Finite element analysis method for strength of small-load 3D printing gear

Abstract

The invention discloses a small-load 3D printing gear strength finite element analysis method. The method comprises the following steps that the stress condition of a research object is analyzed; determining material parameters of the research object; simplifying the model of the research object; determining a grid unit form; determining a grid transition mode; performing static structure analysis; adding the determined material parameters into an engineering material library, and importing a simplified gear assembly file; determining boundary conditions, loads and grid division of statics analysis; solving and analyzing a simulation result; performing transient structure analysis; adding the determined material parameters into an engineering material library, and importing a simplified gear assembly file; determining a boundary condition, a load and grid division of transient structure analysis; and solving and analyzing a simulation result. According to the analysis method, key parameters in the finite element analysis process of the gear strength are analyzed and configured, and an accurate analysis result is obtained.

Description

Technical Field

[0001] The present invention relates to a gear strength analysis method, and in particular to a finite element analysis method for the strength of a small-load 3D-printed gear. Background Art

[0002] With the rapid development of 3D printing technology, 3D-printed gears are increasingly being used in small-load transmission systems due to their low cost, lightweight design, and high degree of customization. They are particularly gaining attention in areas such as robotics and small, lightweight devices. In agriculture, particularly in crop phenotyping equipment, 3D-printed gears have become a crucial component for driving lightweight mechanical structures due to their flexible design and rapid manufacturing capabilities. For example, in high-throughput phenotyping platforms, 3D-printed gears are often used to drive the precision motion systems of cameras or sensor modules, enabling dynamic monitoring of crop growth. These devices often require highly customized gear designs to adapt to complex operating environments. However, traditional gear production processes, with their high material and processing costs, struggle to meet the demands of small-batch, diverse production. 3D printing technology, through its rapid prototyping and material optimization capabilities, significantly reduces production costs and cycle times, meeting the lightweight and highly adaptable requirements of agricultural phenotyping equipment.

[0003] However, the strength and durability of 3D-printed gears are key issues for their successful application. Agricultural phenotyping equipment often operates in outdoor environments, and gears must withstand stresses caused by complex operating conditions such as temperature differences, humidity, and frequent starts and stops. This places higher demands on the mechanical properties of 3D-printed gears. Because the mechanical properties of 3D-printed materials (such as tensile strength and fatigue life) differ from those of traditional metals or engineering plastics, verifying whether their strength is sufficient to support actual working conditions and ensure the reliability of gears in crop phenotyping equipment has become a technical challenge that urgently needs to be solved. To this end, using finite element analysis software such as ANSYS to perform gear strength analysis has become a common and effective method. By precisely setting key parameters such as the gear's mesh density, material properties (such as the mechanical parameters of PLA, ABS, or nylon commonly used in 3D printing), and load conditions (such as the dynamic torque and vibration loads borne by gears in phenotyping equipment), ANSYS can simulate the stress distribution and deformation of gears under different working conditions, thereby predicting their performance and service life.

[0004] Therefore, how to accurately configure these key parameters in ANSYS and obtain reliable analysis results is not only an important step to ensure the performance of 3D printed gears, but also a key link in promoting the widespread application of 3D printing technology in agricultural phenotyping equipment. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above-mentioned problems and provide a finite element analysis method for the strength of 3D printed gears under small loads. The analysis method obtains accurate analysis results by analyzing and configuring the key parameters in the finite element analysis process of gear strength.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A finite element analysis method for the strength of a 3D printed gear under a small load comprises the following steps:

[0008] S1. Analyze the stress of the research object;

[0009] S2. Determine the material parameters of the research object;

[0010] S3. Simplify the model of the research object;

[0011] S4. Determine the grid unit form;

[0012] S5. Determine the grid transition method;

[0013] S6, perform static structural analysis; add the material parameters determined in step S2 to the engineering material library,

[0014] Combine the results of steps S1, S4, and S5 to determine the boundary conditions, loads, and meshing for static analysis;

[0015] Solve and analyze simulation results;

[0016] S7, perform transient structural analysis; add the material parameters determined in step S2 to the engineering material library; import the gear assembly file simplified in step S3;

[0017] Combine the results of steps S1, S4, S5, and S6 to determine the boundary conditions, loads, and meshing for transient structural analysis;

[0018] Solve and analyze the simulation results.

