Contact deformation of spur gears based on accurat

2022-08-14
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Contact deformation analysis of spur gears based on accurate division of tooth surface grids

gears are widely used in the power transmission of automobiles, rail vehicles and other mechanical equipment. This paper analyzes the finite element analysis of gears based on solidworks/cosmosworks and the method of tooth surface contact deformation, and obtains the deformation value of tooth surface nodes by establishing tooth surface displacement sensors. According to this method, the contact deformation of gears with different parameters in meshing can be analyzed quickly and effectively, and the purpose of improving the meshing performance and running stability of gears can be achieved by adjusting the design parameters

I. preface

spur gear transmission, as an important form of mechanical transmission, is widely used in power transmission in automobiles, rail vehicles and other means of transportation, such as automobile engine transmission gears, traction gears in rolling stock and transmission gears in railway cars

gear transmission in transportation equipment is developing towards large load transmission, high-speed and light weight structure. The speed of high-speed gear transmission device is usually 3000r/min, and the linear speed is more than 22m/s. Under the operating conditions of large load and high speed, due to the elastic deformation of the bearing gear teeth, the correct Meshing Conditions of the gear are destroyed, resulting in the contact deformation of the gear in the meshing process, which may cause serious eccentric load and excessive transmission error of the gear, and finally lead to serious impact load and noise. For example, some automobile gearboxes will have gear beating and excessive noise. The periodic noise or scuffing of the transmission gears of the running gear of rail vehicles is often caused by the contact deformation of the gears or other parts

the contact deformation of gears is closely related to the material, geometric dimension and load of gears. How to accurately analyze the meshing contact deformation of gears plays an important role in improving the running performance of gears. Traditional gear design methods and calculation formulas are difficult to accurately analyze the meshing deformation of gears. The application of finite element analysis method based on cad/cae integration and its software tools is an effective way to accurately analyze the contact deformation of gears

solidworks is a three-dimensional mechanical CAD software, which has the functions of three-dimensional design of parts, surface design and assembly modeling. The finite element analysis plug-in CosmosWorks integrated with Solidworks has the functions of finite element analysis and optimization. It is completely embedded in SolidWorks. When the 3D design or assembly design of parts is completed in SolidWorks environment, finite element analysis and optimization can be directly carried out with the help of CosmosWorks. So as to design better products faster and more conveniently

this paper focuses on the methods and steps of accurate analysis and calculation of the displacement value (i.e. deformation) on the gear tooth surface under the solidworks/cosmosworks environment. Using this method, the specific deformation value of the mesh points on the tooth surface of the transmission gear in the meshing process can be obtained, so that the meshing deformation of the transmission gear can be analyzed and controlled more effectively

II. Basic analysis process of gear contact deformation

in order to implement the analysis of gear tooth contact deformation under the solidworks/cosmosworks software environment, it is necessary to carry out two main steps: gear finite element analysis and gear face displacement value detection on the basis of establishing the three-dimensional model of the gear. The specific process is shown in Figure 1

gear contact deformation analysis flow chart

III. gear finite element analysis based on solidworks/cosmoworks

1 Establish a three-dimensional model of the gear in SolidWorks

set the basic parameters of a gear as follows: the number of teeth is 25, the modulus is 2.5, and the tooth width is 75mm. The three-dimensional model of the gear established in SolidWorks is shown in Figure 2. The gear finite element analysis and tooth surface displacement detection described below take the gear parameters as an example

2. Generate an example in cosmoworks

start the cosmoworks plug-in to start the finite element analysis of the gear, and take the drawn gear entity as an example for static analysis

3. Define gear material

open the material dialog box of CosmosWorks, define the material of the gear as 45 steel in the self library file, and "apply this material to all"

4. Define constraint

select "constraint" in CosmosWorks "load/constraint" option, select fixed constraint in "constraint type", and select inner hole and keyway of gear in "constrained face"

5. Applied load

(1) stress analysis of gear teeth

during the meshing process of a pair of gears, the load action point on the gear teeth changes, and the one that causes the maximum bending moment at the tooth root should be taken as the load action point during calculation. Since it is complex to calculate at this point, the tooth top can generally be used as the load action point. The force direction is the normal direction of the tooth surface contact line. The stress analysis of gears is shown in Figure 3

the torque, circumferential force and normal force of the gear are calculated according to equations (1), (2) and (3):

torque (1)

circumferential force ft=2t/da (2)

normal force fn=ft/cos α (3)

Where, α Is the pressure angle of the addendum circle (°), P is the power transmitted by the motor (kw), n is the gear speed (r/min), Da is the diameter of the addendum circle (mm)

set the transmission power of the motor driving the gear to be 7.3Kw and the speed to be 960r/min. According to the above formula, the normal force borne by the gear can be calculated, which is the load borne by the gear at the meshing part of the tooth top

