- Email: [email protected]
Method for enhanced accuracy in machining curvilinear profiles on wire-cut electrical discharge machines
Precision Engineering 44 (2016) 75–80
Contents lists available at ScienceDirect
Precision Engineering journal homepage: www.elsevier.com/locate/precision
Method for enhanced accuracy in machining curvilinear profiles on wire-cut electrical discharge machines Andrzej Werner ∗ Bialystok University of Technology, Faculty of Mechanical Engineering, Wiejska 45 C, 15-351 Bialystok, Poland
a r t i c l e
i n f o
Article history: Received 3 March 2015 Received in revised form 27 August 2015 Accepted 14 October 2015 Available online 21 October 2015 Keywords: CAD/CAM system Coordinate measurements Curvilinear profile Wire-cut electrical discharge machine
a b s t r a c t The present article describes a method for enhanced accuracy in machining components produced on CNC wire-cut electrical discharge machines. In this method, machining programs are generated on the basis of nominal geometric models of the produced objects, developed in CAD/CAM systems. After the initial machining, coordinate measurements are performed. On the basis of these measurement results, the values and distribution of the machining deviations are determined. The obtained information is then used to modify the nominal geometric models of the produced objects and to correct the machining programs. After that, the machining process and measurements are repeated. The method described in the present article was verified using the example of a curvilinear profile, produced with the use of a wire-cut electrical discharge machine. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Wire electrical discharge machining (WEDM) is one of the most popular methods for producing precise machine parts. The method is used in the manufacture of tooling for production (injection mould dies, blanking dies, etc.) [1]. In this case, achieving the appropriate machining precision depends on a number of parameters: for example, the course of the electrical discharge, wire tension and feed rate, motion, and dielectric flow rate [2–4]. The presently used methods for increasing the accuracy of components produced using this technology focus either on the in-process adjustment of the wire position, or on the development of analytical models of processes, and on applying these models at the machining preparation stage. A system based on tracking and controlling the wire position is presented in [5]. In this system, deviations of the actual wire position in relation to the programmed position are measured and corrections are made to the wire position during the machining process. In comparison to conventional cutting, this method allows for cutting complex shapes and simple contours at greater speed. A phenomenon of key importance in machining accuracy is wire lag in the inter-electrode gap region, described in [6]. In the article, Sarkara et al. propose an innovative method to measure the force intensity and wire lag, depending on the selected cutting parameters. Based on that, an analytical
∗ Tel.: +48 85 746 92 60; fax: +48 85 746 92 10. E-mail address: [email protected] http://dx.doi.org/10.1016/j.precisioneng.2015.10.004 0141-6359/© 2015 Elsevier Inc. All rights reserved.
model of the process has been developed, which successfully eliminates unfavourable phenomena and increases the cutting accuracy. Obtaining the appropriate angular accuracy while cutting ruled surfaces is another issue. The experiments presented in [7] aimed to create an analytical model describing the dependence of the cutting angle error on the selected machining parameters, and applying this model at the preparation stage of the cutting process results in a significant decrease in the angular deviation of the cut surfaces. Another, universal method of increasing the accuracy of components manufactured using CNC machines, is a method using coordinate measurements. This method is applied predominantly in machining at milling machine centres. The machining process correction is conducted on the basis of coordinate measurements performed on a machine tool, or on a coordinate-measuring machine. Article [8] presents a method where, after the initial machining of the object, the coordinate measurements were performed on the CNC machine. Once the component was machined, it could be measured by the probe-inspection system. Based on these measurement data, a deterministic surface was established according to a bicubic B-spline surface. Through the spatial statistical analysis of the residual errors of a regression model, the machining errors were broken down into systematic errors and random errors. For the systematic errors, the numeric control program was modified, and the compensation for the calculated machining errors could be conducted without altering the machining benchmarks. The CNC machine-tool interpolator, using a path compensation method for a repeated contour machining process, is presented in paper [9]. In addition to a conventional contour interpolation