[0019] In a preferred embodiment of the present invention, in step S2, the material parameters include density, Young's modulus, Poisson's ratio, tensile yield strength, compressive yield strength and ultimate tensile strength.

[0020] In a preferred embodiment of the present invention, in step S4, the grid unit forms include tetrahedral units and hexahedral units.

[0021] Furthermore, the specific operations of step S4 are:

[0022] Create a new static structure module for preliminary experiments in ANSYS Workbench;

[0023] Import the simplified gear model file in step S3;

[0024] Set the overall mesh size parameters of the model;

[0025] Insert the method in the mesh, set the tetrahedron and hexahedron in the method respectively, and compare the number of nodes and elements after generating the mesh;

[0026] After the mesh is generated, some boundary conditions are simply set according to the results of step S1, and the equivalent stress results of the tetrahedron and hexahedron are compared to observe the quality of the mesh division.

[0027] In a preferred embodiment of the present invention, in step S5, the grid transition method includes adaptive size adjustment and custom growth rate.

[0028] Furthermore, the specific operations of step S5 are:

[0029] Create a new transient structure module for preliminary experiments in ANSYS Workbench;

[0030] Import the simplified gear model file in step S3;

[0031] Set the overall mesh size parameters of the model;

[0032] According to the cell type determined in step S4, a tetrahedron or hexahedron cell is selected, and after the insertion surface size is adjusted, the local mesh size is set for the tooth of the meshing part and the two surrounding teeth.

[0033] Select the transition method of adaptive size adjustment and custom growth rate. By adjusting the growth rate value multiple times, it is found that the mesh units and mesh nodes generated by the two transition methods are similar.

[0034] After the mesh is generated, the boundary conditions are set according to the results of step S1, and the equivalent stress results of the two transition methods are compared to observe the quality of the mesh division.

[0035] In a preferred embodiment of the present invention, the specific operation of step S6 is as follows:

[0036] Create a cylindrical coordinate system based on the axial surface of the driving wheel;

[0037] Set up a friction connection for the two surfaces in contact at the gear mate and define the friction coefficient;

[0038] Setting a fixed support for the driven wheel and a displacement constraint for the driving wheel, using the cylindrical coordinate system to ensure that the gear retains only one degree of freedom of rotation, and setting a torque on the driving wheel according to the calculation in step S1;

[0039] According to the results of steps S4 and S5, the mesh is set to tetrahedral elements, adaptive transition mode, and global mesh size of 1 mm. The units of the local mesh are adjusted multiple times until the results of the equivalent stress cloud map converge.

[0040] In a preferred embodiment of the present invention, the specific operation of step S7 is as follows:

[0041] Select the tooth surface of the gear and define the tooth surface of the driving wheel and the driven wheel;

[0042] Set the contact settings of the master and slave wheels, determine the friction coefficient, and set the rotation connection width of the axial surface of the master and slave wheels to ensure that the movement is rotation;

[0043] Setting the grid parameters determined in step S6;

[0044] Set the rotation speed for the connecting span of the driving wheel and the reverse torque for the connecting span of the driven wheel;

[0045] According to the rotation speed of the driving wheel, the time it takes to rotate three teeth is calculated as the end time of the transient simulation; the time step size is adjusted multiple times according to the simulation results to ensure that the curve is smooth and the number of steps is less than the total time length divided by the minimum time step.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1. The analysis method of the present invention first determines the stress distribution and deformation of the gear under normal working conditions by performing a static structural analysis on the gear. Then, the response of the gear under dynamic load is further considered through transient structural analysis. Multiple preliminary experiments are performed to determine the optimal parameter configuration, thereby obtaining an accurate finite element analysis result of the gear strength.

[0048] 2. The method of the present invention does not limit the parameters and stress conditions of the gears, and the most suitable parameters can be configured according to the solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flowchart of the finite element analysis method for the strength of a small-load 3D-printed gear according to the present invention.

