The plastic helical gear of COSMOSWorks meshes with the steel worm. Let us look at the following. The only designated mold design training base of China Mould Industry Association---Qinghua Technology will give you a detailed introduction. Hex Flange Bolt,Flange Head Screws,Flanged Button Head Screw,Flanged Hex Head Bolt Shaoxing Grace International Trade Co.,Ltd , https://www.shaoxinggrace.com
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The plastic helical gear of COSMOSWorks meshes with the steel worm. Let us look at the following. The only designated mold design training base of China Mould Industry Association---Qinghua Technology will give you a detailed introduction.
Plastic helical gears and steel worms are common transmission mechanisms that transmit motion and power between two axes that are interlaced in space. The angle between the two axes is generally 90o. This type of gear transmission has been widely used in the fields of car seats and home appliances. Since the involute worm Z1 is equivalent to an involute cylindrical helical gear with a small number of teeth and a large helix angle, the transmission can be simply referred to as a helical gear transmission. This kind of gear transmission is equivalent to the two spaces intersecting cylinders rolling each other, and the contact is point contact, thus reducing the bearing capacity and meshing efficiency of the gear, and finally limiting the application range. However, in the plastic helical gear and steel worm drive process, since the plastic has a lower modulus of elasticity than the steel, the gear is partially contacted after being loaded. The entire gear transmission wear is almost on the plastic gear, and the frictional heat of the meshing zone is also accelerated, which directly affects the service life of the plastic helical gear, and the worm can be used repeatedly. Plastics have many advantages over steel, such as low price, light weight, anti-noise and non-conductivity, and better friction characteristics during meshing. The helical gear drive of this material is currently being used more and more widely. Therefore, it is of great significance to carry out finite element analysis on the sensitivity of plastics to temperature, the bearing capacity and service life of such transmissions, and the regularity of meshing of plastic gears.
1 gear 3D modeling
First of all, the establishment of a three-dimensional finite element model is the premise of the contact analysis of the tooth surface. Based on the 3D parametric design function of SolidWorks software, the accurate involute cylindrical worm model and the helical gear model are generated, and the well is assembled correctly.
1.1 Establish a gear model
According to the profile size of the tooth profile and the structural dimensions of the gear (see Table 1), three effective and convenient modeling methods are summarized.
1.1.1 Using SolidWorks' Geartrax Plugin
First establish the blank and then cut the slot to facilitate the actual processing sequence. The operation method is: selecting the Geartrax function, drawing the gear system; inputting the basic parameters of the gear; automatically generating the tensile body and the curve in the SolidWorks drawing area, as shown in Fig. 1 on the helical gear end plane and the worm axis plane The surface closure curve (closed and curved in the figure) is performed by the scanning path (the spiral line in the figure); then, the resection characteristic generated by the helical gear is subjected to a circumferential array operation to obtain a three-dimensional model of the helical gear and the worm with the required parameters.
In Fig. la, the tooth surface closure curve generated on the end surface of the helical gear can be determined by the gear plane parameter and the helix angle, and the scanning path is a helix of β2 = 7.507o. Considering that the root circle of the helical gear is close to the base circle, the transition curve of the root is a circular arc with a radius of 0.38 mm. In Figure 1b, the tooth surface closure curve generated on the plane of the involute cylindrical worm axis can be approximated by the following equation. Determine that the scan path is a helix of β1 = 82.493o. Since the curve between the root circle and the addendum circle is close to a straight line, the tooth profile curve on the worm axis plane can also be replaced by a straight line approximation. The root transition curve of the worm is an arc with a radius of 0.48 mm.
1.1.2 Using the spline curve to fit the tooth ISIS curve
When the 3D parametric aided design software cannot generate complex curves, a multi-point fitting method is required. The involute curve on the end section of the helical gear can be determined from the cross-section parameters of the helical gear method and the helix angle. The polar coordinate parameter equation from the involute:
As shown in Fig. 2, the base circle, the index circle, the addendum circle and the corresponding Ak angle are drawn to obtain three feature points. In order to improve the accuracy of the spline curve fitting and better approach the involute, 3~5 points should be added. Since the involute angle of the top of the tooth is higher than the angle of the root of the root, a point is added to the root involute, and two points are added to the involute.
When the base circle is larger than the root circle (number of teeth z ≤ 41), the tooth profile is composed of an involute and a transition line. When the base circle is smaller than the root circle (number of teeth z>41), the tooth profile is theoretically an involute. However, due to the existence of the arc of the tool tip, there is still a transition curve at the root portion. Therefore, the above 6 points are connected by a spline curve to form a desired involute. The transition curve is used to achieve a smooth connection between the root circle and the involute. Finally, through the operation, form a complete tooth surface.
