulted in a good agreement for those experiments which were not considered during the calibration process. The computation time for the simulation of the material removal process and for the force-control operations mainly depends on the amount of height values and the large number of simulation steps. In the following results, 1.7 million height values were intersected with the tool model in each step. By using the simulation system presented in this paper, this leads to a computation time of about 160 s for each rotation of the workpiece when using a standard desktop computer. In order to speed up the computation, the default algorithm was parallelized using the computer graphics hardware. Applying a parallel computation of the force calculation algorithm, the computation time for a single rotation could be decreased to 3 s. 4.2. Statistical analysis In order to compare the effects observed in the experiments (Section 3) with simulation data, the simulated and measured maximum height of profile Rz is presented in Fig. 7 and an additional second order multiple regression model [16] with t-statistic-based parameter selection was fitted to the simulated roughness values. For the calculation of a suitable regression model, one extreme simulation result (vt = 5 m/min) leading to the prediction of too high roughness values was not taken into account (cf. ‘‘Extreme result’’ in Fig. 7). This problem occurred because the elastic behavior of the finishing belt was not yet taken into account in the process model. The comparison of the simulated and measured data presented in Fig. 7 shows an overestimation of the Rz value by the simulation, but the regression analysis indicated that the simulation approach presented here is able to predict the main parameter effects (cf. Section 3). Again, the contact force had the strongest effect (b = 0.17, p < 0.01), followed by the process time (b = 0.16,
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P. Kersting et al. / CIRP Annals - Manufacturing Technology 64 (2015) 321–324
Fig. 7. Measured and simulated maximum height of profile Rz. The extreme result (red) was removed for the statistical analysis. The green points illustrate the variation of the measured Rz value.
p < 0.01). The magnitude of both coefficients was close to the corresponding values of the experiments. In addition, the better reproducibility of the simulation results led to the inclusion of higher-level terms into the regression model. The quadratic effect of the force (b = 0.20, p < 0.01) and the interaction with the time (b = 0.18, p < 0.01), as well as the linear (b = 0.07, p < 0.05) and quadratic (b = 0.39, p < 0.01) effect of the tangential velocity and its interaction with the time (b = 0.12, p < 0.05) became significant. Hence, the simulation allows all important parameter effects to be studied. 4.3. Analysis of surface topographies In addition to the qualitative results and the statistical analysis of the process parameters and their influence on the surface roughness values, the resulting angle between the crossing grooves on the workpiece surface can also be predicted by the simulation system. In Fig. 8, the influence of different values of the tangential velocity vt on the surface topography is shown.
Fig. 8. Microscopic views of measured and simulated surface topographies for different values of vt.
A comparison of the microscopic views indicates that the simulation is able to qualitatively predict the different directions of the grooves on the resulting surfaces depending on the tangential velocity chosen. This is especially noticeable for vt = 5 m/min since the roughness value was too high for this tangential velocity (Section 4.1). This result demonstrates that the model of the process kinematic allows, even in these cases, for a qualitative prediction of the resulting surfaces. 5. Conclusion and outlook In this paper, a simulation system for modeling the forcecontrolled micro-finishing process was presented. This system is
based on numerical models for the workpiece and the tool, utilizing data from topographic scans. Based on the geometrical description of the engagement of the tool with the workpiece, the process forces can be determined and used in a force-controlled model to reach a predefined contact force during the honing process. In an experimental and simulative analysis, the influence of different process parameters was analyzed. Both the statistical evaluation and the analysis of the workpiece topography show the applicability of the simulation system to predict the main parameter effects in the approach used here. In order to make this simulation system manageable for the analysis of different process parameter combinations, the computation time was drastically reduced by applying a parallel computation of the intersection algorithm using computer graphics hardware. Nevertheless, the results presented in this paper also showed the limitations of this modeling approach. The simulation of processes with high contact forces leads to unrealistic predictions since the elasticity of the finishing belt is not modeled. This will be analyzed and modeled in future studies. Acknowledgements This work is based on the research project ‘‘Experimentelle und simulationsgestu¨tzte Grundlagenuntersuchungen zur Oberfla¨chenstrukturierung durch das Kurz-und Langhubhonen’’ (DFG BI 498/40-1), which has been kindly funded by the German Research Foundation (DFG).