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algorithm, the proposed interpolator also included contour-error calculation, data extraction and contour-error interpolation algorithms, so that the previous contour machining result could be introduced to improve the accuracy of the subsequent repeated machining. Mathematical analysis and experimental evaluation are presented in this paper. The previous machining result (i.e. the machined contour) could be recorded by the feedback devices (e.g. encoders) in the CNC machine, or by a coordinate-measuring machine (CMM). The method for increase machining accuracy proposed in the article is applied in the machining of curvilinear profiles. In this method, the creation of functions describing the distribution of machining deviations is omitted. The correction of the part programs is carried out indirectly by rebuilding the nominal CAD model of the object into a corrected geometrical model, taking into account the deviations observed after the initial machining of a workpiece. Reconstruction of the CAD model is done by direct use of the coordinate-measurement results (deviations observed), carried out after pre-treatment. The expected effects of the application of the proposed method are an increase in the accuracy of the manufacturing curvilinear profiles and a simplification of the whole process of the enhanced machining accuracy. The present article is an attempt to apply this method to machining objects on computer numerically controlled, wire-cut, electrical discharge machines. 2. Machining error correction method 2.1. Procedure As has already been mentioned above, the machining error correction method described in the present article is based on coordinate-measurement results. This, first of all, requires that a nominal geometric model of the machined workpiece is created (1) (Fig. 1). In the case of manufacturing flat parts using of wire-cut electrical discharge machines, two-dimensional wireframe models are sufficient. This model is a basis for generating a program in the CAD/CAM system to control the machining process (2). After a workpiece has been produced on the WEDM machine (3), coordinate measurements are performed (4). Owing to the fact that it is not possible to install a machine-tool measuring probe on a wire-cut electrical discharge machine, measurements are conducted using a coordinate-measuring machine. In the next stage of the process, the machining deviations and their components in the X and Y axes are determined from the results of coordinate measurements (5). Further decisions are made on the basis of the provided information for the observed machining errors (6). If the desired accuracy is obtained, the correction process is not necessary. If the required accuracy of the machined profile has not been achieved, correction
of machining errors is performed, which requires the construction of a corrected geometric model of the produced object (7). Such a model is developed after the nominal model has been modified on the basis of the coordinate-measurement results. The components of the deviations observed on the X and Y axes are determined on the basis of the information included in the measurement program. These components are used to create corrected geometric models of workpieces. The method of determining the deviation components and modifying nominal geometric models is described in Section 2.2 of the article. Corrected geometric models are the basis for generating new machining programs (2). After the workpiece under examination has been machined again (3), coordinate measurements are repeated (4). This allows for the evaluation of the efficiency of the performed correction (5). If the required machining accuracy is achieved, the process can be finished, and if the observed deviations are too large, the procedure can be repeated. 2.2. Determining machining deviations and modifying geometric model of profile Owing to the nature of the process, objects produced on wirecut electrical discharge machines are always described using ruled surfaces. Coordinate measurements consist of measuring a single contour on the surface describing the walls of the cut profile. A surface-scanning procedure of the UVScan type (the PC-DMIS system) can be used for this purpose. The procedure makes use of the fact that parametric surfaces used in CAD systems are objects described with the use of two parameters, u and v [10]. In the case of ruled surfaces, the number of measurement points is adopted in the u parameterization direction, whereas the height at which the cut profile is going to be measured is established in the v parameterization direction. In order to determine the shape accuracy of machining the curvilinear profile describing the manufactured object, the machining deviations at the measurement points should be determined. The degree of the determined deviations (Fig. 2) is described by the distances between the points located on the nominal profile of the CAD model and their corresponding points, observed as a result of measurements conducted on a coordinate-measuring machine. Deviations are determined in the normal direction to the machined profile in the machining plane (the XY plane in wirecut electrical discharge machines). The initial data for determining the observed deviations and their components are coordinatemeasurement results, including information on the coordinates of both the nominal points and the points observed during the measurement, the observed global machining deviations, and the direction cosines determining the deviation direction. After this information has been obtained, the correction process of the curvilinear profile describing the shape of the produced
Fig. 1. Machining error correction method.
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Fig. 3. Creating corrected profile.
