2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 International Journal of Modeling, Simulation, and Scientiﬁc Computing Vol. 9, No. 2 (2018) 1850013 (17 pages) c World Scientiﬁc Publishing Company DOI: 10.1142/S1793962318500137 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. The structural optimization of roadheader conical picks based on fatigue life Zhenguo Lu, Lirong Wan∗ , Qingliang Zeng, Xin Zhang and Kuidong Gao College of Mechanical and Electronic Engineering Shandong University of Science and Technology 266590 Qingdao, Shandong, P. R. China ∗[email protected] Received 16 March 2017 Accepted 28 September 2017 Published 27 October 2017 Conical picks are the key cutting components used on roadheaders, and they are replaced frequently because of the bad working conditions. Picks did not meet the fatigue life when they were damaged by abrasion, so the pick fatigue life and strength are excessive. In the paper, in order to reduce the abrasion and save the materials, structure optimization was carried out. For static analysis and fatigue life prediction, the simulation program was proposed based on mathematical models to obtain the cutting resistance. Furthermore, the ﬁnite element models for static analysis and fatigue life analysis were proposed. The results indicated that fatigue life damage and strength failure of the cutting pick would never happen. Subsequently, the initial optimization model and the ﬁnite element model of picks were developed. According to the optimized results, a new type of pick was developed based on the working and installing conditions of the traditional pick. Finally, the previous analysis methods used for traditional methods were carried out again for the new type picks. The results show that new type of pick can satisfy the strength and fatigue life requirements. Keywords: Structure optimization; static analysis; fatigue life prediction; the new type of pick. 1. Introduction Picks have been widely used, e.g., in roadheader, coal mining machine and continuous mining machine. As the store conditions of coal/rock are complex, picks are subject to random load and wear, loss, tipping, crack, alloy head fall-oﬀ, which often occur in the process of coal/rock cutting. This situation would aﬀect the working stability and reliability of roadheader. Therefore, it is necessary to improve the pick structure that can reduce occurrence of the pick damage and save materials. ∗ Corresponding author. 1850013-1 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Z. Lu et al. In the past decades, many scholars have done a lot of theoretical and laboratorial researches on the cutting force and the technique methods in the progress of coal/rock cutting. Evans1–5 was the ﬁrst to put forward the pick cutting theory. Evans pointed out that the main characteristics inﬂuencing the cutting process are tensile and compressive strengths, and these basic criteria have been widely used in guiding the design of roadheader picks and coal mining machines. Roxborough6 veriﬁed the Evans theory through experimental method and concluded that experimental and theoretical data have a strong correlation. Goktan7 corrected the Evans’ cutting theory and applied to point attack tools, the theory that he proposed is closer to experimental data and has better practical value. Roxborough and Liu8 also put forward point attack tool-modiﬁed cutting theory based on the Evans’ cutting theory, and the average peak forces they got through the modiﬁed cutting theory were consistent with experiments. Nishimatsu9 found that shear failure is the main damage form of the coal with high tensile strength, and the equations of cutting force were discussed. Bilgin10 carried out 22 groups of experiments with diﬀerent rock properties, and concluded that the major factors aﬀecting the pick cutting performance are uniaxial tensile strength, uniaxial compressive strength, dynamic and static elasticity modulus. Liu11 measured cutting force by experimental method and investigated the relationship between the cutting parameters and the geometry of pick. Li12,13 considered the load of the pick as stationary random process, and established random load model of the pick in simple structure coal seam and complex coal seam by Rayleigh distribution and χ2 distribution, and established the mathematical model of cutting head load based on the force of a single pick in hard rock condition. Sun14 presented quantitative analysis methods for the cutting force interaction between the picks. Hurt15 measured service life and cutting eﬃciency of the pick under controlled experimental conditions. Parameters investigated included pick type and quality, depth and speed of cutting and the cobalt content of