CN112643143B - Profile design method for drum-shaped worm grinding wheel of grinding face gear - Google Patents
Profile design method for drum-shaped worm grinding wheel of grinding face gear Download PDFInfo
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Abstract
The invention discloses a method for designing the outline of a drum-shaped worm grinding wheel for grinding a face gear. Based on the profile of the gear shaper cutter, a pair of tooth profiles consistent with the profile of the gear shaper cutter is constructed on the normal section of a drum-shaped worm matrix, the pair of tooth profiles are taken as generatrices to do specific spiral motion along the surface of the drum-shaped worm grinding wheel matrix, and the profile of the drum-shaped worm grinding wheel is formed by a generatrix spiral sweeping method. In addition, the helix angle of the grinding wheel is calculated according to the surface helix equation of the drum worm grinding wheel matrix, and the normal section position of the drum worm grinding wheel is determined by the nominal helix angle of the grinding wheel. The method designs and calculates the profile of the drum-shaped worm grinding wheel without solving a complex meshing equation, has simple calculation process, avoids the limitation of a profile calculation result by singular points, and obtains the profile of the worm grinding wheel with high precision.
Description
Technical Field
The invention belongs to the field of gear manufacturing, in particular relates to grinding processing of a face gear, and particularly relates to a method for designing a profile of a drum-shaped worm grinding wheel for grinding the face gear.
Technical Field
The face gear transmission has the advantages of compact structure, convenience in installation and adjustment, large contact ratio and the like, and is applied to the fields of airplanes, automobiles, wind power, robots and the like. In order to apply the face gear to the working conditions of high speed and heavy load, the hardness and the precision of the face gear tooth surface must be improved, the heat treatment process is generally adopted for improving the tooth surface hardness, after the heat treatment process, the tooth grinding is the essential finish machining process for improving the tooth surface precision, however, the grinding machining of the face gear is always the key point and the difficulty in the face gear manufacturing process.
LITVIN (China) and 1992 and 2000 successively propose a method for grinding face gears by using a disc grinding wheel and a worm grinding wheel, and develop a corresponding special gear grinding machine tool for the face gears. The ConIFACE grinding method is introduced by Gleason corporation, and a special involute edge disc-shaped grinding wheel is adopted to grind a face gear, but the method can only obtain an approximate tooth surface and has higher requirements on machine tool parameter adjustment. The theory and method of the grinding face gear of the disc grinding wheel are researched by the national northwest industrial university Fangzong, Zhaoning and the like and the Chinese-south university Tangjinyuan and the like, and research on the grinding face gear generated by the worm grinding wheel is developed by Zhurupeng and the like of Nanjing aerospace university, so that a large number of achievements are obtained, and the grinding processing of the face gear is also realized on a small part of domestic gear grinding machine tools. However, most of the design calculation aiming at the worm grinding wheel profile of the grinding face gear is based on the meshing theory at present, the worm grinding wheel profile is obtained by solving the meshing equation, the calculation process and the result are complex, and the obtained profile is limited by singular points. In order to avoid solving a complex meshing equation, the Wangzaizhong of Beijing aerospace university proposes that a cylindrical gear is evolved into a spherical hob for a rolling tangent face gear, the method can avoid the limitation of singular points on a base worm of the hob, but the size of the spherical hob is limited by the size of the cylindrical gear. Therefore, the development significance of designing the worm grinding wheel which does not need to solve a complex meshing equation and is not limited by the size of the gear before evolution in the face gear generating grinding technology in the engineering practice is great.
