Variable-thickness gear three-dimensional entity parameterized modeling method

Abstract

The present application relates to variable-thickness gear three-dimensional manufacturing technology, and particularly to a variable-thickness gear three-dimensional entity parameterized modeling method based on Solidworks, which can effectively improve gear three-dimensional modeling efficiency and reduce repeated modeling time, wherein the variable-thickness gear parameterized model is designed based on the involute formation principle under the Solidworks three-dimensional modeling software, and various sizes of variable-thickness gears can be obtained by modifying the basic parameters in the "equation" of the design tree, the parameterized modeling of the variable-thickness gear greatly saves the repeated modeling time in scientific research, improves the design efficiency, and liberates the design resources.

Description

Technical fields:

[0001] This invention relates to 3D manufacturing technology for variable-thickness gears, specifically a Solidworks-based parametric modeling method for 3D solid models of variable-thickness gears that can effectively improve the efficiency of 3D gear modeling and reduce repetitive modeling time. Background technology:

[0002] The variable-thickness gear was first proposed by ASBeam in the United States. Its characteristic is that different end sections have different displacement coefficients in the axial direction. When the displacement coefficient on the end face changes linearly with the axial distance of the end face, the variable-thickness gear is visually similar to a bevel gear. When backlash occurs in such a variable-thickness gear, it can be adjusted by changing the axial position of the gear without replacing it, achieving backlash-free transmission and improving gear life. The excellent reliability and long lifespan of variable-thickness gears have led to their wide application, resulting in increasing research by scholars, which inevitably involves three-dimensional modeling of variable-thickness gears with different parameters.

[0003] Traditional gear modeling suffers from drawbacks such as high workload and numerous repetitive steps. Some gear modeling methods use spline curves to approximate asymptotes, resulting in insufficient modeling accuracy. Currently, there are some open-source gear 3D modeling plugin toolkits, but they cannot directly generate 3D models of modified gears and gears with varying thicknesses, thus still having certain limitations. Summary of the Invention:

[0004] This invention addresses the shortcomings and deficiencies of existing technologies by proposing a Solidworks-based parametric modeling method for 3D solid models of variable-thickness gears that can effectively improve the efficiency of 3D gear modeling and reduce repetitive modeling time.

[0005] To save modeling time, this invention uses the involute formation principle to parametrically model thickened gears in Solidworks 3D modeling software. After modeling, simply changing the basic parameters of the thickened gear, such as normal module, number of teeth, cone angle, and helix angle, can generate thickened gears and modified helical gears of various sizes.

[0006] This invention can be achieved through the following measures:

[0007] A parametric modeling method for three-dimensional solids of variable-thickness gears, characterized by the following steps:

[0008] Step 1: Parameter Setting: Establish global variables at the beginning of modeling. In subsequent modeling, these variable names will be used to represent specific numerical values. The global variables will be created using the parameter calculation formula for the variable-thickness gear.

[0009]

[0010] In the formula h at * —End face tooth addendum coefficient;

[0011] h an * —Addition height coefficient of the normal surface;

[0012] β—Helix angle (rad);

[0013] δ—cone angle (rad);

[0014]

[0015] In the formula α tl —Left tooth surface pressure angle (rad);

[0016] α tr —Right tooth surface pressure angle (rad);

[0017] α n —Pressure angle (rad);

[0018]

[0019] In the formula β l —Helix angle of the left tooth pitch cylinder (rad);

[0020] β r —Helix angle of the right-hand pitch cylinder (rad);

[0021] The calculation formula for the parameters of variable thickness gears is universal. When the cone angle δ = 0° is set, the calculation formula for the basic parameters of variable thickness gears is the same as that for modified helical gears. When the helix angle β = 0° is set, the calculation formula for the basic parameters of variable thickness gears is the same as that for straight variable thickness gears.

