Method for modifying the tooth profile of a cylindrical involute gear

Abstract

The application discloses a method for modifying the tooth profile and tooth direction of a cylindrical involute gear, and comprises the following steps: 1) defining horizontal coordinates and vertical coordinates by using a tooth profile development diagram, establishing a mathematical model for modifying the tooth profile of the cylindrical gear, and solving a tooth profile modification equation of the cylindrical gear; 2) defining the tooth direction modification in a measuring cylindrical development plane, taking the tooth line length direction as the horizontal coordinates, establishing a mathematical model for modifying the tooth direction of the cylindrical gear, and solving a tooth direction modification equation of the cylindrical gear; 3) taking the center of the cylindrical gear as the coordinate system origin, establishing a mathematical model for the tooth profile curve of the gear end face, and solving a curve equation of the tooth profile of the cylindrical gear end face; and 4) solving a tooth surface equation and a normal vector equation of the cylindrical gear according to the curve equation of the tooth profile of the cylindrical gear end face and the tooth direction modification equation. The application utilizes the characteristics of the involute gear, and obtains the tooth surface of the involute cylindrical gear after micro modification, thereby solving the problem of the meshing noise of the cylindrical gear.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gear design, and particularly relates to a method for tooth profile and tooth direction modification of a cylindrical involute gear. BACKGROUND

[0002] During the meshing process of the involute cylindrical gear, due to the deformation of the shaft system, the deformation of the box and the bearing clearance, the gear will be misaligned, which will cause the gear to be partially loaded during the actual working process, thereby causing the gear meshing noise to be large.

[0003] There have been some researches on the tooth surface modification of the involute cylindrical gear, and the existing tooth surface modification methods mainly include the following three kinds: one is the drum modification of the gear tooth profile, which can improve the partial load in the tooth height direction, but the modification expression is not comprehensive enough, and the improvement of the meshing noise is limited; one is the tooth tip modification of the gear tooth profile, which can reduce the meshing impact, but the modification expression is not comprehensive enough, and the improvement of the meshing noise is limited; one is the tooth root modification of the gear tooth profile, which can reduce the meshing impact like the tooth tip modification of the gear tooth profile, but the modification expression is not comprehensive enough, and the improvement of the meshing noise is limited. SUMMARY

[0004] The present application provides a method for tooth profile and tooth direction modification of a cylindrical involute gear, which utilizes the characteristics of the involute gear to obtain the tooth surface of the involute cylindrical gear after micro-modification, thereby solving the problem of the meshing noise of the cylindrical gear.

[0005] The technical solution to solve the above problems is as follows:

[0006] The method for tooth profile and tooth direction modification of the cylindrical involute gear comprises the following steps:

[0007] 1) The horizontal coordinate and the vertical coordinate are defined by using the tooth profile development diagram, a mathematical model for the modification of the tooth profile of the cylindrical gear is established, and a modification equation of the tooth profile of the cylindrical gear is solved;

[0008] 2) The tooth direction modification is defined in the measurement cylindrical development plane, the tooth line length direction is taken as the horizontal coordinate, a mathematical model for the modification of the tooth direction of the cylindrical gear is established, and a modification equation of the tooth direction of the cylindrical gear is solved;

[0009] 3) The center of the cylindrical gear is taken as the coordinate system origin, a mathematical model for the tooth profile curve of the gear end face is established, and a curve equation of the tooth profile of the gear end face is solved;

[0010] 4) The tooth surface equation and the normal vector equation of the cylindrical gear are solved according to the curve equation of the tooth profile of the gear end face and the modification equation of the tooth direction.

[0011] The beneficial effects of the above technical solution are as follows:

[0012] 1. This calculation method calculates the microscopic modified involute cylindrical gear tooth surface by spiraling the modified end section tooth profile curve around the center line. It provides a method to solve gear meshing noise and can be applied to various involute cylindrical gear products with different tooth surfaces.

