阅读说明：本技术 一种摆线齿锥齿轮整体刀盘设计方法 (Design method for integral cutter head of cycloidal-tooth bevel gear ) 是由 郭文超 毛世民 于 2019-10-29 设计创作，主要内容包括：本发明公开了是一种摆线齿锥齿轮整体刀盘设计方法,属于摆线齿锥齿轮加工领域。一种摆线齿锥齿轮整体刀盘设计方法,按照如下步骤：(1)确定产形轮基本参数；(2)确定产形轮齿线方程；(3)确定铲磨圆半径；(4)确定刀齿设计与安装参数；(5)规划刀盘上刀齿总体布置。利用本发明的设计方法得到的刀盘,能够采用传统铲齿工艺加工,无需专用的磨刀机与检刀机,大大降低了刀盘设计与加工难度；适用于现有的弧齿锥齿轮铣齿机,使之同时具备了加工弧齿锥齿轮和摆线齿锥齿轮的能力；弧铣刀盘铲齿工艺技术成熟,且设备充足,降低了设计与制造成本,同时弥补了现阶段摆线齿锥齿轮机床与刀具加工能力差的缺陷。(The invention discloses a design method for an integral cutter head of a cycloidal-tooth bevel gear, and belongs to the field of processing of cycloidal-tooth bevel gears. A method for designing an integral cutter head of a cycloidal-tooth bevel gear comprises the following steps: (1) determining basic parameters of the production wheel; (2) determining a gear tooth line equation of the shape; (3) determining the radius of a relief grinding circle; (4) determining design and installation parameters of the cutter teeth; (5) and planning the overall arrangement of cutter teeth on the cutter head. The cutter head obtained by the design method can be processed by adopting the traditional relieving process, and a special knife grinder and a knife detecting machine are not needed, so that the design and processing difficulty of the cutter head is greatly reduced; the spiral bevel gear milling machine is suitable for the existing spiral bevel gear milling machine, and has the capability of processing spiral bevel gears and cycloidal bevel gears; the arc milling cutter disc relieving process is mature in technology and sufficient in equipment, the design and manufacturing cost is reduced, and meanwhile the defect that the machining capability of a cycloidal bevel gear machine tool and a cutter at the present stage is poor is overcome.)

1. A design method for an integral cutter head of a cycloidal-tooth bevel gear is characterized by comprising the following steps:

1) determining the tooth number of the shaping wheel, the radial cutter position and the angular cutter position of the cutter head according to the gear pair parameters and the cutter basic parameters;

2) determining a shape-generating gear tooth line equation in a plane where the nominal radius of the cutter head is located;

3) determining the effective range of the tooth trace of the shaping wheel in the step 2) according to the actual tooth width of the shaping wheel and the avoidance of interference of a rear cutter face; discretizing the shape-producing gear tooth line in the effective range, and fitting a discretized curve by using an approximate circular arc so as to determine the radius and the circle center position of the grinding circle;

4) determining the center offset distance of the cutter groove, the height of the theoretical groove bottom and the offset angle of the cutter tooth according to the selected blade parameters and relief grinding circle parameters;

5) and planning the cutter tooth sequence and the cutter tooth included angle in the circumferential direction of the cutter head according to the cutter tooth design and the installation parameters.

2. The method for designing the cutter head of the cycloidal-tooth bevel gear according to claim 1, wherein in step 1), the number of the generating gear teeth is determined according to the following formula:

wherein z is_pTo produce the number of teeth of the gear, z₁Number of teeth of small gear, z₂The number of teeth of the big gear is,

3. The method for designing the cutter head of a cycloidal-tooth bevel gear according to claim 1, wherein the radius of the midpoint of the shaping wheel is equal to the pitch of the midpoint cone of the gear pair;

the middle point helical angle of the shape generating wheel is equal to the middle point helical angle of the gear pair;

the gear pair midpoint conical distance and the gear pair midpoint spiral angle are obtained by design.

4. The method for designing the cutter head of a cycloidal-tooth bevel gear according to claim 3, wherein when the gear pair has an offset, the radius of the midpoint and the helix angle of the forming wheel both take the parameters corresponding to the bull wheel.

5. The design method of the overall cutterhead of the cycloidal-tooth bevel gear according to claim 1, wherein in step 2), the equation of the generated gear tooth line is as follows:

wherein r is₀Nominal cutter radius, M_dIs a radial tool position, q is an angular tool position, theta₀The included angle theta between the cutterhead radius vector and the shape-generating wheel radius vector when the cutterhead reference point is coincident with the middle point of the shape-generating wheel tooth surface_kAt the angle of rotation of the cutter head, theta_cIn order to generate the rotation angle of the shape wheel, the rotation relation of the shape wheel and the rotation angle satisfies:

z₀the number of the cutter heads.