[0022] Step 2: Generation of the involute tooth profile:

[0023]

[0024] In the formula r b — Gear base circle radius (mm);

[0025] r k —Radius (mm) at point K on the tooth profile;

[0026] α k —Pressure angle (rad) at point K on the tooth profile;

[0027] θ k —Angle of development (rad) at point K on the tooth profile.

[0028] The coordinates (x) of any point K on the involute k ,y k ) written as

[0029]

[0030] Combining equations (4) and (5), the equation for the left tooth profile from the base circle to the addendum circle can be written as follows:

[0031]

[0032] In the formula r a — Gear tip circle radius (mm);

[0033] The expression for the right tooth profile simply requires changing the ordinate to a negative number. To form a reasonable left and right tooth profile, the right tooth profile also needs to be rotated counterclockwise around the origin by an angle γ, where γ is...

[0034]

[0035] In the formula, s represents the thickness of the gear pitch circle tooth (mm).

[0036] Combining equations (6) and (7), the tooth profile equation from the base circle to the addendum circle is written as follows:

[0037]

[0038] In the formula, i represents the left and right tooth profiles of the gear, 1 for the right tooth profile and 2 for the left tooth profile; γ i — The counterclockwise rotation angle of the left and right tooth profiles. When the value is negative, it represents clockwise rotation, and γ1-γ2=γ, (rad);

[0039] r bi —Base circle radius of the left and right tooth profiles (mm)

[0040] At the small displacement end, when the root circle radius is smaller than the base circle radius, the involute tooth profile can be extended inwards along a straight line into the base circle. The equation of the extension line is:

[0041]

[0042] t is a dimensionless parameter that is proportional to the length of the extension line and can be taken as 0 to 2;

[0043] Step 3: Generating the helix: In Solidworks, enter the sketch and draw the base circle, defining the base circle diameter as 2r. bl Enable the helix function, select "height and pitch" as the definition method, set the helix rotation direction to counterclockwise, set the height to the tooth width h, and the pitch to... Set the starting angle to Drawing a right-hand spiral is similar; you only need to change the parameters.

[0044] In addition to providing a parametric modeling design method for variable-thickness gears, this invention also provides a parametric modeling program. When there is a need for 3D models of gears of different sizes, the parameters in the parametric modeling program can be modified to generate them one by one.

[0045] To generate variable-thickness gears of different sizes, simply modify the attachment. Figure 1 Some basic parameters, such as the number of teeth, normal module, pressure angle, helix angle, cone angle, maximum displacement coefficient of the end face, and tooth width, can be obtained.

[0046] To generate modified helical gears of different sizes, simply set the attachment. Figure 1 The middle cone angle is 0, then modify the appendix. Figure 1 Some basic parameters, such as the number of teeth, normal module, pressure angle, helix angle, maximum displacement coefficient of the end face, and tooth width, can be obtained.

[0047] To generate gears of different sizes with varying thicknesses, simply set the attachment... Figure 1 The helix angle is 0. Then, a negative sign is added before the formula for the helix angle of the pitch cylinder on the right tooth face. Finally, the appendix is ​​modified. Figure 1 Some basic parameters, such as the number of teeth, normal module, pressure angle, cone angle, maximum displacement coefficient of the end face, and tooth width, can be obtained.

[0048] To generate left-hand variable-thickness gears of different sizes, simply add a negative sign before the formulas for the helix angle and the helix angle of the pitch cylinders on the left and right tooth surfaces, then change the rotation direction of the helix to clockwise, and finally modify the appendix. Figure 1 Some basic parameters, such as the number of teeth, normal module, pressure angle, cone angle, helix angle, maximum displacement coefficient of the end face, and tooth width, can be obtained.