Fig. 2. Graphical representation of machining deviation.
object can be implemented. First, the components of the observed machining deviations for each of the axes of the coordinate system of the machine tool are determined (for each measurement point). The following dependencies are used in the calculations: Tix = Ti × cos ˇi Tiy = Ti × cos ˛i
(1)
where i is the number of measurement point; Ti is the deviation observed at ith measurement point; Tix , Tiy are the components of observed deviation; and cos ˛ , cos ˇ are the direction cosines at subsequent measurement points. After determining the components of the observed deviations, the nominal geometric model of the produced object is corrected. New, corrected point coordinates should be determined first, according to the dependencies: xikor = xinom − Tix yikor = yinom − Tiy
• passes of the wire were programmed (rough cutting and two finishing passes) in order to achieve the highest machining accuracy. • In addition to the shaped hole, base surfaces were also cut in the process. The surfaces were then used to define the measurement-coordinate system, which aimed at minimizing setting errors, resulting from moving the machined workpiece from the machine tool to the coordinate-measuring machine. • The cutting operation was performed with a brass wire of 0.25 mm in diameter. • The machining of the part was performed on the WEDM machine, Accutex AU-300i. (bidirectional accuracy of positioning of an axis: X 1.436 m, Y 1.309 m; bidirectional repeatability of positioning of an axis: X 0.80548 m, Y 1.099 m—ISO 230-2:2006). • The basic parameters of the last finishing wire pass were as follows: feed rate 10 mm2 /min; gap voltage 44 V.
(2)
where xinom , yinom are the nominal coordinates of machined curvi-
linear profile; and xikor , yikor are the corrected coordinates of machined curvilinear profile. The newly determined point coordinates are used to create a corrected profile to be machined. It includes information on the occurring errors in machining the object under concern. In developing the curvilinear profile, interpolation techniques are applied. After the coordinates of the corrected points have been determined, a curve describing the corrected profile is interpolated through these coordinates (Fig. 3). In order to create the corrected profile, the NURBS technique is used. 3. Experimental verification The methodology presented above has been verified on an example of machining a curvilinear profile, described with the use of a NURBS curve. This curve was constructed on the control polygon with 9 vertices. The degree of the B-spline basis function was n = 3. Fig. 4 shows the curve describing the cut shape, including the control polygon and the machine profile, implemented using a Mastercam system. The technological assumptions were as follows: • A hole was cut in a flat bar made of 2017 aluminium alloy.
Fig. 4. Curve describing the cut shape.
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Fig. 5. Machined workpiece.
Before the machining was carried out, the condition of the wirecut electrical discharge machine was inspected thoroughly. The upper and lower wire guides, as well as the power contactors, were checked, and the procedure of verticality calibration was carried out. After the machining, the workpiece (Fig. 5) was removed from the machine tool and transferred to the coordinate-measuring machine. Control measurements were taken on a Hexagon Metrology Global Performance measuring machine (PC-DMIS software, MPEE = 1.5 + L/333, equipped with a Renishaw SP25M measuring probe and a 20 mm stylus with the ball tip of 2 mm in diameter). The geometric model of the ruled surface, describing the nominal shape of the cut hole, was used to program the measurements. This made it possible for the UVScan command (for automatic measurements of surface objects) to be used. In this case, the u direction was used for determining the number of measurement points, and 200 measurement points were selected, which, taking the length of the profile into consideration, resulted in a distance of 1 mm between the points. The v scanning direction was used to determine the height at which the machined profile was measured. Adopting that v = 0.5, the measurement was conducted in the middle of the height of the cut hole. The obtained distribution of the measurement points is illustrated in Fig. 6. As a result of the performed measurements, information concerning the 200 observed deviations was obtained. Fig. 7a presents the values of 200 deviations at measurement points. The values of all the determined deviations ranged from −0.0114 to 0.0081 mm and their distribution on the machined profile is shown in Fig. 7b. Considering the obtained values of the machining deviations, the decision to carry out the machining error correction process was taken. The construction of a corrected geometric model of the workpiece was performed according to the procedure described in Section 2.2 of the present article. First, the nominal coordinates, the direction cosines and the deviations observed for the 200 measurement points were obtained from the measuring program. Using Eqs. (1) and (2), corrected coordinates were determined for each point. On the basis of these coordinates, a corrected geometric model of the machined profile was created in the Mastercam system; i.e. a NURBS curve was interpolated through the 200 corrected points. On the basis of the corrected geometric model of the workpiece, programs controlling the machining were generated again, using the same parameters that were adopted for the previous machining of the workpiece. The generated corrected machining programs were used for cutting a new shaped hole. Coordinate measurements
Fig. 6. Distribution of measurement points.
