阅读说明：本技术 一种获取滚切倒棱刀具前刀面廓形的方法 (Method for obtaining profile of front cutter face of hobbing chamfering cutter ) 是由 何坤 何晓虎 于 2021-09-30 设计创作，主要内容包括：本发明公开了一种获取滚切倒棱刀具前刀面廓形的方法,其包括步骤：1)建立滚切倒棱刀具与圆柱齿轮的空间展成运动关系坐标系,2)建立各坐标系之间的坐标变换矩阵,3)将圆柱齿轮倒棱目标廓形表示在齿轮静坐标系中,4)建立滚切倒棱刀具与圆柱齿轮端面廓形的接触点模型；5)求解滚切倒棱刀具前刀面与齿轮齿廓接触点的坐标；6)圆滑连接滚切倒棱刀具前刀面与齿轮倒棱目标廓形的各接触点,得到滚切倒棱刀具前刀面刃口曲线。本发明获取滚切倒棱刀具前刀面廓形的方法,其基于滚切连续展成切削运动原理,通过连续求解刀具前刀面与齿轮倒棱目标廓形的接触点,得到滚切倒棱刀具前刀面廓形,能用于滚切倒棱刀具设计,提高圆柱齿轮齿廓倒棱效率。(The invention discloses a method for obtaining the profile of the front cutter face of a hobbing chamfering cutter, which comprises the following steps: 1) establishing a space generation motion relation coordinate system of the hobbing and chamfering tool and the cylindrical gear, 2) establishing a coordinate transformation matrix among the coordinate systems, 3) expressing the chamfering target profile of the cylindrical gear in a gear static coordinate system, and 4) establishing a contact point model of the hobbing and chamfering tool and the cylindrical gear end surface profile; 5) solving the coordinate of the contact point of the front cutter face of the hobbing and chamfering cutter and the tooth profile of the gear; 6) and smoothly connecting each contact point of the front cutter face of the hobbing and chamfering cutter and the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the hobbing and chamfering cutter. The method for obtaining the profile of the front cutter face of the hobbing and chamfering cutter is based on the principle of hobbing continuous generating cutting motion, and the profile of the front cutter face of the hobbing and chamfering cutter is obtained by continuously solving the contact point of the front cutter face of the cutter and the gear chamfering target profile, so that the method can be used for designing the hobbing and chamfering cutter and improving the tooth profile chamfering efficiency of a cylindrical gear.)

1. A method for obtaining the profile of the front tool face of a hobbing chamfering tool is characterized by comprising the following steps: the method comprises the following steps:

1) establishing a space expansion motion relation coordinate system of the roll-cutting chamfering tool and the cylindrical gear according to the installation pose of the roll-cutting chamfering tool, wherein the space expansion motion relation coordinate system comprises: gear static coordinate system o_m-x_my_mz_mMoving coordinate system o of gear_g-x_gy_gz_gTool static coordinate system o₁-x₁y₁z₁And the tool moving coordinate system o_d-x_dy_dz_d，

Gear moving coordinate system o_g-x_gy_gz_gFixedly connected with the cylindrical gear, and at the initial position, a gear moving coordinate system o_g-x_gy_gz_gAnd gear static coordinate system o_m-x_my_mz_mOverlapping;

moving coordinate system o of tool_d-x_dy_dz_dFixedly connected with a hobbing chamfering tool, and a tool moving coordinate system o at an initial position_d-x_dy_dz_dAnd a tool static coordinate system o₁-x₁y₁z₁Overlapping;

2) establishing a coordinate transformation matrix M from a gear moving coordinate system to a gear static coordinate system_mg：

WhereinFor gear winding z_mThe angle of counterclockwise rotation of the shaft;

establishing a coordinate transformation matrix M from a gear static coordinate system to a cutter static coordinate system_1m：

Wherein h is the geometric center of the hobbing chamfering tool in z_mThe height difference between the axial direction and the end surface of the cylindrical gear, p is x_mThe distance from the axis of the cylindrical gear in the axial direction to the axis of the hobbing chamfering tool;

establishing a coordinate transformation matrix M from a tool static coordinate system to a tool moving coordinate system_d1：