[0049] This invention utilizes Solidworks 3D modeling software to design a parametric model of variable-thickness gears based on the involute formation principle. By modifying the basic parameters in the "equations" of the design tree, variable-thickness gears of various sizes can be obtained. Parametric modeling of variable-thickness gears significantly reduces repetitive modeling time in scientific research, improves design efficiency, and frees up design resources. Attached image description:

[0050] Appendix Figure 1 This is a diagram showing the global variables for the parameters of a variable-thickness gear in Solidworks.

[0051] Appendix Figure 2 This is a rough sketch of the blank in this invention.

[0052] Appendix Figure 3 This is a diagram showing the forming process of the gear blank in this invention.

[0053] Appendix Figure 4This is a schematic diagram illustrating the involute formation principle in this invention.

[0054] Appendix Figure 5 This is a diagram showing the involute tooth profile forming process in this invention.

[0055] Appendix Figure 6 A pattern diagram of the spiral base circle in this invention is drawn.

[0056] Appendix Figure 7 This is a schematic diagram of the "spiral / vortex" menu bar settings in this invention.

[0057] Appendix Figure 8 This is a schematic diagram illustrating the modification of the helical pitch, height, and starting angle in this invention.

[0058] Appendix Figure 9 This is a diagram showing the left and right tooth profiles and the spiral forming process in this invention.

[0059] Appendix Figure 10 This is a diagram showing the forming of the left and right tooth surfaces in this invention.

[0060] Appendix Figure 11 This is a sketch of the tooth groove in this invention.

[0061] Appendix Figure 12 This is a diagram showing the forming process of the tooth groove blank in this invention.

[0062] Appendix Figure 13 This is a solid forming diagram of the tooth groove in this invention.

[0063] Appendix Figure 14 This is a diagram showing the generation of the toothed array in this invention.

[0064] Appendix Figure 15 This is a diagram showing the forming process of the variable thickness gear in this invention. Detailed implementation method:

[0065] The following description, in conjunction with the accompanying drawings, further explains this law.

[0066] The variable-thickness gear studied in this invention has a displacement coefficient that varies with thickness, which complicates its 3D modeling. In simulation studies of gear systems, gears of different sizes and parameters are often required. Repeatedly drawing 3D models of gears with different parameters wastes a significant amount of time. Therefore, designing parametric models for variable-thickness gears will greatly save 3D modeling time. Solidworks is a commonly used 3D modeling software, known for its powerful functions and wide application; therefore, Solidworks was chosen as the modeling platform for parametric modeling of variable-thickness gears.

[0067] Because the variable-thickness gear has both a helix angle β and a cone angle δ, the tooth profiles on the left and right sides of its end face are different and not symmetrically distributed like ordinary helical gears. Furthermore, the helix angles of the left and right tooth profiles are also different, so they need to be designed separately. First, the left and right tooth profiles are generated based on the involute formation principle. The left and right tooth profiles are then rotated around the left and right helical lines to obtain the left and right tooth surfaces of the variable-thickness gear. These surfaces are then tangent to the solid formed by the addendum cylindrical (conical) surface, root cylindrical (conical) surface, top surface, and bottom surface of the helical (variable-thickness) gear to obtain the tooth space solid. After rotation, all tooth space solids are obtained. Finally, the solid is tangent to the variable-thickness gear blank to obtain the three-dimensional model of the variable-thickness gear.

[0068] Example 1:

[0069] 1. Parameter settings

[0070] Open Solidworks, create a new part, and list the parameters required for modeling the variable-thickness gear according to the basic parameter calculation formula, as shown in Table 1. When the cone angle δ = 0°, the basic parameter calculation formula for the variable-thickness gear is the same as that for the modified helical gear; when the helix angle β = 0°, the basic parameter calculation formula for the variable-thickness gear is the same as that for the straight variable-thickness gear. In the Solidworks menu bar, select "Tools" - "Equation", and input the parameters of the variable-thickness gear in Table 1 into the "Equation", as shown below. Figure 1 As shown.