the tungsten carbide pick tips. Hkimoglu16 described the underground and laboratory trails with radial type picks and examined the optimal pick position with respect to the radial line. Chen17 designed and fabricated Fe-based alloy coating with high toughness and high wear resistance on the positon of heavy wear by suing plasma jet surface metallurgy. Huang18 simulated the rock cutting progress in deep mining condition used LS-DYNA software, and compared the simulation results with the theoretical and experimental results. Su19 attempted to model rock cutting tests and the mean peak cutting force was obtained and discussed. He pointed out that there is a strong correlation between simulation, theoretical and experimental results. Dai20 proposed a new type cutter and established the DEM model for excavation progress. Menezes21 used the LS-DYNA to predict the fragmentation process during rock cutting and obtained a valuable result that the chip morphology as signiﬁcantly inﬂuenced by cutting depths and velocities. Jaime22 developed an FEM procedure that was able to obtain the cutting forces and fragments. In his research, an element erosion critical was applied where the elements were removed when the element energy equalled fracture energy. 1850013-2 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. The structural optimization of roadheader conical picks based on fatigue life Fig. 1. Topology optimization process of the pick. Although until now considerable cutting theories and experimental studies have been done by researchers, and all these researches have improved our understanding of rock cutting, however, fatigue life analysis and structure optimization of the pick have never been mentioned. In other ﬁelds, fatigue life analysis and structure optimization are important research contents. Holmberg23 researched the structure strength under the variable load, proposed a topology optimization method that was constrained by the structure fatigue life. Domazet24 took roller as the research object and developed the fatigue life optimization program. Shim25 ﬁnished the optimal design of the pulley based on the response surface method. In this paper, fatigue life prediction and topology optimization of the pick were carried out. The prediction of fatigue life can evaluate the production quality of the pick eﬀectively, and the structure optimization can reduce materials in the premise of the pick reaching the strength requirement. The cutting pick optimization method (Fig. 1) is established in this paper. In the considered method, the cutting head dynamic model was established for simulating the cutting force of the pick in each position, a load spectrum and maximum cutting force can be got from this simulation for fatigue life analysis and static analysis, respectively. On this basis, the topological optimization of the pick was carried out. 2. Prediction of the Cutting Forces and Results Discussion The pick’s performance and service life are aﬀected by the situation of cutting forces directly, and this is the main fundamental index to evaluate pick performances. 1850013-3 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Z. Lu et al. However, the forces on cutting head and picks have no uniﬁed and accepted calculation method due to nonlinear contact, inhomogeneous coal and rock material. The former Soviet Union, Germany, France and other countries have their own calculation theory and methods. Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. 2.1. Mathematical modeling A number of researchers have formulated a mathematical model for coal and rock cutting progress. The pioneering work on pure coal cutting mechanics was performed by a Former Soviet Union scholar. The theory has been widely used to calculate the average loads of cutting picks by the following empirical equation26 : 1 0.35bp + 0.3 htkz kφ ky kc kot , Z0 = 10A 0.5 B b + h cos β p Y0 = Yn Z0 , (1) C1 h X0 = Z0 C + h + C3 t , 2 where X0 , Y0 , and Z0 are the three-axis force, side resistance, tractive resistance, cutting resistance; A is average value of cutting intensity; bp is the working part width of pick shaped cutter equivalent to the cutting ﬂat pick; h is the average value of cutting thickness; B is the brittleness degree of coal; t is the average line spacing of pick arrangement; kz is the coal bared coeﬃcient; kφ is the front cutter face shape inﬂuence coeﬃcient of pick-shaped cutter equivalent to the cutting ﬂat pick; ky is the inﬂuence factor of cutting angle to energy consumption of cutting ratio; kc is the inﬂuence factor of the cutting method; kot is the coal pressure coefﬁcient; β is the installation angle of the pick axial direction and feed direction; Yn is a ratio of cutting