Universal gear modification method

Abstract

The invention discloses a universal gear modification method, which comprises the following steps of: establishing a standard involute profile equation according to common known quantity of a gear; constructing a modification quantity function equation by adopting a figure interaction mode; and superposing the constructed modification quantity functional equation to the established standard involute tooth profile equation to obtain a modification involute tooth profile equation, and modifying the gear according to the modification involute tooth profile equation. According to the method, a figure interaction mode is adopted, the design information of the K-shaped graph in the two-dimensional electronic chart is extracted, and the modification curve in the K-shaped graph can be adjusted at will according to the requirements of the K-shaped graph; the design requirements of all K-shaped graphs can be met; various shaping modes such as edge and root shaping, drum shape shaping, slope shaping and combined shaping can be realized; and the universality and the flexibility are high.

Description

Technical Field

[0001] The invention belongs to the technical field of involute gear tooth profile modification, and in particular relates to a universal gear profile modification method. Background Art

[0002] As a transmission component, involute gears have been widely used in aerospace, automobile, wind power, shipbuilding and many other fields due to their excellent characteristics such as high precision, high efficiency and high transmission ratio. Due to the manufacturing errors and assembly errors in the assembly process of the gear pair, during the transmission process, as the load continues to increase, the tooth surface will produce elastic deformation and thermal deformation, causing the meshing state of the gear pair to deteriorate. If there is interference in the transmission process, impact, noise, vibration and other undesirable phenomena will be generated during the meshing and disengaging process, resulting in the reduction of the transmission stability, load-bearing performance, service life and other indicators of the gear, which can no longer meet the high efficiency and low noise requirements of the gear transmission. Therefore, in order to suppress the transmission whistle, reduce the gear pair load deformation, meshing impact, and improve the comprehensive transmission performance of the gear, the gear needs to be modified.

[0003] Tooth profile modification refers to superimposing a normal deviation on the normal direction of the standard tooth profile curve. This normal deviation is usually called the modification amount. The modification amount has a certain functional relationship with the gear extension or angular parameter. This function is usually called the modification amount function. Currently, the commonly used modification amount functions are usually straight lines, arcs, parabolas, high-order polynomials, or a combination of the above forms. The above methods all require manual construction of the modification amount function and solve the modification coefficient based on the modification parameters. When using a high-order polynomial as the modification amount function, there may be no accurate modification coefficient solution to meet the K-shaped diagram requirements.

[0004] The invention with application number 202210249365.2 provides a gear modification design method, device and storage medium, the method comprising: establishing a gear pair model corresponding to the target gear pair, and simulating the gear pair model to obtain the gear contact spots and gear misalignment of the target gear pair during operation; the target gear pair includes a driving gear and a driven gear; determining the relative tooth profile inclination deviation range of the target gear pair according to the gear contact spots, and determining the relative tooth direction inclination deviation range of the target gear pair according to the gear misalignment; determining the parameter standard corresponding to the preset working condition, and performing parametric analysis on the relative tooth profile inclination deviation range and the relative tooth direction inclination deviation range based on the parameter standard to obtain the parameter analysis value, and determining the tooth profile modification amount and tooth direction modification amount of the driving gear and the driven gear according to the parameter analysis value. However, the above invention also has poor versatility. Summary of the invention

[0005] In view of the technical problems that the current shaping methods are not universal and have poor flexibility, the present invention proposes a universal gear shaping method. Compared with the traditional shaping method, the present invention has strong universality and high flexibility. The user can change the shaping amount function at will according to the K-shaped diagram, and automatically construct the shaping amount function until the shaping design requirements are met.