[0013] 2. This calculation method offers comprehensive shaping expressions and is flexible in application. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention;

[0015] Figure 2 This is a schematic diagram of the tooth profile drum-shaped modification of the present invention;

[0016] Figure 3 This is a schematic diagram of the tooth profile and tooth tip trimming of the present invention;

[0017] Figure 4 This is a schematic diagram of the tooth profile pressure angle modification of the present invention;

[0018] Figure 5 This is a schematic diagram of the tooth profile modification of the present invention;

[0019] Figure 6 This is a schematic diagram of the end face tooth profile curve of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the embodiments of the present invention will be described in more detail with reference to the accompanying drawings. The described embodiments are some, but not all, of the embodiments of the present invention. The embodiments described with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be simply construed as limiting the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0021] The present invention will now be described in detail with reference to the accompanying drawings.

[0022] like Figures 1 to 6 As shown, the method for modifying the tooth profile and tooth direction of a cylindrical involute gear according to the present invention includes the following steps:

[0023] 1) Define the horizontal and vertical coordinates using the tooth profile development diagram, establish a mathematical model for the modification of the cylindrical gear tooth profile, and solve the equation for the modification of the cylindrical gear tooth profile.

[0024] The equation for modifying the tooth profile of the cylindrical gear in step 1) is as follows:

[0025] 1-1) The tooth profile evaluation range is modified by a quadratic parabolic bulge shape, with the following equation:

[0026]

[0027] In the formula, δ PC ρ is the amount of the quadratic parabolic bulge of the tooth profile. ST ρ is the starting point for evaluating tooth profile modification. END ρ is the endpoint for tooth profile modification evaluation. M Δρ is the midpoint for evaluating tooth profile modification, ρ is the amount of tooth profile modification, and ρ is the gear extension.

[0028] In step 1), the highest point of the gear tooth profile is at the center ρ of the evaluation range. M It can be calculated using the following equation:

[0029] ρ M =(ρ ST +ρ END ) / 2.

[0030] 1-2) Perform a quadratic parabolic tooth tip trimming on the tooth profile, with the following equation:

[0031]

[0032] In the formula, δ PT ρ is the amount of tooth tip trimming for a quadratic parabolic tooth profile. T This is the starting point for trimming the tooth profile and tooth tip;

[0033] 1-3) The pressure angle is modified within the tooth profile evaluation range, and the equation is as follows:

[0034]

[0035] In the formula, δ PA This is the amount of material used to modify the pressure angle of the tooth profile.

[0036] 1-4) Based on steps 1-1), 1-2), and 1-3), the equation for modifying the tooth profile of the involute cylindrical gear is obtained:

[0037]

[0038] 2) Tooth profile modification is defined in the development plane of the measuring cylinder. With the tooth line length direction as the abscissa, a mathematical model of tooth profile modification of cylindrical gear is established, and the equation of tooth profile modification of cylindrical gear is solved.

[0039] Step 2) Solve the equation for the tooth profile modification of the cylindrical gear as follows:

[0040]

[0041] In the formula, δ L For gear tooth profile modification and bulging amount, β LFor measuring the helix angle on the cylinder, b is the gear tooth width, L is the length of the tooth trace, and V is the transverse modification.

[0042] 3) Taking the center of the cylindrical gear as the coordinate system origin, a mathematical model of the gear end face tooth profile curve is established, and the curve equation of the cylindrical gear end face tooth profile is solved. The curve equation of the cylindrical gear end face tooth profile is as follows:

[0043]

[0044] In the formula, r b is the base circle radius of the gear, u is the curve parameter, σ0 is the half angle of the gear base circle tooth groove, x0 is the component of the gear end face tooth profile curve in the x direction, y0 is the component of the gear end face tooth profile curve in the y direction, and Δρ is the tooth profile modification;

[0045] 4) According to the curve equation of the cylindrical gear end face tooth profile and the transverse modification equation, the gear surface equation and the normal vector equation of the cylindrical gear are solved. The equation of the cylindrical gear surface is as follows:

[0046]

[0047] In the formula, x0 is the component of the gear end face tooth profile curve in the x direction, y0 is the component of the gear end face tooth profile curve in the y direction, θ is the rotation angle of the gear end face tooth profile curve, β L For measuring the helix angle on the cylinder, L is the length of the tooth trace, V is the transverse modification, X is the X direction coordinate of the gear surface, Y is the Y direction coordinate of the gear surface, and Z is the Z direction coordinate of the gear surface.

