raction transission gearbox echanical properties nuerical calculation and strength analysis Jialin ian,a, Zheng Liang,b, Lin Yang,c, Xueqing Mei 2,d, Baichuan Xiao 3, e, Bei Zhang 4 Southwest Petroleu University, Chengdu, 65, China 2 ChangZhou RuiYang ransission echnology Co., Ltd, Changzhou, 2325, China 3 Structure Departent of Southwest Electronic Equipent Research Institute, Chengdu, 636, China 4 Design Departent of China Offshore Oil Engineering Co., Ltd. ianjin, 345, china a tianjialin@swpu.edu.cn, b liangz_2242@26.co, c ylin@swpu.edu.cn, d xqei3@sina.co, e xiaobc24@63.co Keywords: traction, transission, gearbox, echanical properties, nuerical calculation, FEA Abstract. raction devices are power transission coponents of railbound vehicle. his article discusses the gearbox echanical properties nuerical calculation and strength analysis. It established calculation odel based on field test paraeters. And it finished analysis about elastic deforation of large displaceent and contact proble of nonlinear finite eleent ethod during nuerical calculation. With coparison of energy strength theory and ASME VIII-2 standard, it chooses the suitable strength ethod for gearbox. With definition of key paraeters, the echanical properties nuerical calculation results were given in different load conditions. According to displaceent, strain and stress analysis, the gearbox strength is analyzed based on ASME VIII-2 standard. he results show: under field test loads, the gearbox satisfies strength requireent. But there is stress concentration phenoenon. During independent analysis process of gearbox, hanging and assebly, the results of displaceent, strain and stress assue certain regularity. Introduction raction transission device is the power source of railbound vehicle, and the power transission process is as follows: the traction otor installed in the bogie generates the torque to rotate the wheels through the traction gear and gearbox. he rotation wheels produce locootive traction force with the friction function between wheel and track. he force passes the axle-box guide to the bogie frae, and then passes to vehicle body and realizes the train traction through vehicle hook buffer device. It is the sae transfer process to braking force when brake happens. his article carries on echanical properties nuerical calculation and strength analysis of traction transission gearbox. With field paraeter tested, the load distribution values are obtained. he definition of vertical, horizontal and longitudinal vibration acceleration is shown in figure. Especially, the value of g is 9.8 /s 2. Bogie vibration acceleration (Longitudinal :X axis direction)±4g Bogie vibration acceleration (Vertical:Y axis direction)±g Longitudinal : X axis direction Horizontal :Z axis direction Vertical : Y axis direction Bogie vibration acceleration (Horizontal:Z axis direction) ± 4g Wheel vibration acceleration (Longitudinal :X axis direction)±8g Wheel vibration acceleration (Vertical:Y axis direction)±5g Wheel vibration acceleration (Horizontal:Z axis direction) ± 5g a) b) Fig. traction transission gearbox odel and load condition
a-gearbox test odel, b-the vertical, horizontal and longitudinal definition of vibration acceleration Nuerical Calculation and strength analysis basic Calculation of elastic deforation of large displaceent. his ethod expresses the forula of large displaceent (geoetrical nonlinear) in this article while it is elastic deforation. On this basis, large displaceent and plastic deforation can be derived under the forula [-3]. With the principle of virtual displaceent, it establishes finite eleent equilibriu equations. According to the principle, the energy produced by external force with virtual displaceent equals to the strain energy produced by structure virtual strain, and then the equation () is tenable: { dδ } { ψ } = { dε} { σ} dv { dε} { p} = () In which { d δ} is virtual displaceent. { d ε} is virtual strain. {p} represents load vector array. {ψ } expresses each node vector su of generalized internal forces and external force. According