6. The design method of the overall cutterhead of the cycloidal-tooth bevel gear according to claim 5, wherein the angular cutting position machining left-hand gear is positive and the right-hand gear is negative.

7. The method for designing the integral cutterhead of the cycloidal-tooth bevel gear according to claim 5, wherein in step 3), the effective range of the generating gear tooth line is discretized and an approximate circular arc is used for fitting the discretized curve, and the equation expression is as follows:

and (3) shoveling and grinding the circle center and the radius:

wherein the number of discrete points on the gear tooth line of the shaping gear is n, and the coordinate of the discrete point i is (x)_i,y_i) And a, b and c are solution variables of equation (4).

8. The method for designing the integral cutterhead of the cycloidal-tooth bevel gear according to claim 7, wherein the radius of the grinding circle is the theoretical mounting radius of the cutter teeth during grinding, the mounting base distance of the cutter teeth of the grinding tool is calculated according to the value, and the top edge clearance angle of the cutter teeth is 12 degrees.

9. The method for designing the overall cutterhead of the cycloidal-tooth bevel gear according to claim 7, wherein the parameters of the tool loading slot are determined in step 4) according to the selected blade parameters and relief rounding parameters, and specifically:

the parameter formulas of the tool loading groove are respectively obtained from the geometrical relationship:

D_k＝r₀cosβ＝r₀cos(α+υ_b) (10)

E_k＝E_bsinγ＝E_bsin(ε-α) (11)

wherein E is_kIs the center offset of the tool groove D_kV is the theoretical tank bottom height_bIn order to offset the angle of the cutter teeth,

10. The design method of the overall cutterhead of the cycloidal-tooth bevel gear according to claim 1, wherein in step 5), the step of planning the cutter tooth sequence and the cutter tooth included angle in the peripheral direction of the cutterhead is specifically as follows:

each group of cutter teeth consists of inner cutter teeth and outer cutter teeth, the cutter teeth are arranged in sequence that the inner cutter is in front and the outer cutter is behind, and the inner cutter teeth and the outer cutter teeth are alternately and uniformly arranged in the circumferential direction;

the included angle of the knife teeth is 360 degrees/z according to the included angle between adjacent knife teeth with the same name₀The inner and outer cutter holder angles of the same group of cutter teeth are 180 DEG/z₀。

Technical Field

The invention belongs to the field of processing of a cycloid tooth bevel gear, and particularly relates to a design method of an integral cutter head of the cycloid tooth bevel gear.

Background

The cycloid tooth bevel gear is named after the tooth trace of the generating wheel is an extended epicycloid, and the tooth milling processing is carried out by adopting a constant-height tooth system and a Face-hobbing method (plane-hobbing) based on the principle of a plane generating wheel. The cycloid tooth bevel gear has three types: manufactured by Klingelnberg, germany, by orlikon, switzerland (Oerlikon) and by Gleason, usa, abbreviated as kreb, ohn and kreb, respectively.

The forming principle of the generating surface of the generating wheel of the imaginary plane of the cycloidal tooth bevel gear is as follows: the cutter head and the shaping wheel are respectively provided with a rounding circle, and the movement of the cutter head relative to the shaping wheel can be regarded as that the rounding circle of the cutter head rolls on the rounding circle of the shaping wheel in a pure rolling way, namely, the ratio of the diameter of the rounding circle of the cutter head to the diameter of the rounding circle of the shaping wheel is equal to the ratio of the number of cutter teeth of the cutter head to the number of teeth of the shaping wheel. When the cutter disc rolls on the rolling circle of the shaping wheel, the curved surface swept out by the cutting edge relative to the shaping wheel is the tooth surface of the shaping wheel, and the track of the point on the cutting edge in the plane of the shaping wheel is an extended epicycloid. The tooth surface of the processed gear is formed by winding the tooth surface of the forming gear. In actual processing, a machine tool rocking disc is used for representing a shaping wheel, cutter teeth of a cutter disc are divided into a plurality of groups, each group is provided with at least one inner cutter and one outer cutter, and a convex surface and a concave surface of a gear to be processed are respectively processed. In order to realize the local contact of actual requirements, a split double-layer cutter head with a very complicated mechanical structure is adopted, and an integral cutter head and a cutter inclining mechanism are adopted in an Australia system and a grid system, and the calculation of the integral cutter head and the cutter inclining mechanism is very complicated. In order to better control the tooth surface contact area, arc cutting edges are introduced into the three tooth systems to carry out tooth height direction modification, and tooth surface mismatch is more reasonable and controllable by combining with the drum shape in the tooth length direction.

