Asymmetric involute spline and modeling method thereof

Abstract

The invention discloses an asymmetric involute spline and a modeling method thereof, and the method comprises the following steps: firstly determining basic parameters of the asymmetric involute spline, then determining a size calculation formula of an external spline, defining involute curves of a non-working side and a working side of the external spline, mirroring and rotating the involute curve of the working side to obtain two curves, defining involute root circle curve equations of a non-working side and a working side, and defining that a straight line is tangent to two root circle curves to obtain an external spline tooth profile; determining an internal spline size calculation formula, defining a non-working side involute curve and a working side involute curve of the internal spline, mirroring the non-working side involute curve, rotating the working side involute curve to obtain two curves, defining a dedendum circle curve equation, and enabling the dedendum circle curve equation to be tangent to the two curves to obtain an internal spline tooth profile; and finally modeling and assembling the internal and external splines in modeling software. The problems that the working side bearing capacity, the tooth root bending strength and the tooth surface contact strength of the spline are insufficient under the actual working condition of one-way stress can be solved.

Description

Technical Field

[0001] The invention belongs to the field of spline tooth profile design and relates to an asymmetric involute spline and a modeling method thereof. Background Art

[0002] The involute tooth profile spline has the characteristics of large root arc, small stress concentration, high bending strength of the teeth, and can withstand large bending stress. However, in some scenarios such as heavy machinery and large engineering equipment, its load-bearing capacity still cannot meet the needs. In addition, the existing spline modeling method has certain limitations. On the one hand, it does not support the design of the involute pressure angles on both sides separately. In some application scenarios with high requirements for transmission accuracy and mechanical properties, it is impossible to flexibly adjust the pressure angles on both sides according to actual needs, thereby limiting the adaptability and performance optimization space of the spline under different working conditions. On the other hand, the tolerance cannot be accurately modeled on the model during the modeling process. Summary of the invention

[0003] The object of the present invention is to provide an asymmetric involute spline and a modeling method thereof, which can solve the problems of insufficient working side bearing capacity, tooth root bending strength and tooth surface contact strength of the spline under actual working conditions of unidirectional force.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A method for modeling an asymmetric involute spline comprises the following steps:

[0006] Step 1: Determine the basic parameters of the asymmetric involute spline;

[0007] Step 2: Determine the calculation formula for the external spline size, and define the involute curves θ1 and θ2 on the non-working side and the working side of the external spline, mirror θ2 to obtain θ′2, and then rotate θ′2 clockwise 360 / z to obtain θ″2; define the equations of the involute root circle curves θ3 and θ4 on the non-working side and the working side, and define a straight line l4 so that its curves θ3 and θ4 are tangent at the same time. The final closed curve is the external spline tooth profile;

[0008] Step 3: Determine the calculation formula for the internal spline size, and define the involute curves θ5 and θ6 on the non-working side and working side of the internal spline, mirror θ5 to obtain θ′5, and then rotate θ6 clockwise 360 / z to obtain θ′6; define the tooth root circle curve equation θ7, and make the curve θ7 tangent to θ′5 and θ′6 at the same time. The final closed curve is the internal spline tooth profile;

[0009] Step 4: Model and assemble the internal and external splines in the modeling software.

[0010] Furthermore, the specific contents of the basic parameters in step 1 include:

[0011] (1) Determine the pressure angle: The involutes on both sides of the spline are divided into two types: the working side and the non-working side. The pressure angle of the involute on the non-working side is set to α1, and the pressure angle of the involute on the working side is set to α2. Both α1 and α2 are selected from 30°, 37.5° and 45°, and the values ​​of α1 and α2 are different;

[0012] (2) Determine the tolerance e: The total tolerance of the total tooth width and tooth thickness is calculated as follows: (T+λ)=40i1±160i2, where i1 is the tolerance based on the pitch circle diameter D; the tolerance unit i is: When D≤500mm, When D>500mm, i=0.004D+2.1, i2 is the basic tolerance based on the basic tooth gap width E or basic tooth gap thickness S, and the tolerance unit i is: or Where T is the machining tolerance, λ is the comprehensive tolerance;

[0013] Comprehensive tolerance λ:

[0014] Cumulative tolerance of tooth pitch F p : Where L is half of the circumference of the graduation circle;

[0015] Tooth profile tolerance f f : in is the tolerance factor,

[0016] Tooth tolerance F β : Where g is the spline length;

[0017] The tolerance e should be between T+λ and λ, that is, the maximum actual tooth thickness is 0.5πz-λ, and the minimum actual tooth thickness is 0.5πz-(T+λ);

[0018] (3) Determine the change angle x that reflects the tolerance when using the mirror command during the modeling process:

[0019] 2x*r=Se; Where r is the pitch circle radius; S = 0.5πm; then

[0020] Furthermore, the external spline tooth profile in step 2 is determined by the following steps:

[0021] (1) Determine the calculation formula for external spline size:

[0022] Pitch circle diameter d = mz, where z is the number of teeth and m is the module;

[0023] Two different pressure angle major diameter formulas for external splines: da1 = D ee1 , da2=D ee2 , where da1 is the major diameter corresponding to the involute on the non-working side, D ee1 is the basic size of the major diameter of the non-working side, da2 is the major diameter corresponding to the involute of the working side, D ee2 Is the basic size of the major diameter of the working side; among them, 30° flat tooth root and round tooth root: D ee =m(z+1); 37.5° round tooth root: D ee =m(z+0.9); 45° round tooth root: D ee = m(z+0.8);

[0024] The base circle formula of the external spline is: db1 = dcos(α1), db2 = dcos(α2), where db1 is the base circle diameter corresponding to the involute on the non-working side, and db2 is the base circle diameter corresponding to the involute on the working side;

[0025] Two different pressure angle minor diameter formulas for external splines: df1 = D ie1 , df2=D ie2 , where df1 is the minor diameter corresponding to the involute on the non-working side, D ie1 is the basic size of the minor diameter on the non-working side, df2 is the minor diameter corresponding to the involute on the working side, D ie2 It is the basic size of the working side path;

[0026] The basic dimensions of the external spline minor diameter are as follows:

[0027] 30° flat tooth root: D ie =m(z-1.5); 30° round tooth root: D ie =m(z-1.8); 37.5° round tooth root: D ie =m(z-1.4); 45° round tooth root: D ie = m(z-1.2);

[0028] Root fillet radius of external spline:

[0029] 30° flat tooth root: ρ Fe =0.2m; 30° round tooth root: ρ Fe =0.4m; 37.5° round tooth root: ρ Fe =0.3m; 45° round tooth root: ρ Fe =0.25m;

[0030] (2) Define the involute equations of the non-working side and the working side

[0031] Non-working side involute θ1:

[0032]

[0033] Where, t1 is the angle parameter controlling the generation of the involute θ1 on the non-working side, and the value is t1 = 0;

[0034] Working side involute θ2:

[0035]

[0036] Where, t2 is the angle parameter for controlling the generation of the involute θ2 on the working side, and the value is t2 = 0;

[0037] The two curves θ1 and θ2 intersect with the pitch circle respectively, and two intersection points are obtained. The intersection points are connected with the center of the circle to obtain two straight lines l1 and l2. The angles α3 and α4 between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively. l2 is rotated in the counterclockwise direction by an angle α5=x-(α4-α3) / 2 to obtain the mirror center line l3. The curve θ2 is mirrored with l3 as the mirror center line to obtain θ′2. Then θ′2 is rotated clockwise by 360 / z to obtain θ″2.

[0038] (3) Define the involute root circle curve equations of the non-working side and the working side

[0039] Non-working side involute tooth root circle curve θ3:

[0040]

[0041] In the formula, ρ Fe1 is the radius of the tooth root circle on the non-working side, a3 and b3 are the horizontal and vertical coordinates of the center position of the curve θ3;

[0042] Working side involute tooth root circle curve θ4:

[0043]

[0044] In the formula, ρ Fe2 is the radius of the tooth root circle on the non-working side, a4 and b4 are the horizontal and vertical coordinates of the center position of the curve θ4;

[0045] (4) Determine the external spline tooth profile

[0046] Let curve θ3 be tangent to df1 and tangent to curve θ1, and let curve θ4 be tangent to df2 and tangent to curve θ″2. Create a new straight line l4, which is tangent to curve θ3 and θ4 at the same time, and keep the closed curve composed of da2, curve θ1, θ3, straight line l4, curve θ4 and θ″2 to obtain the external spline tooth profile.

[0047] Furthermore, the internal spline tooth profile in step 3 is determined by the following steps:

[0048] (1) Determine the calculation formula for internal spline size:

[0049] Pitch circle diameter d = mz, where z is the number of teeth and m is the module;

[0050] Two different pressure angle major diameter formulas for internal splines: da5 = D ei1 , da6 = D ei2 , where da5 is the major diameter corresponding to the involute on the non-working side, D ei1 is the basic size of the major diameter of the non-working side, da6 is the major diameter corresponding to the involute of the working side, D ie2 Is the basic size of the major diameter on the working side; among which, 30° flat tooth root: D ei =m(z+1.5); 30° round tooth root: D ei =m(z+1.8); 37.5° round tooth root: D ei =m(z+1.4); 45° round tooth root: D ei = m(z+1.2);

[0051] The base circle formula of the internal spline is: db5 = dcos (α1), db6 = dcos (α2), where db5 is the base circle diameter corresponding to the involute on the non-working side, and db6 is the base circle diameter corresponding to the involute on the working side;

[0052] Two different pressure angle minor diameter formulas for internal splines:

[0053]

[0054] Where, df5 is the minor diameter corresponding to the involute on the non-working side, df6 is the minor diameter corresponding to the involute on the working side, and es v / tan(α1) and es v / tan(α1) are the upper deviations of the inner spline diameter; h s1 、h s2 h is the tooth root working height; s1 and h s2 The specific formula is: 30° flat tooth root, round tooth root: h s =0.2m; 37.5° round tooth root: h s =0.55m; 45° round tooth root: h s =0.5m;

[0055] Root fillet radius of internal spline:

[0056] 30° flat tooth root: ρ Fe =0.2m; 30° round tooth root: ρ Fe =0.4m; 37.5° round tooth root: ρ Fe =0.3m; 45° round tooth root: ρ Fe =0.25m;

[0057] (2) Define the involute equations of the non-working side and the working side

[0058] Non-working side involute θ5:

[0059]

[0060] Wherein, t5 is the angle parameter controlling the generation of the involute θ5 on the non-working side, and the value is t5 = 0;

[0061] Working side involute θ6:

[0062]

[0063] Wherein, t6 is the angle parameter for controlling the generation of the involute θ6 on the working side, and the value is t6 = 0;

[0064] The two curves θ5 and θ6 intersect with the pitch circle respectively, and two intersection points are obtained. The intersection points are connected with the center of the circle to obtain two straight lines l5 and l6. The angles α6 and α7 between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively. l5 is rotated clockwise by an angle α8=x-(α7-α6) / 2 to obtain the mirror center line l7. The curve θ5 is mirrored with l7 as the mirror center line to obtain θ′5. Then θ6 is rotated clockwise by 360 / z to obtain θ′6.

[0065] (3) Define the tooth root circle curve equation

[0066] Tooth root circle curve θ7:

[0067]

[0068] In the formula, ρ Fe1 is the root circle radius of the smaller pressure angle side, a7 and b7 are the horizontal and vertical coordinates of the center position of curve θ7;

[0069] (4) Determine the internal spline tooth profile

[0070] Let curve θ7 be tangent to curves θ′5 and θ′6 at the same time, retain the closed curve formed by df6, curves θ′5, θ7 and θ′6, and obtain the internal spline tooth profile.