WhereinFor rolling chamfering tools around z₁The angle of the shaft rotating anticlockwise, the gear rotating around z in the process of continuously generating chamfering_mAngle of counterclockwise rotation of the shaftThe roll-cutting chamfering tool is wound around z₁Angle of counterclockwise rotation of the shaftStatic coordinate system x of front cutting edge and gear of chamfering tool for hobbing_mo_my_mThe included angle of the face;

wherein k is the tooth number of the hobbing and chamfering tool, and z is the tooth number of the cylindrical gear;

3) expressing the cylindrical gear chamfering target profile in a gear static coordinate system o on the basis of the step 2)_m-x_my_mz_mThe cylindrical gear chamfering target profile comprises a cylindrical gear chamfering target left tooth profile, a cylindrical gear chamfering target left tooth profile transition arc, a cylindrical gear chamfering target right tooth profile and a cylindrical gear chamfering target right tooth profile transition arc;

whereinAn equation is expressed for a cylindrical gear chamfering target left tooth profile in a gear dynamic coordinate system,an equation is expressed for the right tooth profile of the cylindrical gear chamfering target in a gear dynamic coordinate system,an equation is expressed for a cylindrical gear chamfering target left tooth profile transition circular arc in a gear dynamic coordinate system,representing an equation for a right tooth profile transition circular arc of a cylindrical gear chamfering target in a gear dynamic coordinate system, wherein alpha is an expansion angle of a left tooth profile and a right tooth profile, and r is_bThe base radius of the cylindrical gear is shown, and delta is an initial deflection angle; r is_cIs the tooth profile transition arc radius, alpha_sIs the starting spread angle of the tooth profile transition arc, (x)_c，y_c) Is the circle center coordinate of the transition arc of the left tooth profile;

4) establishing a contact point model of the hobbing chamfering tool and the cylindrical gear end face profile:

the axial lead of the over-rolling chamfering tool makes an inclination angle of the cylindrical gear relative to the end facePlane M, plane M being the coordinate system o_d-x_dy_dz_dX of_do_dz_dPlane, plane M and coordinate system o_m-x_my_mz_mX of_mo_my_mThe faces intersect at a line L, the equation for which is:

the straight line L and the cylindrical gear end face profile curve are intersected at a point G, and the point G is a contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile;

5) solving the coordinates of the contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile:

solving the coordinate of the G point simultaneously with the formula (9) according to the cylindrical gear chamfered target profile equation determined by the formula (5) to the formula (8);

converting the obtained G point coordinate into a chamfering tool moving coordinate system to obtain the rotation angle of the hobbing chamfering toolRotation angle of cylindrical gearContour points of the hobbing chamfering tool at the positions:

the cylindrical gear is rotated continuously by the angle delta theta, the rolling cutting chamfering tool is rotated by the angle delta eta according to the generated motion relation,

Δη＝zΔθ/k (12)

obtain the corresponding cylindrical gear cornerCorner of cutterPoint G' of contact point; repeatedly carrying out the calculation, and continuously solving a series of contact points of the front cutter face of the roll-cutting chamfering cutter and the gear chamfering target profile;

6) and smoothly connecting each contact point of the front cutter face of the hobbing and chamfering cutter and the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the hobbing and chamfering cutter.

Technical Field

The invention relates to the technical field of hobbing cutter design, and relates to a design method of a cylindrical gear hobbing chamfering cutter.

Background

The cylindrical gear is widely used in high-speed and heavy-load occasions due to compact structure, strong bearing capacity and stable transmission ratio. In order to improve the transmission precision and prolong the service life, chamfering is a common process means, burrs generated due to collision can be avoided through the chamfered cylindrical gear, and meanwhile, the noise influence of the gear is reduced.

The types of processes currently used are mainly edge grinding and edge extrusion. The edge grinding method adopts a grinding mode to carry out chamfering, and has the problems of low processing efficiency, difficult control of edge grinding shape and the like; the edge-extruding method adopts the edge-extruding cutter and the gear to be processed to perform the backlash-free meshing motion to perform complete and uniform chamfering on the whole tooth profile of the gear, but the cutters need to be used in pairs, and the design of the cutters is complex. With the increasing requirements on the performance of the processed gear, the chamfering principle research and the chamfering machine development become more and more important.