Disclosure of Invention
Aiming at the defects of the existing method, the invention provides a method for designing the profile of a drum-shaped worm grinding wheel for grinding a face gear, which is characterized in that a gear shaper cutter is converted into the drum-shaped worm grinding wheel according to the working principle of the gear shaper cutter for processing the face gear; the process of evolution and calculation of the profile of the drum-shaped worm grinding wheel by the method is simple, the precision of the obtained profile is controllable, and the calculation efficiency and the design precision are greatly improved.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for designing the profile of a drum-shaped worm grinding wheel for grinding face gears comprises the following steps:
1) establishing a coordinate system formed by evolution from a slotting cutter to a drum worm grinding wheel: as shown in FIG. 1, wherein Ow-XwYwZwA moving coordinate system, O-XYZ and O, fixedly connected with the drum-shaped worm grinding wheeln-XnYnZnAre all fixed coordinate systems and the YOZ plane and YnOnZnThe plane is respectively superposed with the cross section of the worm shaft and the normal cross section, and the included angle between the plane and the normal cross section is lambda0，Os-XsYsZsA motion coordinate system of an imaginary tooth line, O1-X1Y1Z1As an auxiliary coordinate system, O1-X1Y1Z1And On-XnYnZnThe shortest distance between the two origins is E;
2) establishing a tooth profile equation which is consistent with the tooth profile of the gear shaper cutter on the section of the drum-shaped worm method, taking the tooth profile as a bus forming the molded surface of the drum-shaped worm grinding wheel, and setting the tooth profile equation in a coordinate system Os-XsYsZsIs represented as:
in the formula: x is a radical of a fluorine atomsIs a tooth line in a coordinate system Os-XsYsZsIn X-axis coordinate, ysIs a tooth line in a coordinate system Os-XsYsZsIn the Y-axis coordinate of (1), zsIs a tooth line in a coordinate system Os-XsYsZsZ axis coordinate of (1), rbIs the base radius of the pinion cutter, theta0For the half angle of the tooth space of the slotting cutter, the formula theta0＝π/2zs-invα0Is determined wherein zsAnd alpha0The number of teeth and the pressure angle of the slotting cutter are respectively, theta is an involute variable parameter, plus or minus is plus or minus, plus or minus corresponds to a right tooth profile, and minus corresponds to a left tooth profile;
3) determining the motion mode of a bus sweep forming the molded surface of the drum-shaped worm grinding wheel: in one aspect, the busbar is wound around O in normal sectionsZsThe shaft rotates at a constant speed, and the rotation angle is alpha; on the other hand, the generatrix is integrally formed on the crowned worm base about the worm axis OwZwRotating at a constant speed, wherein the rotating angle is beta; the two rotary motions are synthesized into a spiral motion of a bus, so that the bus is swept on the drum-shaped worm matrix to form a spiral surface of the drum-shaped worm grinding wheel;
4) and determining the transformation relation among the coordinate systems according to the motion relation: from the coordinate system Os-XsYsZsTo Ow-XwYwZwThe transformation matrix of (a) is:
in the formula, MwsTo be derived from the coordinate system Os-XsYsZsTo Ow-XwYwZwOf the transformation matrix, MwoFrom the coordinate system O-XYZ to Ow-XwYwZwOf the transformation matrix, MonTo be derived from the coordinate system On-XnYnZnTransformation matrix to O-XYZ, Mn1To be derived from the coordinate system O1-X1Y1Z1To On-XnYnZnOf the transformation matrix, M1sTo be derived from the coordinate system Os-XsYsZsTo O1-X1Y1Z1Of the transformation matrix, λ0The included angle between the section of the axis of the drum-shaped worm and the normal section is adopted;
5) the surface equation of the drum-shaped worm grinding wheel can be obtained through the transformation relation of a generatrix equation and a spiral motion coordinate, and is expressed as follows:
in the formula, xwIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwIn X-axis coordinate, ywIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwIn the Y-axis coordinate of (1), zwIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwThe Z-axis coordinate of (a) is,
for the generatrix in the coordinate system Os-XsYsZsThe equation in (1).
As a preferred embodiment of the present invention, the coordinate system O1-X1Y1Z1And On-XnYnZnThe shortest distance E between the original points of the worm grinding wheel and the gear shaping cutter shaft represents the shortest distance between the axis of the worm grinding wheel and the gear shaping cutter shaft, the size of the worm grinding wheel determines the size of the worm grinding wheel, and the worm grinding wheel can be selected at will within a reasonable size range of the worm grinding wheel.
As a preferred scheme of the invention, the bus bar is wound by OsZsAngle of rotation of the shaft alpha and about the worm axis OwZwThe relationship between the rotation angles β is: α/β ═ nw/zsWherein z issIs the number of teeth of the slotting cutter, nwThe number of the worm heads.