were then repeated using the measurement program developed previously. A plot presenting the measurement results before and after performing the correction is shown in Fig. 8a. The ‘flatter’ characteristics of the plot representing the deviation, observed after the correction was performed, can be easily noticed here. Distribution of the deviations observed before and after performing the machining error correction is illustrated in Fig. 8b. It shows a significant improvement in accuracy for most workpiece profiles. There are two regions on the right side of the profile where the sign of the deviations changed from “ + ” to “−”. Subsequent adjustments of the profile in these positions did not affect the further increase in machining accuracy. It should be noted that the absolute values of deviations in these regions are 25% smaller after performed correction. After an analysis of the results obtained once the coordinate measurements had been made, it appeared that the deviations observed after the machining error correction ranged from −0.0066 to 0.0057 mm. In comparison to the previously obtained results, there was a significant increase in the accuracy of the curvilinear profile. The verification of the presented method was performed on the two next profiles. The obtained results were very similar to the results presented in the article.
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79
Fig. 7. The results of the coordinate measurements: (a) values of deviations at measurement points; and (b) distribution of the observed deviations on machined profile.
Fig. 8. Distribution of deviations observed before and after performing machining error correction: (a) graph of the machining deviations; and (b) distribution of the observed deviations on machined profile.
Table 1 Observed machining deviations. Observed deviations
Before correction
After correction
Max. negative deviation [mm] Max. positive deviation [mm] Average absolute values of deviations for 200 measurement points
−0.0114 0.0081 0.0046
−0.0066 0.0057 0.0023
4. Conclusions The implementation of the method of correcting curvilinear profile errors, described in the present article, allowed for a significant increase in the machining accuracy. Table 1 presents the results observed before and after performing the correction process. The results show a considerable decrease in the maximum observed machining deviations. The average absolute values of the deviations determined for all the measurement points after the correction were much lower in comparison to the values before the correction. Therefore, the obtained scatter of the occurring machining deviations was smaller. The implementation of the method of correcting machining errors is relatively simple. It does not require any additional investments because typical equipment of production departments of companies can be used in this case (CAD/CAM systems, CNC machine tools, coordinate measuring machines). The fact that modern CAD/CAM systems are capable of parametrically connecting the generated tool paths and the geometry of the machined workpieces is an additional advantage here. It means that once processed, technological data do not need to be entered into systems again. As a consequence, after the geometric models of workpieces have been
modified, the tool paths are changed automatically. It should be mentioned that in the case of performing the whole process of machining error correction on the same workpiece, it is necessary to machine this workpiece initially (before the correction) with a uniformly distributed machining allowance, which makes it possible to continue the process of machining error correction if too much material is removed during the pre-treatment stage. Acknowledgement The work is supported by the Polish Ministry of Science and Higher Education under the statute activity under project No. S/WM/3/2010. References [1] Newman KH, Ho ST, Rahimifard S, Allen RD. State of the art in wire electrical discharge machining (WEDM). Int J Mach Tools Manuf 2004;44(12–13): 1247–59. [2] Cabanes I, Portillo E, Marcos M, Sanchez JA. On-line prevention of wire breakage in wire electro-discharge machining. Rob Comput Integr Manuf 2008;24(2):287–98. [3] Aniza A, Bulan A, Norliana MA. Influence of machine feed rate in WEDM of Titanium Ti-6al-4v with constant current (6a) using brass wire. Procedia Eng 2012;41:1806–11. [4] Sanchez JA, Rodil JL, Herrero A, Lopez de Lacallea LN, Lamiki A. On the influence of cutting speed limitation on the accuracy of Wire-EDM corner-cutting. J Mater Process Technol 2007;182(1–3):574–9. [5] Dauw DF, Beltrami I. High-precision wire-EDM by online wire positioning control. CIRP Ann Manuf Technol 1994;43(1):193–7. [6] Sarkara S, Sekhb M, Mitraa S, Bhattacharyya B. A novel method of determination of wire lag for enhanced profile accuracy in WEDM. Precis Eng 2011;35(2):339–47.
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[7] Sanchez JA, Plaza S, Ortega N, Marcos M, Albizuri J. Experimental and numerical study of angular error in wire-EDM taper-cutting. Int J Mach Tools Manuf 2008;48(12–13):1420–8. [8] Chen Y, Gao J, Deng H, Zheng D, Chen X, Kelly R. Spatial statistical analysis and compensation of machining errors for complex surfaces. Precis Eng 2013;37(1):203–12.