[0071] Table 1 Modeling Parameters for Variable Thickness Gears

[0072]

[0073]

[0074]

[0075] 2. Sketching the rough draft

[0076] Select the "Front View Plane" and enter the sketching stage to draw. Figure 2 The trapezoid shown is configured with its lower base set to r using the "Smart Size" function. at +m t x1, and coincide with the x-axis; set the upper base of the trapezoid to r. at +m t x2; Set the height of the trapezoid to h, and make it coincide with the y-axis.

[0077] Exit the sketch, select the "Revolve Boss / Base" function, use the entire trapezoid as the rotation profile and the height of the trapezoid as the rotation axis, and rotate to obtain the gear blank, as shown below. Figure 3 After generating the blank, it can be hidden to facilitate subsequent drawing.

[0078] 3. Drawing a spiral surface

[0079] Depend on Figure 4 From the geometric relations and properties of involutes, we can know

[0080]

[0081] In the formula r b — Gear base circle radius (mm);

[0082] r k —Radius (mm) at point K on the tooth profile;

[0083] α k —Pressure angle (rad) at point K on the tooth profile;

[0084] θ k — Angle of development (rad) at point K on the tooth profile.

[0085] The coordinates (x) of any point K on the involute k ,y k It can be written as

[0086]

[0087] Combining equations (10) and (11), the equation for the left tooth profile from the base circle to the addendum circle can be written as follows:

[0088]

[0089] In the formula r a — Gear tip circle radius (mm);

[0090] The expression for the right tooth profile simply requires changing the ordinate to a negative number. To form a reasonable left and right tooth profile, the right tooth profile also needs to be rotated counterclockwise around the origin by an angle γ, where γ is...

[0091]

[0092] In the formula, s represents the thickness of the gear pitch circle tooth (mm).

[0093] Combining equations (12) and (13), the tooth profile equation from the base circle to the addendum circle can be written as follows:

[0094]

[0095] In the formula, i represents the left and right tooth profiles of the gear, 1 represents the right tooth profile, and 2 represents the left tooth profile;

[0096] γ i —The counterclockwise rotation angle of the left and right tooth profiles; a negative value indicates clockwise rotation.

[0097] And γ1-γ2=γ,(rad).

[0098] r bi —The base circle radius of the left and right tooth profiles, r b1 and r b2 r in Table 1 br and r bl ,(mm).

[0099] At the small displacement end, the root circle radius may be smaller than the base circle radius. In this case, simply extend the involute tooth profile inwards along a straight line into the base circle. The equation for the extension line is:

[0100]

[0101] t is a dimensionless parameter that is proportional to the length of the extension line, and is generally taken to be between 0 and 2.

[0102] Based on the above theory, the involute tooth profile is drawn in Solidworks. Select "Top Plane" to enter the sketch, click the Insert Spline Curve button in the sketch operation bar, and select "Equation-Driven Curve". Enter the "Equation-Driven Curve" menu bar, select the "Parametric" type equation, and let i = 2 in equation (14). x k y k and α k The range is filled into the equation and parameters to generate the left tooth profile. Reopen "Equation-Driven Curves" and set i = 2 in equation (15). Fill in the ranges of x, y, and t into the equation and parameters to generate the extension line of the left tooth profile, such as... Figure 5 The part with black lines.

[0103] Similarly, open "Equation-Driven Curves", and let i = 1 and γ1 = θ in equations (14) and (15). r Enter the parameters in "Equation-Driven Curve" to generate the right tooth profile extension line, such as... Figure 5 The gray line section.

[0104] Next, we will draw the helix. First, draw the helix on the left tooth surface. Select the "Top Plane" to enter the sketch, draw a circle with the origin as the center, and use the "Smart Dimension" function to modify the diameter of the circle to 2r. bl ,like Figure 6 .

[0105] In the top menu bar, select "Insert" - "Curve" - ​​"Helix / Swirl". In the "Helix / Swirl" operation bar, select "Define Method" as "Height and Pitch". Since we are drawing a right-handed gear here, select "Counterclockwise" for the rotation direction. Figure 7 .