[0071] Furthermore, the specific process of modeling described in step 4 is as follows:

[0072] (1) Determine the basic parameters of asymmetric involute splines

[0073] The side with a larger involute pressure angle is selected as the working side, and the side with a smaller pressure angle is selected as the non-working side, that is, α2>α1, and the pressure angle of the non-working side of the involute spline is set to 30° and the pressure angle of the working side is set to 37.5° to enhance the load-bearing effect of the asymmetric involute spline during operation; when m=1.5mm, z=12, according to the tolerance e value between T+λ and λ, the tolerance is selected as e=0.126mm, then the angle in the mirror command required in the modeling process is

[0074] (2) Application of UG NX modeling software

[0075] Model the internal and external splines separately, and create sketches on the xoy plane. First, draw the pitch circle, major diameter, and minor diameter according to the relevant parameters through the circle command; then use the command to create a regular curve, select the curve driven by the equation, draw two involutes with different pressure angles, use the mirror command for one of the involutes, and implement the command to rotate around the center point for the other involute; then the external spline draws the root circles of different pressure angles on both sides according to the relevant parameters of the root circle, and implements the command that the root circle is tangent to the involute drawn with the same pressure angle and the minor diameter of the external spline drawn with the same pressure angle. According to the relevant parameters of the root circle, the root circle corresponding to the smaller pressure angle of the internal spline is tangent to the two involutes with different pressure angles on both sides at the same time, and finally form closed curves to obtain the tooth profiles of the internal and external splines; then stretch the matrix to get a single tooth, and finally set the number of teeth to 12 with the center of the pitch circle as the center, and complete the modeling of the internal and external splines through the circular array surface.

[0076] Furthermore, the specific assembly process described in step 4 is: create a new assembly file, import the inner and outer spline models into the assembly file, enter the command to move the component to rotate the outer spline or the inner spline 180° around the axis or axis direction, enter the concentricity constraint in the assembly constraint command to ensure the concentricity of the inner and outer splines, apply contact alignment to make the stretching surfaces with the same involute pressure angle fit together.

[0077] According to the asymmetric involute spline generated by the above modeling method, the pressure angles on both sides of the spline are different, and the involutes on both sides of the spline tooth profile and the external spline tooth root transition curve are also asymmetric.

[0078] Compared with the prior art, the present invention has the following beneficial effects:

[0079] The present invention proposes an asymmetric involute spline. When the working tooth surface adopts a large pressure angle and the non-working tooth surface adopts a small pressure angle, the large pressure angle on the working side enhances the bearing capacity of the spline teeth, which can reasonably distribute the contact stress of the tooth surface and effectively disperse the force when transmitting torque. For example, the bending stress of the tooth root can be reduced under the same torque, because the direction of the force is more conducive to resisting bending deformation, thereby improving the bending strength of the spline to withstand a larger load and not easy to bend and deform; the small pressure angle on the non-working side makes the tooth shape relatively flat, reduces the difficulty of manufacturing and assembly, and can maintain the overall elasticity and flexibility of the spline, avoiding excessive decrease in flexibility due to the increase in the pressure angle on the working side. At the same time, the small pressure angle on the non-working side helps to maintain flexibility, so that the spline can better adapt to complex working conditions such as impact and vibration, reduce stress concentration and fatigue damage caused by excessive rigidity, and can also play a buffering role when the spline is subjected to torque changes or external impacts, reduce the sudden stress change of the root of the working side, and thus reduce the risk of broken teeth, effectively avoiding the hazards of reduced flexibility and increased risk of broken teeth caused by only increasing the pressure angle, and ensuring the excellent bending strength of the spline.

[0080] The modeling method of the present invention provides a solution for the root transition curve, using an asymmetric curve at the root of the external spline, using the non-working side pressure angle root circle at the non-working side root, and using the working side pressure angle root circle at the working side root, thereby ensuring the bending strength of the roots on both sides, and the design method is the same as that of the involute spline. If the internal spline still adopts the design method of the involute spline, the root circle on the smaller pressure angle side will interfere with the involute on the larger pressure angle side. Therefore, a solution in which the root circle on the smaller pressure angle side is tangent to the involutes on both sides is used, which can ensure the bending strength of the non-working side root and the bending strength of the working side root. In addition, the present invention can calculate and accurately model the tolerance of the internal and external splines during the modeling process, specifically, by calculating the actual tooth thickness formed by the involutes on both sides on the pitch circle through the tolerance. Since the involute needs to be mirrored and rotated to construct the tooth profile, the actual tooth thickness under the same pressure angle of the involutes on both sides can be obtained by changing the mirror angle. In view of the fact that the intersection points of the involutes on both sides and the pitch circle do not coincide, it is also necessary to measure the angle between the intersection points of the involutes and the pitch circle on both sides and the line connecting the center of the circle. After calculation, the mirror angle is adjusted again to achieve accurate modeling of the internal and external spline tolerances. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 The 2D sketch of the involute of the external spline for 30° and 37.5° splines;

[0082] Figure 2 2D sketch of the mirroring process of the external spline for 30° and 37.5° splines;

[0083] Figure 3 2D sketch of the external spline root transition for 30° and 37.5° splines;

[0084] Figure 4 The 2D sketch of the single tooth profile of the external spline for 30° and 37.5° splines;

[0085] Figure 5 The three-dimensional part drawing of the external spline for 30° and 37.5° splines;

[0086] Figure 6 The 2D sketch of the internal spline involute for 30° and 37.5° splines;

[0087] Figure 7 The 2D sketch of the internal spline mirroring process for 30° and 37.5° splines;

[0088] Figure 8 The 2D sketch of the internal spline root transition for 30° and 37.5° splines;

[0089] Fig. 9 The 2D sketch of the single tooth profile of the internal spline with 30° and 37.5° splines;

[0090] Fig.10 The three-dimensional part drawing of the internal spline of 30° and 37.5° splines;

[0091] Fig.11 The internal and external spline assembly drawings are for 30° and 37.5° splines;

[0092] Fig.12 Meshing of spline tooth surfaces for 30° and 37.5° splines;

[0093] Fig.13 This is the load distribution diagram of the external spline with a working surface pressure angle of 30°;

[0094] Fig.14 This is the load distribution diagram of the internal spline with a working surface pressure angle of 30°;

[0095] Fig.15 This is the load distribution diagram of the external spline with a working surface pressure angle of 37.5°;

[0096] Fig.16 This is the load distribution diagram of the internal spline with a working surface pressure angle of 37.5°. DETAILED DESCRIPTION

[0097] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0098] A method for modeling an asymmetric involute spline according to this embodiment comprises the following steps:

[0099] Step 1: Determine the basic parameters of the asymmetric involute spline

[0100] (1) Determine the asymmetric pressure angle: The pressure angle of the involute spline specified in the national standard is usually 30°, 37.5° and 45°. The involutes on both sides of the spline are divided into two types: the working side and the non-working side. Set the pressure angle of the involute on the non-working side to α1, and the pressure angle of the involute on the working side to α2. Both α1 and α2 are selected from 30°, 37.5° and 45°, and the values ​​of α1 and α2 are different.

