A tooth-scratching tool for cycloidal wheel machining and a design method thereof

Abstract

The present invention discloses a tooth-cutting tool for cycloidal wheel machining and a design method thereof. The tooth-cutting tool comprises a tool body and a plurality of teeth evenly distributed along the circumference of the tool body, each of the teeth comprising a rake face, a flank face and a cutting edge; the rake face is a curved surface; the cutting edge is a conjugate line of the cycloidal wheel tooth surface to be machined, and the working rake angles at any point on the cutting edge are equal; the flank face is a curved surface composed of a plurality of the cutting edges. The rake angles of the cutting edges of the tooth-cutting tool are consistent when cutting, which can effectively improve the tooth surface machining quality and reduce machine tool vibration.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical processing design, and in particular to a tooth-scratching tool for cycloidal wheel processing and a design method thereof. Background Art

[0002] As China's industrial automation level continues to improve, the quality requirements for RV reducers are getting higher and higher, and the demand is growing. Since China does not have the mass production process for RV reducers, the market is basically monopolized by foreign companies.

[0003] The cycloid wheel is one of the most critical parts in the RV reducer, and its manufacturing accuracy is crucial to the precision index of the reducer. At present, the cycloid wheel tooth surface processing generally uses the forming grinding process, which adopts the intermittent indexing method. The indexing accuracy is not easy to control and needs to rely on expensive high-precision equipment. Obviously, this method cannot meet the mass production requirements of RV reducers.

[0004] The gear skiving method has the processing characteristics of continuous indexing, high efficiency, energy saving and environmental protection, and has more advantages in cycloidal gear tooth processing. In the gear skiving process system, the gear skiving cutter is one of the important factors. At present, the front cutting surface of the gear skiving cutter basically adopts a spherical or conical shape, which leads to inconsistent working front angles at various points of the cutting edge and unreasonable working front angles of some cutting segments. When using this type of tool for gear skiving, the machine tool chatters significantly and the tooth surface processing quality is uneven. Therefore, in order to promote the widespread application of gear skiving technology, especially to promote the application of gear skiving technology in the field of key parts processing of RV reducers, it is very necessary to develop new gear skiving cutter design methods. Summary of the invention

[0005] The purpose of the present invention is to provide a tooth scraping tool for cycloidal wheel processing to solve the technical defects of the existing tooth scraping tool, that is, the obvious machine tool chatter and uneven tooth surface processing quality caused by structural reasons.

[0006] Another object of the present invention is to provide a design method for the above-mentioned tooth-scratching tool for cycloidal wheel machining.

[0007] The technical solution adopted to achieve the purpose of the present invention is:

[0008] A tooth cutting tool for cycloidal wheel machining comprises a tool body and a plurality of teeth evenly distributed along the circumference of the tool body, each of the teeth comprising a rake face, a flank face and a cutting edge; the rake face is a curved surface; the cutting edge is a conjugate line of the cycloidal wheel tooth surface to be machined, and the working rake angle at any point on the cutting edge is equal; the flank face is a curved surface composed of a plurality of cutting edges.

[0009] In the above technical solution, the blade teeth are helical teeth, the rotation direction is left-handed or right-handed, and the helix angle of the blade teeth is 15-25°.

[0010] In the above technical solution, the working front angle is 8-20°.

[0011] In the above technical solution, the top circle diameter of the flank surface gradually decreases from the front end to the rear end of the tooth-scraping tool, and the designed back angle of the flank surface is 6-15°.

[0012] Another object of the present invention is a design method of a cycloidal wheel machining equal rake angle tooth cutter, comprising the following steps:

[0013] Step 1: According to the positional relationship and motion relationship between the workpiece and the tool, three coordinate systems are established, namely the workpiece coordinate system S1, the tool coordinate system S2 and the auxiliary coordinate system Sp;

[0014] Step 2: Obtain the mathematical model of the cycloid gear tooth surface in the workpiece coordinate system according to the workpiece parameters;

[0015] Step 3: Assign values ​​to the number of tool teeth, axis angle, workpiece speed and feed rate respectively, and then obtain the mathematical model of the motion speed of any point on the cycloid gear tooth surface relative to its conjugate surface according to the kinematic principle, and then obtain the mathematical model of the conjugate surface in the tool coordinate system according to the surface conjugation principle;