[0048] The rotation angle θ of the gear end face tooth profile curve in step 4) can be calculated according to the following equation:

[0049]

[0050] S = e + L sin β L + V cos β L

[0051] In the formula, e is half of the end face tooth groove width of the middle section of the tooth width measured on the cylinder, and S is the arc length of the gear measured in the developed plane of the cylinder.

[0052] The normal vector of the gear surface in step 4) is calculated according to the following equation:

[0053]

[0054] Wherein,

[0055]

[0056]

[0057] wherein, N is the normal vector of the gear tooth surface, X N is the X-direction component of the normal vector of the gear tooth surface,

[0058] N is the Y-direction component of the normal vector of the gear tooth surface, Y N is the Y-direction component of the normal vector of the gear tooth surface, Z N is the Z-direction component of the normal vector of the gear tooth surface, N is the partial derivative of the Y-direction component of the gear tooth surface with respect to the u parameter, N is the partial derivative of the X-direction component of the gear tooth surface with respect to the u parameter, N is the partial derivative of the Z-direction component of the gear tooth surface with respect to the u parameter, N is the partial derivative of the X-direction component of the gear tooth surface with respect to the L parameter, N is the partial derivative of the Y-direction component of the gear tooth surface with respect to the L parameter, N is the partial derivative of the Z-direction component of the gear tooth surface with respect to the L parameter.

[0059] In Example 1, the macro parameters of the input gear of the main reduction gear pair of an automobile transmission are taken as an example, and the macro parameters of the gear are shown in Table 1:

[0060] Table 1

[0061] Gear 1 Gear 2 Teeth 15 64 Normal module 3.1 3.1 Normal pressure angle 20° 20° Helical angle 28° 28° Tip circle diameter 62.1 228.7 Transverse contact ratio 1.37 1.37 Axial contact ratio 1.42 1.42 Total contact ratio 2.78 2.78

[0062] According to the method for calculating the tooth profile modification of the involute cylindrical gear of the application, the modification amounts of the tooth profile of the gear are shown in Table 2:

[0063] Table 2

[0064] Gear 1 Gear 2 Transverse crowning 10 8 Profile crowning 5 5 Profile tilt 0 -10 Profile tip relief 8 30 Profile tip relief start point 16.8 44.1

[0065] According to the modification amounts of the tooth profile of the semi-axle bevel gear shown in Table 2, the modified cylindrical gear tooth surface is obtained, and the design data can be used for three-dimensional modeling and gear measurement.

[0066] The method of the application can be used to solve the gear meshing noise by calculating the involute cylindrical gear tooth surface through the modified end section tooth profile curve and spiral motion around the center line, and can be applied to various involute cylindrical gear products with different tooth surfaces. Moreover, the application is a method for modifying the tooth profile of the involute cylindrical gear, which includes tooth profile modification of the secondary parabolic drum shape, pressure angle modification, secondary parabolic drum shape modification, secondary parabolic modification of the tooth top, and comprehensive modification expression, which is very flexible to apply. In addition, the application can directly process the calculation results, which can be used for three-dimensional modeling and gear measurement.