(2) load the gear in CosmosWorks

in order to apply additive load to the addendum dome of the gear within the whole tooth width range, select an end face of the gear as the sketch reference plane, and make a straight line perpendicular to the involute of the tooth profile along the addendum dome point on one side of a single tooth. Using the "dividing line" function, the end face line is projected onto the gear end face, and the projection line can be used to define the direction of the normal force. In the "load/constraint" option of CosmosWorks, select the addendum edge line as the force part, select the projection line made above in the direction of the force, and define the load size, that is, complete the load application, as shown in Figure 4

6. Generation of gear solid lattice

open the "generation lattice" dialog box of CosmosWorks, determine the size and tolerance of the lattice, and then carry out the steps of "evaluating geometry" and "processing boundary". The generated gear solid lattice is shown in Figure 5

7. The results of finite element analysis

are calculated in cosmoworks environment. After running, three results are generated: stress, displacement (combined displacement) and strain. Double click the result file respectively to display the stress nephogram, displacement diagram and strain diagram

IV. gear tooth surface node displacement detection under SolidWorks environment

1 After the finite element analysis and calculation results are generated, in order to obtain the position of several specified points on the tooth surface, "we must improve the performance displacement value, we need to establish a sensor that can detect the displacement value on the tooth surface. Before establishing the sensor, we need to construct the tooth surface lattice and several lattice points on the tooth surface. If the tooth surface of the gear is divided into 15 (axial) × 4 (radial), the specific method is as follows

(1) divide the tooth surface along the axial direction of the gear

select one end face of the gear to draw a sketch, and draw three circles with the gear center as the center, and the radius is the average score from the root circle radius to the addendum circle radius respectively. Using the "projection" function of the "division line", select the drawn division circle in the "sketch to be projected" and select a single tooth surface in the "face to be divided", then three straight lines can be generated in the tooth width direction of the tooth surface, so as to realize the axial division of the tooth surface

(2) divide the tooth surface along the radial direction of the gear

insert 14 datum planes parallel and equidistant with the gear end face between the two gear end faces according to the environmental protection industry standard conditions formulated in the subdivision field. Select the function of "intersection" to split the surface in the split line, select and insert 14 datum planes in the "split datum plane", and select the tooth surface of the gear tooth in the "surface to be divided", and the generated curve can divide the tooth surface along the radial direction. These curves and the straight line along the gear axis obtained in the previous step form the passing point of the tooth surface grid, as shown in Figure 6

2. Define the tooth surface displacement detection sensor

the tooth surface grid intersection established above constitutes 90 cold-rolled strip on the tooth surface. It is a uniformly distributed node produced by the ingot hot rolling method. Using these nodes, we can define a virtual sensor that can detect the tooth surface displacement. The specific methods are as follows:

(1) open the sensor Definition dialog box in the CosmosWorks environment

(2) in the "sensor (select a vertex)" option, select the evenly distributed nodes of the gear tooth surface in turn

(3) after "OK", a tooth displacement detection sensor named "sensor-1" with 90 uniformly distributed nodes on the tooth surface is defined

3. Use the tooth surface displacement sensor to detect the tooth surface displacement

apply the "detection" function in the "result tool", select "slave sensor", and introduce the "sensor-1" just defined. Then the displacement values of 90 tooth surface nodes after stress will be displayed in the table of detection results, and the corresponding displacement values will also be displayed next to each detection node of the tooth surface, as shown in Figure 7

4. Tooth surface displacement detection value export

select "save" in the "report options" of the detection results to save the displacement values of 90 tooth surface nodes in Excel format, as shown in the table, which can be used for later analysis, query, analysis and comparison

v. conclusion

the contact deformation of cylindrical gears has an important impact on the running stability and noise of the power transmission of transportation vehicles. Using modern cad/cae technology and software tools, the contact deformation of gear teeth can be accurately analyzed and calculated. Through the above methods and steps, a more accurate visual analysis and calculation of the contact deformation of the gear tooth surface can be carried out in the solidworks/cosmosworks integrated environment, and the analysis results of the contact deformation of the gear tooth surface can be saved in Excel format. According to the contact deformation of the tooth surface, the material and design parameters of the transmission gear can be further modified and optimized, so as to improve the meshing performance of the gear and improve the running stability of the gear. With reference to the above methods, the contact stress and strength of the gear tooth surface can also be effectively analyzed during the just concluded 10th processing and trade products exhibition (hereinafter referred to as the "fair"). (end)

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