[0016] Step 4: Select the conjugate line of the cycloid wheel end face tooth profile as the cutting edge on the conjugate surface obtained in step 3, and obtain a mathematical model of the motion speed of any point on the cutting edge relative to the cycloid wheel tooth surface;

[0017] Step 5: According to the mathematical model of the motion speed of any point on the cutting edge relative to the cycloidal wheel tooth surface obtained in step 4, a tool angle reference system is established to determine the base surface, cutting plane and main section; then, according to the definition of the working rake angle and the given value of the working rake angle, the shape value points of the rake face are constructed, and a cubic B-spline surface is constructed by interpolating these shape value points. The cubic B-spline surface is the rake face;

[0018] Step 6: Calculate the change in the axial distance after each regrinding according to the set change in the cutting edge tooth vertex position after each regrinding and the designed clearance angle of the tool, then obtain the axial distance after regrinding in combination with the initial axial distance between the workpiece and the tool calculated in step 3, and then obtain the cutting edge after regrinding according to the methods of steps 3 and 4;

[0019] By analogy, several reground cutting edges are obtained, and several shape value points are discretized on each cutting edge. A cubic B-spline surface is constructed by interpolating all the shape value points on the obtained cutting edges. The cubic B-spline surface is the back face.

[0020] Step 7: Based on the mathematical model of the cutting edge obtained in step 4, the mathematical model of the front cutting face obtained in step 5, and the mathematical model of the back cutting face obtained in step 6, a three-dimensional model of the equal rake angle cutter is established.

[0021] In the above technical solution, in step 1, the z of the workpiece coordinate system 1 The axis coincides with the workpiece axis, x 1 o 1 y 1 The plane coincides with the lower end surface of the workpiece and rotates with the workpiece;

[0022] The tool coordinate system z 2 The axis coincides with the tool axis, x 2 o 2 y 2 The plane coincides with the upper end face of the tool and rotates with the tool;

[0023] The auxiliary coordinate system is a fixed coordinate system in space, corresponding to the initial position of the workpiece coordinate system and the tool coordinate system, x p The axis coincides with the x-axis, and the z-axis p The angle between the axis and the z axis is the axis intersection angle, p The distance between the axis and the z-axis is the axis distance between the workpiece and the tool.

[0024] In the above technical solution, in step 2, the workpiece parameters include the eccentricity between the rolling circle and the base circle, the number of pinwheel teeth, the number of cycloid gear teeth, the radius of the pinwheel distribution circle, the displacement modification amount, the pinwheel radius, the equidistance modification amount and the angular modification amount;

[0025] The mathematical model of the cycloid gear tooth surface in the workpiece coordinate system is:

[0026]

[0027] In the above formula,

[0028] It is the short-width coefficient of the tooth profile when the cycloid tooth surface has a displacement modification;

[0029] A is the eccentricity between the rolling circle and the base circle required to form the cycloid tooth surface;

[0030] Z p ,Z c are the number of pinwheel teeth and the number of cycloid wheel teeth respectively;

[0031] r p is the radius of the pinwheel distribution circle, Δr p is the displacement modification amount;

[0032] r rp is the radius of the pinwheel, Δrrp is the isometric shaping amount;

[0033] δ is the amount of corner modification;

[0034] and h are the independent variables of the cycloid wheel parameter equation.

[0035] In the above technical solution, in step 3,

[0036] The mathematical model of the motion speed of any point on the cycloid gear tooth surface relative to its conjugate surface is:

[0037] v 12 =v x i+v y j+v z k(3)

[0038] in,

[0039]

[0040]

[0041] ω 1 ,ω 2 are the angular velocities of the workpiece and tool rotating around their own axes respectively;

[0042] Indicates the angle that the workpiece has rotated relative to its initial position;

[0043] (x 1 ,y 1 ,z 1 ) is the coordinate of the conjugate contact point in the workpiece coordinate system;

[0044] a is the axial distance between the workpiece and the tool, where a = a 0 ;

[0045]