to the increental relation, the equation between strain and displaceent can be ade explicit as equation (2): { d ε} = [ B ]{ dδ} (2) Using equation (2) eliinating{ d δ }, it obtains the general equilibriu equation of nonlinear proble: { ( δ )} = { B} { σ} dv { p} = ψ (3) In the forula the integral operator is the usual application ethod, therefore, equation (3) is suitable in the large or sall displaceent and strain situation. In large displaceent nonlinear proble, displaceent and strain is nonlinear relationship, so {B} is function of (δ ) in equation (3), {B} can be written as: { B } [ B ] + [ ({ δ})] = (4) B L In which [ B ] is atrix of linear strain analysis, and it is independent of {δ }. B L is linear function of displaceent array {δ }. Under large displaceent and elastic deforation condition, stress-strain relation is still linear elastic equation, so it can be given as: { σ } = [ D ]({ ε} { ε }) + { σ } (5) Here [D] is the aterial elastic atrix. { ε } is initial strain array, and { σ } is initial stress array. Equation (3) can be solved with Newton-Raphson ethod; therefore, with differential of {ψ }, the relationship can be established { d ψ} between and { d δ} as equation (6): d[ B ] { σ} dv + { d } = [ B ] { dσ} dv ψ (6) With initial value and boundary condition, it can solve the displaceent, strain and stress value. Strength analysis standard. With results of echanical properties nuerical calculation of traction transission gearbox, it needs analyzing strength. First, it need choose appropriate strength
standard [4-6]. Based on coparison of energy strength theory (the fourth strength theory) and ASME standard, it deterines the strength analysis standard for gearbox. Stress intensity is obtained according to the third strength theory, and von ises stress is obtained with the fourth strength theory, so does the ebrane stress P and bending stress P b, then it carries on strength analysis (shown in table ). ASME VIII-2 standard distinctively checks whether strength eets the requireents under two conditions of axiu working load and axiu experiental load [7-8]. According to stress classification theory of ASME standard, when object subjects to internal pressure and tension force, the equivalent stress of axiu stress point is coposed of linear ebrane stress, linear bending stress, quadratic stress and peak stress. able ASME VIII-2 standard analysis stresses Mebrane stress Su of Mebrane stress and bending stress otal stress P (MPa) P + P (MPa) P + P Q (MPa) b b + he strength exaination of axiu working load is given in equation (7): P 2P 3P he S < ks <.5kS + P + Q < 3S b σ b =, coefficient k=. in analysis. 3. (7) Nuerical calculation and strength analysis Calculation odel definition with experient test. According to gearbox size, the analysis odel is established, before the calculating, engineering data are inputted consistent with product real aterials. And the engineering data is given in table 2. It includes Q45-, 45 steel and rubber in gearbox and hanging structure. Condition yield strength σ and tensile ultiate strength σ b are usually used for perforance indicators in testing aterial strength. Q45- has no obvious yield point. herefore, it usually takes stress value in condition of residual plastic deforation of.2% as condition yield strength. It is expressed by σ.2. he axiu stress value before achieving fracture is tensile ultiate strength. It is σ b. σ s eans tensile yield strength. able 2 structure aterial engineering data Content Q45-45 Steel Rubber Young s odulus (Mpa) 2.e5 2.e5 7.8 Poisson s ratio.3.3.47 Density (Kg/ 3 ) 7.85e 3 7.85e 3 e 3 (MPa) σ b 46 σ b =6 bulk odulus=43.33 (MPa) σ.2 25 σ s =355 shear odulus=2.65 Nuerical calculation odel is established according to physical odel, and the load and boundary condition is shown in figure 2. It is the coparison result of sae position point stress value in experient test and nuerical calculation. It shows that the analysis odel, engineering data and boundary setting is consistent with experient. he following nuerical siulations are based on these setting.