At present, chamfering of spiral bevel gears is a research hotspot, a disk-shaped cutter is generally adopted to indirectly index and cut chamfers one by one for chamfering processing, but the chamfering method taking the spiral bevel gears as research objects is not suitable for chamfering processing of cylindrical gears.

Because the profile of the hobbing chamfering tool and the profile of the end face of the cylindrical gear to be machined are not conjugate tooth profiles any more, the tool profile cannot be solved by adopting an analytical method based on the gear meshing principle. And the premise of designing the hobbing chamfering tool is to obtain the profile of the front tool face of the chamfering tool correctly.

Disclosure of Invention

In view of this, the present invention provides a method for obtaining a profile of a rake face of a hobbing and chamfering tool, so as to solve the technical problem of how to obtain the profile of the rake face of the hobbing and chamfering tool for a cylindrical gear.

The invention discloses a method for obtaining the profile of the front cutter face of a hobbing chamfering cutter, which comprises the following steps:

1) establishing a space expansion motion relation coordinate system of the roll-cutting chamfering tool and the cylindrical gear according to the installation pose of the roll-cutting chamfering tool, wherein the space expansion motion relation coordinate system comprises: gear static coordinate system o_m-x_my_mz_mMoving coordinate system o of gear_g-x_gy_gz_gTool static coordinate system o₁-x₁y₁z₁And the tool moving coordinate system o_d-x_dy_dz_d，

Gear moving coordinate system o_g-x_gy_gz_gFixedly connected with the cylindrical gear, and at the initial position, a gear moving coordinate system o_g-x_gy_gz_gAnd gear static coordinate system o_m-x_my_mz_mOverlapping;

moving coordinate system o of tool_d-x_dy_dz_dFixedly connected with a hobbing chamfering tool, and a tool moving coordinate system o at an initial position_d-x_dy_dz_dAnd a tool static coordinate system o₁-x₁y₁z₁Overlapping;

2) establishing a coordinate transformation matrix M from a gear moving coordinate system to a gear static coordinate system_mg：

WhereinFor gear winding z_mThe angle of counterclockwise rotation of the shaft;

establishing a coordinate transformation matrix M from a gear static coordinate system to a cutter static coordinate system_1m：

Wherein h is the geometric center of the hobbing chamfering tool in z_mThe height difference between the axial direction and the end surface of the cylindrical gear, p is x_mThe distance from the axis of the cylindrical gear in the axial direction to the axis of the hobbing chamfering tool;

establishing a coordinate transformation matrix M from a tool static coordinate system to a tool moving coordinate system_d1：

WhereinFor rolling chamfering tools around z₁The angle of the shaft rotating anticlockwise, the gear rotating around z in the process of continuously generating chamfering_mAngle of counterclockwise rotation of the shaftThe roll-cutting chamfering tool is wound around z₁Angle of counterclockwise rotation of the shaft Static coordinate system x of front cutting edge and gear of chamfering tool for hobbing_mo_my_mThe included angle of the face;

wherein k is the tooth number of the hobbing and chamfering tool, and z is the tooth number of the cylindrical gear;

3) expressing the cylindrical gear chamfering target profile in a gear static coordinate system o on the basis of the step 2)_m-x_my_mz_mThe cylindrical gear chamfering target profile comprises a cylindrical gear chamfering target left tooth profile, a cylindrical gear chamfering target left tooth profile transition arc, a cylindrical gear chamfering target right tooth profile and a cylindrical gear chamfering target right tooth profile transition arc;

whereinAn equation is expressed for a cylindrical gear chamfering target left tooth profile in a gear dynamic coordinate system,an equation is expressed for the right tooth profile of the cylindrical gear chamfering target in a gear dynamic coordinate system,an equation is expressed for a cylindrical gear chamfering target left tooth profile transition circular arc in a gear dynamic coordinate system,representing an equation for a right tooth profile transition circular arc of a cylindrical gear chamfering target in a gear dynamic coordinate system, wherein alpha is an expansion angle of a left tooth profile and a right tooth profile, and r is_bThe base radius of the cylindrical gear is shown, and delta is an initial deflection angle; r is_cIs the tooth profile transition arc radius, alpha_sIs the starting spread angle of the tooth profile transition arc, (x)_c，y_c) Is the circle center coordinate of the transition arc of the left tooth profile;

