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5-Axis machining speed enhancement by step length optimization
Journal of Materials Processing Technology 187–188 (2007) 2–5
5-Axis machining speed enhancement by step length optimization B.S. So a , Y.H. Jung b,∗ , T.R. Kurfess c , S.M. Hwang b a
Department of Precision Mechanical Engineering, Pusan National University, Geumjeong-gu, Busan 609-735, South Korea b School of Mechanical Engineering, Pusan National University, Geumjeong-gu, Busan 609-735, South Korea c Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA
Abstract In this paper, an NC data optimization approach for enhancing 5-axis machining speed is presented. It is usual to use expensive commercial CAD/CAM programs for NC data of 5-axis machining, since it needs very large calculations for optimal tool positioning and orientation, tool path planning, and collision-free tool path generation. Since commercial CAD/CAM systems have similar functions and efficiency based on common algorithms of reliable theories, they do not have their own unique features for machining speed and efficiency. In other words, most commercial CAD/CAM systems consider only the characteristics of part geometry to be machined, which means that they generate almost the same NC data if the part to be machined is the same, even though different machines are used for the part. A new approach is proposed for optimizing NC data of 5-axis machining, which is based on the characteristics of the machine to be operated. As a result, the speed of 5-axis machining can increase without losing machining accuracy and surface quality. © 2007 Elsevier B.V. All rights reserved. Keywords: 5-Axis; Optimization; Machining speed; Feed angle; CAD/CAM
1. Introduction Due to the presence of two additional rotational axes, 5-axis machining enables cutting that is considered impossible by 3axis machining, along with reduced setup time and high surface quality. It is well known in the die and mold industry that the gain of 5-axis machining is up to 20 times on 3-axis machining. Most researchers in the early stage of 5-axis machining were focused on tool path planning with collision-free algorithms. Recently, their focus has moved to research on enhancing machining speed and surface quality. Sarma and Rao [1] had proposed a method for 5-axis machining interpolation, which takes into consideration angular feedrate in parametric curve interpolation, in order to improve low surface quality due to inadequate angular velocity. Fleisig and Spence [2] had applied the “nearly arc-length parameterized quintic-spline interpolation” method [3] to multiaxis machining, proposing an interpolation algorithm that simultaneously satisfies translational and rotational move of constant speed. Xua et al. [4] has proposed an angular interpolation algorithm for the bi-parametric curve of intersection between surfaces, resolving the cut-off error problem of the Taylor series that is used in interpolation algorithms for com∗
Corresponding author. Tel.: +82 51 510 2469; fax: +82 51 512 1722. E-mail address: [email protected] (Y.H. Jung).
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.11.167
mercial controllers. In order to use the interpolation function of commercial controllers, Cheng et al. [5] has proposed a method to input the NURBS parameters as NC data, after representing the tool path data as NURBS. In this study, an NC optimizing algorithm is proposed, which takes into account the characteristics of 5-axis machine behavior, can maximize real machining speed and can smooth machine operation for high surface quality. 2. Influence factors on 5-axis machining time The major machining parameters that affect machining speed and surface quality are feedrate, spindle speed, tool path and orientation. In 5-axis machining, the most effective influence factors on machining speed may be defined as the step length, the block processing time, and the ratio between translational and rotational motion of 5-axis machining, which are described in detail in the following sections. 2.1. Step length and feed angle It is known that shorter step length of NC data guarantees better machining quality in general. In the case of shorter step length, the same length of cut requires the controller to process more NC commands. Step length is set as long as the tolerance can allow. Therefore, the machining time is generally inversely
B.S. So et al. / Journal of Materials Processing Technology 187–188 (2007) 2–5
3
