A modeling method, device, equipment and medium for precise full tooth surface of cycloidal high equal teeth

Abstract

The present invention provides a precise full tooth surface modeling method, device, equipment and medium for cycloidal equal-height teeth, belonging to the technical field of tooth surface modeling. The method includes the following steps: According to the relative position in space and the relative motion relationship between the cycloidal equal-height tooth workpiece and the cutter head, the time-varying position of the cutter head in the cycloidal equal-height tooth workpiece coordinate system is expressed through a coordinate transformation matrix, and the digital model of cycloidal equal-height tooth machining is built; The cutter profile is modified, and the cutter root is relieved to complete the establishment of the cutter mathematical model; Based on the established cutter mathematical model and the digital model of cycloidal equal-height tooth machining, the meshing equation is solved according to the meshing principle to obtain the cutter height parameter. The cutter height parameter is obtained by solving based on the meshing principle, and the precise tooth point coordinates are obtained by solving based on tooth surface discretization and the tooth surface equation expression. The present invention realizes the precise modeling of the full tooth surface of cycloidal equal-height teeth.

Description

Technical Field

[0001] The present invention belongs to the technical field of tooth surface modeling, and particularly relates to a precise full tooth surface modeling method, device, equipment and medium for cycloid equal-height teeth. Background Art

[0002] The cycloid equal-height hypoid gear is an important basic unit in the transmission device for realizing the motion transmission of intersecting axes. Due to its advantages such as high contact ratio, smooth transmission, strong load-bearing capacity, and low transmission noise, it is widely used in the transmission devices of aerospace, transportation tools, and cutting processing equipment. There is a definite relationship between the macroscopic tooth surface shape of the cycloid equal-height hypoid gear and its processing parameters, and the macroscopic tooth surface shape largely determines the transmission performance of the spiral bevel gear pair. Therefore, it is very important to establish an accurate macroscopic tooth surface shape.

[0003] Currently, tool software such as GEM and KIMOS can output tooth surface detection point files, but their regions only include the unmodified region, and cannot output the convex corner region related to the contact performance and the transition region related to the bending stress calculation. Therefore, it is far from enough to rely solely on the tooth surface detection point files of GEM and KIMOS tool software for the design and analysis of cycloid equal-height hypoid gears, and there is a lack of a method for precise full tooth surface modeling.

[0004] This is the deficiency of the prior art. Therefore, in view of the above-mentioned defects in the prior art, it is very necessary to provide a precise full tooth surface modeling method, device, equipment and medium for cycloid equal-height teeth. Summary of the Invention

[0005] In view of the above-mentioned fact that it is very important to establish an accurate macroscopic tooth surface shape in the prior art, and the existing tool software such as GEM and KIMOS can only output tooth surface detection files, lacking the output of the convex corner region and the transition region, and unable to perform precise full tooth surface modeling, the present invention provides a precise full tooth surface modeling method, device, equipment and medium for cycloid equal-height teeth to solve the above technical problems.

[0006] In the first aspect, the present invention provides a precise full tooth surface modeling method for cycloid equal-height teeth, including the following steps:

[0007] S1. According to the relative position in space and the relative motion relationship between the cycloid equal-height tooth workpiece and the cutter head, express the time-varying position of the cutter head in the cycloid equal-height tooth workpiece coordinate system through a coordinate transformation matrix, and complete the construction of the digital model for cycloid equal-height tooth machining;

[0008] S2. Modify the cutter profile and chamfer the cutter root to complete the establishment of the cutter mathematical model;

[0009] S3. Based on the established tool mathematical model and the digital model of cycloid and equal-height tooth machining, solve the meshing equation according to the meshing principle to obtain the tool height parameter;

[0010] S4. Solve to obtain the tool height parameter based on the meshing principle, and solve to obtain the accurate tooth point coordinates based on tooth surface discretization and the tooth surface equation expression.

[0011] Furthermore, the specific steps of step S1 are as follows:

[0012] S11. Establish the first transformation matrix from the machine tool coordinate system to the cycloid and equal-height tooth workpiece coordinate system, and establish the second transformation matrix from the cutting edge to the cutter head coordinate system;

[0013] S12. Construct an expression for the time-varying position of the tool in the cycloid and equal-height tooth workpiece coordinate system based on the first transformation matrix and the second transformation matrix;

[0014] S13. Represent the coordinate transformation by translating or rotating around any axis of the three-dimensional Cartesian coordinate system to obtain the transformation matrix for rotation around any axis, and complete the mapping from the machine tool processing parameters to the digital model.

