Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 174 (2017) 878 – 884
13th Global Congress on Manufacturing and Management, GCMM 2016
Tool Orientation Planning Method Based on Divided Surface Li Mina, Shuai Donga,*, Dian Lia a
Shenyang Jianzhu University College of Mechanical Engineering, Liaoning Shenyang 110168, China
Abstract In the process of complex curved surface, the curvature change is often too large, which will lead to the sharp fluctuation of the cutter axis vector of the adjacent cutter contact, and affect the quality of the machining process. This paper presented a planning methodology of tool orientation for 5-axis sculptured surface CNC machining base on divided surface. Frist, the discrete points of surface were generated, then Gaussian curvature and mean curvature was calculated. By using Gaussian curvature and mean ,the surface was divided into multiple regions. We planned orderly tool orientation in each regions, mutational local area were optimized. The method reduce the rate of change with tool orientation effectively. Finally, the effectiveness of this method were verified by computer implementation and examples. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2017 2016Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management. Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management Keywords: Five-axis NC machining; Tool orientation; Divided surface; Curvature;
1. Introduction Five-axis machining has become one of the means of machining complex curved surface. Five-axis machining is different from three axis. In normal conditions, the three-axis NC machining of tool orientation is fixed in the workpiece coordinate system, but the five axes machining of tool orientation is change. Although the flexibility of five-axis machine tools was improved by the property, constraint problem of cutter axis vector control is emerged, the problem affects directly the quality and efficiency of machining. At the same time, the machining process stability and cutting force will be affected, so it is significant to control reasonably of cutter axis vector.
* Corresponding author. Tel.: +8618842358427. E-mail address:
[email protected]
1877-7058 © 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management
doi:10.1016/j.proeng.2017.01.236
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Li Min et al. / Procedia Engineering 174 (2017) 878 – 884
The method of normal machining is the most commonly used tool orientatin planning method in CAM software [1], the ideal that the direction of tool axis is same as the normal vector. In the complex surface processing, we usually find the curvature change enormously in some areas. As show in Fig.1(a), the normal direction and tool axis vector of the surface changes dramatically within a short distance, it will cause larger processing error. The preset tool axis is another method, allowing the tool axis vector and the surface normal vector to set a certain angle, as show in Fig.1(b), it is likely to cause local gouging.
Fig. 1. Traditional tool orientation planning method: (a) The method of normal processing; (b) The method of Preset tool axis.
Tool orientation planning should satisfy the following two aspects˖(1) The tool orientation with adjacent tool contacts should have less variation in the same trajectory; (2) The tool needs to avoid local interference. This paper presents a methodology of tool oriebtation planning based on surface division. First, the surface area is divided according to the curvature and surface features, then the tool paths are programmed according to the surface area boundary line, the tool orientation is designed on the tool path using normal machining. For regions where the local curvature change is too large, cubic spline interpolation is used to smooth the tool orientation. Finally we achieve the purpose of reducing the vector rate of change. 2. Surface division 2.1. Surface model The NURBS(Non-Uniform Rational B-Splines) are the most commonly used parametric surface representations in CAD/CAM/CNC systems [2]. It calculates stably and fast. Here we briefly introduce the basic definitions and geometric properties of NURBS. A NURBS surface is defined as follows: Q
6 X Y
P
¦ M¦ 1 L S X 1 M T Y : L M 3 L M L
Q
(1)
P
¦ ¦ 1 L S X 1 M T Y : L M
L M
Where 6 X Y is the NURBS surface with parameters
u and v , Vi , j are control points, :L M are weights %L N X
and % M O Y are normalized B-spline basis functions of degree k and l, they are decided by vectorU={u0,u1,…,un+k+1} andV={v0,v1,…,vm+l+1}, and the knot vectors are defined by De Boor-Cox formula [3]. 2.2. Geometric Parameters of Complex Surfaces Sculptured surfaces include concave surface, convex surface, saddle surface, flat and so on. In this paper, we divide the sculptured surface into different basic surfaces based on surface curvature properties, such as Gaussian curvature K and mean curvature H. Then the surface characters are defined as shown below. For each point of a given NURBS surface S(u,v), the 2-dimension tangent space is made of the tangent vector Su(u,v) and Sv(u,v). E, F and G are the typeĉbase parameters, defined as Eq.2.