Nomenclature Ai , Bi , Ci orientation data of the cutter at the ith NC block ratio between translational and rotational motion Hi during the ith NC block Si step length between the ith and (i + 1)th NC blocks vi unit velocity vector of the cutter at the ith NC block Xi , Yi , Zi location data of the cutter at the ith NC block Greek symbols γi radius of curvature at the ith NC block θi feed angle between the ith and (i + 1)th NC blocks rotational feed angle at the ith NC block θiR R θOPT optimal feed angle for rotational motion translational feed angle at the ith NC block θiT T θOPT optimal feed angle for translational motion
proportional to step length. Recently, most controllers of milling machines have a look-ahead interpolating function for contour cutting. As a result, the machining speed reaches maximum at a specific step length. In the case of look-ahead interpolating controllers, the machining speed depends not only on the step length of NC data, but also on the tool path curvature. In order to consider both of these factors, we have the feed angle θ i as the ratio between the step length and radius of curvature during two successive NC blocks as in Eq. (1). It means direction change during the step length, which can be an independent variable defining the dynamic behavior of the machine tool. θi =
Si γi
(1)
2.2. NC block processing speed Experiments showed that the real feedrate is lower than the command feedrate when a 5-axis machine operates with a too short step length. One of the reasons is the speed of the controller for processing input NC data, since too short step length needs large NC blocks. The block processing speed is defined as the number of NC blocks that a controller can process in 1 s. Therefore, the number of NC blocks to be processed in 1 s should be below the block processing speed of the controller, so that the machine can follow the command feedrate. The block processing speed is the dominant factor for machine speed. 2.3. Ratio of translational to rotational motion Since the servo motor power and gear ratio of translational and rotational motion of 5-axis machines are different, the translational speed may be different from the rotational speed during each NC block. Therefore, these two speeds affect the resulting machining speed of a 5-axis machine. In this study, we have defined the ratio Hi at the ith NC block as in Eq. (2) in order to represent the ratio of translational motion to rotational motion
Fig. 1. Schematic diagram of NC data optimization steps.
of 5-axis machining. The ratio Hi will be used to determine the optimal feed angle for maximum resulting speed. Xi2 Yi2 + Zi2 (2) Hi = A2i Bi2 + Ci2 3. NC data optimization When the actual feedrate does not follow the input feedrate, it becomes impossible to schedule machining time and expect good machined quality. In this study, a step length optimization algorithm is proposed, in order to have the actual machining speed follow the input feedrate by taking into account the behavior of 5-axis machine and controller. An overview of the proposed algorithm is presented in Fig. 1. First, a continuous curved region of the original NC data is derived in order to generate an interpolated spline curve. Then, the optimal feed angle is determined from the machine characteristic database that is established with experiments for machine behavior. Finally, NC data are regenerated on the interpolated curve with new step lengths of the optimal feed angle. Each of the major steps is described in detail in the following subsections. 3.1. Curved section extraction from NC data The NC blocks to be optimized in this study are continuous curved regions. If we generate new NC blocks on the original tool path by changing step lengths of the regions that include a straight line segment or corners, we may cause severe dimensional errors in the machined surfaces. Therefore, continuous curved sections for new NC blocks are extracted by the following criteria (Fig. 2): (a) The feed angle between two successive NC blocks should be less than a specific value, as shown in Eq. (3). In this study, the specific value of θ max is set to be 10◦ mm−1 by the rule of thumb. θi = cos−1 (vi−1 · vi ) ≤ θmax
(3)
4
B.S. So et al. / Journal of Materials Processing Technology 187–188 (2007) 2–5
(c) The step length should be sufficiently short as in Eq. (5), where emax is the tolerance defined when NC data are generated. Si ≤ 8γi emax (5) 3.2. Spline interpolation The tool position and orientation data within the selected sections are interpolated to C2 continuous cubic spline for new NC data. The data can be interpolated with a well-known algorithm [6]. The optimized new NC data will be generated on the interpolated curve, which is described in the following subsection. Fig. 2. Curved section extraction from the given NC data.