Point 2 3 4 5 6 Stress value(mpa) 3.5 3 2.5 2.5 Nuerical calculation stress value Experient test stress value.5 8 7 2 3 4 5 6 7 8 Point nuber a) b) Fig.2 stress test points nuber and position (the value is vertical acceleration=6g.) a-points nuber and position, b-stress coparison of experient and nuerical calculation Load conditions. With the result of acceleration superiposition, the longitudinal (x axis direction) axiu acceleration can reach ±2g, the horizontal (z axis direction) axiu acceleration can reach ±9g, and the vertical (y axis direction) axiu acceleration can reach ± 6g. aking g=9.8/s 2, it gives eight kinds of load value (given in table 3). With every result of different load, it can analyze displaceent, strain and stress nuerical calculation. able 3 Different load value Serial nuber Sybol Explanation X+Y+Z+ longitudinal (X axis) acceleration=2g vertical (Y axis) acceleration=6g Horizontal (Z axis) acceleration=9g 2 X-Y+Z+ X: -2g, Y: 6g, Z: 9g 3 X+Y-Z+ X: 2g, Y: -6g, Z: 9g 4 X-Y-Z+ X: -2g, Y: -6g, Z: 9g 5 X+Y+Z- X: 2g, Y: 6g, Z: -9g 6 X-Y+Z- X: -2g, Y: 6g, Z: -9g 7 X+Y-Z- X: 2g, Y: -6g, Z: -9g 8 X-Y-Z- X: -2g, Y: -6g, Z: -9g Considering the contact between hanging and gearbox, including the contact between rubber and hanging, the assebly is analyzed about the echanics properties and strength. Calculation results. hese are the results of axiu value of displaceent, strain and stress of traction transission gearbox in eight different load conditions (shown in figure 3). displaceent axiu value().22.2.8.6.4.2..8.6.4.2.74.937.924.728.728.924.937 2 3 4 5 6 7 8 Load nuber.74 Strain axiu value.25.2.5..5.822.86.979.979.86.6924.6924.822.7.49.67.67.49.9984.9984.7 von ises strain axiu value of different load strain intensity axiu value of different load 2 3 4 5 6 7 8 Load nuber a) b) Stress axiu value(mpa) 28 27 26 25 24 23 22 2 2 257.92 228.4 263.47 233.38 272.67 24.74 257.3 257.3 272.67 263.47 257.92 24.74 233.38 228.6 228.6 228.4 von ises stress axiu value of different load stress intensity axiu value of different load 2 3 4 5 6 7 8 Load nuber c)
Fig.3 Nuerical calculation result of different load value a-displaceent axiu value, b-axiu value of von ises strain and strain intensity, c-axiu value of von ises stress and stress intensity he results of displaceent, strain and stress assue certain regularity. he largest stress was produced in the third and the sixth load condition, and the value is equal. he reason is that the gearbox is siilar to surface syetrical structure. Strength analysis. Based on results of nuerical calculation, the strength analysis accords ASME VIII-2 standard. It analyzes the stress result of the sixth load condition. During independent analysis process of gearbox, hanging and assebly, the largest stress appears in hanging odel (figure 4). So the strength analysis bases on hanging nuerical calculation result. According to ASME VIII-2 standard, the axiu stress intensity point is through the stress dangerous section. a) b) c) Fig.4 Stress coparison of gearbox, hanging and assebly a- Gearbox independent analysis stress, b-hanging independent analysis stress, c-assebly analysis stress he path definition. he definition of path and the stresses value are shown in figure 5. he path is through the section area including the axiu stress intensity node. POS SEP= SUB = IME= PAH PLO NOD=75463 NOD2=7538 S S2 S3 SIN SEQV 92.85 78.866 64.879 POS SEP= SUB = IME= SECION PLO NOD=75463 NOD2=7538 92.85 SIN MEMBRANE 84.572 MEM+BEND OAL 76.296 he path definition 5.892 36.95 22.98 8.93-5.56-9.43-33.3 68.2 59.744 SIN 5.468 43.92 34.96 26.64 8.364-47.7.88 2.392 24.784 37.76 49.568 6.956 6.96 8.588 3.98 43.372 55.764 DIS 2.392 24.784 37.76 49.568 6.956 6.96 8.588 3.98 43.372 55.764 DIS SubwayGearbox--Static Structural (W5) SubwayGearbox--Static Structural (W5) a) b) c) Fig.5 the path definition and the stresses through the path a-the path