FEM Calculation and Optimization for the Cutting Tooth of Stump Grinder

Transcription

1 FEM Calculation and Optimization for the Cutting Tooth of Stump Grinder Xianglong Zhang 1, Jie Sun 1 and Jiangming Kan 1 1 College of Engineering Beijing Forestry University Beijing , China Abstract Cutting tooth is one of the key parts of stump grinder. The structure and the dimension of the tooth affects the efficiency of grinding. In order to predict the state of stress, decrease stress concentration and cut the manufacturing cost of the tooth, a finite element method (FEM) was used to achieve the goals. After getting the model geometry of tooth through 3D laser scanner system, static analysis, transient dynamical analysis and shape optimization were finished in commercial software Workbench. Results show that the tooth meets the strength requirement of material. The maximum stress decreases by 6.7% and the fatigue life will be extended. The tooth is divided into two parts and the cost of material reduces by 15.4%. Numerical method greatly short the design time and reduce the manufacturing costs. Keywords - cutting tooth, dimension, FEM, optimization, structure I. INTRODUCTION Factors other than the type of tree being cut can affect the wear of cutter teeth. Everything from nails and rocks to fence posts and other unusual items are found in stumps because trees grow around anything around in their way. These foreign objects can cause major headaches for operators by bending and breaking cutter teeth. Dull cutter teeth can have a huge financial impact on a machine. What s more, too much vibration can be detrimental to any machine, causing welds to crack and fasteners to loosen and fail. Going through an extra stump( with dull or broken teeth ) may save money in the short term to get the job done faster, but it may be worse in the long run on engine performance and engine life. So, operators can easily be shredding years off the life of their machines simply by not replacing stump cutter teeth when they turn dull or bend [1]. However, a better structure of cutter teeth can expand the safe working hours and reduce the replaceable parts of cutter teeth. To achieve this goal, we need to optimize it in a reliable method. The optimal structure design contains many aspects: if the form of the component is allowed to change, it can help us to select a best form; if the form is fixed, we can use it to search the best structure dimension. The issue includes confirming the constraint condition, selecting design variable and making the objective function reaching maximum or minimum. In all, using optimal design can help us to search the best designing scheme which meets the design requirement, costs least and be most efficient [2]. Jiang Huaitong made the static analysis of the beam which is a key part of autoclaved brick machine. From the stress and strain nephogram, he drew a conclusion that the strength and stiffness of the beam met the requirements. On the premise that strength and stiffness are sufficient, he made the structure optimization for the beam in order to reduce the weight of beam. Genetic algorithm was used to get a globally optimal solution. The results shown that the weight of beam reduced by 10.21% and the distribution of stress was more reasonable. The optimal beam had been used on a 1300t autoclaved brick machine, it was safe and reliable [3]. In order to reduce the fabricating cost of elevator, Ge Jianbing made a structure optimization for the spindle. Based on the finite element model of spindle, stress and strain analysis of the spindle was made by using ANSYS Workbench software. Diameters of the spindle d1 and d2 were independent variable. Minimum volume of spindle was the objective function. The restricted condition was meeting stress and strain requirement. The results shown that the volume is sensitive to d2, stress is sensitive to d1 and strain is insensitive to neither d1 nor d2. The best solution can make the machine working safely and improve economic returns [4]. Xie Zhijiang built a 3d model of the manipulator with Pro/E software, then he did the static analysis by using ANSYS Workbench. The results shown that the maximum displacement was 0.36mm and the maximum stress is 61 Mpa, which is far from the yield limit of material (205 Mpa). As natural frequencies is relevant to the mass and stiffness of the part, before structural optimization of the manipulator, static analysis and modal analysis was done. The first natural frequency is 96Hz, which is lower than the frequency of motor. So the structural optimization is necessary. By using the function of Shape Finder, the mass of manipulator reduced by 23.7kg, first natural frequency rise to 127.2Hz. The static and dynamic characteristics got a maximum improvement. The mass reduced by 43% [5]. Optimum structural design is a design method which is based on modern mathematics, mechanics and numerical methods. By using computer, it focuses on the theories and methods of structures optimization and automation. Compared with classical design method, it can make the design more reasonable, scientific and convictive. At last, a better design can be more practical and cut the cost [6]. As one of the popular CAE software, Workbench is widely used for mechanical structure design and optimization because of DOI /IJSSST.a.16.5A ISSN: x online, print