[0006] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0007] A universal gear shaping method comprises the following steps:

[0008] S1. According to the commonly known quantities of gears, the end face standard involute tooth profile equation is established, and the modification quantity function to be solved is superimposed on the standard involute tooth profile equation to obtain the modified involute tooth profile equation to be solved;

[0009] S2. Adopting the digital-graphic interaction mode, constructing the modification amount function: drawing the K-shaped diagram including the modification information of each position on the tooth profile in the form of a two-dimensional electronic drawing board in a two-dimensional electronic drawing file, keeping the origin of the K-shaped diagram coincident with the origin in the two-dimensional electronic drawing board, using programming software to read the data information of the entity segment of the modification curve in the two-dimensional electronic drawing file, so as to solve the modification amount function corresponding to each segment of the modification curve, and forming a set of the modification amount functions corresponding to all the modification curves to obtain the modification amount function;

[0010] S3, substituting the modification amount function constructed in step S2 into the modified involute tooth profile equation to be solved established in step S1, obtaining the modified involute tooth profile equation, and modifying the gear according to the modified involute tooth profile equation.

[0011] The method of superimposing the modification amount function to be solved on the standard involute tooth profile equation in step S1 to obtain the modified involute tooth profile equation to be solved is:

[0012] Assume that the commonly known quantity of the gear is the normal pressure angle α n , normal modulus m n , number of teeth z, helix angle β, modification factor x n , the vector equation of the diameter of any point on the standard involute tooth profile is expressed as: 0 (φ)=[x 0 ,y 0 ,z 0 ],in, Since the tooth profile modification is performed on the end face tooth profile, the normal surface parameters are converted into end surface parameters: m t =m n / cos(β),tan(α t )=tan(α n ) / cos(β), r b =m t zcos(αt ) / 2, where m t is the end pressure angle, r b is the base circle radius, δ 0 is the base circle half angle, φ is the angle parameter, α t is the end pressure angle;

[0013] Assume r t (φ)=[x 0 ',y 0 ',z 0 '] is the unit tangent vector of the standard involute, then the unit normal vector of the standard involute is r n (φ)=r t (φ)×k, let r n (φ)=[n x ,n y ,n z ], k is the Z-axis unit vector, k = [0, 0, 1];

[0014] Assume that the modification function is Q(φ), and superimpose the modification function on the normal direction of the standard involute to obtain the modified involute tooth profile equation r 1 (φ), then r 1 (φ)=r 0 (φ)+Q(φ)·r n (φ), let r 1 (φ)=[x 1 ',y 1 ',z 1 '], it can be known that the modified involute tooth profile equation to be solved is:

[0015] The K-shaped diagram includes a modification curve and a design tolerance range of the K-shaped diagram. The horizontal axis of the coordinate of the K-shaped diagram is the modification amount, and the vertical axis of the coordinate of the K-shaped diagram is the extension, extension angle or the diameter corresponding to the corresponding extension.

[0016] The modified curve in the K-shaped diagram includes, but is not limited to, a straight line, an arc, or a combination of a straight line and an arc; the modified curve is defined by one or a combination of the following methods:

[0017] Ⅰ. Single shaping function: The shaping curve is represented by a single shaping function, which is a straight line function, circular arc function or other known mathematical functions;

[0018] II. Combination of two or more shaping functions: The shaping curve is composed of two or more shaping function segments, each of which is independently represented by a straight line function, an arc function or other mathematical function; these shaping function segments are continuously connected.

[0019] The shaping curve entity segment in the two-dimensional electronic drawing file is composed of a number of group codes and group values. The group code is the code of the data type, and the group value is a numerical value in the conventional sense. The group code and the group value together represent the characteristics of the entity segment.

[0020] The data information of the shaping curve entity segment includes the curve type, the number of curve segments, and the curve position; the curve type includes the line type of each shaping curve segment: straight line segment, arc segment; the curve position information includes the starting point, end point, initial angle, end angle, center coordinates and radius of each shaping curve segment; the number of curve segments is the number of endpoint elements of each shaping curve segment.

[0021] The method for constructing the shaping amount function is: extracting the data information of the shaping curve entity segment in the two-dimensional electronic drawing file in which the vertical axis of the K-shaped graph is the extension and the horizontal axis of the K-shaped graph is the shaping amount through programming software. Since n known points are given in the K-shaped graph, there are (n-1) shaping curves in total. Therefore, the shaping curve is a piecewise function. Let the number of straight line segments be n. 1 , the number of arc segments is n 2 , then (n-1) = n 1 +n 2 ; Let the shaping function corresponding to each straight line segment be expressed as q i (φ), where i = 1, 2, ..., n 1 , then the set of all straight line segment shaping functions is Suppose the shaping function corresponding to each arc segment is expressed as f j (φ), where j = 1, 2, ..., n 2 , then the set of all arc segment shaping functions is Therefore, the modification function Q(φ) = Q 1 (φ)∪Q 2 (φ).