References [1] Biermann D, Goeke S, Tillmann W, Nebel J (2013) Improvement of Wear Resistant Thermally Sprayed Coatings by Microfinishing. Annals of the CIRP 62(1):559–562. [2] Khellouki A, Rech J, Zahouani H (2013) Micro-scale Investigation on Belt Finishing Cutting Mechanisms by Scratch Tests. Wear 308(1):17–28. [3] Karpuschewski B, Goldau H, Stolze R (2014) Process Force and Technology Model for Designing and Controlling Finishing Operations with Rotating Grinding Tools. Annals of the CIRP 63(1):337–340. [4] Aurich JC, Kirsch B (2012) Kinematic Simulation of High-performance Grinding for Analysis of Chip Parameters of Single Grains. CIRP Journal of Manufacturing Science and Technology 5:164–174. [5] Transchel R, Leinenbach C, Wegener K (2014) Cutting and Ploughing Forces for Sall Clearance Angles of Hexa-octahedron Shaped Diamond Grains. Annals of the CIRP 63(1):325–328. [6] Brinksmeier E, Aurich JC, Govekar E, Heinzel C, Hoffmeister H-W, Klocke F, Peters J, Rentsch R, Stephenson DJ, Uhlmann E, Weinert K, Wittmann M (2006) Advances in Modeling and Simulation of Grinding Processes. Annals of the CIRP 55(2):667–696. [7] Altintas Y, Kersting P, Biermann D, Budak E, Denkena B, Lazoglu I (2014) Virtual Process Systems for Part Machining Operations. Annals of the CIRP 63(2): 585–605. [8] Feng Q, Ren C, Pei Z (2015) A Physics-Based Predictive Model for Number of Contact Grains and Grain Depth of Cut in Honing. Machining Science and Technology 19(1):50–70. [9] Voronov SA, Gouskov AM, Bobrenkov OA (2009) Modelling of Bore Honing. International Journal of Mechatronics and Manufacturing Systems 2(5): 566–579. [10] Gouskov AM, Voronov SA, Butcher EA, Sinha SC (2004) Simulation of Machined Surface Formation while Honing. ASME International Mechanical Engineering Congress and Exposition, 947–954. [11] Reizer R, Pawlus P (2012) Modelling of Plateau Honed Cylinder Surface Topography. Journal of Engineering Manufacture 226(9):1564–1578. [12] Goeldel B, El Mansori M, Dumur D (2012) Macroscopic Simulation of the Liner Honing Process. Annals of the CIRP 61(1):319–322. [13] Covington P, Sabri L, Le-Lan JV (2009) Macroscopic Cylinder Honing Process Simulation. 12th CIRP Conference on Modeling of Machining Operations, San Sebastian, 7–8 May 2009. [14] Buj-Corral I, Vivancos-Calvet J, Coba-Salcedo M (2014) Modelling of Surface Finish and Material Removal Rate in Rough Honing. Precision Engineering 38(1):100–108. [15] Joliet R, Kansteiner M, Kersting P (2014) A Process Model for Force-controlled Honing Simulations. 3rd CIRP Global Web Conference on Production Engineering Research, 3–5 June 2014. [16] Myers RH, Montgomery DC, Anderson-Cook CM (2009) Response Surface Methodology, Wiley, New York. [17] Kienzle O (1952) Die Bestimmung von Kra¨ften und Leistungen an spanenden. Werkzeugen und Werkzeugmaschinen VDI-Z 94(11):299–305.
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Modeling and simulative analysis of the micro-finishing process Petra Kersting a,b,*, Raffael Joliet a, Michael Kansteiner a a
Institute of Machining Technology, TU Dortmund University, Baroper Straße 303, 44227 Dortmund, Germany Institute of Manufacturing Technology and Quality Management, Universita¨tsplatz 2, 39106 Magdeburg, Germany Submitted by Klaus Weinert (1), Dortmund, Germany. b
A R T I C L E I N F O
A B S T R A C T
Keywords: Honing Modeling Surface
Honing operations are primarily applied to enhance tribologically loaded surfaces. In order to reduce the experimental effort during process design and optimization, a prediction of the specific surface topography resulting from a particular honing operation is necessary. Therefore, a high-resolution geometric process model for force-controlled honing operations was developed, which utilizes numerical data of tools and workpieces from topographic scans. In this paper, the modeling approach is presented and applied to a micro-finishing process with different process parameter values. The simulation results are also compared to surface topographies generated in experiments in order to validate the simulation model. ß 2015 CIRP.