In recent years, both the clinbeck and the gleisen develop six-axis full-numerical control bevel gear machine tools, a disc rocking mechanism is cancelled, a hard alloy sharp-toothed strip integral cutter head tool tilting method is adopted to process cycloidal-tooth bevel gears, and part of the machine tools can be dry-cut at high speed, but the clinbeck double-layer cutter head has a complex structure and is difficult to design and process, and only the clinbeck can be manufactured at present; the sharp-tooth cutter head of the Orlikang and the Grisson has high requirements on design and processing precision, and needs a special knife sharpener and a knife detecting machine. The inner cutter teeth and the outer cutter teeth of the double-layer cutter head are respectively arranged on two independent cutter bodies and are embedded together, the inner cutter head body and the outer cutter head body are eccentric through the crosshead shoe mechanism, the structure is complex, the crosshead shoe structure causes poor rigidity of a machine tool, the cutting speed is influenced, and high-speed dry cutting machining cannot be performed. Both the Australian and the gridding adopt an integral cutter head, the restrained defect is overcome, but the cutter tilting processing method adds a cutter tilting and rotating mechanism to the machine tool, the machine tool has a complex structure and the calculation and adjustment are complex.

Disclosure of Invention

The invention aims to overcome the defect that a spiral bevel gear machine tool cannot be used for machining a cycloidal bevel gear, and provides a design method of an integral cutter head of the cycloidal bevel gear.

A method for designing an integral cutter head of a cycloidal-tooth bevel gear comprises the following steps:

1) determining the tooth number of the shaping wheel, the radial cutter position and the angular cutter position of the cutter head according to the gear pair parameters and the cutter basic parameters;

2) determining a shape-generating gear tooth line equation in a plane where the nominal radius of the cutter head is located;

3) determining the effective range of the tooth trace of the shaping wheel in the step 2) according to the actual tooth width of the shaping wheel and the avoidance of interference of a rear cutter face; discretizing the shape-producing gear tooth line in the effective range, and fitting a discretized curve by using an approximate circular arc so as to determine the radius and the circle center position of the grinding circle;

4) determining the center offset distance of the cutter groove, the height of the theoretical groove bottom and the offset angle of the cutter tooth according to the selected blade parameters and relief grinding circle parameters;

5) and planning the cutter tooth sequence and the cutter tooth included angle in the circumferential direction of the cutter head according to the cutter tooth design and the installation parameters.

Further, in step 1), the number of the forming gear teeth is determined according to the following formula:

wherein z is_pTo produce the number of teeth of the gear, z₁Number of teeth of small gear, z₂The number of teeth of the big gear is,

for gear pair pitch angle correction, delta₀₁At a small pitch cone angle, delta₀₂Is a large wheel-knuckle cone angle.

Further, the radius of the middle point of the shaping wheel is equal to the middle point cone distance of the gear pair;

the middle point helical angle of the shape generating wheel is equal to the middle point helical angle of the gear pair;

the gear pair midpoint conical distance and the gear pair midpoint spiral angle are obtained by design.

Furthermore, when the gear pair has offset distance, the midpoint radius and the midpoint spiral angle of the shaping wheel both adopt corresponding parameters of the large wheel.

Further, in step 2), the equation of the gear tooth line of the shape-generating gear is as follows:

wherein r is₀Nominal cutter radius, M_dIs a radial tool position, q is an angular tool position, theta₀The included angle theta between the cutterhead radius vector and the shape-generating wheel radius vector when the cutterhead reference point is coincident with the middle point of the shape-generating wheel tooth surface_kAt the angle of rotation of the cutter head, theta_cIn order to generate the rotation angle of the shape wheel, the rotation relation of the shape wheel and the rotation angle satisfies:

z₀the number of the cutter heads.

Furthermore, the angle cutter position processing left-hand gear is positive, and the right-hand gear is negative.

Further, in step 3), the effective range of the gear tooth line of the product shape is dispersed and an approximate circular arc is used for fitting a discretized curve, and the equation expression is as follows:

and (3) shoveling and grinding the circle center and the radius:

wherein the number of discrete points on the gear tooth line of the shaping gear is n, and the coordinate of the discrete point i is (x)_i,y_i) And a, b and c are solution variables of equation (4).

Further, the relief grinding circle radius is the theoretical installation radius of the cutter tooth during relief grinding, the installation base distance of the cutter tooth of the cutter grinding tool is calculated according to the value, and the top edge back angle of the cutter tooth is 12 degrees in standard.