Pagination
1.1.3 Drawing the tooth profile using CAXA electronic version
When multiple gear wells need to be drawn and not used by the Geartrax plug-in, it is not advisable to use a multi-point fit. CAXA can be used to easily draw complex curves to easily and efficiently generate involute profiles. The next two operations can be followed. The specific steps are as follows:
(1) Open CAXA electronic drawing - drawing - advanced curve - gear - input gear basic parameters - complete - file - data interface - DWG / DXF
File output
(2) Open SolidWorks - Open File *.DWG - Enter the sketch into the new part;
(3) Perform characteristic operation according to the size of the gear structure.
1.2 to achieve the correct assembly of the gear
For high-level surfaces (such as involute surfaces) to achieve high secondary meshing, it should be based on the specific type of gear.
(1) Gears with parallel axes. For any tooth profile, such as involute, cycloid, arc, etc.; any tooth type, such as straight teeth, helical teeth, SolidWorks provides the function. A tangent fit is achieved by selecting an indexing circle of a pair of gears, at which point the teeth are not properly engaged. With the function, set the 'Stop when you hit' check box to finally achieve the correct assembly of the spur gear.
(2) Gear coordination of the axis. If the helical gear in this example is engaged with the worm, the position between the gears is determined by setting the reference plane of the parts of each gear. The two front reference planes coincide on the center plane; set the distance between the two top planes according to the center distance dimension: use the function and select the 'stop when touched' checkbox. The correct engagement of the gears is achieved.
2 gear finite element analysis pre-processing
COSMOS/Works is a finite element analysis module for SolidWorks plug-ins. Various types of analysis can be quickly performed according to the model, such as static analysis, frequency analysis, thermal analysis, bending analysis, etc. The well outputs various diagrams such as stress, strain, deformation, displacement, and the like. Before the finite element analysis of the mathematical model, the following steps must be made:
(1) Analysis types and options. The type of analysis is selected based on the analysis requirements and the purpose of the analysis. In this case, static analysis is selected. Then for each type of topic, there are also attributes of different options, the settings of which directly affect the analysis results and output results.
(2) Material setting. Before running the topic, you must first define the material properties required for the response of the specified analysis type. In an assembly, each part can be a different material. The surface properties are defined for the shell, each shell having a different material and thickness. It can be defined in three ways: from the COSMOS/M material library; manually specify the attribute bits of the material; specified from CENTOR MATERIAL LIBRARY (a plugin). For example, in this example, the helical gear and the worm are respectively set to plastic PA6 and alloy steel 16MnCr5.
(3) Loads and constraints. COSMOS/ Works provides a smart dialog to define loads and constraints and define working conditions for the model. As shown in Fig. 3, the setting method is as follows: the fixed helical gear, three kinds of direction movement and rotation restriction symbols appear on the selected fixed surface (see both ends of the helical gear); the bearing support is arranged at both ends of the worm, so that The movement and rotation of the worm in the radial direction are restricted (both ends of the worm); the temperature of the gear ring is set to 100 ° C; finally, the external load force acting on the worm is set. The axial thrust is set at the end face of the worm, and the thrust symbol (the left end of the worm) appears in the figure.
(4) Contact/gap. For contact analysis, setting the contact options correctly and selecting the contact type reasonably is the key point for smooth finite element analysis, which directly affects the analysis results. The contact surface of the helical gear and the worm is set as a contact group, and the well is defined as a non-penetration type of the curved surface to the curved surface.
(5) Divide the grid with second-order h-element. The quality of the meshing determines the accuracy of the finite element analysis results. The smaller the meshing, the higher the calculation accuracy, the smaller the human influence caused by the unit definition, but the more computer resources and computing time required. . As shown in Fig. 4, in order to improve the accuracy at the contact surface, the tooth profile at the contact is partially subdivided by a mesh. The total number of nodes is 125 032, the total number of units is 89 009, the total number of node degrees of freedom is 372 8910, and the number of degrees of freedom is greater than 3 x 105. This is a large finite element problem, so the FFE solution method is adopted.
3 gear finite element analysis post processing
After the finite element analysis is completed, COSMOS/Works automatically generates various diagrams. Define the corresponding diagrams as needed. For example, you can view the dynamic changes of stress, strain and deformation. By generating a section view (see Figure 5), you can observe the stress-strain state on any section of the model; you can generate a special report for inspection. Staff or others provide good materials, and can also be placed on the website.