1. Introduction Honing operations are used to reduce form and dimensional errors and to influence frictional properties of tribologically loaded surfaces. A typical application of short-stroke honing processes, so called micro-finishing, is the manufacturing of crankshaft bearings [1]. Due to the complexity of the material removal mechanisms [2] and the strong effects and interactions of the process parameter values on the topography of the resulting workpieces, the manufacturing of surfaces with the desired characteristics is a great challenge. Often a great deal of process expertise and many experiments are necessary to achieve the required properties [3]. In order to gain deeper process knowledge and to reduce the number of experiments, simulation systems can be used, which allow a virtual analysis and optimization of processes. An extensive overview of recent developments in the simulation of machining and grinding processes [4,5] is given by Brinksmeier et al. [6] and Altintas et al. [7]. For the simulation of honing operations, different models focusing on specific aspects of the process are known in literature [8–14]. Voronov et al. [9,10] used numerical models to simulate the dynamic tool behavior of a bore-honing process on the macroscopic level. Reizer and Pawlus [11] developed a method for computer-generated topographies of plateau-honed cylinder surfaces based on measured data. A macroscopic simulation of the honing process was developed by Goeldel et al. [12], which takes the cylinder and tool geometry as well as the initial roughness values into account. Covington et al. [13] presented a macroscopic simulation using FEM, while statistical models were investigated by Buj-Corral et al. [14]. In contrast to these approaches which are based on characteristic values (e.g., roughness), the system proposed in this paper
* Corresponding author. E-mail address: [email protected] (P. Kersting). http://dx.doi.org/10.1016/j.cirp.2015.04.014 0007-8506/ß 2015 CIRP.
allows the prediction of the resulting surface characteristics based on original topographic data. A high resolution geometrical representation combined with a force-control model allows for an accurate prediction of the resulting surface characteristics. This simulation system, the experimental setup for the validation experiments, and a comparison of simulated and machined results will be presented in this paper. 2. Modeling of the micro-finishing process The simulation of honing processes requires a geometric modeling of the tool and the workpiece and of their engagement situation [7]. In this article, a simulation system is presented which represents the workpiece and the finishing belt by height fields [15]. By geometrically intersecting the tool and the workpiece model, the uncut chip shape can be described and analyzed in order to predict the cutting forces. These forces are used in an additional control model in order to simulate force-controlled operations. 2.1. Geometric models of the tool and the workpiece For a detailed modeling of the resulting surfaces which are free of undercuts, both the workpiece and the tool are geometrically represented by height fields (Fig. 1a). The basic idea of this efficient modeling technique is to discretize an object by parallel line segments of variable length which are arranged on a grid-like structure over a defined domain (Fig. 1b) [7]. In order to analyze the micro-finishing process, this domain is curved so as to model the finishing belt and the geometry of the workpiece. In order to be able to analyze the resulting honing structures on the workpiece surface, a high resolution of the grid is necessary. The values of the height fields are initialized utilizing measured data of the tool and the workpiece. For this purpose, topography
322
P. Kersting et al. / CIRP Annals - Manufacturing Technology 64 (2015) 321–324
Fig. 3. Calculation of the uncut chip thickness h for each row of the removed material in order to calculate the normal force on the tool. In the cutting direction, the uncut chip thickness is determined by using the maximum and the minimum values. All force values are summed up perpendicular to the cutting direction.
Fig. 1. (a) Experimental setup and simulated workpiece surface. For the simulation of the process, only a very small area of 0.4 mm 0.4 mm is taken into account. (b) The height values are defined with respect to a two-dimensional reference area.
scans had to be made using, e.g., a confocal white light microscope. The model of the finishing belt is limited to the contact area and is assumed to be representative for the whole belt. Since the model does not take tool wear into account, the belt feed is neglected in the simulation model. 2.2. Modeling of the material removal process The approach developed here is based on a time-domain simulation system [15]. For each discrete time step, the relative position of the tool and the workpiece is updated and the intersection between the two models has to be computed in order to calculate the current material removal. Since the finishing belt, which is pressed against the workpiece by an elastic roller, adapts to the shape of the workpiece in the contact area and, thus, the radii of the finishing belt and the outer shaft are equal, the engagement can be limited to this twodimensional region (Fig. 2a). For each height value of the workpiece model, the nearest height value of the tool model in surface normal direction is determined and this value is used to clip the height value of the workpiece (Fig. 2b). As a result, the intersected and removed parts define a model of the uncut chip, which is used for the force calculation.