[9] Lo CC, Hsiao CY. CNC machine tool interpolator with path compensation for repeated contour machining. Comput-Aided Des 1998;30(1): 55–62. [10] Piegl L, Tiller W. The NURBS Book. New York, NY: Springer; 1997.
Contents lists available at ScienceDirect
Precision Engineering journal homepage: www.elsevier.com/locate/precision
Method for enhanced accuracy in machining curvilinear profiles on wire-cut electrical discharge machines Andrzej Werner ∗ Bialystok University of Technology, Faculty of Mechanical Engineering, Wiejska 45 C, 15-351 Bialystok, Poland
a r t i c l e
i n f o
Article history: Received 3 March 2015 Received in revised form 27 August 2015 Accepted 14 October 2015 Available online 21 October 2015 Keywords: CAD/CAM system Coordinate measurements Curvilinear profile Wire-cut electrical discharge machine
a b s t r a c t The present article describes a method for enhanced accuracy in machining components produced on CNC wire-cut electrical discharge machines. In this method, machining programs are generated on the basis of nominal geometric models of the produced objects, developed in CAD/CAM systems. After the initial machining, coordinate measurements are performed. On the basis of these measurement results, the values and distribution of the machining deviations are determined. The obtained information is then used to modify the nominal geometric models of the produced objects and to correct the machining programs. After that, the machining process and measurements are repeated. The method described in the present article was verified using the example of a curvilinear profile, produced with the use of a wire-cut electrical discharge machine. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Wire electrical discharge machining (WEDM) is one of the most popular methods for producing precise machine parts. The method is used in the manufacture of tooling for production (injection mould dies, blanking dies, etc.) [1]. In this case, achieving the appropriate machining precision depends on a number of parameters: for example, the course of the electrical discharge, wire tension and feed rate, motion, and dielectric flow rate [2–4]. The presently used methods for increasing the accuracy of components produced using this technology focus either on the in-process adjustment of the wire position, or on the development of analytical models of processes, and on applying these models at the machining preparation stage. A system based on tracking and controlling the wire position is presented in [5]. In this system, deviations of the actual wire position in relation to the programmed position are measured and corrections are made to the wire position during the machining process. In comparison to conventional cutting, this method allows for cutting complex shapes and simple contours at greater speed. A phenomenon of key importance in machining accuracy is wire lag in the inter-electrode gap region, described in [6]. In the article, Sarkara et al. propose an innovative method to measure the force intensity and wire lag, depending on the selected cutting parameters. Based on that, an analytical
∗ Tel.: +48 85 746 92 60; fax: +48 85 746 92 10. E-mail address: [email protected] http://dx.doi.org/10.1016/j.precisioneng.2015.10.004 0141-6359/© 2015 Elsevier Inc. All rights reserved.
model of the process has been developed, which successfully eliminates unfavourable phenomena and increases the cutting accuracy. Obtaining the appropriate angular accuracy while cutting ruled surfaces is another issue. The experiments presented in [7] aimed to create an analytical model describing the dependence of the cutting angle error on the selected machining parameters, and applying this model at the preparation stage of the cutting process results in a significant decrease in the angular deviation of the cut surfaces. Another, universal method of increasing the accuracy of components manufactured using CNC machines, is a method using coordinate measurements. This method is applied predominantly in machining at milling machine centres. The machining process correction is conducted on the basis of coordinate measurements performed on a machine tool, or on a coordinate-measuring machine. Article [8] presents a method where, after the initial machining of the object, the coordinate measurements were performed on the CNC machine. Once the component was machined, it could be measured by the probe-inspection system. Based on these measurement data, a deterministic surface was established according to a bicubic B-spline surface. Through the spatial statistical analysis of the residual errors of a regression model, the machining errors were broken down into systematic errors and random errors. For the systematic errors, the numeric control program was modified, and the compensation for the calculated machining errors could be conducted without altering the machining benchmarks. The CNC machine-tool interpolator, using a path compensation method for a repeated contour machining process, is presented in paper [9]. In addition to a conventional contour interpolation
76
A. Werner / Precision Engineering 44 (2016) 75–80