resistance and tractive resistance; C1 , C2 , C3 are inﬂuence coeﬃcients of pick arrangement on the cutting head. In this paper, the meaning of coeﬃcients is emblematic of inﬂuence extent generated by the relevant parameters in the equations. The values of the coeﬃcients are determined by empirical data. The pick suﬀered the random load because the coal/rock as the anisotropic material and heterogeneous. The cutting resistance and tractive resistance are usually according with the Gamma distribution, and the modiﬁed Rayleigh distribution can ﬁt the Gamma distribution better. Rayleigh random processes can be determined by two normal random processes which have same independent variance. The random coeﬃcient can be determined by the following equation: (2) k = ξ12 (t) + ξ22 (t) − 1.25, where ξ1 (t), ξ2 (t) are two independent and standard normal random processes with the mean value as 0, the variance value as 1. According to superposition principle, random load of cutting resistance can be determined by a combination of the average load and random components as the 1850013-4 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 The structural optimization of roadheader conical picks based on fatigue life following equations: Z[n] = σz kz [n] + Z0 , Y [n] = σy ky [n] + Y0 , X[n] = σ k [n] + X , x x (3) 0 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. where n are the simulation points of cutting resistances n = 1, 2, 3, . . . , X[n], Y [n], Z[n] random cutting resistance sequence; σx , σy , σz are standard deviations of random cut resistance under Rayleigh distribution; kx [n], ky [n], kz [n] are random sequences of pick cutting resistance coeﬃcient. 2.2. Numerical simulations of the cutting force The main purpose of the cutting force simulation was to determine the parameters for static analysis and fatigue life analysis. In this paper, MATLAB program was written to simulate the random cutting force of the pick. There are 51 cutting picks (Fig. 2) distributed on the cutting head (Fig. 3) forming a helical line, picks in diﬀerent installing positions have diﬀerent work conditions and suﬀered diﬀerent cutting forces. In the MATLAB simulation, the rotational speed and transverse speed of the cutting head took 50 r/min and 2 m/min, the cutting head rotated 10 circles, the resistance of the coal/rock took 30 MPa. The histories of the tool forces were recorded at frequent intervals such as 18,000 data per minute. According to the histories of the force, the random forces of pick were estimated. The variations of cutting force are depicted in Fig. 4, we took pick 23 as an example. It is apparent Fig. 2. Pick shape and size. 1850013-5 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Z. Lu et al. Fig. 3. Picks distribution on the cutting head. (a) Fig. 4. force. (b) The cutting force history of the pick 23: (a) Random cutting force, and (b) theory cutting that the theory cutting force follows the sine, and random cutting force has no regularity. Since the picks in diﬀerent positions suﬀered diﬀerent three-axis force, it is necessary to ﬁnd out the biggest force for static analysis. The three-axis force of each pick has been compared. Pick 1 bore the smallest cutting force and pick 51 bore the biggest cutting force, along with the serial number increase in and cutting force, so the three-axis cutting force of pick 51 will be applied for static analysis. Table 1 shows the theoretical forces and random forces of pick 1, pick 7 and pick 51. It indicated that the minimum value of the side cutting forces is negative because in the MATLAB program, the positive direction for cutting force must be speciﬁed. In the progress of calculation, if the cutting forces are in opposite direction, the 1850013-6 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 The structural optimization of roadheader conical picks based on fatigue life Table 1. Cutting pick 1 Cutting pick 7 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Cutting pick 51 Results of the three-axis force. Theory force (KN) Random force (KN) Z X Z Y X Y Max Min Mean 10.197 0 8.134 7.564 0 5.137 3.256 0 1.766 24.784 0 8.180 15.179 0 5.431 6.387 −0.403 1.880 Max Min Mean Max Min Mean 12.864 0 9.015 21.868 0 13.964 8.562 0 6.012 13.889 0 9.584 4.012 0 1.875 5.979 0 3.087 25.497 0 9.164 45.301 0 14.035 15.134 0 6.132 25.011 0 9.621 7.178 −1.397 1.895 11.032 −0.009 3.112 Z = Cutting resistance; Y = Tractive resistance; X = Side resistance; Max = Maximum value; Min = Minimum value; Mean = Mean value. value of the cutting forces should be shown as a negative number. The theoretical model of the random cutting force is complex, the negative value indicated that the cutting pick bore the side cutting forces both in