[0022] The method for constructing the shaping function corresponding to the straight line segment is as follows: if the entity segment is a straight line segment, the straight line segment information is saved in the matrix M 1 middle: Matrix M 1 The number of rows is the number of straight line segments n 1 , the curve position information is the coordinates of the endpoints of the straight line segment, [x i ,y i ,x i+1 ,y i+1 ],i=1:(2n 1 -1);

[0023] According to the matrix M 1 The element information of each row can be used to solve the slope of the straight line segment modification curve:

[0024] If the slope k of the modified curve of the straight line segment t does not exist, then the shaping function q corresponding to this shaping curve i (φ)=x i =x i+1 , domain φ∈[min[y i / r b ,y i+1 / r b ],max[y i / r b ,y i+1 / r b ]], at this time if x i =x i+1 = 0, indicating that the tooth profile in this section is not modified to a standard involute. i =x i+1 ≠0, indicating that the modified tooth profile in this section is the standard tooth profile normal equidistance x i Or the result after rotating a certain angle clockwise around the Z axis;

[0025] If the slope k of the modified curve of the straight line segment t When exists, the shaping function corresponding to this shaping curve is Domain φ∈[min[y i / r b ,y i+1 / r b ],max[y i / r b ,y i+1 / r b ]], this case is pressure angle shaping or slope shaping.

[0026] The method for constructing the shaping function corresponding to the arc segment is as follows:

[0027] If the entity segment is an arc segment, save the arc segment information to the matrix M 2 middle: Matrix M 2 The number of rows is the number of arc segments n 2 , the curve position information is the endpoint coordinates of the arc segment [xc j ,yc j ,r j ,α j ,α' j ],j=1:n 2 , (x, y) is the coordinate value of the center of the circle, r is the radius, α j is the starting angle, α' j is the end angle;

[0028] When the solid segment is an arc, since the modification curves are all convex, the positive pressure angle is maintained at all locations of the tooth profile. Therefore, the modification amount function when the solid segment is an arc is

[0029] After the shaping function of each arc segment is determined, the definition domain of each segment shaping function needs to be solved. At this time, the starting angle α j The value of the end angle α' j There are two cases:

[0030] ③When α j >α' j When α' j =α' j +360;

[0031] ④When α j <α' j When α' j =α' j :

[0032] Both of the above situations satisfy the formula: L(α)=yc j +r j sin(α), where α is the angular parameter of the arc segment and L(α) refers to the corresponding modification amount at the endpoint;

[0033] Therefore, the domain of the independent variable is: φ∈[min[L(α j ) / r b ,L(α' j ) / r b ],max[L(α j ) / r b ,L(α j ') / r b ]], this case is drum shaping, which can achieve the effects of parabola shaping, high-order parabola shaping, and high-order polynomial shaping.

[0034] The shaping amount function is: When the entity segment is a straight line, the shaping amount equation set is: The set of shaping equations when the solid segment is an arc is: According to the definition domain, sort and merge the modification equations of each segment from the root to the top of the tooth to obtain the modification function

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] 1. The present invention automatically constructs the corresponding modification equation in each angular parameter interval through an algorithm program using the extracted data information and superimposes it on the standard involute tooth profile equation to obtain the modified involute tooth profile equation, which is convenient and fast with a high degree of automation.

[0037] 2. The present invention adopts a digital-shape interactive mode to extract the design information of the K-shaped diagram in the two-dimensional electronic drawing plate, and the user can arbitrarily adjust the shaping curve in the K-shaped diagram according to the requirements of the K-shaped diagram.

[0038] 3. The present invention can realize various shaping modes such as edge shaping, root shaping, drum shaping, slope shaping, and combined shaping.

[0039] 4. The present invention has strong versatility and can meet all K-shaped diagram design requirements.