algorithm, the proposed interpolator also included contour-error calculation, data extraction and contour-error interpolation algorithms, so that the previous contour machining result could be introduced to improve the accuracy of the subsequent repeated machining. Mathematical analysis and experimental evaluation are presented in this paper. The previous machining result (i.e. the machined contour) could be recorded by the feedback devices (e.g. encoders) in the CNC machine, or by a coordinate-measuring machine (CMM). The method for increase machining accuracy proposed in the article is applied in the machining of curvilinear profiles. In this method, the creation of functions describing the distribution of machining deviations is omitted. The correction of the part programs is carried out indirectly by rebuilding the nominal CAD model of the object into a corrected geometrical model, taking into account the deviations observed after the initial machining of a workpiece. Reconstruction of the CAD model is done by direct use of the coordinate-measurement results (deviations observed), carried out after pre-treatment. The expected effects of the application of the proposed method are an increase in the accuracy of the manufacturing curvilinear profiles and a simplification of the whole process of the enhanced machining accuracy. The present article is an attempt to apply this method to machining objects on computer numerically controlled, wire-cut, electrical discharge machines. 2. Machining error correction method 2.1. Procedure As has already been mentioned above, the machining error correction method described in the present article is based on coordinate-measurement results. This, first of all, requires that a nominal geometric model of the machined workpiece is created (1) (Fig. 1). In the case of manufacturing flat parts using of wire-cut electrical discharge machines, two-dimensional wireframe models are sufficient. This model is a basis for generating a program in the CAD/CAM system to control the machining process (2). After a workpiece has been produced on the WEDM machine (3), coordinate measurements are performed (4). Owing to the fact that it is not possible to install a machine-tool measuring probe on a wire-cut electrical discharge machine, measurements are conducted using a coordinate-measuring machine. In the next stage of the process, the machining deviations and their components in the X and Y axes are determined from the results of coordinate measurements (5). Further decisions are made on the basis of the provided information for the observed machining errors (6). If the desired accuracy is obtained, the correction process is not necessary. If the required accuracy of the machined profile has not been achieved, correction
of machining errors is performed, which requires the construction of a corrected geometric model of the produced object (7). Such a model is developed after the nominal model has been modified on the basis of the coordinate-measurement results. The components of the deviations observed on the X and Y axes are determined on the basis of the information included in the measurement program. These components are used to create corrected geometric models of workpieces. The method of determining the deviation components and modifying nominal geometric models is described in Section 2.2 of the article. Corrected geometric models are the basis for generating new machining programs (2). After the workpiece under examination has been machined again (3), coordinate measurements are repeated (4). This allows for the evaluation of the efficiency of the performed correction (5). If the required machining accuracy is achieved, the process can be finished, and if the observed deviations are too large, the procedure can be repeated. 2.2. Determining machining deviations and modifying geometric model of profile Owing to the nature of the process, objects produced on wirecut electrical discharge machines are always described using ruled surfaces. Coordinate measurements consist of measuring a single contour on the surface describing the walls of the cut profile. A surface-scanning procedure of the UVScan type (the PC-DMIS system) can be used for this purpose. The procedure makes use of the fact that parametric surfaces used in CAD systems are objects described with the use of two parameters, u and v [10]. In the case of ruled surfaces, the number of measurement points is adopted in the u parameterization direction, whereas the height at which the cut profile is going to be measured is established in the v parameterization direction. In order to determine the shape accuracy of machining the curvilinear profile describing the manufactured object, the machining deviations at the measurement points should be determined. The degree of the determined deviations (Fig. 2) is described by the distances between the points located on the nominal profile of the CAD model and their corresponding points, observed as a result of measurements conducted on a coordinate-measuring machine. Deviations are determined in the normal direction to the machined profile in the machining plane (the XY plane in wirecut electrical discharge machines). The initial data for determining the observed deviations and their components are coordinatemeasurement results, including information on the coordinates of both the nominal points and the points observed during the measurement, the observed global machining deviations, and the direction cosines determining the deviation direction. After this information has been obtained, the correction process of the curvilinear profile describing the shape of the produced
Fig. 1. Machining error correction method.
A. Werner / Precision Engineering 44 (2016) 75–80
77
Fig. 3. Creating corrected profile.