an empirical model according to [15]. For this purpose, the uncut chip thickness h is necessary, which can be determined using the model of the removed material (Section 2.2). For each row of the height values the uncut chip thickness h is determined (Fig. 3). These values are used to calculate local force values, which are then combined to compute the normal force. By dividing this value by the contact area, the surface pressure is obtained [15]. The calculated pressure value is used in the control model to adapt the radial infeed rinf of the tool. For each time step t, the radial infeed rinf,t is updated, based on the smoothed pressure difference Dpsmooth,t, which is a weighted sum of currently and previously calculated pressure values: r inf;t ¼ r inf;t1 þ f correction ðD psmooth;t Þ;
f correction > 0
D psmooth;t ¼ D psmooth;t1 ð1 aÞ þ ð psim;t ptarget Þ a; a 1:
(1) 0 (2)
The parameters fcorrection and a characterize the behavior of the control mechanism, and ptarget defines the pressure value used in the real experiments. This value was calculated by assuming a constant contact area. If the simulated pressure value psim,t is too high, the radius of the tool model is increased, which leads to a lower engagement of the grains. By applying this approach, the simulation of the force-controlled process becomes possible. The influence of the parameter a is presented in Fig. 4. Using both parameter values, a = 0.25 and a = 0.5, the simulation is able to match the predefined force of 400 N. With a = 0.25, the control tends to overshoot the predefined force value. Higher values for a resulted in an unstable control behavior.
Fig. 2. (a) The outer shell of a cylinder was used to model both the shaft perimeter and the finishing belt during the contact situation. (b) For each time step, the relative position of the tool and the workpiece is calculated by intersecting each height value with the nearest value of the tool model.
Fig. 4. Parameterization of the infeed control model and its effect on the process kinematics. The model corrects the radial infeed of the tool model in order to reach a predefined contact force.
2.3. Force calculation and control feedback
3. Experimental setup
In order to model the force-controlled operation, the normal forces and the pressure on the workpiece surface have to be calculated. The forces are determined in each simulation step using
To validate the simulation model, experiments with different values for the parameters process time, tangential velocity, feed of the finishing belt, and contact force were conducted. The
P. Kersting et al. / CIRP Annals - Manufacturing Technology 64 (2015) 321–324
323
Table 1 Process parameters varied in the experiments.
Process time t Tangential velocity vt Feed velocity (belt) vfb Contact force F
Unit
Minimum
Maximum
s m/min mm/min N
10 5 6 60
60 125 64 540
Fig. 6. Simulated transient maximum height of profile Rz for the central point of the experimental design plan. The lines correspond to different parameter values m of the force model and a constant value for kc of 10,000 N/mm2.
Fig. 5. Setup for the validation experiments. A Supfina finishing device is mounted onto a turning machine. The finishing belt is pressed against the rotating workpiece with a predefined force. The belt and the elastic roller used oscillate in the axial direction.
0.3 mm and a tool model of size 1.4 mm 5.5 mm with a resolution of 0.6 mm were chosen. The time step has to be adapted to the resolution of the workpiece [15]. For this purpose, the tool movement is limited to 0.5 mm in each time step in the experiments. In addition to the parameter values of the general simulation setup, those of the empirical force model based on the Kienzle equation [17] F ¼ b kc
experimental investigations are based on a central composite design with 29 experiments. As the axial distance was set to aCCD = 2, the five levels of the design equidistantly cover the experimental region (Table 1). The grounded workpieces made of unhardened 100Cr6 with a diameter of 50 mm were finished using a finishing belt with electrostatically directed Al2O3 grains of size 30 mm. The experiments were conducted under dry conditions utilizing a Supfina finishing device, mounted onto a MAG Boehringer M 670 turning machine (Fig. 5). The oscillation frequency was 21 Hz for all experiments. The experiments were evaluated by fitting a second order multiple regression model to the resulting roughness values. In order to determine the coefficients b integrated into the regression model, the t-statistic was considered [16]. This statistic transforms the effect magnitude, its uncertainty, and the number of experiments used for its estimation, into a p-value which reflects the probability of seeing the results in case of no actual effect of the parameter. The lower the p-value the higher is the evidence for the corresponding parameter effect. The statistic model indicated a significant effect of the force (b = 0.17, p < 0.01) and the process time (b = 0.13, p < 0.01), whereas the tangential velocity seemed to slightly effect the results (b = 0.09, p = 0.09), and the feed of the finishing belt likely has no influence on the roughness values (b = 0.02, p = 0.38). This latter result supported the assumption made in the simulation model presented that the feed of the finishing belt can be neglected for the finishing of ductile materials. 4. Simulation results For the initialization and validation of the developed simulation model, the corresponding simulations were conducted and compared to the real experiments. In order to achieve accurate simulation results, appropriate values for the model resolution and the time step are necessary. 4.1. Simulation setup While the resolution of the workpiece model mainly defines the computational speed, the accuracy of the tool model only affects the memory requirements. For the following results, a workpiece model of size 0.4 mm 0.4 mm (Fig. 1a) with a resolution of