[0040] 5. The present invention can achieve smoothing of the tooth profile after modification. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 It is a schematic diagram of tooth profile modification of the present invention.

[0043] Figure 2 K-shaped schematic diagram

[0044] Figure 3 A flow chart is constructed for the shaping amount function of the present invention.

[0045] Figure 4 Schematic diagram of a K-shaped diagram according to an embodiment of the present invention.

[0046] Figure 5 Schematic diagram of the relationship between the shaping amount and the extension length according to an embodiment of the present invention.

[0047] Figure 6 is a shaping amount function according to an embodiment of the present invention.

[0048] Figure 7 1 is a comparison diagram of a standard tooth profile and a modified tooth profile according to an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] A universal gear shaping method comprises the following steps:

[0051] S1. According to the common known quantities of gears, the end face standard involute tooth profile equation is established, and the modification quantity function to be solved is superimposed on the standard involute tooth profile equation to obtain the modified involute tooth profile equation to be solved.

[0052] During the grinding process of involute spur gears and helical gears, the helical surface obtained by the spiral motion of the end face involute is used to calculate the grinding wheel section. Therefore, it is necessary to establish the end face standard involute tooth profile equation and the modified involute tooth profile equation. For the convenience of calculation, this embodiment establishes the vector equation of the diameter of any point on the standard involute tooth profile and the modified involute tooth profile equation in the Cartesian coordinate system.

[0053] Furthermore, the commonly known quantities of gears are the normal pressure angle α n , normal modulus m n , number of teeth z, helix angle β, modification factor x n Taking the tooth shape at the right end of the tooth groove as an example, Figure 1 It can be seen that the vector equation of the diameter of any point on the standard involute tooth profile is expressed as: 0 (φ)=[x 0 ,y 0 ,z 0 ],in:

[0054]

[0055] Since the tooth profile modification is performed on the end face tooth profile, it is necessary to convert the normal surface parameters into end surface parameters:

[0056] m t =m n / cos(β) (2)

[0057] tan(α t )=tan(α n ) / cos(β) (3)

[0058] r b =m t zcos(α t ) / twenty four)

[0059] In the formula, m t is the end pressure angle, r b is the base circle radius, δ 0 is the base circle half angle, φ is the angle parameter, α t is the end pressure angle.

[0060] Assume r t (φ)=[x 0 ',y 0 ',z 0'] is the unit tangent vector of the standard involute, then the unit normal vector of the standard involute is r n (φ)=r t (φ)×k, let r n (φ)=[n x ,n y ,n z ]. k is the unit vector of the Z axis, k = [0, 0, 1].

[0061] Assume that the modification function is Q(φ), and superimpose the modification function on the normal direction of the standard involute to obtain the modified involute tooth profile equation r 1 (φ), then r 1 (φ)=r 0 (φ)+Q(φ)·r n (φ), let r 1 (φ)=[x 1 ',y 1 ',z 1 '], it can be known that the modified involute tooth profile equation to be solved is:

[0062]

[0063] S2. Use the digital-graphic interaction mode to construct the shaping amount function: draw the K-shaped diagram including the shaping information of each position on the tooth profile in the form of a two-dimensional electronic drawing board in a two-dimensional electronic drawing file, and keep the origin of the K-shaped diagram coincident with the origin in the electronic drawing board. Use programming software to read the data information of the entity segments (ENTITIES) of the shaping curve in the two-dimensional electronic drawing file to solve the shaping amount function corresponding to each segment of the shaping curve, and combine the shaping amount functions corresponding to all the shaping curves into a set to obtain the shaping amount function.

[0064] The shaping curve entity segment in the two-dimensional electronic drawing file is composed of several group codes and group values. The group code is the code of the data type, and the group value is a numerical value in the conventional sense, specifically the location information of the entity segment, including the starting point, end point, initial angle, end angle, center coordinates and radius. The group code and group value together represent the characteristics of the entity segment.

[0065] The entity segment data information includes the curve type (name), the number of curve segments (number), and the curve position (position); the curve type includes the line type of each segment of the modified curve: straight line segment, arc segment; the position information includes the starting point, end point, initial angle, end angle, center coordinates and radius of each segment of the modified curve; the number of curve segments is the number of endpoint elements of each segment of the modified curve.