[0015] Furthermore, the specific steps of step S11 are as follows:

[0016] S111. Determine the workpiece rotation angle expression, swivel table rotation angle expression, and bed position expression in the machine tool coordinate system;

[0017] S112. Through the tool inclination angle σ, tool rotation angle ζ, radial tool position S r , angular tool position φ 0 , workpiece rotation angle φ P , swivel table angle φ C , vertical wheel position E M , horizontal wheel position X D , bed position X B , installation angle γ m establish the first transformation matrix from the machine tool coordinate system to the cycloid and equal-height tooth workpiece coordinate system;

[0018] where the expression of the workpiece rotation angle φ P is: φ P = R a (φ C - Cφ 2 C - Dφ 3 C ), the expression of the swivel table rotation angle φ C is: φ C = φ P / R a - (Z c θ) / (Z 0 Ra ),bed X B The expression for it is: X B = X B0 + H 1 φ C + H 2 φ 2 C ;

[0019] Through the tool rotation parameter θ, the initial installation angle β of the blade i , the tool radius r 0i , the tool offset angle δ i , the rake angle α of the tool h Establish the second transformation matrix from the cutting edge to the cutter head coordinate system;

[0020] S113. Taking the machine tool coordinate system as an intermediary and based on the first transformation matrix and the second transformation matrix, express the time-varying position of the cutter head in the workpiece coordinate system.

[0021] Furthermore, the specific steps of step S2 are as follows:

[0022] S21. Determine the parametric equation of the flank part of the tool, determine the range of the modified arc, determine the boundary calculation equation of the modified arc, and parametrically express the center of the modified arc;

[0023] S22. Determine the parametric equation of the tip flange part, determine the range of the flange arc, determine the boundary calculation equation of the flange arc, and parametrically express the center of the flange arc;

[0024] S23. Determine the parametric equation of the tip rounding part, determine the range of the rounded modified arc, and parametrically express the center of the tip arc;

[0025] S24. Integrate the parametric expressions of the center of the modified arc, the center of the flange arc, and the center of the tip arc into the tool mathematical model.

[0026] Furthermore, the specific steps of step S3 are as follows:

[0027] S31. Obtain the expression of the time-varying position of the tool in the cycloidal equal-height tooth workpiece coordinate system;

[0028] S32. Obtain the parametric equations in the tool mathematical model;

[0029] S33. Based on the meshing principle of the cycloidal equal-height tooth workpiece and the cutter head, and according to the expression of the time-varying position of the tool in the cycloidal equal-height tooth workpiece coordinate system and the parametric equations in the tool mathematical model, construct the meshing equation;

[0030] S34. Solve the meshing equation to obtain the tool height.

[0031] Further, the specific steps of step S4 are as follows:

[0032] S41. Calculate the discrete height of the tool corresponding to the discrete points on the tooth tip, and combine the tool parameters to obtain the tool height boundary of the tooth surface;

[0033] S42. For each given discrete degree, determine the discrete height of the tool and make the projection points of the discrete points on the axial section fall on the corresponding straight lines to obtain the precise discrete points of the tooth blank section;

[0034] S43. According to the precise discrete points of the tooth blank section and combined with the tooth surface equation expression, solve the coordinates and normal vectors of the discrete points on the tooth surface;

[0035] S44. In the three-dimensional modeling software, import the tooth point coordinates to establish a three-dimensional model to obtain the precise full tooth surface model.

[0036] In a second aspect, the present invention provides a precise full tooth surface modeling device for cycloidal equal-height teeth, including:

[0037] A tool disk time-varying position representation module, which is used to express the time-varying position of the tool disk in the cycloidal equal-height tooth workpiece coordinate system through a coordinate transformation matrix according to the relative position in space and the relative motion relationship between the cycloidal equal-height tooth workpiece and the tool disk, and complete the construction of the digital model for cycloidal equal-height tooth machining;

[0038] A tool mathematical model establishment module, which is used to modify the tool profile and trim the tool root to complete the establishment of the tool mathematical model;

[0039] A tooth surface equation expression module, which is used to solve the meshing equation based on the established tool mathematical model and the digital model for cycloidal equal-height tooth machining according to the meshing principle to obtain the tool height parameters;

[0040] A tool height parameter solving and tooth surface solving module, which is used to solve the tool height parameters based on the meshing principle and solve the precise tooth point coordinates based on tooth surface discretization and the tooth surface equation expression.

[0041] Further, the tool disk time-varying position representation module includes:

[0042] A transformation matrix establishment unit, which is used to establish a first transformation matrix from the machine tool coordinate system to the cycloidal equal-height tooth workpiece coordinate system and a second transformation matrix from the cutting edge to the tool disk coordinate system;

[0043] A time-varying position expression construction unit, which is used to construct an expression of the time-varying position of the tool in the cycloidal equal-height tooth workpiece coordinate system based on the first transformation matrix and the second transformation matrix;

[0044] A digital model mapping unit, which is used to represent coordinate transformation by translating or rotating based on any coordinate axis of a three-dimensional Cartesian coordinate system, obtain a transformation matrix selected around any coordinate axis, and complete the mapping of machine tool processing parameters to the digital model;

[0045] The tool mathematical model establishment module includes:

[0046] A tool flank parametric modification unit, which is used to determine the parametric equation of the tool flank part, determine the modification radian range, determine the boundary calculation equation of the modification radian, and parametrically express the center of the modification arc;