Further, determining a knife loading groove parameter according to the selected blade parameter and the relief grinding circle parameter in the step 4), specifically:

the parameter formulas of the tool loading groove are respectively obtained from the geometrical relationship:

D_k＝r₀cosβ＝r₀cos(α+υ_b) (10)

E_k＝E_bsinγ＝E_bsin(ε-α) (11)

wherein E is_kIs the center offset of the tool groove D_kV is the theoretical tank bottom height_bIn order to offset the angle of the cutter teeth,

E_bthe distance from the center of the relief grinding to the center of the cutter head.

Further, in step 5), the step of planning the cutter tooth sequence and the cutter tooth included angle in the cutter head circumferential direction is specifically as follows:

each group of cutter teeth consists of inner cutter teeth and outer cutter teeth, the cutter teeth are arranged in sequence that the inner cutter is in front and the outer cutter is behind, and the inner cutter teeth and the outer cutter teeth are alternately and uniformly arranged in the circumferential direction;

the included angle of the knife teeth is 360 degrees/z according to the included angle between adjacent knife teeth with the same name₀The inner and outer cutter holder angles of the same group of cutter teeth are 180 DEG/z₀。

Compared with the prior art, the invention has the following beneficial effects:

the invention relates to a design method of an integral cutter head of a cycloidal tooth bevel gear, wherein the nominal radius of the designed integral relieving cutter head is selected according to the diameter and the tooth width of a gear to be processed, the cutter heads for processing large and small gears of a gear pair have the same nominal radius and opposite rotation directions, the cutting edges of the cutter teeth adopt circular arcs to replace straight lines, and the tangent points of the circular arcs and the straight lines are in the reference plane of the cutter heads; the cutter teeth of the designed cutter head take the extended epicycloidal tooth trace of the shaping wheel as the rear cutter face of the cutter teeth, and the cutter teeth are machined by adopting an approximate arc instead of a relieving process, so that the cutter can be machined on an arc milling cutter relief grinding machine tool without a special cutter grinder and a special cutter checking machine; the designed cutter head can be used for the existing spiral bevel gear machine tool, the spiral bevel gear machine tool comprises a traditional cradle type machine tool and a numerical control machine tool, machining of a cycloid tooth bevel gear can be carried out as long as a cutter main shaft is set to be in a servo mode, the introduction of the cycloid tooth bevel gear machine tool is not needed, and machining cost of the cycloid tooth bevel gear is greatly reduced. The cutter head designed according to the design method of the invention is processed by adopting the traditional relieving process, and a special knife grinder and a knife checking machine are not needed, so that the design and processing difficulty of the cutter head is greatly reduced; the spiral bevel gear milling machine is suitable for the existing spiral bevel gear milling machine, and has the capability of processing spiral bevel gears and cycloidal bevel gears; the arc milling cutter disc relieving process is mature in technology and sufficient in equipment, the design and manufacturing cost is reduced, and meanwhile the defect that the machining capability of a cycloidal bevel gear machine tool and a cutter at the present stage is poor is overcome.

Drawings

FIG. 1 is a schematic view of a flat forming wheel; .

FIG. 2 is a schematic diagram of a coordinate system and a relative movement relationship between a left-handed cutter and a shaping wheel;

FIG. 3 is a schematic diagram of the calculation of the relief grinding radius of the integral cutter tooth according to the present invention;

FIG. 4 is a schematic diagram of the design and installation parameters of a single cutter tooth of the left-hand cutter head of the present invention;

FIG. 5 is a schematic view of the overall arrangement of the left-hand cutter head teeth of the present invention;

FIG. 6 is a schematic view of the installation of inner and outer cutter teeth sharpening of the left-handed small-wheel cutter head in the embodiment;

wherein: 1-a small wheel; 2-big wheel; 3-a planar shaping wheel; 4-inner cutter teeth; 5-outer cutter teeth.

Detailed Description

In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.

The invention is described in further detail below with reference to the accompanying drawings:

1) determining basic parameters of a forming wheel

The basic parameters of the shape-producing wheel include the number of teeth, the radius of the middle point and the helix angle of the middle point, see fig. 1, fig. 1 is a schematic diagram of a planar shape-producing wheel, δ₀₁、δ₀₂Taper angle of small and large wheel segments, d₀₂、d₀₂The diameter of the outer pitch circle of the small wheel and the big wheel is set as z₁Number of teeth of small gear, z₂The number of teeth of the big gear is,

and if the gear pair pitch cone angle is corrected, the number of the formed gear teeth is:

the radius of the middle point of the shaping wheel is equal to the distance between the middle points of the gear pairsR_mThe midpoint helix angle of the shape-producing wheel is equal to the midpoint helix angle β of the gear pair_mThe pitch of the middle point of the shaping wheel is equal to that of the gear pair; the gear pair midpoint conical distance, the gear pair midpoint spiral angle and the gear pair midpoint tooth distance are obtained by design.