As a preferable embodiment of the present invention, the included angle λ between the axial section and the normal section of the crowned worm0Is determined by the following method:
a. changing the tooth profile line in the step 2) into a point Q (0, R,0), wherein the point is subjected to the spiral motion in the step 3) to obtain a spiral line on the surface of the drum-shaped worm matrix, and the equation is as follows:
in the formula, xQIs the X-axis coordinate, y, of the helixQIs the Y-axis coordinate of the helix, zQIs the Z-axis coordinate of the spiral line, and R is the base point and the origin of coordinates O of the spiral linesThe distance of (d);
b.Q at any position, the derivative is obtained for beta to obtain the tangent vector of the spiral line at the point Q:
c. on the end section circle where the Q point is located, the tangent vector passing through the Q point is as follows:
d.
and
included angle of (A) is the helix angle lambda of the drum worm grinding wheelwNamely:
e. nominal helix angle lambda of drum worm grinding wheel0That is, the included angle between the section of the axis of the crowned worm and the normal section, and substituting β as 0 into the above formula and simplifying to obtain:
the invention has the beneficial effects that: according to the invention, the drum-shaped worm grinding wheel profile is obtained through evolution from the gear shaping cutter to the worm grinding wheel, a complex meshing equation does not need to be solved, the calculation process is simple, the size of the obtained worm grinding wheel is not limited by the size of the gear shaping cutter or the cylindrical gear before evolution, an analytical expression of the worm grinding wheel profile is directly obtained, and the profile precision is controllable. And the method can be used for trimming the worm grinding wheel according to the principle that the profile of the worm grinding wheel is generated by the method, and is also easy to realize through a multi-shaft linkage numerical control technology, so that the method has a good guiding effect on the trimming process of the worm grinding wheel for grinding the face gear in engineering practice.
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FIG. 1 is a coordinate system diagram of the evolution of a pinion cutter to a drum worm grinding wheel;
FIG. 2 is a three-dimensional model diagram of a drum worm grinding wheel.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description.
Taking grinding of a standard orthogonal straight-tooth face gear as an example, a method for designing a profile of a drum-shaped worm grinding wheel for grinding the face gear comprises the following steps:
1) the basic parameters of the evolved pinion cutter were first determined as follows: modulus m is 3, pressure angle α020 deg. and number of teeth zs25, addendum coefficient haThe tip clearance coefficient c is 0.25 when the value is 1, and the base radius r of the pinion cutter is obtainedb＝mzscosα035.24 mm/2. Determining the number n of grinding heads of drum wormwThe shortest distance E between the axis of the worm grinding wheel and the gear shaping cutter shaft line is 89.5mm which is 1.
2) And establishing a coordinate system formed by the evolution of the pinion cutter to the drum-shaped worm grinding wheel. As shown in FIG. 1, wherein Ow-XwYwZwA moving coordinate system, O-XYZ and O, fixedly connected with the drum-shaped worm grinding wheeln-XnYnZnAre all fixed coordinate systems and the YOZ plane and YnOnZnThe plane is respectively superposed with the cross section of the worm shaft and the normal cross section, and the included angle between the plane and the normal cross section is lambda0，Os-XsYsZsA motion coordinate system of an imaginary tooth line, O1-X1Y1Z1As an auxiliary coordinate system, O1-X1Y1Z1And On-XnYnZnThe shortest distance between the two origins is E.
3) And establishing a tooth profile equation of the section of the drum worm method, which is consistent with the tooth profile of the gear shaper cutter, and taking the tooth profile as a bus for forming the molded surface of the drum worm grinding wheel. Tooth form line equation in coordinate system Os-XsYsZsIs represented as:
in the formula: x is the number ofsIs a tooth line in a coordinate system Os-XsYsZsIn (2) X-axis coordinate, ysIs a tooth line in a coordinate system Os-XsYsZsIn the Y-axis coordinate of (1), zsIs a tooth line in a coordinate system Os-XsYsZsZ-axis coordinate of (1), rbIs the base radius of the pinion cutter, theta0Is the half angle of the tooth slot of the slotting cutter theta0＝π/2zs-invα0The angle is approximately equal to 2.75 degrees, theta is an involute variable parameter, plus or minus in plus or minus is plus or minus, which corresponds to a right tooth profile, and minus corresponds to a left tooth profile.