[0047] A tool tip flange parametric modification unit, which is used to determine the parametric equation of the tool tip flange part, determine the flange radian range, determine the boundary calculation equation of the flange radian, and parametrically express the center of the flange arc;

[0048] A tool tip fillet parameter modification unit, which is used to determine the parameter equation of the tool tip fillet part, determine the fillet modification radian range, and parametrically express the center of the tool tip arc;

[0049] A tool mathematical model integration unit, which is used to integrate the parametric expressions of the centers of the modification arc, the flange arc, and the tool tip arc into a tool mathematical model;

[0050] The tooth surface equation expression module includes:

[0051] A tool time-varying position expression acquisition unit, which is used to acquire the expression of the time-varying position of the tool in the cycloid equal-height tooth workpiece coordinate system;

[0052] A tool parameter equation acquisition unit, which is used to acquire the parameter equations in the tool mathematical model;

[0053] A meshing equation construction unit, which is used to construct a meshing equation based on the meshing principle of the cycloid equal-height tooth workpiece and the cutter head, and according to the expression of the time-varying position of the tool in the cycloid equal-height tooth workpiece coordinate system and the parametric equations in the tool mathematical model;

[0054] A tool height solving unit, which is used to solve the meshing equation to obtain the tool height;

[0055] The tool height parameter solving and tooth surface solving module includes:

[0056] A tooth surface tool height boundary acquisition unit, which is used to calculate the discrete height of the tool corresponding to the discrete points at the tooth top, and combine the tool parameters to obtain the tool height boundary of the tooth surface;

[0057] A tooth blank cross-section discrete point acquisition unit, which is used to determine the discrete height of the tool for each given discrete degree, and make the projection points of the discrete points on the axial cross-section fall on the corresponding straight lines to obtain accurate tooth blank cross-section discrete points;

[0058] The tooth surface discrete point coordinate solving unit is used to solve the coordinates and normal vectors of the tooth surface discrete points according to the accurate discrete points of the blank cross-section and in combination with the tooth surface equation expression.

[0059] The accurate full tooth surface model obtaining unit is used to import the tooth point coordinates in 3D modeling software to establish a 3D model and obtain an accurate full tooth surface model.

[0060] In a third aspect, the present invention provides a device, including a processor and a memory;

[0061] Wherein, the memory is used to store a computer program, and the processor is used to call and run the computer program from the memory, so that the computer device executes the method described in the first aspect above.

[0062] In a fourth aspect, the present invention provides a storage medium,

[0063] Instructions are stored in the storage medium, and when it runs on a computer, it causes the computer to execute the method described in the first aspect above.

[0064] The beneficial effects of the present invention are as follows:

[0065] The cycloid equal-height tooth accurate full tooth surface modeling method, device, equipment and medium provided by the present invention are based on the relative position and relative motion relationship between the workpiece and the cutter head in space. Through the coordinate transformation matrix, a mathematical model of the relative motion between the workpiece and the cutter head is considered by high-order correction of the machine tool processing parameters, and in combination with the meshing principle, a tooth surface equation expression is obtained; the tooth surface is discretized by using the tool height parameter, the tooth surface discrete equation is simplified, and the coordinates and normal vectors of the tooth surface discrete points are solved; finally, based on the output accurate tooth points, CAD modeling and CAE analysis are completed, realizing the high efficiency and accuracy of the design and analysis of cycloid equal-height tooth hypoid gears.

[0066] In addition, the design principle of the present invention is reliable, the structure is simple, and it has a very wide application prospect.

[0067] It can be seen that compared with the prior art, the present invention has substantial features and progress, and the beneficial effects of its implementation are also obvious. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

[0069] Figure 1 It is a schematic flowchart of an embodiment of the cycloid equal-height tooth accurate full tooth surface modeling method of the present invention.

[0070] Figure 2 It is a schematic flow diagram of another embodiment of the cycloidal isometric tooth precise full tooth surface modeling method of the present invention.

[0071] Figure 3 It is a schematic diagram of the cycloidal isometric tooth precise full tooth surface modeling device of the present invention.

[0072] Figure 4 It is a processing model of the cycloidal isometric tooth hyperboloid gear of the present invention.

[0073] Figure 5 It is a schematic diagram of the straight cutting edge of the present invention.

[0074] Figure 6 It is a schematic diagram of the tooth surface discretization driven by the tool height parameter of the present invention.

[0075] Figure 7 It is a schematic diagram of the precise full tooth surface CAD model of the present invention. Specific embodiments

[0076] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0077] Embodiment 1:

[0078] As Figure 1 shown, the present invention provides a cycloidal isometric tooth precise full tooth surface modeling method, including the following steps:

[0079] S1. According to the relative position in space and the relative motion relationship between the cycloidal isometric tooth workpiece and the cutter head, through the coordinate transformation matrix, express the time-varying position of the cutter head in the cycloidal isometric tooth workpiece coordinate system, and complete the construction of the digital model for cycloidal isometric tooth machining;

[0080] S2. Modify the cutter profile and chamfer the cutter root to complete the establishment of the cutter mathematical model;

[0081] S3. Based on the established cutter mathematical model and the digital model for cycloidal isometric tooth machining, solve the meshing equation according to the meshing principle to obtain the cutter height parameter;

[0082] S4. Solve the cutter height parameter based on the meshing principle, and solve the precise tooth point coordinates based on tooth surface discretization and the tooth surface equation expression.