3.3. Optimal feed angle
(b) The radius of curvature defined by three successive NC blocks should be within specific values as in Eq. (4). The minimum radius of curvature (γ min ) in this study is set to be the cutting tool radius, and the maximum radius of curvature (γ min ) is set to be the maximum length of workpiece to be cut. γmin < γi < γmax , where γi =
|Si−1 | |Si | (|Si−1 | + |Si |) 2 |Si−1 × Si |
(4)
The optimal feed angle is the key factor for the purpose of this research. In order to get the optimal feed angle from 5-axis machining behavior, we measured machining time according to feed angle for translational and rotational motion (Fig. 3). For these experiments, we generated a simple circular tool path for each motion and measured the real machining time in dry-run conditions. Fig. 3 shows that there are ranges of optimal feed angle with minimum machining time for each input feedrate. We took the mid value of each range as the optimal feed angle in each motion. We will generate new NC blocks with optimal step length based on these optimal values.
Fig. 3. 5-Axis machining time vs. feed angle. (a) Translational motion, (b) rotational motion.
Fig. 4. New NC data generation algorithm by reparameterization.
B.S. So et al. / Journal of Materials Processing Technology 187–188 (2007) 2–5
5
Fig. 5. Applications. (a) Impeller, (b) saddle.
3.4. Optimal NC data generation
5. Concluding remarks
Since the optimal feed angles for translational and rotational motion are independent characteristics, they may not have the same values as in Fig. 3a and b. Therefore, new NC blocks can be calculated by considering both optimal feed angles with the ratio Hi . When each interpolated curve is defined by the parameter u from 0 to 1, new NC blocks can be calculated on the interpolated curve with the new parametric increment by Eq. (6). This process of new NC block generation continues until the parameter is below 1, as in Fig. 4. As a result, new NC data with the optimal feed angle are generated.
5-Axis machines may have various configurations, servo motors with different capacity, and different controllers, which result in different operational behavior, even with the same NC data. However, commercial CAD/CAM programs do not take into account these characteristics, but only consider the workpiece geometry to generate NC data. In this study, an NC data-optimizing algorithm was proposed, which takes into account the characteristics of 5-axis machining behavior, which can maximize machining speed and smooth the machine operation for high surface quality. The proposed algorithm has proven its efficiency with more than 25% of machining gain compared with a commercial CAD/CAM system.
u =
uTi Hi + uR i , 1 + Hi
where uTi =
T R θOPT θOPT , uR i = T θi θiR (6)
4. Application and results For the application of the proposed algorithm, a Swiss-made MIKRON machine [7] model UCP710 was used; it is of the table rotating and tilting type, the most popular in the mid size die and mold industry. In order to prove the efficiency of the proposed algorithm, the machining times obtained with the optimized NC data by the proposed algorithm were compared with those of the original NC data obtained by a commercial CAD/CAM program. For this purpose, machining times were measured for a part of impeller (Fig. 5a) and a saddle (Fig. 5b). For the impeller, the machining time with NC data from the commercial CAD/CAM system was 1390 s, whereas with the optimized NC data by the proposed algorithm it was 580 s. For the saddle, the former was 429 s, and the latter was 319 s.
References [1] R. Sarma, A. Rao, Discretizors and interpolators for five-axis CNC machines, J. Manuf. Sci. Eng. ASME, Trans. ASME 122 (2000) 191–197. [2] R.V. Fleisig, A.D. Spence, A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining, Comput.-Aid. Des. 33 (2001) 1–15. [3] F.C. Wang, D.C.H. Yang, Nearly arc-length parameterized quintic-spline interpolation for precision machining, Comput.-Aid. Des. 25 (1993) 281–288. [4] H.Y. Xua, Y.H. Zhoua, J.J. Zhangb, Angular interpolation of bi-parameter curves, Comput.-Aid. Des. 35 (2003) 1–10. [5] M.Y. Cheng, M.C. Tsai, J.C. Kuo, Real-time NURBS command generators for CNC Servo controllers, Int. J. Mach. Tools Manuf. 42 (2002) 801– 813. [6] K. Lee, Principles of CAD/CAM/CAE Systems, first ed., Addison Wesley Longman, Inc., 1999. [7] Mikron Technology Group, http://www.mikron.com, 2006.