4) And determining the motion mode of the profile of the drum type worm grinding wheel formed by scanning the generatrix. In one aspect, the busbar is wound around O in normal sectionsZsThe shaft rotates at a constant speed, and the rotation angle is alpha; on the other hand, the generatrix is integrally formed on the crowned worm base about the worm axis OwZwRotating at constant speed and the rotating angle is beta. The two rotary motions are combined into a spiral motion of a generatrix, so that the generatrix is swept on the drum-shaped worm matrix to form a spiral surface of the drum-shaped worm grinding wheel. Wherein the bus is wound around OsZsAngle of rotation of the shaft alpha and about the worm axis OwZwThe relationship between the rotation angles β is: α/β ═ nw/zs＝1/25。
5) And determining the transformation relation among the coordinate systems according to the motion relation. From the coordinate system Os-XsYsZsTo Ow-XwYwZwThe transformation matrix of (d) is:
in the formula, MwsTo be derived from the coordinate system Os-XsYsZsTo Ow-XwYwZwOf the transformation matrix, MwoFrom coordinate system O-XYZ to Ow-XwYwZwOf the transformation matrix, MonTo be derived from the coordinate system On-XnYnZnConversion to O-XYZMatrix, Mn1To be derived from the coordinate system O1-X1Y1Z1To On-XnYnZnOf the transformation matrix, M1sTo be derived from the coordinate system Os-XsYsZsTo O1-X1Y1Z1Of the transformation matrix, λ0The included angle between the section of the axis of the drum-shaped worm and the normal section is adopted.
6) Worm axis cross-section and normal cross-section, i.e. YOZ plane and YnOnZnAngle between the planes lambda0Is determined by the following method:
a. by a point Q (0, r) on the base circle of the gear shaping cutterbAnd 0) is taken as a base point, a spiral line on the surface of the drum-shaped worm base body is obtained, and the equation is as follows:
in the formula, xQIs the X-axis coordinate, y, of the helixQIs the Y-axis coordinate of the helix, zQIs the Z-axis coordinate of the helix, rbIs a base point of the spiral line and a coordinate origin OsThe distance of (d);
b.Q, when moving to a certain position, the derivative is made to beta, and the tangent vector of the spiral line at the point Q is:
c. on the end section circle where the Q point is located, the tangent vector passing through the Q point is as follows:
d.
and
included angle of (A) is the helix angle lambda of the drum worm grinding wheelwNamely:
e. nominal helix angle lambda of drum worm grinding wheel0That is, the included angle between the section of the axis of the crowned worm and the normal section, and substituting β as 0 into the above formula and simplifying to obtain:
6) the surface equation of the drum-shaped worm grinding wheel can be obtained through the transformation relation of a generatrix equation and a spiral motion coordinate:
in the formula, xwIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwIn X-axis coordinate, ywIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwIn the Y-axis coordinate of (1), zwIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwZ-axis coordinate of (1).
Calculating discrete points of the profile by using the obtained profile equation of the drum-shaped worm grinding wheel through MATLAB, introducing the discrete points into SolidWorks for accurate modeling of the drum-shaped worm grinding wheel, and obtaining a three-dimensional model of the drum-shaped worm grinding wheel by using the parameters as shown in figure 2. Thus, the profile design of the drum-shaped worm grinding wheel for grinding the face gear is completed.
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.
Claims (4)
1. A method for designing the profile of a drum-shaped worm grinding wheel for grinding face gears is characterized by comprising the following steps:
1) establishing a coordinate system formed from a slotting cutter to a drum worm grinding wheel evolution: wherein O isw-XwYwZwA moving coordinate system, O-XYZ and O, fixedly connected with the drum-shaped worm grinding wheeln-XnYnZnAre all fixed coordinate systems and the YOZ plane and YnOnZnThe plane is respectively superposed with the cross section of the worm shaft and the normal cross section, and the included angle between the plane and the normal cross section is lambda0，Os-XsYsZsA motion coordinate system of an imaginary tooth line, O1-X1Y1Z1As an auxiliary coordinate system, O1-X1Y1Z1And On-XnYnZnThe shortest distance between the two origins is E;
2) establishing a tooth profile equation which is consistent with the tooth profile of the gear shaper cutter on the section of the drum-shaped worm method, taking the tooth profile as a bus forming the molded surface of the drum-shaped worm grinding wheel, and setting the tooth profile equation in a coordinate system Os-XsYsZsIs represented as:
in the formula: x is the number ofsIs a tooth line in a coordinate system Os-XsYsZsIn X-axis coordinate, ysIs a tooth line in a coordinate system Os-XsYsZsIn the Y-axis coordinate of (1), zsIs a tooth line in a coordinate system Os-XsYsZsZ-axis coordinate of (1), rbIs the base radius of the pinion cutter, theta0For the half angle of the tooth space of the slotting cutter, the formula theta0＝π/2zs-invα0Is determined wherein zsAnd alpha0The number of teeth and the pressure angle of the slotting cutter are respectively, theta is an involute variable parameter, plus or minus is plus or minus, plus or minus corresponds to a right tooth profile, and minus corresponds to a left tooth profile;
3) determining the motion mode of a bus sweep forming the molded surface of the drum-shaped worm grinding wheel:in one aspect, the busbar is wound around O in normal sectionsZsThe shaft rotates at a constant speed, and the rotation angle is alpha; on the other hand, the generatrix is integrally formed on the crowned worm base about the worm axis OwZwRotating at a constant speed, wherein the rotating angle is beta; the two rotary motions are synthesized into a spiral motion of a bus, so that the bus is swept on the drum-shaped worm matrix to form a spiral surface of the drum-shaped worm grinding wheel;
4) and determining the transformation relation among the coordinate systems according to the motion relation: from the coordinate system Os-XsYsZsTo Ow-XwYwZwThe transformation matrix of (a) is:
in the formula, MwsTo be derived from the coordinate system Os-XsYsZsTo Ow-XwYwZwOf the transformation matrix, MwoFrom the coordinate system O-XYZ to Ow-XwYwZwOf the transformation matrix, MonTo be derived from the coordinate system On-XnYnZnTransformation matrix to O-XYZ, Mn1To be derived from the coordinate system O1-X1Y1Z1To On-XnYnZnOf the transformation matrix, M1sTo be derived from the coordinate system Os-XsYsZsTo O1-X1Y1Z1Of the transformation matrix, λ0The included angle between the section of the axis of the drum-shaped worm and the normal section is adopted;
5) the surface equation of the drum-shaped worm grinding wheel can be obtained through the transformation relation of a generatrix equation and a spiral motion coordinate, and is expressed as follows:
in the formula, xwIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwIn X-axis coordinate, ywIs drum-shaped worm sandWheel profile in coordinate system Ow-XwYwZwIn the Y-axis coordinate of (1), zwIs a drum-shaped worm grinding wheel profile in a coordinate system Ow-XwYwZwThe Z-axis coordinate of (a) is,
for the generatrix in the coordinate system Os-XsYsZsThe equation in (1).
2. The method of claim 1, wherein the coordinate system O is a contour of a crowned worm grinding wheel1-X1Y1Z1And On-XnYnZnThe shortest distance E between the original points of the worm grinding wheel and the gear shaping cutter shaft represents the shortest distance between the axis of the worm grinding wheel and the gear shaping cutter shaft, the size of the worm grinding wheel determines the size of the worm grinding wheel, and the worm grinding wheel can be selected at will within a reasonable size range of the worm grinding wheel.
3. The method of claim 1, wherein the generatrix is wound around OsZsAngle of rotation of the shaft alpha and about the worm axis OwZwThe relationship between the rotation angles β is: α/β ═ nw/zsWherein z issIs the number of teeth of the slotting cutter, nwThe number of the worm heads.
4. The method of claim 1, wherein the included angle λ between the crowning worm axis cross-section and the normal cross-section is a crowning worm grinding wheel profile0Is determined by the following method:
a. changing the tooth profile line into a point Q (0, R,0), and obtaining a spiral line on the surface of the drum-shaped worm matrix through spiral motion, wherein the equation is as follows:
in the formula, xQIs the X-axis coordinate, y, of the helixQIs the Y-axis coordinate of the helix, zQIs the Z-axis coordinate of the spiral line, and R is the base point and the origin of the coordinate O of the spiral linesThe distance of (a);
b.Q at any position, the derivative is obtained for beta to obtain the tangent vector of the spiral line at the point Q:
c. on the end section circle of the Q point, the tangent vector passing through the Q point is as follows:
d.
and
included angle of (A) is the helix angle lambda of the drum worm grinding wheelwNamely:
e. nominal helix angle lambda of drum worm grinding wheel0That is, the included angle between the section of the axis of the crowned worm and the normal section, and substituting β as 0 into the above formula and simplifying to obtain:
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| CN113103080B (en) * | 2021-04-21 | 2022-04-05 | 重庆大学 | Archimedes worm gear hob design method, cutter grinding correction method and worm gear master machine configuration method |
| CN113127993B (en) * | 2021-04-27 | 2023-03-17 | 重庆大学 | Worm gear shaver and design method and modification method thereof |
| CN113400197B (en) * | 2021-06-23 | 2022-07-26 | 重庆大学 | Method for shaping and trimming drum-shaped worm grinding wheel for grinding face gear |
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