[0083] Example 2:

[0084] As Figure 2 shown, the present invention provides a modeling method for the accurate whole tooth surface of cycloidal equal-height teeth, including the following steps:

[0085] S1. According to the relative position in space between the cycloidal equal-height tooth workpiece and the cutter head and their relative motion relationship, through the coordinate transformation matrix, express the time-varying position of the cutter head in the cycloidal equal-height tooth workpiece coordinate system, and complete the construction of the digital model for cycloidal equal-height tooth machining; the specific steps of step S1 are as follows:

[0086] S11. Establish the first transformation matrix from the machine tool coordinate system to the cycloidal equal-height tooth workpiece coordinate system, and establish the second transformation matrix from the cutting edge to the cutter head coordinate system; the specific steps of step S11 are as follows:

[0087] S111. Determine the workpiece rotation angle expression, swing table rotation angle expression, and bed position expression in the machine tool coordinate system;

[0088] As Figure 4 shown, in the machine tool coordinate system, the machining parameters expressing the cutter head position are the tool inclination angle δ, the tool rotation angle ζ, the radial tool position S r , and the angular tool position φ 0 , where the angular tool position can also be called the initial swing table angle, and the workpiece rotation angle φ P changes with the swing table angle φ C , and its change ratio is determined by the gear ratio R a . If the gear ratio correction coefficients 2C and 6D are considered, the expression of the workpiece rotation angle φ P is:

[0089]

[0090] The machining of cycloidal equal-height tooth hypoid gears is hobbing, and the rotation of the swing table is composed of the generating motion of the generating gear and the workpiece and the cycloid motion of the rolling circle centered on the tool axis and the base circle centered on the swing table. The parameters expressing the swing table motion are the number of cutter groups Z c , the number of workpiece teeth Z 0 , and the tool rotation parameter θ. Then the expression of the swing table rotation angle φ C is:

[0091]

[0092] The machining parameters expressing the workpiece position are the vertical wheel position E M , the horizontal wheel position X D , the bed position X B0 , and the installation angle γ m , with a total of one rotational degree of freedom and three translational degrees of freedom. If the bed order correction coefficients H 1 and H2 , then the bed position X B has the following expression:

[0093]

[0094] Since the tilting table angle changes with the rotation of the blank, the positions of the cutter head and the workpiece are time-varying. The tooth surface is the final object to be solved, and it is necessary to use the machine tool coordinate system as an intermediary to express the time-varying position F C of the cutter head in the workpiece coordinate system F C1 :

[0095] F C1 = M b1 (σ, ζ, S r , φ C , E M , X D , X B , γ m )M 1t (θ, β i , r 0i , δ i , α h )F C

[0096] where M b1 is the transformation matrix from the machine tool coordinate system to the workpiece coordinate system, and M 1t is the transformation matrix of the cutting edge in the cutter head coordinate system; where the tool inclination angle σ, the tool rotation angle ζ, the radial tool position S r , the angular tool position φ 0 , and the angular tool position can also be called the initial tilting table angle, the workpiece rotation angle φ P , the tilting table angle φ C , the vertical wheel position E M , the horizontal wheel position X D , the bed position X B , the installation angle γ m , the tool rotation parameter θ, the initial blade installation angle β i , the tool radius r 0i , the tool offset angle δ i , the tool rake angle α h ;

[0097] S112. Through the tool inclination angle σ, the tool rotation angle ζ, the radial tool position S r , the angular tool position φ 0 , the workpiece rotation angle φ P , the tilting table angle φ C , the vertical wheel position E M , the horizontal wheel position X D , the bed position X B , the installation angle γ mEstablish the first transformation matrix from the machine tool coordinate system to the cycloidal high-tooth workpiece coordinate system;

[0098] where the workpiece rotation angle φ P has the expression: φ P = R a (φ C - Cφ 2 C - Dφ 3 C ), the swivel table rotation angle φ C has the expression: φ C = φ P / R a - (Z c θ) / (Z 0 R a ), the bed position X B has the expression: X B = X B0 + H 1 φ C + H 2 φ 2 C ;

[0099] Establish the second transformation matrix from the cutting edge to the cutter head coordinate system through the tool rotation parameter θ, the initial installation angle β i of the blade, the tool radius r 0i , the tool offset angle δ i , and the tool rake angle α h ;

[0100] S113. Taking the machine tool coordinate system as an intermediary and based on the first transformation matrix and the second transformation matrix, express the time-varying position of the cutter head in the workpiece coordinate system;

[0101] S12. Based on the first transformation matrix and the second transformation matrix, construct an expression for the time-varying position of the tool in the cycloidal high-tooth workpiece coordinate system;