[0066] The K-shaped diagram is a diagram that specifies that the tooth profile error fluctuation of the gear after modification is within the two tolerance bands specified in the drawing requirements. The K-shaped diagram is usually a known diagram provided to the customer, and the K-shaped diagram includes the modification information of each position on the tooth profile.

[0067] The horizontal axis of the coordinate of the K-shaped diagram is the shaping amount, and the vertical axis of the coordinate can be the extension length, the extension angle or the diameter corresponding to the corresponding extension length.

[0068] Assume that the K-shaped graph is Figure 2 As shown, the vertical axis of the K-shaped diagram is the extension. The K-shaped diagram has n (usually n ≥ 3) known points. Points A, B, ... N from the tooth root to the tooth top are the known points given in the K-shaped diagram, and the coordinates are (q 1 ,y 1 ), (q 2 ,y 2 )......(q n ,y n ), corresponding to the normal modification amount at each point in the tooth profile. The dotted box in the figure is the design tolerance range of the K-shaped diagram; the red curve is the modification curve, and the form of the modification curve includes but is not limited to a straight line, an arc, or a combination of a straight line and an arc.

[0069] The shaping curve is defined by one or a combination of the following methods:

[0070] Ⅰ. Single shaping function: The shaping curve is represented by a single shaping function, which can be a straight line function, an arc function, or other known mathematical functions;

[0071] II. Combination of two or more shaping functions: A shaping curve can be composed of two or more shaping function segments, each segment can be independently represented by a straight line function, an arc function, or other mathematical functions; these shaping function segments are continuously connected.

[0072] The specific process of constructing the shape modification function is as follows: Figure 3 As shown:

[0073] The vertical axis of the K-shaped graph in this embodiment is the extension. Since n (usually n ≥ 3) known points are given in the K-shaped graph, there are a total of (n-1) shaping curves, so the shaping curve is a piecewise function. Suppose the number of straight line segments is n 1 , the number of arc segments is n 2 , then (n-1) = n 1 +n 2 ; Let the shaping function corresponding to each straight line segment be expressed as q i (φ), where i = 1, 2, ..., n 1 , then the set of all straight line segment shaping functions is Suppose the shaping function corresponding to each arc segment is expressed as fj (φ), where j = 1, 2, ..., n 2 , then the set of all arc segment shaping functions is Therefore, the modification function Q(φ) = Q 1 (φ)∪Q 2 (φ).

[0074] The entity segment (ENTITIES) data in the two-dimensional electronic drawing file is extracted through programming software, including the curve type (name), the number of curve segments (number), and the curve position (position).

[0075] If the entity segment is a straight line segment (LINE), save the straight line segment information to the matrix M 1 middle:

[0076]

[0077] Matrix M 1 The number of rows is the number of straight line segments n 1 (number), the curve position (position) information is the endpoint coordinates of the straight line segment, [x i ,y i ,x i+1 ,y i+1 ],i=1:(2n 1 -1).

[0078] According to the matrix M 1 The element information of each row can be used to solve the slope of the straight line segment modification curve:

[0079] If the slope k of the modified curve of the straight line segment t does not exist, then the shaping function q corresponding to this shaping curve i (φ)=x i =x i+1 , domain φ∈[min[y i / r b ,y i+1 / r b ],max[y i / r b ,y i+1 / r b ]], at this time if x i =x i+1 = 0, indicating that the tooth profile in this section is not modified to a standard involute. i =x i+1 ≠0, indicating that the modified tooth profile in this section is the standard tooth profile normal equidistance x i Or the result after rotating a certain angle clockwise around the Z axis.

[0080] If the slope k of the modified curve of the straight line segment t When exists, the shaping function corresponding to this shaping curve is Domain φ∈[min[y i / r b ,y i+1 / r b ],max[y i / r b ,y i+1 / r b ]], this case is pressure angle shaping or slope shaping.