Pagination
3.1 Stress diagram of gear meshing
In order to facilitate the observation of a clearer stress diagram, a stress profile is illustrated on the center plane of the gear mesh with a stress of Von Mises stress (as shown in Figure 5). When the helical gear load is gradually increased from 10% of the rated load of 30 Nm, the maximum stress of the worm increases from 70 M1"a to 275 M1". The helical gear is plastically deformed at the contact of the tooth profile under the 40 lc rated load. Local stress drop To the ultimate stress of 91 MPa, the contact area changes, and the teeth to be meshed also enter the mesh, so that the total contact area and the gear coincidence increase with the increase of the load, that is, the load distribution of each pair of the meshing teeth changes. .
3. 2 plastic helical gear surface deformation
Since the plastic has a small modulus of elasticity, it has an elliptical shape at the contact of the two flank surfaces, and its area increases as the load increases. It is easy to produce protrusions at the contact between the helical gear tooth tip and the worm tooth profile (Fig. 6). It can be clearly seen from the figure that the gear coincidence degree is continuously increasing. The main failure modes that occur during the transmission process are gear fracture, tooth surface wear and plastic deformation.
3. 3 Hz pressure theory
According to Hertz theory, when two smooth curved surfaces are in contact, two parabolic surface contacts can be approximated in the vicinity of the contact point. After the load is applied, a contact ellipse is formed at the contact point, and the normal force is distributed on the elliptical surface. The maximum normal compressive stress is at the point of contact and passes through the center of the ellipse. The value is:
Therefore, it is theoretically possible to calculate the stress and deformation at the contact of the two tooth profiles to verify the feasibility and correctness of finite element simulation based on COSMOS/Work.
4 Conclusion
The meshing characteristics of plastic helical gears and steel worm gears based on Solid W arks and the modeling process of gear body are described. The COSMOS/Works finite element contact simulation method is used to analyze the variation of tooth profile deformation of plastic helical gears. Hertzian pressure theory verifies the correctness of finite element simulation. Valuable suggestions for the modeling of such complex surface models, the assembly of two irregular surface entities, meshing, and how to simplify complex finite element analysis. According to the analysis results obtained by the above-mentioned parameters, it can be seen that due to the small elastic modulus of the plastic helical gear, the contact state with the steel worm is changed from point contact to a certain area of ​​surface contact, well As the gear load increases, the gear coincidence also increases, and the contact area on each pair of contact tooth faces increases synchronously, so that the stress distribution state on each pair of tooth profiles is repeatedly changed many times.
Author: http: //
(Editor: Xu Yongyan)
Author: http: //
The plastic helical gear of COSMOSWorks meshes with the steel worm. Let us look at the following. The only designated mold design training base of China Mould Industry Association---Qinghua Technology will give you a detailed introduction.
Plastic helical gears and steel worms are common transmission mechanisms that transmit motion and power between two axes that are interlaced in space. The angle between the two axes is generally 90o. This type of gear transmission has been widely used in the fields of car seats and home appliances. Since the involute worm Z1 is equivalent to an involute cylindrical helical gear with a small number of teeth and a large helix angle, the transmission can be simply referred to as a helical gear transmission. This kind of gear transmission is equivalent to the two spaces intersecting cylinders rolling each other, and the contact is point contact, thus reducing the bearing capacity and meshing efficiency of the gear, and finally limiting the application range. However, in the plastic helical gear and steel worm drive process, since the plastic has a lower modulus of elasticity than the steel, the gear is partially contacted after being loaded. The entire gear transmission wear is almost on the plastic gear, and the frictional heat of the meshing zone is also accelerated, which directly affects the service life of the plastic helical gear, and the worm can be used repeatedly. Plastics have many advantages over steel, such as low price, light weight, anti-noise and non-conductivity, and better friction characteristics during meshing. The helical gear drive of this material is currently being used more and more widely. Therefore, it is of great significance to carry out finite element analysis on the sensitivity of plastics to temperature, the bearing capacity and service life of such transmissions, and the regularity of meshing of plastic gears.
1 gear 3D modeling
First of all, the establishment of a three-dimensional finite element model is the premise of the contact analysis of the tooth surface. Based on the 3D parametric design function of SolidWorks software, the accurate involute cylindrical worm model and the helical gear model are generated, and the well is assembled correctly.
1.1 Establish a gear model
According to the profile size of the tooth profile and the structural dimensions of the gear (see Table 1), three effective and convenient modeling methods are summarized.