[0102] S13. Represent coordinate transformation by translating or rotating around any axis of the three-dimensional Cartesian coordinate system to obtain a transformation matrix for rotation around any axis selection, and complete the mapping from machine tool processing parameters to the digital model;

[0103] where the transformation matrix for rotation around any axis can be expressed as:

[0104]

[0105]

[0106]

[0107] The transformation matrix for rotation about any coordinate axis can be expressed as:

[0108]

[0109] S2. Modify the tool profile and chamfer the tool root to establish the mathematical model of the tool. The specific steps of step S2 are as follows:

[0110] S21. Determine the parametric equation of the flank part of the tool, determine the range of the modified arc, determine the boundary calculation equation of the modified arc, and parametrically express the center of the modified arc;

[0111] S22. Determine the parametric equation of the tip flange part of the tool, determine the range of the flange arc, determine the boundary calculation equation of the flange arc, and parametrically express the center of the flange arc;

[0112] S23. Determine the parametric equation of the tip fillet part of the tool, determine the range of the fillet modification arc, and parametrically express the center of the tip arc;

[0113] S24. Integrate the parametric expressions of the center of the modified arc, the center of the flange arc, and the center of the tip arc into the mathematical model of the tool;

[0114] As Figure 4 shown, for the mapping from the machining parameters of the machine tool to the digital model, to improve the contact performance and effectively avoid severe edge contact at the tooth root of the gear, the tool profile is modified using an arc tool profile, and the tool root is chamfered. The arc tool is generally divided into three parts: the flank, the tip flange, and the tip fillet;

[0115] Establish a complete mathematical model of the tool. The parametric equation of the flank part is expressed as follows:

[0116] (x,z)=(x 0 +r x cosα′ x ,z 0 -r x sinα′ x )

[0117] The range of the modified arc α′ x is α′ x ∈[α 1 ,α 0 , and the boundary calculation equation is as follows:

[0118] α 1 =arcsin((r x sinα-(h b -h w )) / r x )

[0119] α0 = arcsin((r x sinα + h d ) / r x )

[0120] (x 0 , z 0 ) is the center of the modified arc and can be specifically expressed as:

[0121] (x 0 , z 0 ) = (-r x cosα, r x sinα)

[0122] There is a variable modified radian α' in the flank part x , and the other structural parameters are the pressure angle α, the tool height h, the modification radius r x , the tool depth h d and the root cutting height h w ;

[0123] The parametric equation of the tool tip flange part is expressed as follows:

[0124] (x, z) = (x 1 + r w cosα' w , z 1 - r w sinα' w )

[0125] The flange radian α' w ranges from α' w ∈ [α 1 , α 2 , and the boundary calculation equations are as follows:

[0126] α 1 = arcsin((r x sinα - (h b - h w )) / r x )

[0127] α 2 = arcsin((r x sinα - (h b - ρ)) / (r x + ρ))

[0128] (x 1 , z 1 ) is the center of the flange arc and can be specifically expressed as:

[0129] (x 1 , z 1) = (-r x cosα + (r x -r w )cosα 1 ,r x sinα - (r x -r w )sinα 1 )

[0130] There is a flange radian α' in the tool tip flange part w , and the other structural parameters are the pressure angle α, the tool height h b , the dressing radius r x , the tool depth h d , the root cutting height h w , the root cutting radius r w and the tool tip rounding radius ρ;

[0131] The parametric equation of the tool tip rounding part is expressed as follows:

[0132] (x, z) = (x 2 -ρ sinη, z 2 +ρ cosη)

[0133] The range of the dressing radian η is η ∈ [0, π / 2 - α 2 , (x 2 , z 2 ) is the center of the tool tip arc, which can be specifically expressed as:

[0134] (x 2 , z 2 ) = (x 1 +(r w +ρ)cosα 2 , z 1 -(r w +ρ)sinα 2 )

[0135] There is a rounding radian η in the tool tip rounding part, and the other structural parameters are the pressure angle α, the root cutting radius r w and the tool tip rounding radius ρ;

[0136] Taking the parametric equation of the cutting tool as an example, the modeling of other types of tools can refer to the content of the present invention. The cutting edge is straight, as shown in Figure 5 , there is a variable tool profile height u in the flank part, where is the cutter head pressure angle, F C1 is any point on the cutter head; there is a variable tool tip radian η in the tool tip rounding part, where h b is the tool height and ρ is the tool tip radius; therefore, the complete tool equation is:

[0137]

[0138] S3. Based on the established tool mathematical model and the digital model of cycloid high equal-height tooth machining, solve the meshing equation according to the meshing principle to obtain the tool height parameters; the specific steps of step S3 are as follows:

[0139] S31. Obtain the expression of the time-varying position of the tool in the cycloid high equal-height tooth workpiece coordinate system;

[0140] S32. Obtain the parameter equations in the tool mathematical model;