[0081] If the entity segment is an arc segment (ARC), save the arc segment information to the matrix M 2 middle:

[0082]

[0083] Matrix M 2 The number of rows is the number of arc segments n 2 (number), the curve position (position) information is the endpoint coordinates of the arc segment [xc j ,yc j ,r j ,α j ,α' j ],j=1:n 2 (x, y) is the coordinate value of the center of the circle, r is the radius, α j is the starting angle, α' j is the ending angle.

[0084] When the solid segment is an arc, since the modification curves are all convex, the positive pressure angle is maintained at all locations of the tooth profile. Therefore, the modification amount function when the solid segment is an arc is

[0085] After the shaping function of each arc segment is determined, the definition domain of each segment shaping function needs to be solved. At this time, the starting angle α j The value of the end angle α' j There are two cases:

[0086] ⑤When α j >α' j When α' j =α' j +360.

[0087] ⑥ When α j <α' j When α' j =α' j .

[0088] Both of the above situations satisfy the following formula:

[0089] L(α)=yc j +r j sin(α) (6)

[0090] Among them, α is the angular parameter of the arc segment, and L(α) refers to the corresponding modification amount at the endpoint.

[0091] Therefore, the domain of the independent variable is: φ∈[min[L(α j ) / r b ,L(α' j ) / r b ],max[L(α j ) / r b ,L(α j ') / r b ]], this case is drum shaping, which can achieve the effects of parabola shaping, high-order parabola shaping, and high-order polynomial shaping. By adjusting the center position of the arc, the radius size, and the definition domain range, the superposition effect of drum shaping and slope shaping can also be achieved.

[0092] From the above, we can see that the set of shaping equations when the solid segment is a straight line is: The set of shaping equations when the solid segment is an arc is: According to the definition domain, the modification equations of each section are sorted and merged from the tooth root to the tooth top, and the modification function Q(φ) is obtained as follows:

[0093]

[0094] S3, substituting the modification amount function constructed in step S2 into the modified involute tooth profile equation to be solved established in step S1, obtaining the modified involute tooth profile equation, and modifying the gear according to the modified involute tooth profile equation.

[0095] The present invention, starting from the perspective of digital-shape interaction, establishes a universal shaping method based on data interaction of two-dimensional electronic drawing files. According to the storage structure of the curve entity segment in the electronic drawing file, the entity segment data including information such as curve type, number of curve segments, and curve position in the two-dimensional K-shaped drawing file is extracted. According to the entity segment data information, the corresponding shaping amount function within different angular parameter ranges is automatically constructed, and the shaping amount of each segment is superimposed on the standard profile to obtain the profile equation and coordinate point information after shaping, which lays the foundation for solving the sand profile in the subsequent grinding process of the gear. Compared with the traditional shaping method, the present invention has strong versatility and high flexibility. The user can change the shaping amount function at will according to the K-shaped diagram, and automatically construct the shaping amount function until the shaping design requirements are met.

[0096] Example

[0097] Assume the gear parameters are as follows: Normal module m n =3.45, number of teeth z=21, normal pressure angle α n =24°, helix angle β = 15°, modification factor x n =0.420419, the design parameters of K-shaped graph are as follows Figure 4 As shown, for ease of observation, the tooth top modification amount is set to 0.1mm, and the tooth root modification amount is set to 0.08mm. The coordinates of the known points in the figure are A (0.08, 10.706), B (0.042, 12.152), C (0.013, 13.917), D (0, 18), E (0.012, 21.878), F (0.055, 24.047), and G (0.1, 25.4).

[0098] according to Figure 4 Draw a two-dimensional electronic drawing with the provided K-shaped drawing dimensions, compile a related program to read the K-shaped drawing design information, and redraw the K-shaped drawing in the programming software as shown below Figure 5 As shown:

[0099] The number of known points is n = 7, there are 6 solid segments, and the number of straight line segments is n 1 =2, the number of arc segments n 2 =4.