[0050] Figure 2 This is a schematic diagram of the three-dimensional structure of the data acquisition platform device, which is the research object of the present invention.

[0051] Figure 3 It is a schematic diagram of the three-dimensional structure of the rotating platform of the data acquisition platform device of the present invention.

[0052] Figure 4 It is a bottom view of the rotating platform of the data acquisition platform device of the present invention.

[0053] Figure 5 This is a bottom view of the gear ring of the data acquisition platform device of the present invention.

[0054] Figure 6 It is a simplified model of the gear ring of the data acquisition platform device of the present invention.

[0055] Figure 7 Schematic diagram of the hexahedral unit grid of the present invention.

[0056] Figure 8 Schematic diagram of the tetrahedral unit grid of the present invention.

[0057] Figure 9 Schematic diagram of the adaptive transition grid of the present invention.

[0058] Figure 10 Schematic diagram of the custom transition grid of the present invention.

[0059] Figure 11 This is the adaptive equivalent stress diagram of the present invention.

[0060] Figure 12 This is the customized equivalent stress diagram of the present invention.

[0061] Figure 13 This is a diagram of the mesh division pre-experimental process of the present invention.

[0062] Figure 14 This is a diagram of the grid pre-experimental results of the present invention.

[0063] Figure 15 This is the total deformation cloud diagram of the static structural analysis of the present invention.

[0064] Figure 16 This is the equivalent stress diagram of the static structural analysis of the present invention.

[0065] Figure 17 This is the equivalent elastic strain diagram of the static structural analysis of the present invention.

[0066] Figure 18 This is the tooth root equivalent stress diagram of the static structural analysis of the present invention.

[0067] Figure 19 This is the static safety factor diagram of the static structural analysis of the present invention.

[0068] Figure 20 This is the total deformation cloud diagram of the transient structural analysis of the present invention.

[0069] Figure 21 This is the equivalent stress diagram of the transient structural analysis of the present invention.

[0070] Figure 22 This is the equivalent elastic strain diagram of the transient structural analysis of the present invention.

[0071] Figure 23 This is the tooth root equivalent stress diagram of the transient structural analysis of the present invention.

[0072] Figure 24 This is the static safety factor diagram of the transient structural analysis of the present invention. DETAILED DESCRIPTION

[0073] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0074] The finite element analysis method for the strength of a small-load 3D-printed gear of this embodiment includes the following steps:

[0075] S1. Determine the research object and analyze its stress conditions. Select a driving mechanism in a data acquisition platform device as the research object for analysis. Figure 2 As shown in the figure, the acquisition device is mainly divided into a rotating platform and a camera position adjustment device. The rotating platform is driven by a gear ring meshing, as shown in Figure 3 shown.

[0076] Table 1 Gear and ring parameters

[0077]

[0078] The gear ring is subjected to force analysis. The gear ring parameters are shown in Table 1. When the mechanism is running, it is mainly affected by the friction between the wheels and the ground. Therefore, the torque provided by the external gear only needs to overcome the torque generated by the ground friction to achieve the movement of the mechanism. The magnitude of the friction torque is calculated by the following formula:

[0079]

[0080] F=η*μ*m*g;

[0081] M=SF*F*r;

[0082] Where m represents the total mass; ρ i represents the density of the i-th unit; v i represents the volume of the i-th unit; t i represents the time of the i-th unit. F represents the magnitude of the force; η represents the efficiency coefficient; μ represents the friction coefficient; g represents the acceleration due to gravity; M represents the torque; SF represents the safety factor; and r represents the length of the lever arm.

[0083] S2. Determine the parameters of the gear material.

[0084] Table 2 Gear material parameters

[0085]

[0086] Figure 3 The 3D printing material used for the gears of the device shown is the widely used PC (polycarbonate) material, which has excellent mechanical properties, good thermal stability and high stimulation. In order to perform finite element strength analysis, the material parameters that need to be obtained are shown in Table 2.