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Li Min et al. / Procedia Engineering 174 (2017) 878 – 884
( X Y ° ®) X Y °* X Y ¯
6 X X Y u 6 X X Y (2)
6 X X Y u 6Y X Y 6Y X Y u 6Y X Y
Here L, M and N are the typeĊbase parameters, defined as Eq. 3.
/ X Y ° ®0 X Y °1 X Y ¯
Q X Y u 6 XX X Y Q X Y u 6 XY X Y
(3)
Q X Y u 6YY X Y
Suppose the tangent vector: dS(u,v)=Su(u,v)du+Sv(u,v)dv, is one of the surface principal direction, and (du,dv)satisfies the linear equations shown as Eq. 4.
/ O( GX 0 O) GY ® ¯ 0 O) GX 1 O* GY
(4)
Therefore, Gaussian curvature K and mean curvature H are calculated as below:
+
.
(1 )0 */ (* )
N PD[ N PLQ
N PD[ N PLQ
(5)
/1 0 (* )
(6)
The mean curvature H and Gaussian curvature K are not relevant, and Gaussian curvature is the intrinsic surface character. Points on a sculptured surface can be grouped into different types using Gaussian curvature K and mean curvature H. The basic types of NURBS surface can be identified by the geometric properties, as shown in Table 1. Table 1. Basic surface types according to parameter K and H. Surface
K0
H>0
Concave saddle
Concave column
Concave ellipsoid
H=0 Hψ), threshold value is determined according to the actual processing conditions. This makes the change of the cutter axis vector produce singularity. In order to solve this problem, the cubic spline interpolation method is used[9]. A cubic spline function is constructed between Vi and Vi+1, and the new cutter axis vector Vj is obtained and inserted to smooth the vector of the cutter shaft. New interpolation tool axis vector calculation, as shown in the formula (7): 6 Y
L
§Y YL · § Y L Y · §Y YL · § Y L Y · OLM ¨ ¸ OL M ¨ ¸ PL KLM ¨ ¸ PL KLM ¨ ¸ © KL ¹ © KL ¹ © KL ¹ © KL ¹
Q
(7)
In the formula, h=vi+1-vi; φ is the interpolation function;
Fig. 4. Tool orientation change.
4. Examples and data analysis In order to verify the effectiveness of the proposed strategy, the simulation analysis is carried out by using MATLAB software. In order to facilitate the analysis, threshold ψ=5°. A surface model is established in Fig.2 (a). According to the previously mentioned surface partitioning algorithm, the surface is divided into three regions as shown in Fig.5. The cutter axis vector diagram, which is generated by the parameter line method and the residual height method, is shown in Fig.6.
Fig. 5. The model of surface divided.
Li Min et al. / Procedia Engineering 174 (2017) 878 – 884
As shown in Fig.6 (a), we compare the tool axis vector map, found that when the tool path from the area along the track from the A region to the B region, the tool inclination occurred more severe deflection, however, as shown in Fig.6(b), the cutter axis vectors on each area of the tool path are consistent with the direction of the partition.
Fig. 6. The tool orientation simulation: (a) Single locus cutter axis vector; (b) Cutter axis vector of curved surface.