[0100]

[0101] The automatically constructed modification function Q(φ) is as follows: Figure 6 As shown in the figure, the modified involute tooth profile equation is obtained by superimposing the modification function on the standard involute tooth profile equation. The curve is shown in Figure 7 shown.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A universal gear shaping method, It is characterized in that The following steps are involved: S1. According to the commonly known quantities of gears, the end face standard involute tooth profile equation is established, and the modification quantity function to be solved is superimposed on the standard involute tooth profile equation to obtain the modified involute tooth profile equation to be solved; S2. Adopting the digital-graphic interaction mode, constructing the modification amount function: drawing the K-shaped diagram including the modification information of each position on the tooth profile in the form of a two-dimensional electronic drawing board in a two-dimensional electronic drawing file, keeping the origin of the K-shaped diagram coincident with the origin in the two-dimensional electronic drawing board, using programming software to read the data information of the entity segment of the modification curve in the two-dimensional electronic drawing file, so as to solve the modification amount function corresponding to each segment of the modification curve, and forming a set of the modification amount functions corresponding to all the modification curves to obtain the modification amount function; S3, substituting the modification amount function constructed in step S2 into the modified involute tooth profile equation to be solved established in step S1, obtaining the modified involute tooth profile equation, and modifying the gear according to the modified involute tooth profile equation.

2. The universal gear shaping method according to claim 1, It is characterized in that The method of superimposing the modification amount function to be solved on the standard involute tooth profile equation in step S1 to obtain the modified involute tooth profile equation to be solved is: Assume that the commonly known quantity of the gear is the normal pressure angle α n , normal modulus m n , number of teeth z, helix angle β, modification factor x n , the vector equation of the diameter of any point on the standard involute tooth profile is expressed as: 0 (φ)=[x 0 ,y 0 ,z 0 ],in, Since the tooth profile modification is performed on the end face tooth profile, the normal surface parameters are converted into end surface parameters: m t =m n / cos(β),tan(α t )=tan(α n ) / cos(β), r b =m t zcos(α t ) / 2, where m t is the end pressure angle, r b is the base circle radius, δ 0 is the base circle half angle, φ is the angle parameter, α t is the end pressure angle; Assume r t (φ)=[x 0 ',y 0 ',z 0 '] is the unit tangent vector of the standard involute, then the unit normal vector of the standard involute is r n (φ)=r t (φ)×k, let r n (φ)=[n x ,n y ,n z ], k is the Z-axis unit vector, k = [0, 0, 1]; Assume that the modification function is Q(φ), and superimpose the modification function on the normal direction of the standard involute to obtain the modified involute tooth profile equation r 1 (φ), then r 1 (φ)=r 0 (φ)+Q(φ)·r n (φ), let r 1 (φ)=[x 1 ',y 1 ',z 1 '], it can be known that the modified involute tooth profile equation to be solved is:

3. The universal gear shaping method according to claim 2, It is characterized in that The K-shaped diagram includes a modification curve and a design tolerance range of the K-shaped diagram. The horizontal axis of the coordinate of the K-shaped diagram is the modification amount, and the vertical axis of the coordinate of the K-shaped diagram is the extension, extension angle or the diameter corresponding to the corresponding extension.

4. The universal gear shaping method according to claim 3, It is characterized in that The modified curve in the K-shaped diagram includes, but is not limited to, a straight line, an arc, or a combination of a straight line and an arc; the modified curve is defined by one or a combination of the following methods: Ⅰ. Single shaping function: The shaping curve is represented by a single shaping function, which is a straight line function, circular arc function or other known mathematical functions; II. Combination of two or more shaping functions: The shaping curve is composed of two or more shaping function segments, each of which is independently represented by a straight line function, an arc function or other mathematical function; these shaping function segments are continuously connected.

5. The universal gear shaping method according to claim 1 or 4, It is characterized in that The shaping curve entity segment in the two-dimensional electronic drawing file is composed of a number of group codes and group values. The group code is the code of the data type, and the group value is a numerical value in the conventional sense. The group code and the group value together represent the characteristics of the entity segment.

6. The universal gear shaping method according to claim 5, It is characterized in that The data information of the shaping curve entity segment includes the curve type, the number of curve segments, and the curve position; the curve type includes the line type of each shaping curve segment: straight line segment, arc segment; the curve position information includes the starting point, end point, initial angle, end angle, center coordinates and radius of each shaping curve segment; the number of curve segments is the number of endpoint elements of each shaping curve segment.