[0141] S33. Based on the meshing principle of the cycloid high equal-height tooth workpiece and the cutter head, and according to the expression of the time-varying position of the tool in the cycloid high equal-height tooth workpiece coordinate system and the parametric equations in the tool mathematical model, construct the meshing equation;

[0142] S34. Solve the meshing equation to obtain the tool height;

[0143] S4. Based on the meshing principle, solve to obtain the tool height parameters, and based on the tooth surface discretization and the tooth surface equation expression, solve to obtain the accurate tooth point coordinates; the specific steps of step S4 are as follows:

[0144] As Figure 6 shown, S41. Calculate the discrete height of the tool corresponding to the discrete points at the tooth tip, and combine the tool parameters to obtain the tool height boundary of the tooth surface;

[0145] S42. For each given discretization, determine the discrete height of the tool and make the projection points of the discrete points on the axial section fall on the corresponding straight line to obtain the accurate discrete points of the tooth blank section;

[0146] S43. According to the accurate discrete points of the tooth blank section and combined with the tooth surface equation expression, solve the coordinates and normal vectors of the tooth surface discrete points;

[0147] S44. In the three-dimensional modeling software, import the tooth point coordinates to establish a three-dimensional model to obtain an accurate full tooth surface model, as Figure 7 shown.

[0148] Embodiment 3:

[0149] As Figure 3 shown, the present invention provides a cycloid high equal-height tooth accurate full tooth surface modeling device, including:

[0150] A cutter head time-varying position representation module, which is used to express the time-varying position of the cutter head in the cycloid high equal-height tooth workpiece coordinate system through a coordinate transformation matrix according to the relative position in space and the relative motion relationship between the cycloid high equal-height tooth workpiece and the cutter head, and complete the construction of the digital model of cycloid high equal-height tooth machining; the cutter head time-varying position representation module includes:

[0151] A transformation matrix establishment unit for establishing a first transformation matrix from the machine tool coordinate system to the cycloidal high-profile gear workpiece coordinate system, and a second transformation matrix from the cutting edge to the cutter head coordinate system;

[0152] A time-varying position expression construction unit for constructing an expression of the time-varying position of the tool in the cycloidal high-profile gear workpiece coordinate system based on the first transformation matrix and the second transformation matrix;

[0153] A digital model mapping unit for representing coordinate transformation by translating or rotating along any axis of the three-dimensional Cartesian coordinate system to obtain a transformation matrix selected along any axis, and completing the mapping from the machine tool processing parameters to the digital model;

[0154] A tool mathematical model establishment module for modifying the tool profile and rounding the tool root to complete the establishment of the tool mathematical model; the tool mathematical model establishment module includes:

[0155] A tool flank parametric modification unit for determining the parametric equation of the tool flank part, determining the modification arc range, determining the boundary calculation equation of the modification arc, and parametrically expressing the center of the modification arc;

[0156] A tool tip flange parametric modification unit for determining the parametric equation of the tool tip flange part, determining the flange arc range, determining the boundary calculation equation of the flange arc, and parametrically expressing the center of the flange arc;

[0157] A tool tip fillet parameter modification unit for determining the parametric equation of the tool tip fillet part, determining the fillet modification arc range, and parametrically expressing the center of the tool tip arc;

[0158] A tool mathematical model integration unit for integrating the parametric expressions of the center of the modification arc, the center of the flange arc, and the center of the tool tip arc into the tool mathematical model;

[0159] A tooth surface equation expression module for obtaining the tool height parameter by solving the meshing equation based on the established tool mathematical model and the cycloidal high-profile gear machining digital model and according to the meshing principle; the tooth surface equation expression module includes:

[0160] A tool time-varying position expression acquisition unit for acquiring the expression of the time-varying position of the tool in the cycloidal high-profile gear workpiece coordinate system;

[0161] A tool parameter equation acquisition unit for acquiring the parameter equations in the tool mathematical model;

[0162] A meshing equation construction unit for constructing a meshing equation based on the meshing principle of the cycloidal high-profile gear workpiece and the cutter head, and according to the expression of the time-varying position of the tool in the cycloidal high-profile gear workpiece coordinate system and the parametric equations in the tool mathematical model;

[0163] The tool height solving unit is used to solve the meshing equation to obtain the tool height;

[0164] The tool height parameter solving and tooth surface solving module is used to solve the tool height parameters based on the meshing principle, and solve the accurate tooth point coordinates based on the tooth surface discretization and the tooth surface equation expression; the tool height parameter solving and tooth surface solving module includes:

[0165] The tooth surface tool height boundary obtaining unit is used to calculate the tool discrete height corresponding to the tooth top discrete points, and combine with the tool parameters to obtain the tool height boundary of the tooth surface;

[0166] The blank cross-section discrete point obtaining unit is used to determine the tool discrete height for each given discretization degree, and make the axial section projection points of the discrete points fall on the corresponding straight lines to obtain accurate blank cross-section discrete points;

[0167] The tooth surface discrete point coordinate solving unit is used to solve the coordinates and normal vectors of the tooth surface discrete points according to the accurate blank cross-section discrete points and combine with the tooth surface equation expression;

[0168] The accurate full tooth surface model obtaining unit is used to import the tooth point coordinates in 3D modeling software to establish a 3D model to obtain an accurate full tooth surface model.