[0106] Click the checkmark to generate a spiral. In the Design Tree, right-click "Annotation" and select "Show Feature Dimensions." After opening the feature dimensions, you will get... Figure 8 In the interface shown, the parameter at position A is the helix pitch. Double-click the parameter to open the parameter editing interface, and change the parameter to... Position B is the height of the helix. Double-click the parameter to open the parameter editing interface and change the parameter to h; Position C is the starting angle of the helix. Double-click the parameter to open the parameter editing interface and change the parameter to h. Degree. Click "Rebuild" in the menu bar to get the left tooth surface helix.

[0107] The right-hand tooth surface helix is ​​generated using the same method, but with different parameter settings, where the base circle radius is set to 2r during base circle drawing. br In drawing a spiral, the position parameter of A is... The position parameter of C is Degree. The final result is the helix of the left and right tooth surfaces as follows: Figure 9 As shown.

[0108] Finally, draw the helical surface. In the menu bar, select "Tools" - "Surface" - "Sweep Surface" to enter the operation panel. In the contour bar, select the generated left contour and its extension line. In the path bar, select the generated left tooth surface helical line and click the checkmark to obtain the left tooth surface. Use the same method to sweep the right tooth contour along the right helical line to obtain the right tooth surface. The left and right tooth surfaces are as follows... Figure 10 As shown.

[0109] 4. Drawing the toothed solid

[0110] This design uses a cutting method to obtain the tooth groove solid.

[0111] Select "Front Plane" to enter sketch editing mode, and draw a line segment on the x-axis. Then draw a line segment from the origin O towards the positive y-axis. Finally, draw a line segment parallel to the x-axis. Where C, D, and M are the same vertical axis. Use the "Smart Size" function to set them sequentially. Last connection and We obtain a parallelogram ABCD and a line segment. like Figure 11 Exit the sketch, and in the "Features" toolbar, select the "Revolve Boss / Base" function to... Using parallelogram ABCD as the axis of rotation, we rotate the contour to obtain... Figure 12 .

[0112] In the top menu bar, select "Insert" - "Features" - "Intersection". Select the tooth blank obtained in this step and the left and right tooth surfaces generated in the previous step. Check "Create Both", and confirm to generate the tooth solid, as shown below. Figure 13 As shown.

[0113] 5. Generation of variable thickness gears

[0114] Select "Front Plane" to enter sketch editing, draw a line segment along the y-axis, and exit the sketch. Select the "Circular Array" function in the "Features" toolbar, select the line segment you just drew in the "Rotation Axis" field, enter the global variable "number of teeth z" in the "Number of Instances" field, select the tooth groove solid in the "Solid" field, and click the checkmark to generate the tooth groove circular array, as shown. Figure 14 As shown.

[0115] To display the gear blank in step 2 of the blank drawing, click "Insert" - "Feature" - "Group" in the menu bar. In the "Group" operation bar, select the "Delete" function in "Operation Type," and select the appropriate entity in the "Main Entity" column. Figure 3 The gear blank shown is selected in the "Entities to be assembled" column. Figure 14 The toothed array shown. This ultimately results in a thickened gear, such as... Figure 15 As shown.

[0116] Compared with existing technologies, this invention designs a parametric model of variable-thickness gears based on the involute formation principle. By modifying the basic parameters in the "equation" of the design tree, variable-thickness gears of various sizes can be obtained. The parametric modeling of variable-thickness gears greatly saves the time of repeated modeling in scientific research, improves work efficiency, and is suitable for industrialization.