7. The universal gear shaping method according to claim 1 or 6, It is characterized in that The method for constructing the shaping amount function is: extracting the data information of the shaping curve entity segment in the two-dimensional electronic drawing file in which the vertical axis of the K-shaped graph is the extension and the horizontal axis of the K-shaped graph is the shaping amount through programming software. Since n known points are given in the K-shaped graph, there are (n-1) shaping curves in total. Therefore, the shaping curve is a piecewise function. Let the number of straight line segments be n. 1 , the number of arc segments is n 2 , then (n-1) = n 1 +n 2 ; Let the shaping function corresponding to each straight line segment be expressed as q i (φ), where i = 1, 2, ..., n 1 , then the set of all straight line segment shaping functions is Suppose the shaping function corresponding to each arc segment is expressed as f j (φ), where j = 1, 2, ..., n 2 , then the set of all arc segment shaping functions is Therefore, the modification function Q(φ) = Q 1 (φ)∪Q 2 (φ).

8. The universal gear shaping method according to claim 7, It is characterized in that The method for constructing the shaping function corresponding to the straight line segment is as follows: if the entity segment is a straight line segment, the straight line segment information is saved in the matrix M 1 middle: Matrix M 1 The number of rows is the number of straight line segments n 1 , the curve position information is the coordinates of the endpoints of the straight line segment, [x i ,y i ,x i+1 ,y i+1 ],i=1:(2n 1 -1); According to the matrix M 1 The element information of each row can be used to solve the slope of the straight line segment modification curve: If the slope k of the modified curve of the straight line segment t does not exist, then the shaping function q corresponding to this shaping curve i (φ)=x i =x i+1 , domain φ∈[min[y i / r b ,y i+1 / r b ],max[y i / r b ,y i+1 / r b ]], at this time if x i =x i+1 = 0, indicating that the tooth profile in this section is not modified to a standard involute. i =x i+1 ≠0, indicating that the modified tooth profile in this section is the standard tooth profile normal equidistance x i Or the result after rotating a certain angle clockwise around the Z axis; If the slope k of the modified curve of the straight line segment t When exists, the shaping function corresponding to this shaping curve is Domain φ∈[min[y i / r b ,y i+1 / r b ],max[y i / r b ,y i+1 / r b ]], this case is pressure angle shaping or slope shaping.

9. The universal gear shaping method according to claim 8, It is characterized in that The method for constructing the shaping function corresponding to the arc segment is as follows: If the entity segment is an arc segment, save the arc segment information to the matrix M 2 middle: Matrix M 2 The number of rows is the number of arc segments n 2 , the curve position information is the endpoint coordinates of the arc segment [xc j ,yc j ,r j ,α j ,α' j ],j=1:n 2 , (x, y) is the coordinate value of the center of the circle, r is the radius, α j is the starting angle, α' j is the ending angle; When the solid segment is an arc, since the modification curves are all convex, the positive pressure angle is maintained at all locations of the tooth profile. Therefore, the modification amount function when the solid segment is an arc is After the shaping function of each arc segment is determined, the definition domain of each segment shaping function needs to be solved. At this time, the starting angle α j The value of the end angle α' j There are two cases: ①When α j > α' j , α' j = α' j + 360; ②When α j <α' j , α' j =α' j : Both of the above cases satisfy the formula: L(α)=yc j +r j sin(α), where α is the angular parameter of the arc segment and L(α) refers to the corresponding modification amount at the endpoint; Therefore, the domain of the independent variable is: φ∈[min[L(α j ) / r b ,L(α' j ) / r b ],max[L(α j ) / r b ,L(α j ') / r b ]], this case is drum shaping, which can achieve the effects of parabola shaping, high-order parabola shaping, and high-order polynomial shaping.

10. The universal gear shaping method according to claim 9, It is characterized in that The shaping amount function is: When the entity segment is a straight line, the shaping amount equation set is: The set of shaping equations when the solid segment is an arc is: According to the definition domain, sort and merge the modification equations of each segment from the root to the top of the tooth to obtain the modification function

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