[0101] (2) Determine the tolerance:

[0102] In the involute spline, the total tolerance calculation formula of the total differential tooth width and tooth thickness is: (T+λ)=40i1±160i2, i1 is the tolerance based on the pitch circle diameter D, and its tolerance unit i is: when D≤500mm, When D>500mm, i=0.004D+2.1. i2 is the basic tolerance based on the basic tooth gap width E or basic tooth gap thickness S, and its tolerance unit i is: or Where T is the machining tolerance and λ is the comprehensive tolerance.

[0103] Comprehensive tolerance λ:

[0104] Cumulative tolerance of tooth pitch F p : Where L is half of the circumference of the graduation circle;

[0105] Tooth profile tolerance f f : in is the tolerance factor,

[0106] Tooth tolerance F β : Where g is the spline length;

[0107] The tolerance e should be between T+λ and λ, that is, the maximum actual tooth thickness is 0.5πz-λ, and the minimum actual tooth thickness is 0.5πz-(T+λ).

[0108] (3) Determine the change angle x that reflects the tolerance when using the mirror command during the modeling process:

[0109] In the modeling process, when using the mirror command, the tolerance e is reflected by controlling the angle between the mirror line and the center line. The principle is that after the mirror command, the arc length intercepted by the involutes on both sides on the pitch circle is the actual tooth thickness. In order to reduce the tolerance e of the tooth thickness of the internal and external splines, it is necessary to determine the angle x between the involutes with different pressure angles on both sides on the pitch circle and the line connecting the center of the circle, 2x*r=Se; Where r is the pitch circle radius; S = 0.5πm; then

[0110] Step 2: Determine the calculation formula for the external spline size, and define the involute curves θ1 and θ2 on the non-working side and the working side of the external spline, mirror θ2 to obtain θ′2, and then rotate θ′2 clockwise 360 / z to obtain θ″2; define the equations of the involute root circle curves θ3 and θ4 on the non-working side and the working side, and define a straight line l4 so that its curves θ3 and θ4 are tangent at the same time. The final closed curve is the external spline tooth profile.

[0111] (1) Determine the calculation formula for external spline size:

[0112] Pitch circle diameter d = mz, where z is the number of teeth and m is the module;

[0113] Two different pressure angle major diameter formulas for external splines: da1 = D ee1 , da2=D ee2 , where da1 is the major diameter corresponding to the involute on the non-working side, D ee1 is the basic size of the major diameter of the non-working side, da2 is the major diameter corresponding to the involute of the working side, D ee2 Is the basic size of the major diameter of the working side; among them, 30° flat tooth root and round tooth root: D ee =m(z+1); 37.5° round tooth root: D ee =m(z+0.9); 45° round tooth root: D ee = m(z+0.8);

[0114] The base circle formula of the external spline is: db1 = dcos(α1), db2 = dcos(α2), where db1 is the base circle diameter corresponding to the involute on the non-working side, and db2 is the base circle diameter corresponding to the involute on the working side;

[0115] Two different pressure angle minor diameter formulas for external splines: df1 = D ie1 , df2=D ie2 , where df1 is the minor diameter corresponding to the involute on the non-working side, D ie1 is the basic size of the minor diameter on the non-working side, df2 is the minor diameter corresponding to the involute on the working side, D ie2 It is the basic size of the working side path;

[0116] The basic dimensions of the external spline minor diameter are as follows:

[0117] 30° flat tooth root: D ie =m(z-1.5); 30° round tooth root: D ie =m(z-1.8); 37.5° round tooth root: D ie =m(z-1.4); 45° round tooth root: D ie = m(z-1.2);

[0118] Root fillet radius of external spline:

[0119] 30° flat tooth root: ρ Fe =0.2m; 30° round tooth root: ρ Fe =0.4m; 37.5° round tooth root: ρ Fe =0.3m; 45° round tooth root: ρ Fe =0.25m;

[0120] (2) Define the involute equations of the non-working side and the working side

[0121] Non-working side involute θ1:

[0122]

[0123] Wherein, t1 is the angle parameter controlling the generation of the involute θ1 on the non-working side, and the value is t1=0.

[0124] Working side involute θ2:

[0125]

[0126] Wherein, t2 is the angle parameter for controlling the generation of the involute θ2 on the working side, and the value is t2=0.

[0127] The two curves θ1 and θ2 intersect with the pitch circle respectively to obtain two intersection points. After connecting the intersection points with the center of the circle, two straight lines l1 and l2 are obtained, and the angles α3 and α4 between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively. l2 is rotated counterclockwise by an angle α5=x-(α4-α3) / 2 to obtain the mirror center line l3, and the curve θ2 is mirrored with l3 as the mirror center line to obtain θ′2, and then θ′2 is rotated clockwise by 360 / z to obtain θ″2.

[0128] (3) Define the involute root circle curve equations of the non-working side and the working side

[0129] Non-working side involute tooth root circle curve θ3:

[0130]

[0131] In the formula, ρ Fe1 is the radius of the root circle of the non-working side tooth, a3 and b3 are the horizontal and vertical coordinate values ​​of the center position of the curve θ3.

[0132] Working side involute tooth root circle curve θ4:

[0133]

[0134] In the formula, ρ Fe2 is the radius of the root circle of the non-working side tooth, a4 and b4 are the horizontal and vertical coordinate values ​​of the center position of the curve θ4.

[0135] (4) Determine the external spline tooth profile

[0136] Let curve θ3 be tangent to df1 and tangent to curve θ1, and let curve θ4 be tangent to df2 and tangent to curve θ″2. Create a new straight line l4, which is tangent to curves θ3 and θ4 at the same time, retain the closed curve composed of da2, curves θ1, θ3, straight line l4, curve θ4 and θ″2, and obtain the external spline tooth profile.