2 its high quality optimization module. A good knowledge of the degree of the optimum structural design can help to achieve the best structure quickly. The remainder of this paper is organized as follows. Section 2 describes the model geometry, static analysis, transient dynamical analysis and shape optimization of the tooth. Section 3 gave the results of analysis and the meaning of numerical analysis. Conclusions are summarized in Section 4. I. MATERIALS AND METHODS A. Model Geometry and Wood Cutting Force Because the tooth was originally designed by Rayco Inc., we didn t have the 3D model. In order to get an accurate model of cutting tooth, we used a 3D laser scanner system to get the 3D data. The detail resolving power of the system is 0.02mm and the geometric tolerance is 0.05mm. What s more, the initial dead zone of single scanning is less than 1%. For only light color part can be scanned by the laser scanner, we paint the tooth into blue. The system is represented in Fig.1. In Scanmechinel software, we got the point cloud of the part firstly. Then by using surface reconstruction, we got the initial surface of the tooth. As the initial model is tanglesome and inaccurate, to get a complete model, we fixed the model with Copycad software on the basis of metrical dimension. At last, we built a STL model [7]. Then we imported it into Workbench software. Cutting tooth is the key part of cutting mechanism. It has a physical contact with the stump. When the tooth is on bad working conditions and bearing complex force, it may occur acutely worn, fatigue damage, breakup of the tool bit and crack of the cutter body. So the structure and parameter of the tooth are important factors that affecting the stump grinder s working ability and the life of tooth. Because of the anisotropy of wood, fiber direction must be considered when calculating the cutting force. Based on the direction of tooth to that of the fiber, the ways of wood cutting was classified into three modes [8]: (1) Upright cutting ( ): Cutting lip and direction of tooth moving are upright to the fiber direction, as is shown in Fig.2, 1 and 2. (2) Lengthwise cutting ( ): Cutting lip is longitudinal to fiber direction, but the direction of tooth is parallel to fiber direction. As is shown in 3 and 4. (3) Broad wise cutting(#): Cutting lip is parallel to fiber direction, the direction of tooth moving is upright to fiber direction, which is 5 and 6. Figure 1. 3D laser scanner system. Figure 2. Three main cutting directions of wood cutting [8]. Besides the fiber direction, the cutting force is also affected by other factors, like tree species, moisture capacity, cutting speed, cutting thickness, feed speed, sharpness of tooth and the cutting angle. These factors have a functional relation with the cutting force [9]. As the stump cutter is working under manual control, the cutting depth and feed rate can vary greatly when cutting the stump. So we chose a bigger value to get a better result. The back force and feeding force are ignored. The main cutting force is confirmed as the cutting force. Based on the design requirement of stump grinder, the diameter of tooth plate is 376mm, the cutting width is 13mm, the cutting angle is 85 and the cutting depth is 5mm. To make sure the safety of stump, the rotate speed is set as 700rpm. The cutting way of stump grinder is lengthwise cutting. For quercus acutissima, its main cutting force is [10, 11]: F x a a H bh u w h x z a a q w q sin u θ t z p N DOI /IJSSST.a.16.5A ISSN: x online, print