[0087] S3. Simplify the model. To improve computational efficiency and reduce computational resource requirements, simplify the model by deleting all other structures except the toothed shaft hole. Also, delete the holes, slots, and keys on the gear ring.

[0088] Figure 4 The bottom power structure of the device is shown. It can be seen that two motors drive two outer gears, which drive the outer ring gear to rotate. By separating the gear ring gear into separate materials, we can get Figure 5 , and since the two external gears are under the same force state, in order to save the amount of calculation, it is simplified to a single gear driving the ring gear. At the same time, after deleting the details on the gear ring gear, we get Figure 6 .

[0089] S4. Compare tetrahedron and hexahedron elements. The mesh types are tetrahedron and hexahedron. According to the shape of the gear, 1mm hexahedron and tetrahedron elements are set to divide the gear. Compare the results. Figure 7-8 It can be seen that under the same grid size, the tetrahedral grid can be divided more densely for models with complex shapes, and the simulation accuracy is higher.

[0090] S5. Compare adaptive and custom transition methods. Since the concentrated force areas of a model are often around the contact surfaces, to save computational effort, the mesh is not refined across the entire model, but rather in the areas of key analysis. For gear meshing mechanisms, the contacting tooth surfaces and tooth roots are often refined. When it comes to localized refinement, the mesh transition method must be considered.

[0091] Table 3 Grid transition results

[0092]

[0093] There are two common transition methods. One is adaptive size adjustment, which can dynamically adjust the density of the grid according to the needs of problem solving. The second is custom growth rate, which sets the grid size to 1mm overall + 0.1mm locally and the custom transition parameter to 1.3. The two methods were tested and the results are shown in Table 3. The number of elements and nodes using the adaptive transition method will be less than that of the custom one. From the preliminary test results, we can see that the combination of the results Figure 9-12It can be seen that although the number of elements and nodes is small, the pressure cloud diagram of the adaptive transition is smoother and rounder, and the analysis results are more reasonable.

[0094] S6. Static structural analysis.

[0095] First, create a static structure module and add the material parameters determined in step S2. Then, import the simplified gear assembly file in step S3.

[0096] Set the surface-to-surface connection between the external and internal gears. In the Connections section of the model tree, insert a Manual Contact area and select the contact and target surfaces. Generally, for convex-concave contact, select the convex surface as the contact surface. Next, select Friction Contact as the contact type. Set the friction coefficient to 0.12, referring to the table of dynamic friction coefficients for common plastics.

[0097] To constrain the motion state of the gears, a fixed support is inserted into the inner gear to prevent displacement, and a displacement constraint is inserted into the outer gear so that it has only one degree of freedom of rotation.

[0098] Analyze the power mechanism, such as Figure 2 As shown, the primary force acting on the entire mechanism during motion is friction between the wheels and the ground. Therefore, the torque provided by the external gear only needs to overcome the torque generated by ground friction to achieve motion. The magnitude of the friction torque is calculated using the formula. Since the power is provided by two external gears, the friction torque is divided by two. Based on the gear ratio, the torque acting on the gears is calculated: the external gear experiences a torque of 1047 N·mm, while the internal gear experiences a torque of 5353.2 N·mm.

[0099] According to the previous preliminary experiments, the grid division settings are:

[0100] Tetrahedron elements, adaptive transition mode, and the specific grid size parameters are obtained through multiple tests, such as Figure 13 As shown in the figure, 5 groups of experimental data are set, namely overall 2mm, overall 1mm, overall 1mm + local 0.5mm, overall 1mm + local 0.1mm, overall 1mm + local 0.05mm. The local division surface is shown in the figure. The 6 groups of parameters are simulated and analyzed respectively, and the maximum equivalent stress value is plotted as Figure 14 ,It can be seen that after the fourth group of experiments, the maximum equivalent stress value is basically converged, so the mesh division parameters of overall 1mm + local 0.1mm can be selected.

[0101] S7. Transient structural analysis

[0102] First, create a transient structure module and add the material parameters determined in step S2. Then, import the simplified gear assembly file in step S3.