[0137] Step 3: Determine the internal spline size calculation formula, and define the involute curves θ5 and θ6 on the non-working side and working side of the internal spline, mirror θ5 to get θ′5, and then rotate θ6 clockwise 360 / z to get θ′6; define the root circle curve equation θ7, and make the curve θ7 tangent to θ′5 and θ′6 at the same time. The final closed curve is the internal spline tooth profile.

[0138] (1) Determine the calculation formula for internal spline size:

[0139] Pitch circle diameter d = mz, where z is the number of teeth and m is the module;

[0140] Two different pressure angle major diameter formulas for internal splines: da5 = D ei1 , da6 = D ei2 , where da5 is the major diameter corresponding to the involute on the non-working side, D ei1 is the basic size of the major diameter of the non-working side, da6 is the major diameter corresponding to the involute of the working side, D ie2 Is the basic size of the major diameter on the working side; among which, 30° flat tooth root: D ei =m(z+1.5); 30° round tooth root: D ei =m(z+1.8); 37.5° round tooth root: D ei =m(z+1.4); 45° round tooth root: D ei = m(z+1.2);

[0141] The base circle formula of the internal spline is: db5 = d cos(α1), db6 = d cos(α2), where db5 is the base circle diameter corresponding to the involute on the non-working side, and db6 is the base circle diameter corresponding to the involute on the working side;

[0142] Two different pressure angle minor diameter formulas for internal splines:

[0143]

[0144] Where, df5 is the minor diameter corresponding to the involute on the non-working side, df6 is the minor diameter corresponding to the involute on the working side, and es v / tan(α1) and es v / tan(α1) are the upper deviations of the inner spline diameter; h s1 、h s2 h is the tooth root working height; s1 and h s2 The specific formula is: 30° flat tooth root, round tooth root: h s =0.2m; 37.5° round tooth root: h s =0.55m; 45° round tooth root: h s =0.5m.

[0145] Root fillet radius of internal spline:

[0146] 30° flat tooth root: ρ Fe =0.2m; 30° round tooth root: ρ Fe =0.4m; 37.5° round tooth root: ρ Fe =0.3m; 45° round tooth root: ρ Fe =0.25m;

[0147] (2) Define the involute equations of the non-working side and the working side

[0148] Non-working side involute θ5:

[0149]

[0150] Wherein, t5 is the angle parameter controlling the generation of the involute θ5 on the non-working side, and the value is t5=0.

[0151] Working side involute θ6:

[0152]

[0153] Wherein, t6 is the angle parameter for controlling the generation of the involute θ6 on the working side, and the value is t6=0.

[0154] The two curves θ5 and θ6 intersect with the pitch circle respectively to obtain two intersection points. After connecting the intersection points with the center of the circle, two straight lines l5 and l6 are obtained, and the angles α6 and α7 between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively. Rotate l5 in the clockwise direction by an angle α8=x-(α7-α6) / 2 to obtain the mirror center line l7, mirror the curve θ5 with l7 as the mirror center line to obtain θ′5, and then rotate θ6 clockwise by 360 / z to obtain θ′6.

[0155] (3) Define the tooth root circle curve equation

[0156] Tooth root circle curve θ7:

[0157]

[0158] In the formula, ρ Fe1is the root circle radius of the smaller pressure angle side, a7 and b7 are the horizontal and vertical coordinate values ​​of the center position of curve θ7.

[0159] (4) Determine the internal spline tooth profile

[0160] Let curve θ7 be tangent to curves θ′5 and θ′6 at the same time, retain the closed curve formed by df6, curves θ′5, θ7 and θ′6, and obtain the internal spline tooth profile.

[0161] Step 4: Model and assemble the internal and external splines in the modeling software

[0162] (1) Determine tolerances and calculate internal and external spline parameters

[0163] The side with a larger involute pressure angle is selected as the working side, and the side with a smaller pressure angle is selected as the non-working side, that is, α2>α1. The pressure angle of the non-working side of the involute spline is set to 30° and the pressure angle of the working side is set to 37.5° to enhance the load-bearing effect of the asymmetric involute spline during operation.

[0164] The design of asymmetric involute spline complies with the following working conditions: torque is 25N·m, speed is 6000, spline length g=9, and machining accuracy is level 7. Select m=1.5mm, z=12, then the pitch circle diameter d=mz=18mm; basic tooth width E=0.5πm=2.3562mm; basic tooth thickness S=0.5πm=2.3562mm, then the basic tolerance Therefore, the total tolerance of the total tooth width and tooth thickness is T+λ=144μm, λ=46.2892mm. According to the tolerance e taking the value between T+λ and λ, the tolerance is selected as e=0.126mm.

[0165] Angles in the mirror command required during modeling

[0166] (2) Application software modeling

[0167] Using UG NX modeling software, first model the external spline and create a sketch on the xoy plane. The centers of the pitch circle, base circle, major diameter, and minor diameter are all (0,0). When m=1.5mm and z=12, it is found that when the non-working side pressure angle α1=30°, the corresponding major diameter da1=19.5mm, base circle diameter db1=15.5884mm, and minor diameter df1=15.3mm; the working side pressure angle α2=37.5°, the corresponding major diameter da2=19.35mm, base circle diameter db2=14.2803mm, and minor diameter df2=15.9mm. Use the circle command to draw the external spline pitch circle, base circle, major diameter, and minor diameter in turn according to the calculated parameters, and then establish the spline size relationship expression. Use the command to create a regular curve, select the equation-driven curve and substitute it into the non-working side involute θ1 and the working side involute θ2. After drawing, it is as follows Figure 1 shown.

[0168] The two curves θ1 and θ2 intersect with the pitch circle respectively to obtain two intersection points. The intersection points are connected with the origin to obtain two straight lines l1 and l2. The angles between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively, which are α3=3.0797° and α4=6.4646°. According to the calculated tolerance, l2 is rotated counterclockwise by an angle α5=5.4076° with the xoy plane (0,0) as the origin to obtain the mirror center line l3. The curve θ2 is mirrored with l3 as the mirror center line to obtain θ′2. Then, with the origin as the center of the circle, θ′2 is rotated 30° clockwise to obtain θ″2. The plot is as follows: Figure 2 shown.