Claims

1. A parametric modeling method for three-dimensional solids of variable-thickness gears, characterized in that, Includes the following steps: Step 1: Parameter Setting: Establish global variables at the beginning of modeling. In subsequent modeling, these variable names will be used to represent specific numerical values. The global variables will be created using the parameter calculation formula for the variable-thickness gear. In the formula h at * —End face tooth tip height coefficient; h an * —Addition height coefficient of the normal surface; β—Helix angle (rad); δ—cone angle (rad); In the formula α tl —Left tooth surface pressure angle (rad); α tr —Right tooth surface pressure angle (rad); α n —Pressure angle (rad); In the formula β l —Helix angle of the left tooth pitch cylinder (rad); β r —Helix angle of the right-hand pitch cylinder (rad); The calculation formula for the parameters of variable thickness gears is universal. When the cone angle δ = 0° is set, the calculation formula for the basic parameters of variable thickness gears is the same as that for modified helical gears. When the helix angle β = 0° is set, the calculation formula for the basic parameters of variable thickness gears is the same as that for straight variable thickness gears. Step 2: Generation of the involute tooth profile: In the formula r b — Gear base circle radius (mm); r k —Radius (mm) at point K on the tooth profile; α k —Pressure angle (rad) at point K on the tooth profile; θ k —Angle of development (rad) at point K on the tooth profile. The coordinates (x) of any point K on the involute k ,y k ) written as Combining equations (4) and (5), the equation for the left tooth profile from the base circle to the addendum circle can be written as follows: In the formula r a — Gear tip circle radius (mm); The expression for the right tooth profile simply requires changing the ordinate to a negative number; to form a reasonable left and right tooth profile, the right tooth profile also needs to be rotated counterclockwise around the origin by an angle γ, where γ is... In the formula, s represents the thickness of the gear pitch circle tooth (mm). Combining equations (6) and (7), the tooth profile equation from the base circle to the addendum circle is written as follows: In the formula, i represents the left and right tooth profiles of the gear, 1 represents the right tooth profile, and 2 represents the left tooth profile; γ i — The counterclockwise rotation angle of the left and right tooth profiles. When the value is negative, it represents clockwise rotation, and γ1-γ2=γ, (rad); r bi —Base circle radius of the left and right tooth profiles (mm) At the small displacement end, when the root circle radius is smaller than the base circle radius, the involute tooth profile can be extended inwards along a straight line into the base circle. The equation of the extension line is: t is a dimensionless parameter that is proportional to the length of the extension line and can be taken as 0 to 2; Step 3: Generating the helix: In Solidworks, enter the sketch and draw the base circle, defining the base circle diameter as 2r. bl Enable the helix function, select "height and pitch" as the definition method, set the helix rotation direction to counterclockwise, set the height to the tooth width h, and the pitch to... Set the starting angle to Drawing a right-hand spiral is similar; you only need to change the parameters.

2. The parametric modeling method for a three-dimensional solid of a variable-thickness gear according to claim 1, characterized in that, To generate variable-thickness gears of different sizes, simply modify the basic parameters: number of teeth, normal module, pressure angle, helix angle, cone angle, maximum end face displacement coefficient, and tooth width.

3. The parametric modeling method for a three-dimensional solid of a variable-thickness gear according to claim 1, characterized in that, To generate modified helical gears of different sizes, simply set the cone angle to 0, and then modify the number of teeth, normal module, pressure angle, helix angle, maximum displacement coefficient of the end face, and tooth width.

4. The parametric modeling method for a three-dimensional solid of a variable-thickness gear according to claim 1, characterized in that, To generate gears of different sizes with varying thicknesses, simply set the helix angle to 0, add a negative sign before the formula for the helix angle of the right tooth surface pitch cylinder, and finally modify the basic parameters.

5. The parametric modeling method for a three-dimensional solid of a variable-thickness gear according to claim 1, characterized in that, To generate left-hand variable-thickness gears of different sizes, simply add a negative sign before the formulas for the helix angle and the helix angle of the pitch cylinders on the left and right tooth surfaces, change the rotation direction of the helix to clockwise, and finally modify the basic parameters.

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