[0103] Transient structure simulation analyzes load transformations during gear meshing. During simulation, the gears rotate, so the boundary conditions and load settings are different from those for static conditions. The specific settings are as follows:

[0104] (1) Set up the connection. Unlike static structures, transient structural analysis requires setting up the contact between each tooth surface. In order to quickly complete the setting, the tooth surfaces of the outer gear and the inner gear can be named, and a group of contacts can be used to complete the contact setting between all tooth surfaces. Friction contact is also set, and the friction coefficient is 0.12.

[0105] In addition, since the movement of the two gears is fixed-axis rotation, two connection pairs need to be set up, and the type is rotation.

[0106] (2) The motion setting of the gear structure is to set the rotation speed of the outer gear to 0.25 rad / s and the torque of the inner gear to 5353.3 N·mm.

[0107] Based on the preliminary experiments mentioned above, the meshing settings are: tetrahedral elements, adaptive transition mode, global 1mm mesh size, and local refinement of 0.1mm. Due to the increased computing power requirements of transient structural simulation, the meshing is adjusted to global 5mm + local 1mm.

[0108] After completing the boundary conditions, loads, and mesh settings for the transient structure, the time step setting needs to be adjusted in real time based on the simulation results. Since the transient structure simulation mainly analyzes the dynamic loads during the gear meshing process, the simulation time is set to a complete meshing process of a single tooth, which is 1.95s.

[0109] The settings for the initial time step, minimum time step, and maximum time step are preset to 1%, 1%, and 10% of the simulation duration. Then, based on the results, if the number of steps is equal to the simulation duration divided by the minimum time step, it means that the minimum time step needs to be further refined and can be set to 0.5%, 0.5%, 5%, and so on.

[0110] According to the test, the final three time steps are set to 0.005s, 0.005s, and 0.05s.

[0111] S8. Results Analysis

[0112] Static structure:

[0113] from Figure 15 The total deformation cloud diagram shows that during the meshing process, the internal gear is slightly deformed due to the torque applied to the external gear. However, at the position where the external gear contacts the inner ring gear, the deformation on the contacting teeth is relatively small because the inner ring gear is fixed. Figure 16The equivalent strain cloud shows that the largest deformation occurs inside the tooth contact point and at the tooth root, with a maximum deformation of 0.0073 mm. Figure 17 The equivalent elastic strain diagram can be used to analyze that these two parts correspond exactly to the positions with the greatest stress; the stress cloud diagram at the contact point of the tooth surface is very similar to the failure form of Hertz stress, which may cause microcracks and local damage on the tooth surface and eventually produce the failure form of gear pitting. The probe was used to measure the position of Hertz failure and found that the part with the highest stress was inside the outer gear, which was 14.31MPa, lower than the yield strength of the material, and the design was reasonable.

[0114] In addition to tooth surface pitting, tooth root fracture must also be considered. Figure 18 It can be seen from the tooth root stress cloud map that the maximum force at the tooth root is 14.31 MPa, which is the area with the greatest force in the entire model. It is also lower than the yield strength of the material. The minimum safety factor is 4.1719, which is safe and reliable and meets the reasonable design.

[0115] Transient Structure:

[0116] Since transient structural analysis is to analyze the mechanical behavior of gear meshing, Figure 20 The total deformation expresses the linear displacement of the gear rotation. On each tooth, the closer to the edge and the farther from the rotation center, the greater the deformation. Figure 21 The equivalent stress cloud shows that since the transient structural analysis is about gear meshing under dynamic load, the maximum stress analyzed under dynamic load is 36.617MPa. Figure 22 The equivalent elastic strain cloud shows that elastic strain exists at the gear contact points and around the outer ring gear hole. The maximum deformation is at the tooth root contact point, which is 0.0003mm. The minimum safety factor is 6.8275. The comprehensive transient structural analysis results show that the gear structural design meets the requirements.