h h0
1m
(3)
have to be determined (Fig. 6). For all simulation runs described in this paper, the process parameter values were set to m = 0.65 and kc = 10,000 N/mm2. These values were determined in calibration experiments by minimizing the mean deviation between the measured and simulated roughness values for a subset of the experimental design. In this subset, only the process time t 2 {10 s, 35 s, 60 s} was varied and the other parameters were fixed to the center of their domain (Table 1). The obtained parameter values also resulted in a good agreement for those experiments which were not considered during the calibration process. The computation time for the simulation of the material removal process and for the force-control operations mainly depends on the amount of height values and the large number of simulation steps. In the following results, 1.7 million height values were intersected with the tool model in each step. By using the simulation system presented in this paper, this leads to a computation time of about 160 s for each rotation of the workpiece when using a standard desktop computer. In order to speed up the computation, the default algorithm was parallelized using the computer graphics hardware. Applying a parallel computation of the force calculation algorithm, the computation time for a single rotation could be decreased to 3 s. 4.2. Statistical analysis In order to compare the effects observed in the experiments (Section 3) with simulation data, the simulated and measured maximum height of profile Rz is presented in Fig. 7 and an additional second order multiple regression model [16] with t-statistic-based parameter selection was fitted to the simulated roughness values. For the calculation of a suitable regression model, one extreme simulation result (vt = 5 m/min) leading to the prediction of too high roughness values was not taken into account (cf. ‘‘Extreme result’’ in Fig. 7). This problem occurred because the elastic behavior of the finishing belt was not yet taken into account in the process model. The comparison of the simulated and measured data presented in Fig. 7 shows an overestimation of the Rz value by the simulation, but the regression analysis indicated that the simulation approach presented here is able to predict the main parameter effects (cf. Section 3). Again, the contact force had the strongest effect (b = 0.17, p < 0.01), followed by the process time (b = 0.16,
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Fig. 7. Measured and simulated maximum height of profile Rz. The extreme result (red) was removed for the statistical analysis. The green points illustrate the variation of the measured Rz value.
p < 0.01). The magnitude of both coefficients was close to the corresponding values of the experiments. In addition, the better reproducibility of the simulation results led to the inclusion of higher-level terms into the regression model. The quadratic effect of the force (b = 0.20, p < 0.01) and the interaction with the time (b = 0.18, p < 0.01), as well as the linear (b = 0.07, p < 0.05) and quadratic (b = 0.39, p < 0.01) effect of the tangential velocity and its interaction with the time (b = 0.12, p < 0.05) became significant. Hence, the simulation allows all important parameter effects to be studied. 4.3. Analysis of surface topographies In addition to the qualitative results and the statistical analysis of the process parameters and their influence on the surface roughness values, the resulting angle between the crossing grooves on the workpiece surface can also be predicted by the simulation system. In Fig. 8, the influence of different values of the tangential velocity vt on the surface topography is shown.
Fig. 8. Microscopic views of measured and simulated surface topographies for different values of vt.
A comparison of the microscopic views indicates that the simulation is able to qualitatively predict the different directions of the grooves on the resulting surfaces depending on the tangential velocity chosen. This is especially noticeable for vt = 5 m/min since the roughness value was too high for this tangential velocity (Section 4.1). This result demonstrates that the model of the process kinematic allows, even in these cases, for a qualitative prediction of the resulting surfaces. 5. Conclusion and outlook In this paper, a simulation system for modeling the forcecontrolled micro-finishing process was presented. This system is
based on numerical models for the workpiece and the tool, utilizing data from topographic scans. Based on the geometrical description of the engagement of the tool with the workpiece, the process forces can be determined and used in a force-controlled model to reach a predefined contact force during the honing process. In an experimental and simulative analysis, the influence of different process parameters was analyzed. Both the statistical evaluation and the analysis of the workpiece topography show the applicability of the simulation system to predict the main parameter effects in the approach used here. In order to make this simulation system manageable for the analysis of different process parameter combinations, the computation time was drastically reduced by applying a parallel computation of the intersection algorithm using computer graphics hardware. Nevertheless, the results presented in this paper also showed the limitations of this modeling approach. The simulation of processes with high contact forces leads to unrealistic predictions since the elasticity of the finishing belt is not modeled. This will be analyzed and modeled in future studies. Acknowledgements This work is based on the research project ‘‘Experimentelle und simulationsgestu¨tzte Grundlagenuntersuchungen zur Oberfla¨chenstrukturierung durch das Kurz-und Langhubhonen’’ (DFG BI 498/40-1), which has been kindly funded by the German Research Foundation (DFG).
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