As shown in Fig.6, we select the tool angle data, namely in bold line tool path, calculate the cutter inclination angle difference of the cutter contact point on the same tool path, and generate a graph as shown in Fig.7. Some problems are found by comparing the difference of the cutter inclination angle between the non partition and the partition. In Fig.7(a), the cutter contact angle difference between the five trace lines on the middle part of the middle part has a great change. And most of the cutter inclination angle difference is greater than the threshold value. The fluctuation of the curve is too severe, which means that the cutter inclination angle between the adjacent knife contacts is more violent. Fig.7(b) shows that, after the surface division, the five trajectory of the cutter angle interpolation is more gentle than the partition, but in the local area, there is a sharp point which is larger than the threshold value ψ. It affects the smoothness of the vector of the cutter shaft. Cubic spline interpolation method is used to optimize the cusp region, and the optimization results are shown in Fig.7 (c). We can see from the graph, the point of the curve is basically eliminated. As shown in Table 2, the deviation of the cutter inclination angle after the partition is decreased by 53.12% compared with that before the partition, and when the interpolation method is used, the deviation value is decreased by 11.72%.
Fig. 7. The same path adjacent cutter con tact Angle difference: (a) Single locus cutter inclination angle difference; (b) Surface division angle difference; (c) Surface area optimization cutter angle difference.
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Li Min et al. / Procedia Engineering 174 (2017) 878 – 884 Table 2. The tool angle deviation. Trail 1
Trail 2
Trail 3
Trail 4
Trail 5
Not partition
23.02881
22.97036
23.19447
23.61857
24.12523
Partition and not optimized
8.586446
5.143779
12.46023
15.40817
13.21319
After optimization
8.730929
5.212194
11.53766
14.56471
8.343117
5. Peroration The fluctuation of cutter inclination angle can greatly affect the machining quality. Due to the cutting force caused by the cutter inclination angle is not uniform, it is possible to produce stress concentration on the surface of the working surface. The main reason that causes the change of the cutter inclination angle is that the curvature of the complex surface is too large. The experimental results show that the partition planning strategy of the curved surface area can avoid the sharp change of the cutter axis vector on the same cutting tool path. The cubic spline interpolation method is used to optimize the local mutation region, which can further improve the variation rate of tool inclination angle. It can effectively improve the processing quality of the complex surface. Acknowledgements The authors acknowledge the financial support from Natural Science Foundation of Liaoning province (201602622), Science research project of Liaoning Provincial Department of Education (L2015447), Key Laboratory of Shenyang Jianzhu University Opening Foundation (SJSC-2015-11) and the research project of Shenyang Jianzhu University (XKHY2-37). References [1] Zhang Yong-chao, Yu-Yang. Using Coordinates Interpolation Algorithm to Control Tool Orientations in 5-axis Machining. Modular Machine Tool & Automatic Manufacturing Technique, 2011(08): 39~42. [2] Farin, G. E. Curves and Surfaces for CAGD, Morgan-Kaufmann, 5th Edition (2001). [3] Zhu Xin-xiong. Free curve surface modeling technology. Beijing: Science Press, 2000: 104~106. [4] Fan Wen-shan, Wang Bin. A Fast KD-Tree Construction Method by Probing the Optimal Splitting Plane Heuristically.Chinese Journal of computers, 2009, 02: 185~192. [5] Wang Jing, Zhang Ding-hua, Luo Ming, etc. A Global Tool Orientation Optimization Method for Five-axis CNC Machining of Sculptured Surfaces. Acta Aeronautica et Astronautica Sinica, 2013, 06: 1452~1462. [6] Bi Qing-zhen, Wang Yu-han, Zhu Li-ming, etc. Whole on Cutter Contact Grid Fairing Five-Axis NC Machining Tool Axis Direction of the Model and Algorithm, Science in China, 2010, 10: 1159~1168. [7] Li Bing-ling, Wang Xue-ling, Hu Yu-jing, etc. Tool Orientation Control Method Based on Divided-area Algorithm. China Mechanical Engineering, 2010, 04: 452~457. [8] Li Zhan-jun, Wang Xia, Li Zhen, Smooth tool-path planning algorithm based on constant scallop-height, Machinery Design & Manufacture, 2010, 06: 243~245. [9] Chen Wen-lue, Wang Zi-yang. The application of cubic splines interpolation in the project fitting, Journal of central China normal university (natural science edition), 2004, 38(4): 418~422.