[0117] The above is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited to the above content. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A finite element analysis method for the strength of a small-load 3D-printed gear, characterized in that: The following steps are involved: S1. Analyze the stress of the research object; S2. Determine the material parameters of the research object; S3. Simplify the model of the research object; S4. Determine the grid unit form; S5. Determine the grid transition method; S6. Perform static structural analysis; Add the material parameters determined in step S2 to the engineering material library, and import the gear assembly file simplified in step S3; Combine the results of steps S1, S4, and S5 to determine the boundary conditions, loads, and meshing for static analysis; Solve and analyze simulation results; S7. Perform transient structural analysis; Add the material parameters determined in step S2 to the engineering material library, and import the gear assembly file simplified in step S3; Combine the results of steps S1, S4, S5, and S6 to determine the boundary conditions, loads, and meshing for transient structural analysis; Solve and analyze the simulation results.

2. The finite element analysis method for strength of a small-load 3D-printed gear according to claim 1, characterized in that: In step S2, the material parameters include density, Young's modulus, Poisson's ratio, tensile yield strength, compressive yield strength and ultimate tensile strength.

3. The finite element analysis method for strength of a small-load 3D-printed gear according to claim 1, characterized in that: In step S4, the grid unit forms include tetrahedral units and hexahedral units.

4. The finite element analysis method for strength of a small-load 3D-printed gear according to claim 3, characterized in that: The specific operations of step S4 are: Create a new static structure module for preliminary experiments in ANSYS Workbench; Import the simplified gear model file in step S3; Set the overall mesh size parameters of the model; Insert the method in the mesh, set the tetrahedron and hexahedron in the method respectively, and compare the number of nodes and elements after generating the mesh; After the mesh is generated, some boundary conditions are simply set according to the results of step S1, and the equivalent stress results of the tetrahedron and hexahedron are compared to observe the quality of the mesh division.

5. The finite element analysis method for strength of a small-load 3D-printed gear according to claim 1, characterized in that: In step S5, the grid transition method includes adaptive size adjustment and custom growth rate.

6. The finite element analysis method for strength of a small-load 3D-printed gear according to claim 5, characterized in that: The specific operations of step S5 are: Create a new transient structure module for preliminary experiments in ANSYS Workbench; Import the simplified gear model file in step S3; Set the overall mesh size parameters of the model; According to the cell type determined in step S4, tetrahedron or hexahedron cells are selected, and after the insertion surface size is adjusted, the local mesh size is set for the tooth of the meshing part and the two surrounding teeth; Select the transition method of adaptive size adjustment and custom growth rate. By adjusting the growth rate value multiple times, it is found that the mesh units and mesh nodes generated by the two transition methods are similar. After the mesh is generated, the boundary conditions are set according to the results of step S1, and the equivalent stress results of the two transition methods are compared to observe the quality of the mesh division.

7. The finite element analysis method for strength of a small-load 3D-printed gear according to claim 1, characterized in that: The specific operations of step S6 are: Create a cylindrical coordinate system based on the axial surface of the driving wheel; Set up a friction connection for the two surfaces in contact at the gear mate and define the friction coefficient; Setting a fixed support for the driven wheel and a displacement constraint for the driving wheel, using the cylindrical coordinate system to ensure that the gear retains only one degree of freedom of rotation, and setting a torque on the driving wheel according to the calculation in step S1; According to the results of steps S4 and S5, the mesh is set to tetrahedral elements, adaptive transition mode, and global mesh size of 1 mm. The units of the local mesh are adjusted multiple times until the results of the equivalent stress cloud map converge.

8. The finite element analysis method for strength of a small-load 3D-printed gear according to claim 1, characterized in that: The specific operations of step S7 are: Select the tooth surface of the gear and define the tooth surface of the driving wheel and the driven wheel; Set the contact settings of the master and slave wheels, determine the friction coefficient, and set the rotation connection width of the axial surface of the master and slave wheels to ensure that the movement is rotation; Setting the grid parameters determined in step S6; Set the rotation speed for the connecting span of the driving wheel and the reverse torque for the connecting span of the driven wheel; According to the rotation speed of the driving wheel, the time it takes to rotate three teeth is calculated as the end time of the transient simulation; the time step size is adjusted multiple times according to the simulation results to ensure that the curve is smooth and the number of steps is less than the total time length divided by the minimum time step.

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