3 B. Static Analysis and Transient Dynamical Analysis of the Tooth The material of tooth is 1045 steel, its Young modulus is 2.0e+11Pa, Poisson s Ration is 0.3 and the density is 7850kg /m3. Workbench has a powerful meshing function, it can generate high quality mesh based on the 3D model. We used the free meshing for the tooth meshing. The total nodes is and the total elements is The mesh is shown in Fig.3. Figure 5. Load curve. Figure 3. Meshing of cutting tooth. C. Structure Parameter and Shape Optimization of Cutting Tooth From Fig.3-1, we could find that the maximum stress concentrated on area A and B, as is shown in Fig.6. We selected the radius of area A as design variable. Meanwhile we kept the other parameter remain unchanged, as is shown in Fig.7. The unit of radius is millimeter. Different values of radius are listed in Table Ⅰ. The stress of area A and B and the displacement at the end of tooth are target variable. Figure 4. Load condition of cutting tooth. Based on the assembly and movement of the cutting mechanism, fixed constraint was applied on the two bolt holes. 461N load was applied on the welding alloying tool bit, as is in Fig.4. Factors other than the type of tree being cut can affect the wear of cutter teeth. Everything from nails and rocks to fence posts and other unusual items are found in stumps because trees grow around anything in their way. These foreign objects can cause major headaches for operators by bending and breaking cutter teeth. So the transient dynamical analysis of the tooth is necessary. The load simulation curve is shown in Fig N is the cutting force of stone. 2500N is the force of cutting metal. Figure 6. Area of A and B. Figure 7. Radius of area A. As the setting of topological optimization is similar with that of static analysis, we input the model, then meshed and applied the load and constraint. By using Shape Finder DOI /IJSSST.a.16.5A ISSN: x online, print

4 function [12, 13], we finished the shape optimization. Because the stress and displacement in the upper half part of the tooth is small, the removal rate was set as 0.5. II. RESULTS AND DISCUSSIONS A. Results and Discussions of Static Analysis and Transient Dynamical Analysis Through finite element method analysis of the tooth model, we got the equivalent stress diagram of tooth, as is shown in Fig.8. Maximum stress happened in the place where the section varied most. The maximum stress is 6.24 Mpa. Maximum displacement is at the end of tooth, as is shown in Fig.9. The maximum displacement is m. Figure 8. Stress distribution of the tooth. Figure 10. Results of transient analysis. B. Results and discussions of structure parameter and shape optimization For viewing the results clearly, we arranged the results into polyline, as is shown in Fig.11. From Table I, we could find that the stress of area A and the displacement increase when the radius decreases. However, the stress of area B increase at first then decreases when the radius decreases. So, the optimal radius should be at the range of 8mm to 25mm, as is shown in Table Ⅱ. Based on the principle that making stress of area B less when keeping the stress of area A least, we selected radius 15mm as the optimal dimension. The stress of area A is 5.82MPa, stress of B area is 5.02MPa and the maximum displacement of tooth is m. Size of area A (mm ) TABLE I. area A(10 6 Pa) ANALYSIS RESULTS OF DIFFERENT DIMENSION Results area B(10 6 Pa) Maximum displacement of tooth (m) Line R R R R R Figure 9. Displacement distribution of the tooth. Seen from Fig.10, we could found that the maximum stress is 34.9Mpa, which is far from the breaking point of So considering the results of static analysis and transient analysis only, the tooth can work safely for a long time. DOI /IJSSST.a.16.5A ISSN: x online, print

5 Figure 13. The removal part after the topology optimization. Size of area A (mm ) TABLE II. Figure 11. Stress variation of area A and B. area A(10 6 Pa) ANALYSIS RESULTS OF DIFFERENT DIMENSION Results area B(10 6 Pa) Maximum displacement of tooth (m) R R R R R R R The results of Shape Finder is shown in Fig.12 and Fig.13. From the results of optimization, the function of upper part of tooth is fixing the tooth. Compared with the half bottom of the tooth, its stress and displacement is smaller. What s more, considering the structure of tooth is complex, we separated the tooth into two parts based on the function of different parts. As is shown in Fig.14 and Fig.15. Figure 14. Ⅰfor fixing the tooth. Figure 12. Topology optimization results. Figure 15. Part Ⅱfor cutting stump. After the static analysis of the new model, we achieved the equivalent stress and displacement of the new part. The maximum stress happened at the place where the stress DOI /IJSSST.a.16.5A ISSN: x online, print