5-Axis machining speed enhancement by step length optimization B.S. So a , Y.H. Jung b,∗ , T.R. Kurfess c , S.M. Hwang b a
Department of Precision Mechanical Engineering, Pusan National University, Geumjeong-gu, Busan 609-735, South Korea b School of Mechanical Engineering, Pusan National University, Geumjeong-gu, Busan 609-735, South Korea c Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA
Abstract In this paper, an NC data optimization approach for enhancing 5-axis machining speed is presented. It is usual to use expensive commercial CAD/CAM programs for NC data of 5-axis machining, since it needs very large calculations for optimal tool positioning and orientation, tool path planning, and collision-free tool path generation. Since commercial CAD/CAM systems have similar functions and efficiency based on common algorithms of reliable theories, they do not have their own unique features for machining speed and efficiency. In other words, most commercial CAD/CAM systems consider only the characteristics of part geometry to be machined, which means that they generate almost the same NC data if the part to be machined is the same, even though different machines are used for the part. A new approach is proposed for optimizing NC data of 5-axis machining, which is based on the characteristics of the machine to be operated. As a result, the speed of 5-axis machining can increase without losing machining accuracy and surface quality. © 2007 Elsevier B.V. All rights reserved. Keywords: 5-Axis; Optimization; Machining speed; Feed angle; CAD/CAM
1. Introduction Due to the presence of two additional rotational axes, 5-axis machining enables cutting that is considered impossible by 3axis machining, along with reduced setup time and high surface quality. It is well known in the die and mold industry that the gain of 5-axis machining is up to 20 times on 3-axis machining. Most researchers in the early stage of 5-axis machining were focused on tool path planning with collision-free algorithms. Recently, their focus has moved to research on enhancing machining speed and surface quality. Sarma and Rao [1] had proposed a method for 5-axis machining interpolation, which takes into consideration angular feedrate in parametric curve interpolation, in order to improve low surface quality due to inadequate angular velocity. Fleisig and Spence [2] had applied the “nearly arc-length parameterized quintic-spline interpolation” method [3] to multiaxis machining, proposing an interpolation algorithm that simultaneously satisfies translational and rotational move of constant speed. Xua et al. [4] has proposed an angular interpolation algorithm for the bi-parametric curve of intersection between surfaces, resolving the cut-off error problem of the Taylor series that is used in interpolation algorithms for com∗
Corresponding author. Tel.: +82 51 510 2469; fax: +82 51 512 1722. E-mail address: [email protected] (Y.H. Jung).
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.11.167
mercial controllers. In order to use the interpolation function of commercial controllers, Cheng et al. [5] has proposed a method to input the NURBS parameters as NC data, after representing the tool path data as NURBS. In this study, an NC optimizing algorithm is proposed, which takes into account the characteristics of 5-axis machine behavior, can maximize real machining speed and can smooth machine operation for high surface quality. 2. Influence factors on 5-axis machining time The major machining parameters that affect machining speed and surface quality are feedrate, spindle speed, tool path and orientation. In 5-axis machining, the most effective influence factors on machining speed may be defined as the step length, the block processing time, and the ratio between translational and rotational motion of 5-axis machining, which are described in detail in the following sections. 2.1. Step length and feed angle It is known that shorter step length of NC data guarantees better machining quality in general. In the case of shorter step length, the same length of cut requires the controller to process more NC commands. Step length is set as long as the tolerance can allow. Therefore, the machining time is generally inversely
B.S. So et al. / Journal of Materials Processing Technology 187–188 (2007) 2–5
3