[0169] Use the circle command to draw the non-working side involute root circle curve θ3 and the non-working side root circle radius ρ Fe1 =0.6mm, use the tangent command to make the curve θ3 tangent to df1 and tangent to θ1, a3=8.2331 and b3=-0.2644 are the horizontal and vertical coordinate values ​​of the center position of the curve θ3; use the circle command to draw the working side involute root circle curve θ4, the working side root circle radius ρ Fe2 =0.45mm, use the tangent command to make the curve θ4 tangent to df2 and θ2″′, a4=8.3482 and b4=-0.9311 are the horizontal and vertical coordinate values ​​of the center position of the curve θ4; finally, create a new straight line l4, use the tangent command to make the straight line tangent to the curves θ3 and θ4 at the same time, and draw as shown Figure 3 shown.

[0170] Keep the closed curves composed of da2, θ1, θ3, l4, θ4, and θ″2 in sequence to obtain the single tooth profile of the external spline, such as Figure 4Select the closed curve, click the feature, thickness b = 9mm, and you can extrude a tooth external spline. Select the tooth profile extrusion surface to execute the array surface command, select the number and interval in the bevel direction, the number is 12, and the interval is 30°, so as to obtain an asymmetric involute external spline, as shown in Figure 5 shown.

[0171] Create a new part and then model the internal spline. Create a sketch on the xoy surface. The centers of the pitch circle, base circle, major diameter, and minor diameter are all (0,0). When m=1.5mm and z=12, it is concluded that: when the non-working side pressure angle α1=30°, the corresponding major diameter da5=20.7mm, base circle diameter db5=15.5884mm, and minor diameter df5=16.7972mm; the working side pressure angle α2=37.5°, the corresponding major diameter da6=20.1mm, base circle diameter db6=14.2803mm, and minor diameter df6=16.7907mm. Use the circle command to draw the internal spline pitch circle, base circle, major diameter, and minor diameter in sequence according to the calculated parameters, and then establish the spline size relationship expression. Use the command to create a regular curve, select the equation-driven curve and substitute it into the non-working side involute θ5 and the working side involute θ6. After drawing, it looks like this: Figure 6 shown.

[0172] The two curves θ5 and θ6 intersect with the pitch circle respectively to obtain two intersection points. The intersection points are connected with the origin to obtain two straight lines l5 and l6, and the angles between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively, which are α6=3.0797° and α7=6.4646°. According to the calculated tolerance, l5 is rotated clockwise by an angle α8=5.4076° with the (0,0) point of the xoy plane as the origin to obtain the mirror center line l7. The curve θ5 is mirrored with l7 as the mirror center line to obtain θ5′. With the origin as the center of the circle, θ6 is rotated 30° clockwise to obtain θ6′. The plot is as follows: Figure 7 shown.

[0173] Use the circle command to draw the root circle curve θ7. The root circle radius uses the non-working side root circle radius ρ Fe1 =0.6mm, use the tangent command to make θ7 tangent to θ5′ and θ6′ at the same time, a7=9.3797 and b7=-2.1219 are the horizontal and vertical coordinates of the center position of curve θ7, and draw it as shown Figure 8 shown.

[0174] Keep the closed curves composed of df6, θ′5, θ7, and θ′6 in sequence to obtain the single tooth profile of the internal spline, such as Fig. 9Select the closed curve, click Stretch, and set the thickness b = 9mm to extrude an internal spline of a tooth. Select the tooth profile stretching surface to execute the array surface command, select the number and interval in the bevel direction, the number is 12, and the interval is 30°, thus obtaining an asymmetric involute internal spline, as shown in Fig.10 shown.

[0175] Create a new assembly file in NX software and import the internal and external spline models into the assembly file. Enter the command to move the component to rotate the external or internal spline 180° around the axis or axis direction. Enter the concentric constraint in the assembly constraint command to ensure the concentricity of the internal and external splines. Apply contact alignment to make the tensile surfaces with the same involute pressure angle fit together. The assembly structure is as follows: Fig.11 shown.

[0176] The pressure angles on the working and non-working sides of the involute spline are set to 30° and 45° and 37.5° and 45° to complete the asymmetric involute spline model, and finite element simulation analysis is performed on the 30° and 37.5° splines, 30° and 45° splines, and 37.5° and 45° splines.

[0177] According to the material properties of 45 steel, the edited material mass density is 7.85e-9, Young's modulus is 2.1e5, and Poisson's ratio is 0.3. In the finite element analysis, the inner spline is fixed, and the bending moment is applied to the outer spline. The total bending moment applied is 50N·m. Since the finite element analysis process is an analysis of a single tooth, the total number of spline teeth is 12, so the bending moment acting on each pair of teeth is 4.1667N·m.

[0178] In the finite element simulation stage, in order to ensure that the simulation results are close to the actual results, the grid needs to be divided evenly and finely, such as Fig.12 As shown in the figure, for the meshing of a single tooth, one of the key teeth of the external spline is divided into 6 parts, and one of the key teeth of the internal spline is divided into 6 parts. The meshing of a single tooth is axisymmetric and symmetrical. According to the properties, the single side of the external spline and the internal spline is divided into 3 types of meshing, namely the involute part, the tooth root transition curve part, and the rest. If the meshing is too fine, there will be too many meshes, causing the computer to waste too much computing power. Therefore, the involute part is meshed more densely, the tooth root transition curve part is divided regularly and orderly according to the tooth root shape, and the rest is arranged with sparse meshes.

[0179] When the working surface pressure angle of 30° and 37.5° splines is 30°, the load distribution of the external spline and the load distribution of the internal spline are as follows: Fig.13 , 14 As shown in Figure 1, the maximum normal contact stress on the outer spline surface is 157.3MPa, and the maximum normal contact stress on the inner spline surface is 123.7MPa. When the pressure angle is 37.5°, the load distribution of the outer spline and the load distribution of the inner spline are as follows: Fig.15 , 16 As shown, the maximum normal contact stress on the outer spline surface is 135.6MPa, and the maximum normal contact stress on the inner spline surface is 141.3MPa.