the positive direction and in the negative direction. The load spectrum also can be obtained from the MATLAB program. In consideration of each pick bearing the diﬀerent forces, pick 51 random spectrum was adopted. In the software for fatigue analysis, the three-axis force coeﬃcient and maximum force should be input, so the random load spectrum had to transform to three-axis force coeﬃcient (Fig. 5), the reason why simulated rotation angle is 1800◦, not 3600◦ is because the pick taking part is cutting only in half cycle, and the load spectrum with no cutting force had been removed. The coeﬃcient can be deﬁned as follows: C = F/Fmax , (4) (a) Fig. 5. The coeﬃcients of three-axis force: (a) The coeﬃcient of X, (b) the coeﬃcient of Y , and (c) the coeﬃcient of Z. 1850013-7 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Z. Lu et al. (b) (c) Fig. 5. (Continued) where C is cutting force coeﬃcient, F is the three-axis force, Fmax is Maximum value of the three-axis force. 3. Prediction of the Fatigue Life and Results The pick’s strength and fatigue life requirement must be modiﬁed ﬁrstly, so it is important to perform static analysis. This would provide the basis for topological optimization if the fatigue life is excessive. The process of the fatigue life analysis is shown in Fig. 6. Finite software was used for static analysis and fatigue life prediction. 3.1. The finite element model The pick is composed of the pick head and the pick bar. There are diﬀerent materials with these two parts, the pick head is tungsten carbide–cobalt, and the pick bar is 1850013-8 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 The structural optimization of roadheader conical picks based on fatigue life Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Fig. 6. Fig. 7. Process of the fatigue life. Numerical model of rock cutting. 42CrMo, so they must be divided with the mesh alone. The mesh size took 1.5 mm, and tetrahedron mesh was taken. Three-axis constant force of pick 51 was exerted on the pick head. The bottom of the pick bar was ﬁxed, and the cylindrical surface of the pick bar was constrained (Fig. 7). 3.2. Static analysis results and discussion The displacement and the von Mises stress results are shown in Fig. 8. The maximum displacement of the pick occurred at the head with 0.14 mm. It was negligible because the deformation was far less than the overall size, and had no inﬂuence on rigidity. The maximum von Mises stress also occurs at head with 747 MPa, and it is less than permissible stress of 950 MPa of the tungsten carbide–cobalt. For the pick bar, the maximum von Mises stress occurred at connection between bar and head with 249 MPa at less than permissible stress 310 MPa of the 42CrMo. As can be seen, the strength requirement of the pick can be satisﬁed, however, the pick head and the connection are damaged easily. 1850013-9 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Z. Lu et al. (a) (b) (c) (d) Fig. 8. Static analysis results of the pick: (a) Displacement of the pick, (b) Von Mises stress of the pick, (c) Von Mises stress of the pick bar, and (d) Von Mises stress of the pick bar. 3.3. Fatigue life analysis and discussion The ﬁnite model built for static analysis was also applicable to fatigue life analysis, but some parameters were replaced. In the cutting progress, the cutting pick only bore the cutting force of the load spectrum. Therefore, load spectrum is the only factor that lead to the fatigue failure of cutting pick, and it can be seen as fatigue load. In Fig. 7, the three-axis forces loaded on the cutting pick were the biggest cutting force that the pick 51 bore, and they should be replaced by the load spectrum as shown in Fig. 5. The 50% survival material S–N curve was took. The material properties are as same as before. Nominal stress method was taken because the pick had no plastic deformation in the cutting progress, and rain ﬂow counting method was set to deal with the stress history data. In order to reduce the computational burden of the computer, one cyclic load contains 12 load spectra. The fatigue life results are shown in Fig. 9, both the pick head and the connection between the bar and the head have the tendency of fatigue failure, besides, there is no fatigue damage tendency. The minimum fatigue life of the connection between the bar and the head is 1.00e19 cyclic loads, less than 1.25e19 cyclic loads of the pick head, reﬂecting that the head has the risk of being detached from the pick. That is agreed with static analysis results. But the pick fatigue failure has not been considered in theory because 1.00e19 cyclic load is very high. The static analysis and fatigue life analysis results indicated that both the strength and the life of 1850013-10 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 The structural optimization of roadheader conical picks based on fatigue life Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. (a) (b) Fig. 9. Results of the fatigue life analysis: (a) Fatigue life cloud of the pick, and (b) fatigue life cloud of the pick bar. pick designed are excessive. The topological optimization will be carried out for material saving and reduce wear under the premise of satisfying strength and life requirement. 