6 concentrated most. The equivalent stress diagram of new tooth is shown in Fig.16. Its maximum stress was 6.83MPa. The maximum displacement still happened at the end of the tooth, its value was m, as is shown in Fig.17. Compared with the part un-optimized, the stress was getting larger. But it s still within a safe range. The tooth is a brittle part. After the optimization, part Ⅰ could work safely for a long time. When the tooth is broken, all we have to do is change part Ⅱ. The volume of these two parts reduces by 15.4% comparing with that of original. This can cut the cost greatly. In addition, as two parts of the tooth is processed separately, the processing efficiency increases and the rate of spoiled products decreases. of radius, the maximum stress decreased by 6.7%. The fatigue life of tooth and the replacement time will be extended. The volume of these two parts reduces by 15.4% comparing with that of original. The optimization of the structure greatly cut the cost of processing. What s more, the processing efficiency increases and the rate of spoiled products decreases. This result clearly demonstrates that the numerical method, such as finite element method, could be used for improving the performance of the cutting tooth. Further works include carrying out experiments for measuring the cost of processing. Effects of the different structure and parameter of tooth will be deeply tested in order to validate and adjust finite element modeling simulations. ACKNOWLEDGMENT 1. This research is financially supported by the National 948 Project from the Chinese State Forestry Administration (Grant No ). Figure 16. Optimized Stress distribution of the tooth. Figure 17. Optimized displacement of the tooth. III. CONCLUSION Based on the results of static analysis and transient dynamical analysis, the main purpose of this study was to optimize the structure and parameter of tooth. Compared with experimental analysis, numerical method can largely reduce the time of designing and improve its economic benefits. By using the function of Static Structural and Shape Finder in commercial software Workbench, the cutting tooth was redesigned. The maximum stress of static analysis and transient dynamical analysis is 34.9MPa, which is far from the breaking point of The main reason for this result is that the cutting force is small and stable. After the optimization REFERENCES [1] M. Rieckhoff, Stump cutter teeth maintenance 101, Tree Care Industry Magazine, vol. 2, pp. 12, [2] Z. H. Zeng, Application of the structure optimization techniques in mechanical design by ANSYS, Machine Design and Manufacturing, vol. 13, pp , [3] W. T. Jiang, M. Li, L. Li, et al, Structure optimization design for lower beam of hydraulic press based on ANSYS Workbench, Machine Design and Manufacturing Engineering, vol. 5, pp , [4] J. B. Ge, P. Zhang, M. Liang, et al, Structure optimization of main shaft based on ANSYS Workbench, Coal Mine Machinery, vol. 12, pp , [5] Z. J. Xie, Y. Sun, C. Li, et al, Structural optimization design of carrying manipulator based on ANSYS Workbench, Machinery & Electronics, vol. 1, pp ,2010. [6] S. Wang, K. Wang, X. W. Sun, Spindle Structure Optimization Design of Whirlwind Cutter, Mechanical Engineering & Automation, vol. 12, pp ,2015. [7] H. Yang, S. Z. Xu, Research on recerse of auto parts based on 3D laser scanning, Journal of Henan Institute of Engineering, vol. 1, pp ,2015. [8] Z. K. Zhang, X. R. Peng et al, Effect of cutting direction on cutting force of wood, China Wood Industry, vol. 6, pp. 7-9, [9] N. Jia, Z. H. Zhang, T. H. Fu, Numerical simulation of wood tool s geometric parameter optimization based on finite element, Forest Engineering, vol. 5, pp , [10] C. M. Yang, B. Yang, W. L. Song, Study on cutting force and cutting power of small artificial forest tracked harcester, Forest Engineering, vol. 9, pp , [11] Y. F. Yang, B. T. Xi, L. Li, Cutting force of moso bamboo, Journal of Beijing Forestry University, vol. 7, pp , [12] Z. J. Xie, Y. Sun, C. Li et al, Structural optimization design of carrying manipulator based on ANSYS Workbench, Machinery & Electronics, vol. 1, pp , [13] H. T. Jiang, M. Li, L. Li et al, Structural optimization design for lower beam of hydraulic press based on ANSYS Workbench, Machine Design and Manufacturing Engineering, vol. 5, pp , DOI /IJSSST.a.16.5A ISSN: x online, print