The Constructing of Gearbox Transmission Mechanism 3D Model based

The Constructing of Gearbox Transmission Mechanism 3D Model based on SolidWorks Jiangsu Jianzhu Institute, Jiangsu China 221116 yuanyuxiang4532@163.com Abstract The gearbox is a complex system component and its core is the gear shafting. The gear system output the power to the drive shaft with speed changing through the engine. In the actual work, because of the installing error, load distortion and shock load situation, the correct meshing condition of gears was destroyed. 3D model of transmission gear was firstly built up by using SolidWorks software, and the Simulation module was utilized for modal analysis of transmission gear by using finite element method. The modal forms and deformation extent of transmission gear under several frequencies were gained and analyzed the maximum displacement deformation of gear with loading. It provides a reference for reverse engineering and optimization design of transmission gear. 1. Introduction Keywords: Transmission Gear, Modal Analysis, SolidWorks In recent years, people have paid more attention to the durability and reliability of commodity. Opposite to the environmental protection and the security of the passenger train, the truck pays more attention on the products efficiency, durability and the reliability. Opposite to other vehicles the trucks state of roads were worse. Therefore a higher request to the transmission system and the load bearing system was set up [1]. As the main center of the transmission system, the power and the reliability of the gearbox appeared especially important [2]. Those mentioned above forced the gear to run with non-uniform speed. At the same time the gears transmission accuracy decreases [3]. And even that can cause the gears fatigue failure very early, which can cause the properties of the whole gearbox decrease. In order to improve the working reliability of the trucks, the modal of the transmission gear in the gearbox was analyzed through SolidWorks Simulation module. The deformation degree of the gears in each frequency order was analyzed. The gears were loaded under the simulation actual situation. The relevant improved method was put forward according those involved form the above. Virtual prototype technology is arisen in the 1980s which is based on a new conception of computer technology. Virtual prototype is a computer model which could reflect the actual product characteristic including appearance, spatial relationships, kinematics and dynamics characteristic. Applying this technique, the technologist could build the model of mechanical system by computer along with 3D visual processing, simulating the sport and dynamic characteristics in the real environment system [4]. According to the simulation results, it downsizes and optimizes the system. However, because each soft-ware has its dedicated place, it couldn't complete independently the whole simulation process very well. For example, multi-body dynamics simulation software ADAMS is professional virtual prototype analysis software which could analyze virtual prototype system static, kinematics and dynamics, output displacement, velocity, acceleration and reaction curve. It has been used by hundreds of major manufacturers from all walks of life around the world. However, compared with professional 3D CAD software system such as SolidWorks and so on, the capability of constructing complex 3D model in ADAMS still has a long way to go. At present, the widely used three-dimensional computer-aided design software is Pro/e, SolidWorks, and UG etc. Though the function of 3D CAD modeling is very strong, the function in accurate kinematics and dynamics analysis is rather weak. Among so many 3D CAD soft-wares, SolidWorks is specialized Windows-production in R&D (research and development) and in sales of mechanical design software. Many famous universities abroad list it obligatory course as their manufacture majors. It shortens the design time greatly, with making the product quickly and effectively to market [6]. Meanwhile, it also wins numerous customer's favor by following the principles of easy-using, stability and innovative. In this paper, a new way how to use SolidWorks and International Journal of Digital Content Technology and its Applications(JDCTA) Volume7,Number3,February 2013 doi:10.4156/jdcta.vol7.issue3.13 95

ADAMS combination simulation is discussed in order to accomplish the simulation of the shaper mechanism. And the conclusion is made that the result of the graphic is the same as that of analytic method 2. The gearbox structure and the transmission gear working parameters The mechanical gearbox of some agricultural vehicle was chosen as a research object. The gear transmission figure showed as fig1. Figure.1 Schematic diagram of gearbox transmission mechanism Found from the strength check of each gear in the gearbox, the strength of the speed-changing gears was lower, which was weak link among the transmission system. At the same time it was the core component among the gearbox. So the modal of the gears should be analyzed mostly. In the actual operation, the transmission gears usually were placed on the top file, which including three files. All loads were distributed on the three files of gears surface uniformly. Table 1 was the major parameters of the transmission gears. Table1 Major Parameters of shift gear Parameter I Files II Files III Files Material Teeth No. Modulus Pressure angle Dislodgement coefficient Poisson's ratio Elasticity coefficient 20CrMnTi 18 3 20 0.38 0.28 2.1 10 11 20CrMnTi 21 3 20 0.4 0.28 2.1 10 11 20CrMnTi 24 3 20 0.83 0.28 2.1 10 11 The three-dimensional model was introduced into the Simulation. According to the material properties showed in Table 1, two step tetrahedral units were chosen as a unit type of the dividing grid. The unit size was 10.2883mm, which include 3583 units and 7223 nodes. The modal generated by grid was showed as fig 2. 96