1.1.1 Using SolidWorks' Geartrax Plugin
First establish the blank and then cut the slot to facilitate the actual processing sequence. The operation method is: selecting the Geartrax function, drawing the gear system; inputting the basic parameters of the gear; automatically generating the tensile body and the curve in the SolidWorks drawing area, as shown in Fig. 1 on the helical gear end plane and the worm axis plane The surface closure curve (closed and curved in the figure) is performed by the scanning path (the spiral line in the figure); then, the resection characteristic generated by the helical gear is subjected to a circumferential array operation to obtain a three-dimensional model of the helical gear and the worm with the required parameters.
In Fig. la, the tooth surface closure curve generated on the end surface of the helical gear can be determined by the gear plane parameter and the helix angle, and the scanning path is a helix of β2 = 7.507o. Considering that the root circle of the helical gear is close to the base circle, the transition curve of the root is a circular arc with a radius of 0.38 mm. In Figure 1b, the tooth surface closure curve generated on the plane of the involute cylindrical worm axis can be approximated by the following equation. Determine that the scan path is a helix of β1 = 82.493o. Since the curve between the root circle and the addendum circle is close to a straight line, the tooth profile curve on the worm axis plane can also be replaced by a straight line approximation. The root transition curve of the worm is an arc with a radius of 0.48 mm.
1.1.2 Using the spline curve to fit the tooth ISIS curve
When the 3D parametric aided design software cannot generate complex curves, a multi-point fitting method is required. The involute curve on the end section of the helical gear can be determined from the cross-section parameters of the helical gear method and the helix angle. The polar coordinate parameter equation from the involute:
As shown in Fig. 2, the base circle, the index circle, the addendum circle and the corresponding Ak angle are drawn to obtain three feature points. In order to improve the accuracy of the spline curve fitting and better approach the involute, 3~5 points should be added. Since the involute angle of the top of the tooth is higher than the angle of the root of the root, a point is added to the root involute, and two points are added to the involute.
When the base circle is larger than the root circle (number of teeth z ≤ 41), the tooth profile is composed of an involute and a transition line. When the base circle is smaller than the root circle (number of teeth z>41), the tooth profile is theoretically an involute. However, due to the existence of the arc of the tool tip, there is still a transition curve at the root portion. Therefore, the above 6 points are connected by a spline curve to form a desired involute. The transition curve is used to achieve a smooth connection between the root circle and the involute. Finally, through the operation, form a complete tooth surface.
Pagination
1.1.3 Drawing the tooth profile using CAXA electronic version
When multiple gear wells need to be drawn and not used by the Geartrax plug-in, it is not advisable to use a multi-point fit. CAXA can be used to easily draw complex curves to easily and efficiently generate involute profiles. The next two operations can be followed. The specific steps are as follows:
(1) Open CAXA electronic drawing - drawing - advanced curve - gear - input gear basic parameters - complete - file - data interface - DWG / DXF
File output
(2) Open SolidWorks - Open File *.DWG - Enter the sketch into the new part;
(3) Perform characteristic operation according to the size of the gear structure.
1.2 to achieve the correct assembly of the gear
For high-level surfaces (such as involute surfaces) to achieve high secondary meshing, it should be based on the specific type of gear.
(1) Gears with parallel axes. For any tooth profile, such as involute, cycloid, arc, etc.; any tooth type, such as straight teeth, helical teeth, SolidWorks provides the function. A tangent fit is achieved by selecting an indexing circle of a pair of gears, at which point the teeth are not properly engaged. With the function, set the 'Stop when you hit' check box to finally achieve the correct assembly of the spur gear.
(2) Gear coordination of the axis. If the helical gear in this example is engaged with the worm, the position between the gears is determined by setting the reference plane of the parts of each gear. The two front reference planes coincide on the center plane; set the distance between the two top planes according to the center distance dimension: use the function and select the 'stop when touched' checkbox. The correct engagement of the gears is achieved.
2 gear finite element analysis pre-processing
COSMOS/Works is a finite element analysis module for SolidWorks plug-ins. Various types of analysis can be quickly performed according to the model, such as static analysis, frequency analysis, thermal analysis, bending analysis, etc. The well outputs various diagrams such as stress, strain, deformation, displacement, and the like. Before the finite element analysis of the mathematical model, the following steps must be made:
(1) Analysis types and options. The type of analysis is selected based on the analysis requirements and the purpose of the analysis. In this case, static analysis is selected. Then for each type of topic, there are also attributes of different options, the settings of which directly affect the analysis results and output results.
(2) Material setting. Before running the topic, you must first define the material properties required for the response of the specified analysis type. In an assembly, each part can be a different material. The surface properties are defined for the shell, each shell having a different material and thickness. It can be defined in three ways: from the COSMOS/M material library; manually specify the attribute bits of the material; specified from CENTOR MATERIAL LIBRARY (a plugin). For example, in this example, the helical gear and the worm are respectively set to plastic PA6 and alloy steel 16MnCr5.