[0046] Among them, r ba is the radius of the tooth top circle of the cycloid gear; r bf Z is the root circle radius of the cycloid gear; d is the number of tool teeth, Z c is the number of cycloid gear teeth;

[0047] v is the feed speed, in mm / s,

[0048]

[0049] f is the feed rate, which is given by the process personnel based on processing experience while meeting the requirements of processing accuracy and cutting efficiency;

[0050] L is the distance the workpiece moves along its own axis relative to the initial position when any point on the cycloid gear tooth surface is in conjugate contact

[0051]

[0052] in, Indicates the angle that the workpiece rotates relative to the initial position;

[0053] N h ·v 12 =0 (4)

[0054] Solve to obtain N b is the normal vector of the cycloid gear tooth surface at each point obtained in step 2.

[0055] In the above technical solution, the mathematical model of the conjugate surface in the tool coordinate system is:

[0056]

[0057] is the angle that the tool rotates relative to the initial position, get;

[0058] (x 1 ,y 1 ,z 1 ) are the coordinates of the conjugate contact point in the coordinate system.

[0059] In the above technical solution, in step 4, the mathematical model of the motion speed of any point on the cutting edge relative to the cycloid gear tooth surface is the opposite vector of the mathematical model of the motion speed of any point on the cycloid gear tooth surface relative to its conjugate surface in step 3, that is, v e =-v 12 .

[0060] In the above technical solution, in step 5, the method for constructing the profile point of the rake face is to construct a straight line in the main section so that the angle between it and the intersection line of the base surface / main section is equal to the given value of the working rake angle, and use the constructed straight line as the construction line of the rake face;

[0061] According to the above method, a plurality of the above construction lines are constructed at a plurality of points on the cutting edge obtained in step 4, and a plurality of discrete points are determined on each construction line, and all the discrete points are used as the profile points of the rake face;

[0062] The mathematical model of the rake face is:

[0063]

[0064] Among them, μ and ω are two parameters of the parametric equation; N i,3(u), N j,3 (w) is the cubic B-spline basis function;

[0065] P i,j Represents the control points of a cubic B-spline surface.

[0066] In the above technical solution, in step 6, the mathematical model of the back cutting surface is:

[0067]

[0068] Among them, m and n are the parameters of the parametric equation; N i,3 (m), N j,3 (n) is the cubic B-spline basis function;

[0069] Q i,j Represents a control point.

[0070] In the above technical solution, a verification step is also included between step 6 and step 7, using the tool angle reference system established in step 5 to calculate the working back angle and verify the feasibility of the designed back angle.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] 1. The tooth cutter designed by the design method provided by the present invention has a consistent working front angle at each point of the cutting edge when participating in cutting, which can effectively improve the tooth surface processing quality and reduce machine tool vibration.

[0073] 2. The tooth cutter designed by the design method provided by the present invention does not need to use high-precision equipment during the cycloidal wheel processing process. Compared with other cycloidal wheel processing methods, this method has high efficiency and low cost.

[0074] 3. The design method provided by the present invention adds a verification step, using the established tool angle reference system to calculate the working back angle and verify the feasibility of the designed back angle, thereby further increasing the feasibility of the tool design. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 This is a schematic diagram of the cycloid wheel tooth cutting process;

[0076] Figure 2 Calculate coordinate system for tool design;

[0077] Figure 3 It is a schematic diagram of the tool angle coordinate system and the rake face structure;

[0078] Figure 4 It is a schematic diagram for designing the back angle and back face structure;

[0079] Figure 5 This is a diagram for calculating the working back angle;

[0080] Figure 6 is the working clearance angle at 50 points on the initial cutting edge of the embodiment;

[0081] Figure 7 A three-dimensional model of the tool designed for the embodiment;

[0082] Figure 8 The structure of the toothed cutter is shown in FIG.

[0083] Fig. 9 The present invention is a flow chart of the design method of the cycloidal wheel tooth cutting cutter with equal rake angle;

[0084] Fig.10 It is a schematic diagram of the conjugate relationship between the cycloid gear tooth surface and the cutting edge;

[0085] Among them, a is a side view and b is a top view.