3. Modal analysis Figure.2 Finite element model of transmission gear 3.1 Analysis of the gear structure vibration mode Using the method of ADAMS and SolidWorks combination simulation, there are some slightly distinction compared with ordinary modeling. Firstly, there is no need to build accurately each components of the three-dimensional model in ADAMS. Only build its rough shape except ignore the detailed features of the parts. These simple mechanical institutions like shaper mechanism just need some simple rods to replace its parts. ADAMS can not only calculate the mass of each part automatically, by setting the parts of the materials, rotation inertia and other physical properties, but also set freely mass, rotation inertia and other physical properties for each part. It simplifies the modeling work greatly. But this simplified must have no impact on the accuracy of the simulation results, and it should depend on the circumstances. Secondly, for extrude boss characteristic in modeling, a lot of people like using symmetry in order to make model centre and coordinate origin superposition. However, we'd better use unilateral rather than symmetry in modeling for in ADAMS simulation. It can avoid each part of virtual prototype producing a new part in original position when import files to ADAMS, to reduce the troubleness of deleting it manually. Again, in addition to satisfy the constraint relation between parts as assemble the virtual prototype, we'd better make it in the initial location place by constraints. This will simplified the work of ADAMS greatly. The mechanism dynamic performance was mainly decided by its modal parameters of natural frequency, the host vibration mode and so on. The inherent characteristics of these systems have a great bearing on the dynamic response of the systems, the creation and transmission of dynamic load and the vibrant form of the systems. The finite element model of the transmission was analyzed in the article. The mass distribution and connection stiffness of the modal was consistent with the actual situation. That can meet the requirement of dynamics analysis. Known from the vibration theory, the mechanical meaning of the modal analysis was to analyze the structure free vibration. From the above the gear s natural frequency and corresponding vibration model can be obtained. Its mathematics essence was to solve the two step linearity homogeneous ordinary differential equation. To an n-degree of freedom system, its free vibration differential equation of motion was as following: M x t C x t K x t 0 (1) In the formula, [M], [C], [K] respectively represents the system quality, the damping and the stiffness matrix; {x} represents each displacement respond vector of the system. The process of modal analysis is to solve eigen value and eigenvector of the differential equation of motion characteristic matrix. Because there are many degrees of freedom in the finite element model of 97

elastic structures, the major work of modal calculation was centralized on the solution of the lager eigen value. There are many mature numerical algorithms in this aspect, such as inverse iteration method, subspace iteration method, Ritz method and Lanczon method, and so on. The equation solver of extracting structure eign value in Simulation is subspace equation solver. Its has advantages of fast operation and high efficiency, and so on. 3.2 Modal of transmission gear analysis results Save the SolidWorks file as "PARASOLID" format, the generated file extension is ".x-t". However, you need to be aware that although both ADAMS and Solid-Works support PARASOLID format, PARASOLID format file generated in SolidWorks only retains each parts' shape, structure and the positional relationship between parts after the load of ADAMS. Other information, such as material, mass of parts, restriction between parts, cannot remain in the ADAMS. They need to redefine in ADAMS. In addition, the PARASOLID format file generated in SolidWorks should be saved in the file path of English. Or they cannot be imported into ADAMS. Through SolidWorks and ADAMS combination simulation, every part from the new imported virtual prototype is no mass and material. If the virtual prototype contains massless component in ADAMS, the result cannot be solved. It requires us to set the initialization data, by means of setting corresponding mass or material properties separately for every single part. If the virtual prototype is very complex and contains lots of parts, we could click the menu "View-Part only..." Then, there is a pop-up window named "Selections". Select each part in turn in this window and complete the setting and simulation according to the general procedure of the ADAMS simulation. Figure 3 showed the modal of transmission gear analysis results under five order frequencies. One order modal frequency of transmission gear was 15530Hz. Minimal distortion appeared when the frequency reached 17218 Hz. When the frequency was 17252 Hz, elliptic vibration model in the open end appeared. In 17865 Hz, three flaps vibration model firstly appeared and in 18559 Hz, four flaps vibration model appeared. Range from 0 to 2000 Hz, transmission gears in all order modal appeared vertical, level and oblique bending vibration model. While the typical vertical bending and torsion modal didn t appear. During the meshing transmission of all the gears in the gearbox, when a pair of meshing gear teeth enter and separate, the load and stiffness of the gear teeth would increase and decrease suddenly. That could cause instantaneous tangential acceleration that is meshing impact. So it can cause vibration of gears. The vibration frequency was the meshing frequency of gears. The frequency can be expressed on f. Its formula is: f n z /60 n z /60( Hz) (2) 1 1 2 2 In the formula, n 1 and n 2 respectively represented the rotational speed of driving gear and driven gear, (r/min) and, z 1 and z 2 respectively represented the teeth of f driving gear and driven gear. This vibration was caused by the gears self-factors. As long as the gear meshing operates, this meshing shock vibration will exist. This was the natural vibration of the gear transmission. Its vibration intensity decided by the high-low of the circumferential velocity and size of the circular force, precise degree of teeth surface state and the concrete teeth number of gears. When the gearbox worked normally, the rotational speed of the transmission gear changed in the condition of the engine being idle speed, the output torque being maximum and the power being maximum. Knowing form the type of engine parameters, the rotational speed of the transmission gear was 600r/min when the engine was idle speed. According to formula 2, the frequency of transmission gear in the three files is 230Hz. When the engine worked under the maximum output torque, the rotational speed of the transmission gear was 1400r/min and the frequency of transmission gear in the three files is 536.7Hz. When the engine worked under the maximum power, the rotational speed of the transmission gear was 2000r/min and the frequency of transmission gear in the three files is 766.7Hz. Seen form the extreme typical condition of gearbox mentioned above, one step natural frequency of the gearbox was 15530Hz. All meshing frequency in all conditions was under the natural frequency. Both of them didn t effect mutually. 98