Fig. 2. Graphical representation of machining deviation.
object can be implemented. First, the components of the observed machining deviations for each of the axes of the coordinate system of the machine tool are determined (for each measurement point). The following dependencies are used in the calculations: Tix = Ti × cos ˇi Tiy = Ti × cos ˛i
(1)
where i is the number of measurement point; Ti is the deviation observed at ith measurement point; Tix , Tiy are the components of observed deviation; and cos ˛ , cos ˇ are the direction cosines at subsequent measurement points. After determining the components of the observed deviations, the nominal geometric model of the produced object is corrected. New, corrected point coordinates should be determined first, according to the dependencies: xikor = xinom − Tix yikor = yinom − Tiy
• passes of the wire were programmed (rough cutting and two finishing passes) in order to achieve the highest machining accuracy. • In addition to the shaped hole, base surfaces were also cut in the process. The surfaces were then used to define the measurement-coordinate system, which aimed at minimizing setting errors, resulting from moving the machined workpiece from the machine tool to the coordinate-measuring machine. • The cutting operation was performed with a brass wire of 0.25 mm in diameter. • The machining of the part was performed on the WEDM machine, Accutex AU-300i. (bidirectional accuracy of positioning of an axis: X 1.436 m, Y 1.309 m; bidirectional repeatability of positioning of an axis: X 0.80548 m, Y 1.099 m—ISO 230-2:2006). • The basic parameters of the last finishing wire pass were as follows: feed rate 10 mm2 /min; gap voltage 44 V.
(2)
where xinom , yinom are the nominal coordinates of machined curvi-
linear profile; and xikor , yikor are the corrected coordinates of machined curvilinear profile. The newly determined point coordinates are used to create a corrected profile to be machined. It includes information on the occurring errors in machining the object under concern. In developing the curvilinear profile, interpolation techniques are applied. After the coordinates of the corrected points have been determined, a curve describing the corrected profile is interpolated through these coordinates (Fig. 3). In order to create the corrected profile, the NURBS technique is used. 3. Experimental verification The methodology presented above has been verified on an example of machining a curvilinear profile, described with the use of a NURBS curve. This curve was constructed on the control polygon with 9 vertices. The degree of the B-spline basis function was n = 3. Fig. 4 shows the curve describing the cut shape, including the control polygon and the machine profile, implemented using a Mastercam system. The technological assumptions were as follows: • A hole was cut in a flat bar made of 2017 aluminium alloy.
Fig. 4. Curve describing the cut shape.
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A. Werner / Precision Engineering 44 (2016) 75–80
Fig. 5. Machined workpiece.
Before the machining was carried out, the condition of the wirecut electrical discharge machine was inspected thoroughly. The upper and lower wire guides, as well as the power contactors, were checked, and the procedure of verticality calibration was carried out. After the machining, the workpiece (Fig. 5) was removed from the machine tool and transferred to the coordinate-measuring machine. Control measurements were taken on a Hexagon Metrology Global Performance measuring machine (PC-DMIS software, MPEE = 1.5 + L/333, equipped with a Renishaw SP25M measuring probe and a 20 mm stylus with the ball tip of 2 mm in diameter). The geometric model of the ruled surface, describing the nominal shape of the cut hole, was used to program the measurements. This made it possible for the UVScan command (for automatic measurements of surface objects) to be used. In this case, the u direction was used for determining the number of measurement points, and 200 measurement points were selected, which, taking the length of the profile into consideration, resulted in a distance of 1 mm between the points. The v scanning direction was used to determine the height at which the machined profile was measured. Adopting that v = 0.5, the measurement was conducted in the middle of the height of the cut hole. The obtained distribution of the measurement points is illustrated in Fig. 6. As a result of the performed measurements, information concerning the 200 observed deviations was obtained. Fig. 7a presents the values of 200 deviations at measurement points. The values of all the determined deviations ranged from −0.0114 to 0.0081 mm and their distribution on the machined profile is shown in Fig. 7b. Considering the obtained values of the machining deviations, the decision to carry out the machining error correction process was taken. The construction of a corrected geometric model of the workpiece was performed according to the procedure described in Section 2.2 of the present article. First, the nominal coordinates, the direction cosines and the deviations observed for the 200 measurement points were obtained from the measuring program. Using Eqs. (1) and (2), corrected coordinates were determined for each point. On the basis of these coordinates, a corrected geometric model of the machined profile was created in the Mastercam system; i.e. a NURBS curve was interpolated through the 200 corrected points. On the basis of the corrected geometric model of the workpiece, programs controlling the machining were generated again, using the same parameters that were adopted for the previous machining of the workpiece. The generated corrected machining programs were used for cutting a new shaped hole. Coordinate measurements
Fig. 6. Distribution of measurement points.