(3) Loads and constraints. COSMOS/ Works provides a smart dialog to define loads and constraints and define working conditions for the model. As shown in Fig. 3, the setting method is as follows: the fixed helical gear, three kinds of direction movement and rotation restriction symbols appear on the selected fixed surface (see both ends of the helical gear); the bearing support is arranged at both ends of the worm, so that The movement and rotation of the worm in the radial direction are restricted (both ends of the worm); the temperature of the gear ring is set to 100 ° C; finally, the external load force acting on the worm is set. The axial thrust is set at the end face of the worm, and the thrust symbol (the left end of the worm) appears in the figure.
(4) Contact/gap. For contact analysis, setting the contact options correctly and selecting the contact type reasonably is the key point for smooth finite element analysis, which directly affects the analysis results. The contact surface of the helical gear and the worm is set as a contact group, and the well is defined as a non-penetration type of the curved surface to the curved surface.
(5) Divide the grid with second-order h-element. The quality of the meshing determines the accuracy of the finite element analysis results. The smaller the meshing, the higher the calculation accuracy, the smaller the human influence caused by the unit definition, but the more computer resources and computing time required. . As shown in Fig. 4, in order to improve the accuracy at the contact surface, the tooth profile at the contact is partially subdivided by a mesh. The total number of nodes is 125 032, the total number of units is 89 009, the total number of node degrees of freedom is 372 8910, and the number of degrees of freedom is greater than 3 x 105. This is a large finite element problem, so the FFE solution method is adopted.
3 gear finite element analysis post processing
After the finite element analysis is completed, COSMOS/Works automatically generates various diagrams. Define the corresponding diagrams as needed. For example, you can view the dynamic changes of stress, strain and deformation. By generating a section view (see Figure 5), you can observe the stress-strain state on any section of the model; you can generate a special report for inspection. Staff or others provide good materials, and can also be placed on the website.
Pagination
3.1 Stress diagram of gear meshing
In order to facilitate the observation of a clearer stress diagram, a stress profile is illustrated on the center plane of the gear mesh with a stress of Von Mises stress (as shown in Figure 5). When the helical gear load is gradually increased from 10% of the rated load of 30 Nm, the maximum stress of the worm increases from 70 M1"a to 275 M1". The helical gear is plastically deformed at the contact of the tooth profile under the 40 lc rated load. Local stress drop To the ultimate stress of 91 MPa, the contact area changes, and the teeth to be meshed also enter the mesh, so that the total contact area and the gear coincidence increase with the increase of the load, that is, the load distribution of each pair of the meshing teeth changes. .
3. 2 plastic helical gear surface deformation
Since the plastic has a small modulus of elasticity, it has an elliptical shape at the contact of the two flank surfaces, and its area increases as the load increases. It is easy to produce protrusions at the contact between the helical gear tooth tip and the worm tooth profile (Fig. 6). It can be clearly seen from the figure that the gear coincidence degree is continuously increasing. The main failure modes that occur during the transmission process are gear fracture, tooth surface wear and plastic deformation.
3. 3 Hz pressure theory
According to Hertz theory, when two smooth curved surfaces are in contact, two parabolic surface contacts can be approximated in the vicinity of the contact point. After the load is applied, a contact ellipse is formed at the contact point, and the normal force is distributed on the elliptical surface. The maximum normal compressive stress is at the point of contact and passes through the center of the ellipse. The value is:
Therefore, it is theoretically possible to calculate the stress and deformation at the contact of the two tooth profiles to verify the feasibility and correctness of finite element simulation based on COSMOS/Work.
4 Conclusion
The meshing characteristics of plastic helical gears and steel worm gears based on Solid W arks and the modeling process of gear body are described. The COSMOS/Works finite element contact simulation method is used to analyze the variation of tooth profile deformation of plastic helical gears. Hertzian pressure theory verifies the correctness of finite element simulation. Valuable suggestions for the modeling of such complex surface models, the assembly of two irregular surface entities, meshing, and how to simplify complex finite element analysis. According to the analysis results obtained by the above-mentioned parameters, it can be seen that due to the small elastic modulus of the plastic helical gear, the contact state with the steel worm is changed from point contact to a certain area of ​​surface contact, well As the gear load increases, the gear coincidence also increases, and the contact area on each pair of contact tooth faces increases synchronously, so that the stress distribution state on each pair of tooth profiles is repeatedly changed many times.
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(Editor: Xu Yongyan)
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