[0169] Embodiment 4:

[0170] The present invention provides a device, including a processor and a memory;

[0171] Wherein, the memory is used to store a computer program, and the processor is used to call and run the computer program from the memory, so that the device executes the method described in the above Embodiment 1 or Embodiment 2.

[0172] Embodiment 5:

[0173] The present invention provides a storage medium,

[0174] Instructions are stored in the storage medium, and when it runs on a computer, it causes the computer to execute the method described in the above Embodiment 1 or Embodiment 2.

[0175] Although the present invention has been described in detail by referring to the accompanying drawings and in combination with the preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, those of ordinary skill in the art can make various equivalent modifications or substitutions to the embodiments of the present invention, and these modifications or substitutions should all be within the scope of the present invention. / Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for accurately modeling the entire tooth surface of cycloidal high-profile teeth, characterized in that, it includes the following steps: S1. According to the relative position in space and the relative motion relationship between the cycloidal high-profile tooth workpiece and the cutter head, through the coordinate transformation matrix, express the time-varying position of the cutter head in the cycloidal high-profile tooth workpiece coordinate system, and complete the construction of the digital model for cycloidal high-profile tooth machining; The specific steps of step S1 are as follows: S11. Establish the first transformation matrix from the machine tool coordinate system to the cycloidal high-profile tooth workpiece coordinate system, and establish the second transformation matrix from the cutting edge to the cutter head coordinate system; S12. Based on the first transformation matrix and the second transformation matrix, construct an expression for the time-varying position of the tool in the cycloidal high-profile tooth workpiece coordinate system; S13. Express the coordinate transformation by translating or rotating along any axis of the three-dimensional Cartesian coordinate system, obtain the transformation matrix for rotation around any axis, and complete the mapping from the machine tool processing parameters to the digital model; S2. Modify the tool profile and chamfer the tool root to complete the establishment of the tool mathematical model; S3. Based on the established tool mathematical model and the digital model for cycloidal high-profile tooth machining, solve the meshing equation according to the meshing principle to obtain the tool height parameter; The specific steps of step S3 are as follows: S31. Obtain the expression for the time-varying position of the tool in the cycloidal high-profile tooth workpiece coordinate system; S32. Obtain the parametric equations of each parameter in the tool mathematical model; S33. Based on the meshing principle of the cycloidal high-profile tooth workpiece and the cutter head, and according to the expression for the time-varying position of the tool in the cycloidal high-profile tooth workpiece coordinate system and the parametric equations of each parameter in the tool mathematical model, construct the meshing equation; S34. Solve the meshing equation to obtain the tool height; S4. Based on the tool height parameter obtained by solving according to the meshing principle, and based on the tooth surface discretization and the tooth surface equation expression, solve to obtain the accurate tooth point coordinates.

2. The method for accurately modeling the entire tooth surface of cycloidal high-profile teeth according to claim 1, characterized in that, the specific steps of step S11 are as follows: S111. Determine the workpiece rotation angle expression, the swivel table rotation angle expression, and the bed position expression in the machine tool coordinate system; S112. Through the inclination angle of the tool σ , the rotation angle of the tool ζ , the radial tool position S r , the angular tool position φ 0 , the workpiece rotation angle φ P , the swivel table angle φ C , the vertical wheel position E M , the horizontal wheel position X D , the bed position X B , the installation angle γ m Establish the first transformation matrix from the machine tool coordinate system to the cycloidal high-tooth workpiece coordinate system; Among them, the workpiece rotation angle φ P The expression is: , the rotary table rotation angle φ C The expression is: , the bed position X B The expression is: ; Through the tool rotation parameters θ , the initial installation angle of the blade β i , the tool radius r 0i , the tool offset angle δ i , the tool rake angle α h Establish the second transformation matrix from the cutting edge to the cutter head coordinate system; S113. Using the machine tool coordinate system as an intermediary, and based on the first transformation matrix and the second transformation matrix, express the time-varying position of the cutter head in the workpiece coordinate system.

3. The method for accurately modeling the entire tooth surface of cycloidal high-profile teeth according to claim 1, characterized in that, the specific steps of step S2 are as follows: S21. Determine the parametric equation of the tool flank part, determine the modification arc range, determine the boundary calculation equation of the modification arc, and parametrically express the center of the modification arc; S22. Determine the parametric equation of the tool tip flange part, determine the flange arc range, determine the boundary calculation equation of the flange arc, and parametrically express the center of the flange arc; S23. Determine the parametric equation of the tool tip fillet part, determine the fillet modification arc range, and parametrically express the center of the tool tip arc; S24. Integrate the parametric expressions of the center of the modification arc, the center of the flange arc, and the center of the tool tip arc into the tool mathematical model.