4. Topological Optimization Based on Fatigue Life 4.1. Topological optimization The volume of the pick bar is far greater than the pick head, the paper took the pick bar as the main optimized objective. In order to better optimize, the initial structure of the pick as shown in Fig. 10 was chosen. This structure is an improved version of the pick as shown in Fig. 7. The pick head was retained and used for Fig. 10. The initial structure of topology optimization model. 1850013-11 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Z. Lu et al. Fig. 11. The volume iterative curve of the pick. applying load. It did not involve optimization. The load spectrum applied on the pick head was same with the fatigue life analysis. Assuming that picks work 24 h a day with the speed of 50 r/min, in these working conditions, its fatigue life must be met in 30 days.27 Volume minimization was taken as the optimization objective based on variable density method. Results for volume decreases are shown in Fig. 11. As can be seen, the convergence occurs many times in the iterative process, e.g., the 13th, 14th, 23th, 26th, 27th, 42th, 43th results satisﬁed the convergence criterion. The ﬁrst ﬁve of them have smaller volume fraction ﬂuctuation with the average value of 45.18%, when the 42th, 43rd steps are reached, the average value is 33.1%. The 43rd step result was taken as the optimum result. The initial volume of pick is 2.69191e5 mm3 , after the topological optimization the volume is 1.01149e5 mm3 . Based on this, the volume decreased 64.42%. Speciﬁc iterative processes are shown in Fig. 12. Figure 12(d) presents the ﬁnal optimization results, compared with the traditional pick structure as shown in Fig. 7. There are some similarities, but also diﬀerences. All of the pick heads have the taper and the taper measures are very similar. After optimization, the bottom half of the pick disappeared, instead of a cavity. The pick bar also emerged as the symmetric groove because of the inﬂuence in the force direction. 4.2. Structure improvement Optimized model is shown in Fig. 13(a), with no pick head and ﬁxed structure, and cannot be applied directly. Based on the pick actual working conditions and characteristics, the improvement is carried out according to the installation method of traditional pick. As shown in Fig. 13(b), the pick with new structure is composed of three sections which are pick head, pick head seat and pick bar. The volume of the new type of pick is 2.1455e5 mm3 , compared with the traditional pick, its volume decreases 23.83%. 1850013-12 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. The structural optimization of roadheader conical picks based on fatigue life (a) (b) (c) (d) Fig. 12. The results of topological optimization: (a) The 10th optimization result, (b) the 20th optimization result, (c) the 30th optimization result, and (d) the 43rd optimization result. (a) (b) Fig. 13. The improvement of the pick: (a) The optimized result model of the pick, and (b) the new structure of the pick. 1850013-13 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Z. Lu et al. Fig. 14. The rotation of the new type of pick. To avoid the wear at the same position, the traditional pick rotation relies on frictional contact, but because the rotational torques are small, the pick is diﬃcult to rotate. This caused the pick one side wear and led to the pick failure. With the new type of picks, the groove can increase the rotational torques, reduce the wear and improve the service life is shown in Fig. 14. 