4) establishing a contact point model of the hobbing chamfering tool and the cylindrical gear end face profile:

the axial lead of the over-rolling chamfering tool makes an inclination angle of the cylindrical gear relative to the end facePlane M, plane M being the coordinate system o_d-x_dy_dz_dX of_do_dz_dPlane, plane M and coordinate system o_m-x_my_mz_mX of_mo_my_mThe faces intersect at a line L, the equation for which is:

the straight line L and the cylindrical gear end face profile curve are intersected at a point G, and the point G is a contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile;

5) solving the coordinates of the contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile:

solving the coordinate of the G point simultaneously with the formula (9) according to the cylindrical gear chamfered target profile equation determined by the formula (5) to the formula (8);

converting the obtained G point coordinate into a chamfering tool moving coordinate system to obtain the rotation angle of the hobbing chamfering toolRotation angle of cylindrical gearContour points of the hobbing chamfering tool at the positions:

the cylindrical gear is rotated continuously by the angle delta theta, the rolling cutting chamfering tool is rotated by the angle delta eta according to the generated motion relation,

Δη＝zΔθ/k (12)

obtain the corresponding cylindrical gear cornerCorner of cutterPoint G' of contact point; repeatedly carrying out the calculation, and continuously solving a series of contact points of the front cutter face of the roll-cutting chamfering cutter and the gear chamfering target profile;

6) and smoothly connecting each contact point of the front cutter face of the hobbing and chamfering cutter and the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the hobbing and chamfering cutter.

The invention has the beneficial effects that:

the method for obtaining the profile of the front cutter face of the hobbing and chamfering cutter is based on the principle of hobbing continuous generating cutting motion, and the profile of the front cutter face of the hobbing and chamfering cutter is obtained by continuously solving the contact point of the front cutter face of the cutter and the gear chamfering target profile, so that the method can be used for designing the hobbing and chamfering cutter and improving the tooth profile chamfering efficiency of a cylindrical gear.

Drawings

FIG. 1 is a schematic view of the installation position of a hobbing and chamfering tool relative to a cylindrical gear;

FIG. 2 is a space generation motion coordinate system of a hobbing chamfering tool and a cylindrical gear;

FIG. 3 is a model of the contact point between the hobbing and chamfering tool and the cylindrical gear;

fig. 4 is a rake face profile of a roll cutting chamfer tool.

Detailed Description

The invention is further described below with reference to the figures and examples.

The method for obtaining the profile of the rake face of the hobbing and chamfering tool comprises the following steps:

1) establishing a space expansion motion relation coordinate system of the roll-cutting chamfering tool and the cylindrical gear according to the installation pose of the roll-cutting chamfering tool, wherein the space expansion motion relation coordinate system comprises: gear static coordinate system o_m-x_my_mz_mMoving coordinate system o of gear_g-x_gy_gz_gTool static coordinate system o₁-x₁y₁z₁And the tool moving coordinate system o_d-x_dy_dz_d，

Gear moving coordinate system o_g-x_gy_gz_gFixedly connected with the cylindrical gear, and at the initial position, a gear moving coordinate system o_g-x_gy_gz_gAnd gear static coordinate system o_m-x_my_mz_mOverlapping;

moving coordinate system o of tool_d-x_dy_dz_dFixedly connected with a hobbing chamfering tool, and a tool moving coordinate system o at an initial position_d-x_dy_dz_dAnd a tool static coordinate system o₁-x₁y₁z₁And (4) overlapping.