[0086] Among them, 1-tool body, 2-tool teeth, 21-front tool face, 22-flank tool face, 23-cutting edge, 3-cycloid wheel to be processed, 4-cycloid wheel tooth surface, 5-conjugate contact point. DETAILED DESCRIPTION

[0087] The present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0088] Example 1

[0089] A tooth-cutting tool for machining a cycloidal wheel comprises a tool body 1 and a plurality of teeth 2 evenly distributed along the circumference of the tool body 1, each of the teeth 2 comprising a rake face 21, a flank face 22 and a cutting edge 23; the rake face 21 is a curved surface; the cutting edge 23 is a conjugate line of the tooth surface of a cycloidal wheel 3 to be machined, and the working rake angles at any point on the cutting edge 23 are equal; the flank face 22 is a curved surface composed of a plurality of the cutting edges. There is a smooth transition between the flank faces of every two adjacent teeth 2. The teeth 2 are helical teeth with a left-handed rotation direction, and the helix angle of the teeth 2 is 20°. The working rake angle is 15°. The top circle diameter of the flank face 22 gradually decreases from the front end to the rear end of the tooth-cutting tool, and the designed flank angle of the flank face is 10°.

[0090] In actual application, the working front angle can be changed to 8-20°, or the design back angle of the back tool face can be changed to 6-15°, or the tooth can be changed to right-hand and the helix angle can be changed to 15-25° according to different workpiece sizes and machine tool performance requirements, without affecting the overall performance of the tooth cutting tool.

[0091] Example 2

[0092] A design method for a tooth-scratching tool for cycloidal wheel machining comprises the following steps:

[0093] Step 1: Establish the coordinate system used by the design method

[0094] During the gear cutting process, the positional relationship and motion relationship between the workpiece to be processed (i.e., the cycloidal wheel) and the tool (i.e., the gear cutting tool to be designed) are as follows: Figure 1 As shown, there is a certain angle between the workpiece axis and the tool axis. The tool and the workpiece rotate synchronously at high speed, and the workpiece is fed along the workpiece axis to complete the processing of the entire workpiece tooth surface.

[0095] according to Figure 1 The positional relationship and motion relationship between the workpiece and the tool shown in the figure establish three coordinate systems, such as Figure 2 As shown in the figure, they are workpiece coordinate system S1, tool coordinate system S2 and auxiliary coordinate system Sp. 1 The axis coincides with the workpiece axis, x 1 o 1 y 1 The plane coincides with the lower end surface of the workpiece and rotates with the workpiece. 2 The axis coincides with the tool axis, x 2 o 2 y 2 The plane coincides with the upper end face of the tool and rotates with the tool. The auxiliary coordinate system Sp is a fixed coordinate system in space, corresponding to the initial positions of the workpiece coordinate system S1 and the tool coordinate system S2. p The axis coincides with the x-axis, and the z-axis p The angle between the axis and the z axis is the axis intersection angle γ, z p The distance between the axis and the z axis is the axis distance a between the workpiece and the tool.

[0096] Step 2: Use MATLAB software to establish the mathematical model of the cycloid gear tooth surface in the workpiece coordinate system S1

[0097] The parameters of the workpiece to be processed are shown in Table 1.

[0098]

[0099] According to the parameters provided in Table 1, the mathematical model of the cycloid gear tooth surface in the workpiece coordinate system S1 is as follows:

[0100]

[0101] In the above formula,

[0102] is the short-width coefficient of the tooth profile when there is a displacement modification;

[0103] A is the eccentricity between the rolling circle and the base circle;

[0104] Z p ,Z c are the number of pinwheel teeth and the number of cycloid wheel teeth respectively;

[0105] r p is the radius of the pinwheel distribution circle, Δr p is the displacement modification amount;

[0106] r rp is the radius of the pinwheel, Δr rp is the isometric shaping amount;

[0107] δ is the amount of corner modification;

[0108] and h are the independent variables of the parametric equation of the cycloid wheel, It represents the rotation angle of the arm relative to the center vector of a certain pin tooth during the formation of the cycloid gear tooth surface; h is the height parameter, and its value range is [0,H].