4. The method for accurately modeling the entire tooth surface of cycloidal high-profile teeth according to claim 3, characterized in that, the specific steps of step S4 are as follows: S41. Calculate the discrete height of the tool corresponding to the discrete points on the tooth tip, and combine with the tool parameters to obtain the tool height boundary of the tooth surface; S42. For each given discretization degree, determine the discrete height of the tool and make the projection points of the discrete points on the axial section fall on the corresponding straight lines to obtain the precise discrete points of the blank cross-section; S43. According to the precise discrete points of the blank cross-section and combined with the tooth surface equation expression, solve the coordinates and normal vectors of the discrete points on the tooth surface; S44. In the 3D modeling software, import the coordinates of the tooth points to establish a 3D model to obtain the precise full tooth surface model.

5. A precise full tooth surface modeling device for cycloidal equal-height teeth, characterized in that, it includes: A cutter head time-varying position representation module, which is used to express the time-varying position of the cutter head in the cycloidal equal-height tooth workpiece coordinate system through a coordinate transformation matrix according to the relative position and relative motion relationship between the cycloidal equal-height tooth workpiece and the cutter head in space, and complete the construction of the digital model for cycloidal equal-height tooth machining; The cutter head time-varying position representation module includes: A transformation matrix establishment unit, which is used to establish the first transformation matrix from the machine tool coordinate system to the cycloidal equal-height tooth workpiece coordinate system, and establish the second transformation matrix from the cutting edge to the cutter head coordinate system; A time-varying position expression construction unit, which is used to construct an expression of the time-varying position of the tool in the cycloidal equal-height tooth workpiece coordinate system based on the first transformation matrix and the second transformation matrix; A digital model mapping unit, which is used to represent the coordinate transformation by translating or rotating around any coordinate axis of the three-dimensional Cartesian coordinate system, obtain the transformation matrix selected around any coordinate axis, and complete the mapping from the machine tool processing parameters to the digital model; A tool mathematical model establishment module, which is used to modify the tool profile and chamfer the tool root to complete the establishment of the tool mathematical model; A tooth surface equation expression module, which is used to solve the meshing equation based on the established tool mathematical model and the digital model for cycloidal equal-height tooth machining, and obtain the tool height parameters; the tooth surface equation expression module includes: A tool time-varying position expression acquisition unit, which is used to acquire the expression of the time-varying position of the tool in the cycloidal equal-height tooth workpiece coordinate system; A tool parameter equation acquisition unit, which is used to acquire the parameter equations in the tool mathematical model; A meshing equation construction unit, which is used to construct a meshing equation based on the meshing principle between the cycloidal equal-height tooth workpiece and the cutter head, and according to the expression of the time-varying position of the tool in the cycloidal equal-height tooth workpiece coordinate system and the parametric equations in the tool mathematical model; A tool height solution unit, which is used to solve the meshing equation to obtain the tool height; A tool height parameter solution and tooth surface solution module, which is used to solve the tool height parameters based on the meshing principle and solve the precise tooth point coordinates based on tooth surface discretization and the tooth surface equation expression.

6. The precise full tooth surface modeling device for cycloidal equal-height teeth according to claim 5, characterized in that, The tool mathematical model establishment module includes: A tool flank parametric modification unit, which is used to determine the parametric equations of the tool flank part, determine the modification radian range, determine the boundary calculation equation of the modification radian, and parametrically express the center of the modification arc; The tool tip flange parametric modification unit is used to determine the parametric equation of the tool tip flange part, determine the flange radian range, determine the boundary calculation equation of the flange radian, and parametrically express the center of the flange arc; The tool tip rounding parameter modification unit is used to determine the parametric equation of the tool tip rounding part, determine the rounding modification radian range, and parametrically express the center of the tool tip arc; The tool mathematical model integration unit is used to integrate the parametric expressions of the centers of the modified arc, the flange arc, and the tool tip arc into a tool mathematical model; The tool height parameter solving and tooth surface solving module includes: The tooth surface tool height boundary obtaining unit is used to calculate the discrete height of the tool corresponding to the discrete points at the tooth top, and combine with the tool parameters to obtain the tool height boundary of the tooth surface; The tooth blank cross-section discrete point obtaining unit is used to determine the discrete height of the tool for each given discretization degree, and make the projection points of the discrete points on the axial section fall on the corresponding straight line to obtain accurate tooth blank cross-section discrete points; The tooth surface discrete point coordinate solving unit is used to solve the coordinates and normal vectors of the tooth surface discrete points according to the accurate tooth blank cross-section discrete points and in combination with the tooth surface equation expression; The accurate full tooth surface model obtaining unit is used to import the tooth surface point coordinates in a 3D modeling software to establish a 3D model and obtain an accurate full tooth surface model.

7. A device, characterized in that, it includes a processor and a memory; wherein, the memory is used to store a computer program, and the processor is used to call and run the computer program from the memory, so that the device executes the method described in any one of claims 1-4 above.

8. A storage medium, characterized in that, the storage medium stores instructions, which when running on a computer, cause the computer to execute the method described in any one of claims 1-4 above.

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