Nomenclature Ai , Bi , Ci orientation data of the cutter at the ith NC block ratio between translational and rotational motion Hi during the ith NC block Si step length between the ith and (i + 1)th NC blocks vi unit velocity vector of the cutter at the ith NC block Xi , Yi , Zi location data of the cutter at the ith NC block Greek symbols γi radius of curvature at the ith NC block θi feed angle between the ith and (i + 1)th NC blocks rotational feed angle at the ith NC block θiR R θOPT optimal feed angle for rotational motion translational feed angle at the ith NC block θiT T θOPT optimal feed angle for translational motion
proportional to step length. Recently, most controllers of milling machines have a look-ahead interpolating function for contour cutting. As a result, the machining speed reaches maximum at a specific step length. In the case of look-ahead interpolating controllers, the machining speed depends not only on the step length of NC data, but also on the tool path curvature. In order to consider both of these factors, we have the feed angle θ i as the ratio between the step length and radius of curvature during two successive NC blocks as in Eq. (1). It means direction change during the step length, which can be an independent variable defining the dynamic behavior of the machine tool. θi =
Si γi
(1)
2.2. NC block processing speed Experiments showed that the real feedrate is lower than the command feedrate when a 5-axis machine operates with a too short step length. One of the reasons is the speed of the controller for processing input NC data, since too short step length needs large NC blocks. The block processing speed is defined as the number of NC blocks that a controller can process in 1 s. Therefore, the number of NC blocks to be processed in 1 s should be below the block processing speed of the controller, so that the machine can follow the command feedrate. The block processing speed is the dominant factor for machine speed. 2.3. Ratio of translational to rotational motion Since the servo motor power and gear ratio of translational and rotational motion of 5-axis machines are different, the translational speed may be different from the rotational speed during each NC block. Therefore, these two speeds affect the resulting machining speed of a 5-axis machine. In this study, we have defined the ratio Hi at the ith NC block as in Eq. (2) in order to represent the ratio of translational motion to rotational motion
Fig. 1. Schematic diagram of NC data optimization steps.
of 5-axis machining. The ratio Hi will be used to determine the optimal feed angle for maximum resulting speed. Xi2 Yi2 + Zi2 (2) Hi = A2i Bi2 + Ci2 3. NC data optimization When the actual feedrate does not follow the input feedrate, it becomes impossible to schedule machining time and expect good machined quality. In this study, a step length optimization algorithm is proposed, in order to have the actual machining speed follow the input feedrate by taking into account the behavior of 5-axis machine and controller. An overview of the proposed algorithm is presented in Fig. 1. First, a continuous curved region of the original NC data is derived in order to generate an interpolated spline curve. Then, the optimal feed angle is determined from the machine characteristic database that is established with experiments for machine behavior. Finally, NC data are regenerated on the interpolated curve with new step lengths of the optimal feed angle. Each of the major steps is described in detail in the following subsections. 3.1. Curved section extraction from NC data The NC blocks to be optimized in this study are continuous curved regions. If we generate new NC blocks on the original tool path by changing step lengths of the regions that include a straight line segment or corners, we may cause severe dimensional errors in the machined surfaces. Therefore, continuous curved sections for new NC blocks are extracted by the following criteria (Fig. 2): (a) The feed angle between two successive NC blocks should be less than a specific value, as shown in Eq. (3). In this study, the specific value of θ max is set to be 10◦ mm−1 by the rule of thumb. θi = cos−1 (vi−1 · vi ) ≤ θmax
(3)
4
B.S. So et al. / Journal of Materials Processing Technology 187–188 (2007) 2–5
(c) The step length should be sufficiently short as in Eq. (5), where emax is the tolerance defined when NC data are generated. Si ≤ 8γi emax (5) 3.2. Spline interpolation The tool position and orientation data within the selected sections are interpolated to C2 continuous cubic spline for new NC data. The data can be interpolated with a well-known algorithm [6]. The optimized new NC data will be generated on the interpolated curve, which is described in the following subsection. Fig. 2. Curved section extraction from the given NC data.