[0109] Step 3: Obtain the mathematical model of the conjugate surface in the tool coordinate system S2

[0110] First, calculate the initial axis distance between the workpiece and the tool according to the following formula:

[0111]

[0112] Among them, r ba is the radius of the tooth top circle of the cycloid wheel, that is, the maximum distance from a point on the tooth surface of the cycloid wheel to the axis of the cycloid wheel; r bf Z is the root circle radius of the cycloid wheel, that is, the minimum distance from a point on the cycloid wheel tooth surface to the cycloid wheel axis; d is the number of tool teeth, Z c is the number of cycloid gear teeth.

[0113] Then, based on the above parameters, according to the position and motion relationship between any point on the cycloid gear tooth surface (represented by M1) and its conjugate point (represented by M2) obtained in step 2, the motion velocity v of M1 relative to its conjugate point M2 during conjugate contact is derived. 12 Mathematical model:

[0114] v 12 =v x i+v y j+v z k(3)

[0115] in,

[0116]

[0117]

[0118] ω 1 ,ω 2 are the angular velocities of the workpiece and tool rotating around their own axes respectively;

[0119] Indicates the angle that the workpiece has rotated relative to its initial position;

[0120] (x 1 ,y 1 ,z 1 ) is the coordinate of the conjugate contact point in the workpiece coordinate system S1;

[0121] a is the axial distance between the workpiece and the tool, where a = a 0 ;

[0122] v is the feed speed, Get, the unit is mm / s, f represents the given feed rate;

[0123] L is the distance that the workpiece feeds along its own axis relative to the initial position when the M1 point is in conjugate contact. The following relationship exists:

[0124]

[0125] According to the conjugate principle of curved surfaces, the normal vector of the cycloid gear tooth surface and the relative motion speed satisfy the following relationship:

[0126] N b ·v 12 =0 (4)

[0127] Among them, N b is the normal vector of the cycloid gear tooth surface at a certain point obtained in step 2. In equation (4), only As the unknown quantity, solving the equation yields

[0128] According to the condition that a certain point on the cycloid gear tooth surface coincides with the corresponding point on the conjugate surface during conjugate contact, the mathematical model of the conjugate surface in the tool coordinate system S2 can be obtained:

[0129]

[0130] in, is the angle that the tool rotates relative to the initial position, get.

[0131] (x 1 ,y 1 ,z 1 ) are the coordinates of the conjugate contact point in the coordinate system S1.

[0132] Step 4: Obtain the mathematical model of the motion speed of the cutting edge and any point on the cutting edge relative to the cycloid gear tooth surface

[0133] Considering the characteristic that the cycloid gear tooth profile is a complete curve, the conjugate line of the cycloid gear end face tooth profile is selected as the cutting edge on the conjugate surface obtained in step 3, that is, the variable h in formula (1) in step 2 is set to a constant, and the cutting edge is obtained, denoted as (x r ,y r ,z r ).

[0134] The velocity v of any point M1 on the cycloid gear tooth surface relative to its conjugate point M2 when in conjugate contact is obtained in step 3 12 The mathematical model of the motion speed of any point on the cutting edge relative to the cycloid gear tooth surface is obtained, that is, the opposite vector of the vector shown in formula (3), v e =-v 12 .

[0135] Step 5: Obtain the mathematical model of the rake face

[0136] According to the tangent vector at any point on the cutting edge obtained in step 4 and the speed of any point on the cutting edge relative to the cycloid gear tooth surface, establish the tool angle reference system. Figure 3 As shown, the plane perpendicular to the direction of relative motion is the base plane P r The plane determined by the tangent vector of the cutting edge and the relative motion speed is the cutting plane P s , and the base surface P r and cutting plane P s The two perpendicular planes are the main sections P o According to metal cutting theory, the working rake angle is defined as the main section P o The angle between the two straight lines inside, these two straight lines are the base plane P r With the main section P o The intersection line and the main section P o The tangent line of the intersection with the front cutting edge. Figure 3 As shown, the base surface P r With the main section P o The intersection line is N1, the rake angle is set to 8°, and the main section P o Construct a straight line tr so that it intersects with the straight line N 1 The angle between the straight line t r Considering the surface construction accuracy requirements, the above straight line t is constructed at 100 points on the cutting edge. r , and on each straight line t rDetermine 20 discrete points within the upper 5mm range, and obtain the coordinate data of 2000 points in total. These points are the shape value points. Then construct a cubic B-spline surface to interpolate through these shape value points. The constructed surface is the front cutting edge, and its mathematical model is as follows:

[0137]

[0138] Among them, μ and ω are two parameters of the parametric equation; N i,3 (u), N j,3 (w) is the cubic B-spline basis function;

[0139] P i,j The control points of the rake face are obtained by inverse calculation of the rake face shape points according to the cubic B-spline interpolation construction principle (Reference: Zhu Xinxiong, Free Curve and Surface Modeling Technology, Beijing: Science Press, 2000 (ISBN

[0140] 9787030074409)).

[0141] Step 6: Obtain the mathematical model of the flank surface

[0142] In order to ensure the machining accuracy after tool regrinding, the back face is constructed by the reground cutting edge. In order to construct the tool back angle, the radius of the tooth top circle of the reground cutting edge should be reduced, and the axis distance between the workpiece and the tool should be reduced during processing. The cutting edge obtained in step 4 is the initial cutting edge r 1 The tooth vertex is taken as the inspection point, and at this point along the initial conjugate surface c 1 The tooth direction establishes the design back angle reference surface P α .like Figure 4 As shown, within this reference plane, according to the given design back angle α d Determine the relationship between the change in axis distance Δa after regrinding and the grinding amount Δg of the tooth vertex:

[0143]

[0144] Among them, α d is the designed back angle of the tool;

[0145] Δa is the change in the axis distance after each regrinding;

[0146] Δg is the change in the cutting edge tooth apex position after each regrinding.

[0147] According to the tool life requirements, the tool can be re-grinded 10 times, and the change in the cutting edge tooth vertex position each time is 0.6 mm. The initial design back angle is set to 6°. The change in the axis distance Δa after each re-grinding is calculated according to formula (7). Combined with the initial axis distance α between the workpiece and the tool calculated in step 3,0 Obtain the axis distance a=a after regrinding 0 -Δa, repeat step 3 and subsequent steps to obtain the re-grinded conjugate surface c 2 Then, according to the method in step 4, the conjugate surface c after regrinding is 2 Determine the curve r 2 As the cutting edge after regrinding 2 . And so on, determine the conjugate surface c after several regrindings 3 , c 4 ..., and the cutting edge after regrinding 2 , r 3 , r 4 ……. 100 profile points are evenly discretized on each cutting edge (including the initial cutting edge and the cutting edge after regrinding), and the coordinate data of 1100 points are obtained in total. These points are the profile points of the back tool face. Then, a cubic B-spline surface is constructed to interpolate through all the profile points. The constructed surface is the back tool face, and its mathematical model is:

[0148]

[0149] Among them, m and n are the parameters of the parametric equation; N i,3 (m), N j,3 (n) is the cubic B-spline basis function;

[0150] Q i,j It represents the control point of the flank surface, which is obtained by inverse calculation from the flank surface value points according to the cubic B-spline interpolation construction principle.

[0151] Step 7: Verify the feasibility of the designed back angle

[0152] In the present invention, the design of the rake face can ensure that the working rake angle at each point of the cutting edge is consistent with the set value. However, the design of the back face uses the designed back angle as a parameter, which cannot ensure that the working back angle at each point of the cutting edge is consistent. For this reason, it is necessary to use the tool angle reference system established in step 5 to calculate the working back angle and verify the feasibility of the designed back angle.

[0153] like Figure 5 As shown in the figure, the working back angle is the angle between two straight lines in the main section, which are the cutting plane P s With the main section P o The unit direction vectors of the intersection line of the back cutting surface and the main section are respectively represented by N 2 ,t α ,in,

[0154] N 2 =N 1 ×N o (9)

[0155] Among them, N 1 Main section P o and base surface P r The unit direction vector of the intersection line;

[0156] N o is the unit direction vector of the intersection of the cutting plane and the base surface.