2) Establishing a coordinate transformation matrix M from a gear moving coordinate system to a gear static coordinate system_mg：

WhereinFor gear winding z_mThe angle of counterclockwise rotation of the shaft;

establishing a coordinate transformation matrix M from a gear static coordinate system to a cutter static coordinate system_1m：

Wherein h is the geometric center of the hobbing chamfering tool in z_mThe height difference between the axial direction and the end surface of the cylindrical gear, p is x_mThe distance from the axis of the cylindrical gear in the axial direction to the axis of the hobbing chamfering tool;

establishing a coordinate transformation matrix M from a tool static coordinate system to a tool moving coordinate system_d1：

WhereinFor rolling chamfering tools around z₁The angle of the shaft rotating anticlockwise, the gear rotating around z in the process of continuously generating chamfering_mAngle of counterclockwise rotation of the shaftThe roll-cutting chamfering tool is wound around z₁Angle of counterclockwise rotation of the shaft Static coordinate system x of front cutting edge and gear of chamfering tool for hobbing_mo_my_mThe included angle of the face;

wherein k is the tooth number of the hobbing and chamfering tool, and z is the tooth number of the cylindrical gear.

3) Expressing the cylindrical gear chamfering target profile in a gear static coordinate system o on the basis of the step 2)_m-x_my_mz_mThe cylindrical gear chamfering target profile comprises a cylindrical gear chamfering target left tooth profile, a cylindrical gear chamfering target left tooth profile transition arc, a cylindrical gear chamfering target right tooth profile and a cylindrical gear chamfering target right tooth profile transition arc;

whereinAn equation is expressed for a cylindrical gear chamfering target left tooth profile in a gear dynamic coordinate system,an equation is expressed for the right tooth profile of the cylindrical gear chamfering target in a gear dynamic coordinate system,an equation is expressed for a cylindrical gear chamfering target left tooth profile transition circular arc in a gear dynamic coordinate system,representing an equation for a right tooth profile transition circular arc of a cylindrical gear chamfering target in a gear dynamic coordinate system, wherein alpha is an expansion angle of a left tooth profile and a right tooth profile, and r is_bThe base radius of the cylindrical gear is shown, and delta is an initial deflection angle; r is_cIs the tooth profile transition arc radius, alpha_sIs the starting spread angle of the tooth profile transition arc, (x)_c，y_c) Is the center coordinate of the transition arc of the left tooth profile.

4) Establishing a contact point model of the hobbing chamfering tool and the cylindrical gear end face profile:

the axial lead of the over-rolling chamfering tool makes an inclination angle of the cylindrical gear relative to the end facePlane M, plane M being the coordinate system o_d-x_dy_dz_dX of_do_dz_dPlane, plane M and coordinate system o_m-x_my_mz_mX of_mo_my_mThe faces intersect at a line L, the equation for which is:

the straight line L intersects with the profile curve of the cylindrical gear end face at a point G, and the point G is a contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile.

5) Solving the coordinates of the contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile:

solving the coordinate of the G point simultaneously with the formula (9) according to the cylindrical gear chamfered target profile equation determined by the formula (5) to the formula (8);

converting the obtained G point coordinate into a chamfering tool moving coordinate system to obtain the rotation angle of the hobbing chamfering toolRotation angle of cylindrical gearContour points of the hobbing chamfering tool at the positions:

the cylindrical gear is rotated continuously by the angle delta theta, the rolling cutting chamfering tool is rotated by the angle delta eta according to the generated motion relation,

Δη＝zΔθ/k (12)

obtain the corresponding cylindrical gear cornerCorner of cutterPoint G' of contact point; and repeating the calculation, and continuously solving a series of contact points of the front cutter surface of the roll-cutting chamfering cutter and the gear chamfering target profile.

6) And smoothly connecting each contact point of the front cutter face of the hobbing and chamfering cutter and the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the hobbing and chamfering cutter.

In the method for obtaining the profile of the front tool face of the hobbing and chamfering tool in the embodiment, based on the principle of hobbing continuous generating cutting motion, the profile of the front tool face of the hobbing and chamfering tool is obtained by continuously solving the contact point between the front tool face of the tool and the gear chamfering target profile, and the method can be used for designing the hobbing and chamfering tool and improving the tooth profile chamfering efficiency of a cylindrical gear.

Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.