Claims

1. A method of modifying the tooth profile of a cylindrical involute gear, characterised in that, Comprise the following steps: 1), with the tooth profile development to define the horizontal coordinate and vertical coordinate, the establishment of cylindrical gear tooth profile modification mathematical model, solution of cylindrical gear tooth profile modification equation; The mathematical model of the involute cylindrical gear tooth profile modification established in step 1) is as follows: 1-1) the tooth profile evaluation range is modified by quadratic parabolic drum shape, the equation is as follows: ； wherein is the tooth profile quadratic parabolic drum amount, is the tooth profile modification evaluation starting point, is the tooth profile modification evaluation end point, is the tooth profile modification evaluation midpoint, is the tooth profile modification amount, is the gear expansion length; 1-2) the tooth profile top is modified by quadratic parabolic tooth tip, the equation is as follows: ； wherein is the profile quadratic parabolic addendum relief, is the profile addendum relief starting point; 1-3) the tooth profile evaluation range is modified by pressure angle, the equation is as follows: ； In the formula, is the profile pressure angle modification amount; 1-4) according to step 1-1), 1-2), 1-3), the expression equation of involute cylindrical gear tooth profile modification is obtained: ； 2), the tooth modification is defined in the measuring cylindrical development plane, the mathematical model of cylindrical gear tooth modification is established with the tooth line length direction as the horizontal coordinate, and the equation of cylindrical gear tooth modification is solved; The equation of the mathematical model of the involute cylindrical gear tooth modification established in step 2) is as follows: ； wherein is the amount of tooth profile modification in the direction of the tooth, is the helix angle on the measuring cylinder, is the tooth width, L is the length of the tooth trace, is the amount of tooth profile modification in the direction of the tooth, 3), with the center of cylindrical gear as the coordinate system origin, the mathematical model of gear end face tooth profile curve is established, and the curve equation of cylindrical gear end face tooth profile is solved; The curve equation of the cylindrical gear end face tooth profile solved in step 3) is as follows: ； wherein is the base circle radius of the gear, is the curve parameter, is the half angle of the base circle tooth space of the gear, is the tooth profile curve of the gear end face is the component of the direction, is the tooth profile curve of the gear end face is the component of the direction, is the tooth profile modification amount; 4), according to the curve equation of the cylindrical gear end face tooth profile and the tooth modification equation, the cylindrical gear tooth surface equation and the normal vector equation are solved, and the equation of the cylindrical gear tooth surface is as follows: ； wherein is a gear end face tooth profile curve is a component of the direction, is a gear end face tooth profile curve is a component of the direction, is a gear end face tooth profile curve rotation angle, is a helix angle on a measuring cylinder, L is a tooth trace length, is a transverse modification amount, is a gear tooth surface is a direction coordinate, is a gear tooth surface is a direction coordinate, is a gear tooth surface is a direction coordinate.

2. The method of cylindrical involute gear tooth profile and tooth direction modification according to claim 1, characterized in that: The highest point of the gear tooth profile in step 1) can be calculated according to the following equation: 。 3. The method of cylindrical involute gear tooth profile and tooth direction modification according to claim 1, characterized in that, The gear end face tooth profile curve rotation angle in step 4) can be calculated according to the following equation: ； ； wherein To measure the half of the face width of the tip of the tooth slot in the middle section of the tooth width on the cylinder, To measure the arc length of the gear in the cylinder development plane.

4. The method of cylindrical involute gear tooth profile and tooth direction modification according to claim 1, characterized in that, The tooth surface normal vector in step 4) is calculated according to the following equation: ； wherein ; ； ； wherein is the normal vector of the gear tooth surface, is the direction of the normal vector of the gear tooth surface component, is the direction of the normal vector of the gear tooth surface component, is the direction of the normal vector of the gear tooth surface component, is the partial derivative of the Y-direction component of the gear tooth surface with respect to the u parameter, is the partial derivative of the X-direction component of the gear tooth surface with respect to the u parameter, is the partial derivative of the Z-direction component of the gear tooth surface with respect to the u parameter, is the partial derivative of the X-direction component of the gear tooth surface with respect to the L parameter, is the partial derivative of the Y-direction component of the gear tooth surface with respect to the L parameter, is the partial derivative of the Z-direction component of the gear tooth surface with respect to the L parameter.

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