[0180] The involute pressure angles on both sides are 30° and 37.5°, 30° and 45°, and 37.5° and 45° respectively. When the working surfaces are tensile surfaces with involute pressure angles of 30°, 37.5°, and 45° respectively, the maximum normal contact stress on the external spline surface obtained by finite element analysis is shown in Table 1.

[0181] Table 1 Comparison of the maximum normal contact stress on the involute tensile surface of the external spline (MPa)

[0182]

[0183] It can be seen that when the involute pressure angle of the working surface is increased, the maximum normal contact stress of the external spline will decrease; when the pressure angle of the working surface remains unchanged, appropriately increasing the pressure angle of the non-working surface will reduce the maximum normal contact stress of the working surface. The same is true for the internal spline. Therefore, when using a large pressure angle as the working side, the root bending strength and tooth surface contact strength are significantly enhanced. At the same time, selecting a smaller pressure angle on the non-working side will significantly increase the tooth top thickness and avoid the risk of broken teeth.

Claims

1. A method for modeling an asymmetric involute spline, characterized in that: The following steps are involved: Step 1: Determine the basic parameters of the asymmetric involute spline; Step 2: Determine the calculation formula for the external spline size, and define the involute curves θ1 and θ2 on the non-working side and the working side of the external spline, mirror θ2 to obtain θ′2, and then rotate θ′2 clockwise 360 / z to obtain θ″2; define the equations of the involute root circle curves θ3 and θ4 on the non-working side and the working side, and define a straight line l4 so that its curves θ3 and θ4 are tangent at the same time. The final closed curve is the external spline tooth profile; Step 3: Determine the calculation formula for the internal spline size, and define the involute curves θ5 and θ6 on the non-working side and working side of the internal spline, mirror θ5 to obtain θ′5, and then rotate θ6 clockwise 360 / z to obtain θ′6; define the tooth root circle curve equation θ7, and make the curve θ7 tangent to θ′5 and θ′6 at the same time. The final closed curve is the internal spline tooth profile; Step 4: Model and assemble the internal and external splines in the modeling software.

2. The method for modeling an asymmetric involute spline according to claim 1, characterized in that: The specific contents of the basic parameters described in step 1 include: (1) Determine the pressure angle: The involutes on both sides of the spline are divided into two types: the working side and the non-working side. The pressure angle of the involute on the non-working side is set to α1, and the pressure angle of the involute on the working side is set to α2. Both α1 and α2 are selected from 30°, 37.5° and 45°, and the values ​​of α1 and α2 are different; (2) Determine the tolerance e: The total tolerance of the total tooth width and tooth thickness is calculated as follows: (T+λ)=40i1±160i2, where i1 is the tolerance based on the pitch circle diameter D; the tolerance unit i is: When D≤500mm, When D>500mm, i=0.004D+2.1, i2 is the basic tolerance based on the basic tooth gap width E or basic tooth gap thickness S, and the tolerance unit i is: or Where T is the processing tolerance, λ is the comprehensive tolerance; Comprehensive tolerance λ: Cumulative tolerance of tooth pitch F p : Where L is half of the circumference of the graduation circle; Tooth profile tolerance f f : in is the tolerance factor, Tooth tolerance F β : Where g is the spline length; The tolerance e should be between T+λ and λ, that is, the maximum actual tooth thickness is 0.5πz-λ, and the minimum actual tooth thickness is 0.5πz-(T+λ); (3) Determine the change angle x that reflects the tolerance when using the mirror command during the modeling process: 2x*r=Se; Where r is the pitch circle radius; S = 0.5πm; then 3. The method for modeling an asymmetric involute spline according to claim 2, characterized in that: Step 2: The external spline tooth profile is determined by the following steps: (1) Determine the calculation formula for external spline size: Pitch circle diameter d = mz, where z is the number of teeth and m is the module; Two different pressure angle major diameter formulas for external splines: da1 = D ee1 , da2=D ee2 , where da1 is the major diameter corresponding to the involute on the non-working side, D ee1 is the basic size of the major diameter of the non-working side, da2 is the major diameter corresponding to the involute of the working side, D ee2 Is the basic size of the major diameter of the working side; among them, 30° flat tooth root and round tooth root: D ee =m(z+1); 37.5° round tooth root: D ee =m(z+0.9); 45° round tooth root: D ee = m(z+0.8); The base circle formula of the external spline is: db1 = dcos(α1), db2 = dcos(α2), where db1 is the base circle diameter corresponding to the involute on the non-working side, and db2 is the base circle diameter corresponding to the involute on the working side; Two different pressure angle minor diameter formulas for external splines: df1 = D ie1 , df2=D ie2 , where df1 is the minor diameter corresponding to the involute on the non-working side, D ie1 is the basic size of the minor diameter on the non-working side, df2 is the minor diameter corresponding to the involute on the working side, D ie2 It is the basic size of the working side path; The basic dimensions of the external spline minor diameter are as follows: 30° flat tooth root: D ie =m(z-1.5); 30° round tooth root: D ie =m(z-1.8); 37.5° round tooth root: D ie =m(z-1.4); 45° round tooth root: D ie = m(z-1.2); Root fillet radius of external spline: 30° flat tooth root: ρ Fe =0.2m; 30° round tooth root: ρ Fe =0.4m; 37.5° round tooth root: ρ Fe =0.3m; 45° round tooth root: ρ Fe =0.25m; (2) Define the involute equations of the non-working side and the working side Non-working side involute θ1: Where, t1 is the angle parameter controlling the generation of the involute θ1 on the non-working side, and the value is t1 = 0; Working side involute θ2: Where, t2 is the angle parameter for controlling the generation of the involute θ2 on the working side, and the value is t2 = 0; The two curves θ1 and θ2 intersect with the pitch circle respectively, and two intersection points are obtained. The intersection points are connected with the center of the circle to obtain two straight lines l1 and l2. The angles α3 and α4 between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively. l2 is rotated in the counterclockwise direction by an angle α5=x-(α4-α3) / 2 to obtain the mirror center line l3. The curve θ2 is mirrored with l3 as the mirror center line to obtain θ′2. Then θ′2 is rotated clockwise by 360 / z to obtain θ″2. (3) Define the involute root circle curve equations of the non-working side and the working side Non-working side involute tooth root circle curve θ3: In the formula, ρ Fe1 is the radius of the tooth root circle on the non-working side, a3 and b3 are the horizontal and vertical coordinates of the center position of the curve θ3; Working side involute tooth root circle curve θ4: In the formula, ρ Fe2 is the radius of the tooth root circle on the non-working side, a4 and b4 are the horizontal and vertical coordinates of the center position of the curve θ4; (4) Determine the external spline tooth profile Let curve θ3 be tangent to df1 and tangent to curve θ1, and let curve θ4 be tangent to df2 and tangent to curve θ″2. Create a new straight line l4, which is tangent to curve θ3 and θ4 at the same time, and keep the closed curve composed of da2, curve θ1, θ3, straight line l4, curve θ4 and θ″2 to obtain the external spline tooth profile.