definition, b-s, S2, S3, von ises stress and stress intensity value through the path, c- P, P, P + Q value through the path ASME VIII-2 standard strength analysis. Based on above calculation result, the stress dangerous section is definite through the axiu stress node. With path definition, able 4 presents the value of P (Mebrane stress, MPa), P (Su of Mebrane stress and bending stress, MPa), P + Q (otal stress, MPa). Under rated load, according to ASME VIII requireents, strength analysis is given below for checking the axiu working load. able 4 Gearbox strength analysis stresses according to ASME VIII-2 standard Su of Mebrane stress Mebrane stress otal stress and bending stress P + P (MPa) P + P Q (MPa) P (MPa) b 25.89 54.46 92.85 b +
S σ b 6 = = = 2MPa, set k=., the analysis equation is: 3. 3. P = 25.89MPa < ks = 2MPa P = 54.46MPa <.5kS = 3MPa (8) P + Q = 92.85MPa < 3S = 6MPa Under working load condition, the traction transission gearbox satisfies ASME VIII-2 strength standard. Conclusions o ensure the correct nuerical calculation result, it needs inputting key paraeters which are consistent with experient result, such as boundary, contact and odel engineering data setting. he stress variation shows rule: during independent analysis process of gearbox, hanging and assebly, the largest stress appears in hanging odel, and the stress value is slightly larger than that of assebly. he reason is that the pin terinal surfaces are fixed in hanging independent analysis process, while during assebly analysis process, the hanging and gearbox established connection via pin. It allows icro relative deforation of the pin terinal surface, and the deforation is deterined by echanical paraeters of assebly various connection coponents. According to eight different load condition strength analyses, the results show the traction transission gearbox eets the strength requireents. It can be safe and stable operating under these load condition. Acknowledgeents his work is supported by National Natural Science Foundation of China (NSFC: 57422), Foundation of Key Laboratory of Oil and Gas Equipent of China Education Ministry (SS), Major Cultivation Foundation of Sichuan Education Departent (9ZZ38) and Science Foundation of Southwest Petroleu University (No.245). References []. S.S. Gill: Int. J. Mech. Engng Educ., 976, 4, 339 355. [2]. D.M. Wei, G.. Yang: Journal of aiyuan University of echnology, 992, 23, (4), 8-3. [3]..X. Yu, G.X. Lu: 'Energy absorption of structures and aterials', 26, Beijing, Cheical Industry Press. [4]..J. McDevitt, J.G. Sionds: Journal of Applied Mechanics, 23, 7, 799-88. [5]. H.S. Harung, M.A. Millar and M.G. Moore: Proc. Int. Conf. on 'Instability and plastic collapse of steel structures', Manchester, UK, 983, 74 83. [6]. Z.H. Wu, J.L. ian, Z. Liang, Y.F. Nie and L. Yang: Oil Field Equipent, 29, 38, (3), 23-27. [7]. ZHAO Guanghui, LIANG Zheng, IAN Jialin, JIANG faguang, ZHANG Liang. Large Deflection Plastic Studying on Preforing of Multilateral ool, Materials Research Innovations, th ASIA-PACIFIC CONFERENCE ON ENGINEERING PLASICIYAND IS APPLICAIONS, Noveber 5-7, 2, Wuhan, China. [8]. LIANG Zheng, REN Liancheng, IAN Jialin, YANG Lin. Research on the Distribution Law of Hydrocyclone Radial Velocity, the 2nd International Conference on Mechanic Autoation and Control Engineering (MACE 2), July 6-8, 2, Inner Mongolia, China.
About the author: Corresponding author: Jialin ian: Assistant Professor of the Departent of Mechanical Engineering at Southwest Petroleu University. He obtained his Ph.D. fro Southwest Petroleu University, China. Major in nuerical calculation of structure and fluid dynaics. Phone: 3882236886, 28-8332949(China). Mail: tianjialin@swpu.edu.cn, tianjialin@live.co, and website: www.tianjialin.net. Lin Yang: Doctor of Southwest Petroleu University, Major in fluid dynaics nuerical calculation and siulation. Phone: 369962(China), Mail: ylin@swpu.edu.cn.