Aiming at the hypoid gear, the parameters of the shape-generating wheel are all corresponding to the parameters of the big wheel.

2) Determining a gear tooth line equation

The tooth trace is the tooth trace of the shape-generating wheel in the plane of the nominal radius of the cutter head, see fig. 2, fig. 2 is a schematic diagram of a coordinate system and a relative motion relationship between the left-handed cutter head and the shape-generating wheel, and S_k、S_cFor being respectively a coordinate system fixedly connected with the cutter head and the shape generating wheel, the shape generating wheel tooth line equation is also a tooth line equation under the cutter head coordinate system, and specifically comprises the following steps:

wherein r is₀Nominal cutter radius, M_dIs a radial cutter position, q is an angular cutter position (a left-hand gear is machined to be positive, a right-hand gear is machined to be negative), theta₀The included angle theta between the cutterhead radius vector and the shape-generating wheel radius vector when the cutterhead reference point is coincident with the middle point of the shape-generating wheel tooth surface_kAnd theta_cThe rotation angles of the cutter head and the shaping wheel are respectively, the coordinate system and the rotation relation of the cutter head and the shaping wheel are shown in figure 2, and the requirements are met:

wherein z is₀The number of the cutter heads.

3) Determining the relief grinding radius of the cutter teeth

Referring to fig. 3, fig. 3 is a schematic diagram of calculating the relief grinding radius of the integral cutter tooth according to the present invention, the effective range of the tooth trace of the shaping wheel is determined according to the actual tooth width of the shaping wheel and the avoidance of interference of the rear cutter face, the obtained effective range is dispersed to obtain discrete data, and the tooth trace is fitted by using an approximate arc by using the least square method, the radius of the fitting tooth trace is the radius of the relief grinding circle, the center of the fitting tooth trace is the center of the relief grinding circle, thereby determining the radius and the center position of the relief grinding circle, and the specific equation can be expressed as:

relief grinding of circle center and radius:

wherein the number of discrete points on the gear tooth line of the shaping gear is n, and the coordinate of the discrete point i is (x)_i,y_i) And a, b and c are solution variables of equation (4).

4) Determining cutter tooth mounting design and mounting parameters

Determining the center offset E of the cutter groove according to the parameters of the grinding circle of the shovel obtained in the step 3) and the selected parameters of the blade_kTheoretical tank bottom height D_kAnd a cutter tooth offset angle v_bThe parameter of (1) is set as the distance | o from the center of the relief grinding to the center of the cutter head_b0o_kL is E_bThen there is

Referring to fig. 4, fig. 4 is a schematic diagram of the design of a single cutter groove of a left-handed cutter head and the installation parameters of the cutter blades of the invention, O_kIs the center of rotation of the cutter head, O_b0For relief grinding of the center of the circle, the M point is a reference point for cutter head design calculation, and the following installation parameter calculation formula can be obtained from the geometric relationship in FIG. 4:

D_k＝r₀cosβ＝r₀cos(α+υ_b) (10)

E_k＝E_bsinγ＝E_bsin(ε-α) (11)

5) planning cutter head upper cutter tooth overall arrangement

The cutter tooth arrangement refers to the distribution of cutter teeth in the circumferential direction of a cutter head, and comprises two aspects of cutter tooth sequence and cutter tooth included angle, each group of cutter teeth in the design comprises inner cutter teeth and outer cutter teeth, the outer cutter is arranged in front, the inner cutter is arranged behind, and the inner cutter teeth and the outer cutter teeth are uniformly arranged in the circumferential direction at intervals, as shown in figure 5, figure 5 is a general arrangement schematic diagram of the cutter teeth of the left-handed cutter head, and 4 and 5 are respectively the inner cutter teeth and the outer cutter teeth. The included angle between adjacent teeth of the same knife is 360 degrees/z₀The inner and outer cutter holder angles of the same group of cutter teeth are 180 DEG/z₀. And the left-handed cutter disc rotates anticlockwise (right against the cutter teeth) to process a left-handed gear, the right-handed cutter disc rotates clockwise to process a right-handed gear, and the cutter teeth are cut into a small end from the large end of the workpiece.

And if the inner cutter and the outer cutter are interfered, modifying the size parameters of the cutter head again.