4. The method for modeling an asymmetric involute spline according to claim 3, characterized in that: Step 3: The internal spline tooth profile is determined by the following steps: (1) Determine the calculation formula for internal spline size: Pitch circle diameter d = mz, where z is the number of teeth and m is the module; Two different pressure angle major diameter formulas for internal splines: da5 = D ei1 , da6 = D ei2 , where da5 is the major diameter corresponding to the involute on the non-working side, D ei1 is the basic size of the major diameter of the non-working side, da6 is the major diameter corresponding to the involute of the working side, D ie2 Is the basic size of the major diameter on the working side; among which, 30° flat tooth root: D ei =m(z+1.5); 30° round tooth root: D ei =m(z+1.8); 37.5° round tooth root: D ei =m(z+1.4); 45° round tooth root: D ei = m(z+1.2); The base circle formula of the internal spline is: db5 = dcos (α1), db6 = dcos (α2), where db5 is the base circle diameter corresponding to the involute on the non-working side, and db6 is the base circle diameter corresponding to the involute on the working side; Two different pressure angle minor diameter formulas for internal splines: Where, df5 is the minor diameter corresponding to the involute on the non-working side, df6 is the minor diameter corresponding to the involute on the working side, and es v / tan(α1) and es v / tan(α1) are the upper deviations of the inner spline diameter; h s1 、h s2 h is the tooth root working height; s1 and h s2 The specific formula is: 30° flat tooth root, round tooth root: h s =0.2m; 37.5° round tooth root: h s =0.55m; 45° round tooth root: h s =0.5m; Root fillet radius of internal spline: 30° flat tooth root: ρ Fe =0.2m; 30° round tooth root: ρ Fe =0.4m; 37.5° round tooth root: ρ Fe =0.3m; 45° round tooth root: ρ Fe =0.25m; (2) Define the involute equations of the non-working side and the working side Non-working side involute θ5: Wherein, t5 is the angle parameter controlling the generation of the involute θ5 on the non-working side, and the value is t5 = 0; Working side involute θ6: Wherein, t6 is the angle parameter for controlling the generation of the involute θ6 on the working side, and the value is t6 = 0; The two curves θ5 and θ6 intersect with the pitch circle respectively, and two intersection points are obtained. The intersection points are connected with the center of the circle to obtain two straight lines l5 and l6. The angles α6 and α7 between the two straight lines and the positive semi-axis direction of the x-axis are measured respectively. l5 is rotated clockwise by an angle α8=x-(α7-α6) / 2 to obtain the mirror center line l7. The curve θ5 is mirrored with l7 as the mirror center line to obtain θ′5. Then θ6 is rotated clockwise by 360 / z to obtain θ′6. (3) Define the tooth root circle curve equation Tooth root circle curve θ7: In the formula, ρ Fe1 is the root circle radius of the smaller pressure angle side, a7 and b7 are the horizontal and vertical coordinates of the center position of curve θ7; (4) Determine the internal spline tooth profile Let curve θ7 be tangent to curves θ′5 and θ′6 at the same time, retain the closed curve formed by df6, curves θ′5, θ7 and θ′6, and obtain the internal spline tooth profile.

5. The method for modeling an asymmetric involute spline according to claim 4, characterized in that: The specific process of modeling described in step 4 is as follows: (1) Determine the basic parameters of asymmetric involute splines The side with a larger involute pressure angle is selected as the working side, and the side with a smaller pressure angle is selected as the non-working side, that is, α2>α1, and the pressure angle of the non-working side of the involute spline is set to 30° and the pressure angle of the working side is set to 37.5° to enhance the load-bearing effect of the asymmetric involute spline during operation; when m=1.5mm, z=12, according to the tolerance e value between T+λ and λ, the tolerance is selected as e=0.126mm, then the angle in the mirror command required in the modeling process is (2) Application of UG NX modeling software Model the internal and external splines separately, and create sketches on the xoy plane. First, draw the pitch circle, major diameter, and minor diameter according to the relevant parameters through the circle command; then use the command to create a regular curve, select the curve driven by the equation, draw two involutes with different pressure angles, use the mirror command for one of the involutes, and implement the command to rotate around the center point for the other involute; then the external spline draws the root circles of different pressure angles on both sides according to the relevant parameters of the root circle, and implements the command that the root circle is tangent to the involute drawn with the same pressure angle and the minor diameter of the external spline drawn with the same pressure angle. According to the relevant parameters of the root circle, the root circle corresponding to the smaller pressure angle of the internal spline is tangent to the two involutes with different pressure angles on both sides at the same time, and finally form closed curves to obtain the tooth profiles of the internal and external splines; then stretch the matrix to get a single tooth, and finally set the number of teeth to 12 with the center of the pitch circle as the center, and complete the modeling of the internal and external splines through the circular array surface.

6. The method for modeling an asymmetric involute spline according to claim 5, characterized in that: The specific assembly process described in step 4 is: create a new assembly file, import the inner and outer spline models into the assembly file, enter the command to move the component to rotate the outer spline or inner spline 180° around the axis or axis direction, enter the concentricity constraint in the assembly constraint command to ensure the concentricity of the inner and outer splines, apply contact alignment to make the stretching surfaces with the same involute pressure angle fit together.

7. The asymmetric involute spline generated by the modeling method according to claim 6, characterized in that: The pressure angles on both sides of the spline are different, and the involutes on both sides of the spline tooth profile and the external spline tooth root transition curve are asymmetric.

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