were then repeated using the measurement program developed previously. A plot presenting the measurement results before and after performing the correction is shown in Fig. 8a. The ‘flatter’ characteristics of the plot representing the deviation, observed after the correction was performed, can be easily noticed here. Distribution of the deviations observed before and after performing the machining error correction is illustrated in Fig. 8b. It shows a significant improvement in accuracy for most workpiece profiles. There are two regions on the right side of the profile where the sign of the deviations changed from “ + ” to “−”. Subsequent adjustments of the profile in these positions did not affect the further increase in machining accuracy. It should be noted that the absolute values of deviations in these regions are 25% smaller after performed correction. After an analysis of the results obtained once the coordinate measurements had been made, it appeared that the deviations observed after the machining error correction ranged from −0.0066 to 0.0057 mm. In comparison to the previously obtained results, there was a significant increase in the accuracy of the curvilinear profile. The verification of the presented method was performed on the two next profiles. The obtained results were very similar to the results presented in the article.
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Fig. 7. The results of the coordinate measurements: (a) values of deviations at measurement points; and (b) distribution of the observed deviations on machined profile.
Fig. 8. Distribution of deviations observed before and after performing machining error correction: (a) graph of the machining deviations; and (b) distribution of the observed deviations on machined profile.
Table 1 Observed machining deviations. Observed deviations
Before correction
After correction
Max. negative deviation [mm] Max. positive deviation [mm] Average absolute values of deviations for 200 measurement points
−0.0114 0.0081 0.0046
−0.0066 0.0057 0.0023
4. Conclusions The implementation of the method of correcting curvilinear profile errors, described in the present article, allowed for a significant increase in the machining accuracy. Table 1 presents the results observed before and after performing the correction process. The results show a considerable decrease in the maximum observed machining deviations. The average absolute values of the deviations determined for all the measurement points after the correction were much lower in comparison to the values before the correction. Therefore, the obtained scatter of the occurring machining deviations was smaller. The implementation of the method of correcting machining errors is relatively simple. It does not require any additional investments because typical equipment of production departments of companies can be used in this case (CAD/CAM systems, CNC machine tools, coordinate measuring machines). The fact that modern CAD/CAM systems are capable of parametrically connecting the generated tool paths and the geometry of the machined workpieces is an additional advantage here. It means that once processed, technological data do not need to be entered into systems again. As a consequence, after the geometric models of workpieces have been
modified, the tool paths are changed automatically. It should be mentioned that in the case of performing the whole process of machining error correction on the same workpiece, it is necessary to machine this workpiece initially (before the correction) with a uniformly distributed machining allowance, which makes it possible to continue the process of machining error correction if too much material is removed during the pre-treatment stage. Acknowledgement The work is supported by the Polish Ministry of Science and Higher Education under the statute activity under project No. S/WM/3/2010. References [1] Newman KH, Ho ST, Rahimifard S, Allen RD. State of the art in wire electrical discharge machining (WEDM). Int J Mach Tools Manuf 2004;44(12–13): 1247–59. [2] Cabanes I, Portillo E, Marcos M, Sanchez JA. On-line prevention of wire breakage in wire electro-discharge machining. Rob Comput Integr Manuf 2008;24(2):287–98. [3] Aniza A, Bulan A, Norliana MA. Influence of machine feed rate in WEDM of Titanium Ti-6al-4v with constant current (6a) using brass wire. Procedia Eng 2012;41:1806–11. [4] Sanchez JA, Rodil JL, Herrero A, Lopez de Lacallea LN, Lamiki A. On the influence of cutting speed limitation on the accuracy of Wire-EDM corner-cutting. J Mater Process Technol 2007;182(1–3):574–9. [5] Dauw DF, Beltrami I. High-precision wire-EDM by online wire positioning control. CIRP Ann Manuf Technol 1994;43(1):193–7. [6] Sarkara S, Sekhb M, Mitraa S, Bhattacharyya B. A novel method of determination of wire lag for enhanced profile accuracy in WEDM. Precis Eng 2011;35(2):339–47.
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