3.3. Optimal feed angle
(b) The radius of curvature defined by three successive NC blocks should be within specific values as in Eq. (4). The minimum radius of curvature (γ min ) in this study is set to be the cutting tool radius, and the maximum radius of curvature (γ min ) is set to be the maximum length of workpiece to be cut. γmin < γi < γmax , where γi =
|Si−1 | |Si | (|Si−1 | + |Si |) 2 |Si−1 × Si |
(4)
The optimal feed angle is the key factor for the purpose of this research. In order to get the optimal feed angle from 5-axis machining behavior, we measured machining time according to feed angle for translational and rotational motion (Fig. 3). For these experiments, we generated a simple circular tool path for each motion and measured the real machining time in dry-run conditions. Fig. 3 shows that there are ranges of optimal feed angle with minimum machining time for each input feedrate. We took the mid value of each range as the optimal feed angle in each motion. We will generate new NC blocks with optimal step length based on these optimal values.
Fig. 3. 5-Axis machining time vs. feed angle. (a) Translational motion, (b) rotational motion.
Fig. 4. New NC data generation algorithm by reparameterization.
B.S. So et al. / Journal of Materials Processing Technology 187–188 (2007) 2–5
5
Fig. 5. Applications. (a) Impeller, (b) saddle.
3.4. Optimal NC data generation
5. Concluding remarks
Since the optimal feed angles for translational and rotational motion are independent characteristics, they may not have the same values as in Fig. 3a and b. Therefore, new NC blocks can be calculated by considering both optimal feed angles with the ratio Hi . When each interpolated curve is defined by the parameter u from 0 to 1, new NC blocks can be calculated on the interpolated curve with the new parametric increment by Eq. (6). This process of new NC block generation continues until the parameter is below 1, as in Fig. 4. As a result, new NC data with the optimal feed angle are generated.
5-Axis machines may have various configurations, servo motors with different capacity, and different controllers, which result in different operational behavior, even with the same NC data. However, commercial CAD/CAM programs do not take into account these characteristics, but only consider the workpiece geometry to generate NC data. In this study, an NC data-optimizing algorithm was proposed, which takes into account the characteristics of 5-axis machining behavior, which can maximize machining speed and smooth the machine operation for high surface quality. The proposed algorithm has proven its efficiency with more than 25% of machining gain compared with a commercial CAD/CAM system.
u =
uTi Hi + uR i , 1 + Hi
where uTi =
T R θOPT θOPT , uR i = T θi θiR (6)
4. Application and results For the application of the proposed algorithm, a Swiss-made MIKRON machine [7] model UCP710 was used; it is of the table rotating and tilting type, the most popular in the mid size die and mold industry. In order to prove the efficiency of the proposed algorithm, the machining times obtained with the optimized NC data by the proposed algorithm were compared with those of the original NC data obtained by a commercial CAD/CAM program. For this purpose, machining times were measured for a part of impeller (Fig. 5a) and a saddle (Fig. 5b). For the impeller, the machining time with NC data from the commercial CAD/CAM system was 1390 s, whereas with the optimized NC data by the proposed algorithm it was 580 s. For the saddle, the former was 429 s, and the latter was 319 s.
References [1] R. Sarma, A. Rao, Discretizors and interpolators for five-axis CNC machines, J. Manuf. Sci. Eng. ASME, Trans. ASME 122 (2000) 191–197. [2] R.V. Fleisig, A.D. Spence, A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining, Comput.-Aid. Des. 33 (2001) 1–15. [3] F.C. Wang, D.C.H. Yang, Nearly arc-length parameterized quintic-spline interpolation for precision machining, Comput.-Aid. Des. 25 (1993) 281–288. [4] H.Y. Xua, Y.H. Zhoua, J.J. Zhangb, Angular interpolation of bi-parameter curves, Comput.-Aid. Des. 35 (2003) 1–10. [5] M.Y. Cheng, M.C. Tsai, J.C. Kuo, Real-time NURBS command generators for CNC Servo controllers, Int. J. Mach. Tools Manuf. 42 (2002) 801– 813. [6] K. Lee, Principles of CAD/CAM/CAE Systems, first ed., Addison Wesley Longman, Inc., 1999. [7] Mikron Technology Group, http://www.mikron.com, 2006.