[0157] The unit normal vector N of the flank surface at each point of the initial cutting edge is obtained by formula (8): h , then N h ⊥t α , while N o ⊥t α , we can get:

[0158] t α =N h ×N o (10)

[0159] The working clearance angle at each point of the cutting edge is calculated by the following formula:

[0160]

[0161] In this embodiment, the working back angles at 50 points on the initial cutting edge are calculated, as shown in the attached figure. Figure 6 From the calculation results, the minimum working clearance angle is 4.1° and the maximum is 6°, which shows that the tool has a significant working clearance angle, thus effectively avoiding interference. Therefore, it is feasible to determine that the design clearance angle is 6°.

[0162] Step 8: Obtain the 3D model of the equal rake angle cutter

[0163] According to the mathematical model of the cutting edge obtained in step 4, the mathematical model of the front cutting face obtained in step 5, and the mathematical model of the back cutting face obtained in step 6, a three-dimensional model of the equal rake angle tooth cutter is established, as shown in FIG. Figure 7 shown.

[0164] The above is only a preferred embodiment of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A design method for a tooth-scratching tool for cycloidal wheel machining, characterized in that: The tooth cutting tool for cycloid wheel machining comprises a tool body and a plurality of teeth evenly distributed along the circumference of the tool body, each of the teeth comprising a rake face, a flank face and a cutting edge; the rake face is a curved surface; the cutting edge is a conjugate line of the cycloid wheel tooth surface to be machined, and the working rake angle at any point on the cutting edge is equal; the flank face is a curved surface composed of a plurality of cutting edges; The design method comprises the following steps: Step 1: According to the positional relationship and motion relationship between the workpiece and the tool, three coordinate systems are established, namely the workpiece coordinate system S1, the tool coordinate system S2 and the auxiliary coordinate system Sp; The z1 axis of the workpiece coordinate system S1 coincides with the workpiece axis, and the x1o1y1 plane coincides with the lower end surface of the workpiece and rotates with the workpiece; the z2 axis of the tool coordinate system S2 coincides with the tool axis, and the x2o2y2 plane coincides with the upper end surface of the tool and rotates with the tool; the auxiliary coordinate system Sp is a fixed coordinate system in space, corresponding to the initial positions of the workpiece coordinate system and the tool coordinate system, x p The axis coincides with the x-axis, and the z-axis p The angle between the axis and the z axis is the axis intersection angle, p The distance between the axis and the z axis is the axis distance between the workpiece and the tool; Step 2: Obtain the mathematical model of the cycloid gear tooth surface in the workpiece coordinate system according to the workpiece parameters; Step 3: Assign values ​​to the number of tool teeth, axis angle, workpiece speed and feed rate respectively, and then obtain the mathematical model of the motion speed of any point on the cycloid gear tooth surface relative to its conjugate surface according to the kinematic principle, and then obtain the mathematical model of the conjugate surface in the tool coordinate system according to the surface conjugation principle; Step 4: Select the conjugate line of the cycloid wheel end face tooth profile as the cutting edge on the conjugate surface obtained in step 3, and obtain the mathematical model of the motion speed of any point on the cutting edge relative to the cycloid wheel tooth surface; the mathematical model of the motion speed of any point on the cutting edge relative to the cycloid wheel tooth surface is the opposite vector of the mathematical model of the motion speed of any point on the cycloid wheel tooth surface relative to its conjugate surface in step 3, that is, v e =-v 12 ; Step 5: According to the mathematical model of the motion speed of any point on the cutting edge relative to the cycloidal wheel tooth surface obtained in step 4, a tool angle reference system is established to determine the base surface, cutting plane and main section; then, according to the definition of the working rake angle and the given value of the working rake angle, the shape value points of the rake face are constructed, and a cubic B-spline surface is constructed by interpolating these shape value points. The cubic B-spline surface is the rake face; Step 6: Calculate the change in the axial distance after each regrinding according to the set change in the cutting edge tooth vertex position after each regrinding and the designed clearance angle of the tool, then obtain the axial distance after regrinding in combination with the initial axial distance between the workpiece and the tool calculated in step 3, and then obtain the cutting edge after regrinding according to the methods of steps 3 and 4; By analogy, several reground cutting edges are obtained, and several shape value points are discretized on each cutting edge. A cubic B-spline surface is constructed by interpolating all the shape value points on the obtained cutting edges. The cubic B-spline surface is the back face. Step 7: Use the tool angle reference system established in step 5 to calculate the working back angle and verify the feasibility of the designed back angle; Step 8: According to the mathematical model of the cutting edge obtained in step 4, the mathematical model of the front cutting face obtained in step 5, and the mathematical model of the back cutting face obtained in step 6, a three-dimensional model of the equal rake angle cutter is established.

2. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 1, characterized in that: The blade teeth are helical teeth, the rotation direction is left-handed or right-handed, and the helix angle of the blade teeth is 15-25°.

3. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 1, characterized in that: The working front angle is 8-20°.

4. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 1, characterized in that: The top circle diameter of the flank surface gradually decreases from the front end to the rear end of the tooth scraping tool, and the designed back angle of the flank surface is 6-15°.

5. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 1, characterized in that: In step 2, the workpiece parameters include the eccentricity between the rolling circle and the base circle, the number of pinwheel teeth, the number of cycloid gear teeth, the radius of the pinwheel distribution circle, the displacement modification amount, the pinwheel radius, the equidistance modification amount and the angle modification amount; The mathematical model of the cycloid gear tooth surface in the workpiece coordinate system is: In the above formula, It is the short-width coefficient of the tooth profile when the cycloid tooth surface has a displacement modification; A is the eccentricity between the rolling circle and the base circle required to form the cycloid tooth surface; Z p ,Z c are the number of pinwheel teeth and the number of cycloid wheel teeth respectively; r p is the radius of the pinwheel distribution circle, Δr p is the displacement modification amount; r rp is the radius of the pinwheel, Δr rp is the isometric shaping amount; δ is the amount of corner modification; and h are the independent variables of the cycloid wheel parameter equation.

6. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 5, characterized in that: In step 3, the mathematical model of the motion speed of any point on the cycloid gear tooth surface relative to its conjugate surface is: v 12 =v x i+v y j+v z k (3) in, ω1 and ω2 are the angular velocities of the workpiece and tool rotating around their own axes respectively; Indicates the angle that the workpiece has rotated relative to its initial position; (x1, y1, z1) are the coordinates of the conjugate contact point in the workpiece coordinate system; a is the axial distance between the workpiece and the tool, where a = a0; Among them, r ba is the radius of the tooth top circle of the cycloid gear; r bf Z is the root circle radius of the cycloid gear; d is the number of tool teeth, Z c is the number of cycloid gear teeth; v is the feed speed, in mm / s, f is the feed rate; L is the distance the workpiece moves along its own axis relative to the initial position when any point on the cycloid gear tooth surface is in conjugate contact in, Indicates the angle that the workpiece rotates relative to the initial position; N b ·v 12 =0 (4) Solve to obtain N b is the normal vector of the cycloid gear tooth surface at each point obtained in step 2.

7. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 6, characterized in that: The mathematical model of the conjugate surface in the tool coordinate system is: is the angle that the tool rotates relative to the initial position, get; (x1, y1, z1) are the coordinates of the conjugate contact point in the coordinate system.

8. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 7, characterized in that: In step 5, the method for constructing the profile point of the rake face is to construct a straight line in the main section so that the angle between the straight line and the intersection line of the base surface / main section is equal to the given value of the working rake angle, and use the constructed straight line as the construction line of the rake face; According to the above method, a plurality of the above construction lines are constructed at a plurality of points on the cutting edge obtained in step 4, and a plurality of discrete points are determined on each construction line, and all the discrete points are used as the profile points of the rake face; The mathematical model of the rake face is: Among them, μ and ω are two parameters of the parametric equation; N i,3 (u), N j,3 (w) is the cubic B-spline basis function; P i,j Represents the control points of a cubic B-spline surface.

9. The design method of a tooth-scratching tool for cycloidal wheel machining according to claim 8, characterized in that: In step 6, the mathematical model of the back cutting surface is, Among them, m and n are the parameters of the parametric equation; N i,3 (m), N j,3 (n) is the cubic B-spline basis function; Q i,j Represents a control point.

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