4.3. Static analysis results and discussion of the new pick The new pick must also satisfy the strength and fatigue life requirement, so the static analysis and fatigue life analysis are carried out. The static analysis method and parameters of the new pick were the same as in Sec. 3.1, and the analysis results shown in Fig. 15. The biggest displacement of the pick still occurred at pick head with 0.0612 mm. Compared with the 0.140 mm of the traditional pick, the strength of pick obviously is reinforced. The biggest von Mises stress occurred at the pick head with 883 MPa. Compared with 747 MPa of the traditional pick, the maximum stress increased, but still less than the pick head material allowable stress with 950 MPa, so the pick head satisﬁed strength requirement. The biggest von Mises stress of the pick head seat occurred at the connection between pick head and the pick head seat with 301 MPa, also bigger than traditional connection stress with (a) (b) Fig. 15. Static analysis of the new type pick: (a) The displacement of the pick, and (b) the von Mises stress of the pick. 1850013-14 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 The structural optimization of roadheader conical picks based on fatigue life Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. (a) (b) Fig. 16. Static analysis of the new type pick: (a) The fatigue life analysis result of the pick, and (b) the fatigue life analysis result of the pick bar. 249 MPa, less than the allowable stress 310 MPa of the material 42CrMo. The pick bar and pick head seat bore the small stress relative to the connection position. On the whole, the new pick satisﬁes application requirements. 4.4. Fatigue life analysis results and discussion of the pick By the previous approach, fatigue life analysis of the new pick was ﬁnished. The results shown in Fig. 16. All of the pick head, pick bar and pick head seat have the tendency of fatigue life, the minimum fatigue life occurred at the connection with 1.92e4 cyclic loads. The working days can be calculated as the following equations: n ∗ n1 ∗ n2 , (5) D= 24 ∗ 60 ∗ r where n is the number of cyclic loads, n1 is the number of load spectrum in one cyclic load, n2 is the number of cutting head rotate circle, r is the speed of cutting head. As mentioned above, n = 1.92e4, n1 = 12, n2 = 10, r = 50 r/min, D can be calculated as 32 days, meet the working requirement 30 days. The static analysis and fatigue analysis of the new pick have shown that topological optimization and structure results are feasible. 5. Conclusions The picks are the important cutting tools used on excavators, especially used on roadheaders, replaced frequently due to bad damage, so it is important to analyze their fatigue life and topological optimization in order to save material and estimate on time. This paper presented the simulation process based on ﬁnite element method. The cutting force of the pick was simulated based on the theory model. Results show that the pick 51 which was installed at the front of the head that bore the maximum three-axis resistance. Additionally, the static analysis of the pick 51 shows that all of the picks’ strength requirements were satisﬁed. The fatigue life analysis 1850013-15 2nd Reading October 25, 2017 18:35 WSPC/262-IJMSSC/S1793-9623 1850013 Z. Lu et al. of the traditional pick showed that fatigue damage is impossible and concluded that material waste always exist. Finally, a new pick initial structure for topological optimization is proposed. The optimized result of the cutting pick cannot be applied directly, so with the improved measures the new type of pick was proposed. The new type of pick can save 23.83% materials compared with the traditional pick and can meet the strength and fatigue life requirement with the pick working for 32 days. Int. J. Model. Simul. Sci. Comput. Downloaded from www.worldscientific.com by VANDERBILT UNIVERSITY on 10/27/17. For personal use only. Acknowledgments The study is ﬁnancially supported by National Natural Science Foundation of China (Grant No. 51674155), China Postdoctoral Science Foundation Funded Project (Project No. 2016M592214) and Natural Science Foundation of Shandong Province (Grant No. ZR2014EEM021). References 1. Evans I., A theory of the basic mechanics of coal ploughing, Mining Research 2:761– 798, 1962. 2. Evans I., Line spacing of picks for eﬀective cutting, Int. J. Rock Mech. Min. Sci. 9(3):355–361, 1972. 3. Evans I., A theory of the cutting force for point-attack picks, Geotech. Geol. Eng. 2:63–71, 1984. 4. Evans I., Basic mechanics of the point attack pick, Colliery Guardian 189–93, May, 1984. 5. Hurt K. G., Evans I., Point attack tools, Mining Engineer 141:673–675, 1981. 6. Roxborough F. F., Cutting rock with picks, Mining Engineer 133:445–455, 1973. 7. Goktan R. M., A suggested improvement on Evans cutting theory for conical bits, in Proc. Fourth Symp. Mine Mechanization Automation, Brisbane, Queensland, Australia, Cooperative Research Center for Mining Technology and Equipment, Vol. 1, pp. 57–61, 1997. 8. Roxborough F. F., Liu Z. C., Theoretical considerations on pick shape in rock and coal cutting, in Proc. Sixth Underground Operator’s Conf., Kalgoorlie, WA, Australia, pp. 189–193, 1995. 9. Nishimatsu Y., The mechanics of rock cutting, Int. J. Rock Mech. Min. Sci. 9(2): 261–270, 1972. 10. Bilgin N., Demircin M. 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