(a) 15330Hz (b)17218hz (c)17252hz (c) 17865Hz 3.3 Import SolidWorks file into ADAMS 3.3.1 Run ADAMS and set working environment. (c) 18559Hz Figure.3 Typical mode of transmission mechanism a. Check and set modeling basic environment. Select the menu: setting units, set the unit to be MMKS, set grid work: working grid, X = 7.5, Y = 10, Spacing = 10mm. b. Check gravity Settings. Select the menu: setting gravity... The working interface after setting is below: 99

Figure 4. The working interface after setting. 3.3.2 Import the file and set each component for initialization. a. Select the menu: file - import, selective the path of the file to import. b. Set the physical properties of each component. Right click on each Part, choose Part- modify order. In the pop-up window named "Modify Body", select "User Input" in the blank of "Define Mass By", and set component 2's Mass value is 0.1, component 3's Mass value is 0.1, component 4's Mass value is 220/9.8, component 5' s Mass value is 0.1, component 6 ' s mass value is 800/9.8. Theoretically component 2> 3 and 5' s Mass value is zero. But in order to make the simulation be normal on, it is set to be 0.1. This has demonstrated in the front. c. Add motion pair for the model, motion for driving link and dynamic working resistance. First, add motion pair for prototype according to the Kinematic sketch. Add cylindricpair between component 2 and ground at point 02; Add cylindricpair between component 4 and ground at point 04; Add sliding pair between component 3 and component 4 along the link 4; Add cylindricpair between component 4 and component 5 at point B; Add cylindricpair between component 5 and component 6 at point C; Add sliding pair between component 6 and ground along the horizontal direction. Then, set the motion for driving link. Click the button of "Rotational Joint Motion" at the main toolbar, set its value to be -384, click joint - 1, and add it in the driving link component 2. Last, add the working resistance on component 6. Here, adopt the step function by ADAMS to simulate the working resistance of planer knives. Step function of basic format: Step(x,x0,h0,xl,hl) x independent variables, it can be the time or any functions of the time; x0 the start value of independent variable in step function; xl the final value of independent variable in step function; h0 the initial value of step function; hi the final value of step function; Figure 5 is the curve of working resistance changes with time: Figure 5. The curves of working resistance changes with time. 100

Figure 6 is the virtual prototype after setting: Figure 6. The virtual prototype after setting 3.3.3 Kinematics and dynamics simulation, post-processing in ADAMS. Click on the simulation button to run the simulation. Obtain the shaper planer knives for machining of displacement, velocity and acceleration chart and resistance torque and work of resistance chart as below. Figure 7. The displacement chart. Figure 8. The velocity chart. 101

Figure 9. The acceleration chart. Figure 10. The resistance torque chart. 4. Conclusions Figure 11. The work of resistance chart. Using finite element method to analyze the modal of transmission gear, the natural frequency and vibration mode changing from 0 Hz to 20000 Hz could be obtained. One step natural frequency of the transmission gear was 15530 Hz. With the improving of natural frequency, the phenomenon of expansion, shrinkage, distortion appeared gradually. And in the open end three flaps and four flaps vibration mode appeared too. But there were not obvious vertical and torsional vibration mode. Through comparing the natural frequency of transmission gears and the meshing frequency of gears, we can find the natural frequency of transmission gears was far lower the natural frequency of he gearbox. So that cannot cause resonance. 5. References [1] Xu Tao and Wang Jian-ping, "United Simulation about Dynamics Based on Pro/E, ANSYS and ADAMS", Mechanical engineering & automation, pp. 37-39,2010 102

[2] Yang Hong-wei, "Discussion on model import from Pro/E to ADAMS", China science and technology information, pp.83-87,2010 [3] Du Zhong-hua, Xue De-qing and Zhao Ying-hong, "Discussion to Some Problems Met When Parts being Transformed from Pro/E to ADAMS" Machinery & Electronics, pp.68-70,2010 [4] Li Xu-rong and Zheng Xiang-zhou, "ADAMS enabled virtual prototyping and dynamical simulation approach into planing mechanism", Chinese journal of construction machinery,pp.438-146,2011 [5] Zhang Xiao-ning, Yang Peng, "Finite Element Analysis of High Modulus Asphalt Pavement", IJACT: International Journal of Advancements in Computing Technology, Vol. 4, No. 2, pp. 72-79, 2012 [6] Fang Yongfeng, Chen Jianjun, "Bezier Curves Based On Trigonometric Polynomial", IJACT: International Journal of Advancements in Computing Technology, Vol. 4, No. 2, pp. 80-87, 2012. 103