CN112541235A - Universal design method for hypoid gear pair - Google Patents

Universal design method for hypoid gear pair Download PDF

Info

Publication number
CN112541235A
CN112541235A CN202011410805.5A CN202011410805A CN112541235A CN 112541235 A CN112541235 A CN 112541235A CN 202011410805 A CN202011410805 A CN 202011410805A CN 112541235 A CN112541235 A CN 112541235A
Authority
CN
China
Prior art keywords
hypoid gear
wheel
parameters
angle
small
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202011410805.5A
Other languages
Chinese (zh)
Other versions
CN112541235B (en
Inventor
宋朝省
刘思远
朱才朝
刘坤明
黄千洪
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guilin Fuda Gear Co ltd
Chongqing University
Original Assignee
Guilin Fuda Gear Co ltd
Chongqing University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guilin Fuda Gear Co ltd, Chongqing University filed Critical Guilin Fuda Gear Co ltd
Priority to CN202011410805.5A priority Critical patent/CN112541235B/en
Publication of CN112541235A publication Critical patent/CN112541235A/en
Application granted granted Critical
Publication of CN112541235B publication Critical patent/CN112541235B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Computer Hardware Design (AREA)
  • General Engineering & Computer Science (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Computational Mathematics (AREA)
  • Gears, Cams (AREA)

Abstract

The invention relates to the technical field of gear pair design, in particular to a general design method of a hypoid gear pair, which provides a hypoid gear space pitch cone parameter design and calculation flow under the working conditions of positive axis intersection angle and small axis intersection angle based on a space meshing theory; solving basic geometric parameters of the hypoid gear based on the geometric characteristics of the hypoid gear blank by the calculated parameters; the method optimizes a local synthesis method, provides a hypoid gear pair meshing characteristic presetting method and a processing parameter calculation flow under the working conditions of positive axis intersection angle and small axis intersection angle, and overcomes the defects that the traditional design method is poor in convergence, complex in design, required to be reversely adjusted for multiple times, only aiming at a single orthogonal working condition and the like; the method has high integration and high calculation efficiency, can cope with any target working condition, and realizes the integrated design and calculation of the geometric parameters of the gear, the basic parameters of the gear blank and the gear tooth processing parameters.

Description

Universal design method for hypoid gear pair
Technical Field
The invention relates to the technical field of gear pair design, in particular to a general design method of a hypoid gear pair, and particularly relates to a general design method of a hypoid gear pair considering working conditions of a positive axis intersection angle and a small axis intersection angle.
Background
The hypoid gear transmission is used as one of hot spot problems in the field of space gear transmission, has the advantages of large contact ratio, strong tolerance capability, high meshing stability, excellent meshing performance and the like, and is widely applied to the fields of high-speed ship power transmission, four-wheel drive vehicle power transfer, aircraft engine accessory transmission, helicopter main rotor transmission, automatic equipment steering transmission and the like. Hypoid gear pairs have high requirements on designers and design methods due to their complexity in geometry. At present, the existing hypoid gear pair design method has the following characteristics:
1) the application range is single: the existing hypoid gear pair design method is based on an orthogonal pitch cone contact theory, a nonlinear equation system is utilized to solve a unique gear geometric design parameter meeting all conditions of a contact point in a space, and due to the limitation of the pitch cone design method, the condition only aims at a positive axis intersection angle working condition (an axis intersection angle is 90 degrees), and the hypoid gear pair design method cannot be applied to other axis intersection angles;
2) the reverse adjustment of the meshing characteristic is complex: the hypoid gear pair is generally set with initial processing parameters firstly, and the processing parameters are reversely adjusted to achieve the target contact characteristic based on a mismatch design method, so that the method has higher accuracy and convergence, but needs to be reversely adjusted for many times, and has higher requirements on the reverse regulation experiment of designers;
3) the calculation efficiency is not high: the existing hypoid gear pair design method solves a space contact nonlinear equation set based on a Newton iteration method, and due to the complexity of the hypoid gear geometry and more parameters, the equation set has longer solving time and lower overall calculation efficiency;
therefore, based on the defects of the existing hypoid gear pair design method and the characteristics of the hypoid gear pair, researchers in the field should invent a new design method aiming at overcoming the defects.
Disclosure of Invention
In view of the above, the present invention provides a general design method of a hypoid gear pair, which considers the working conditions of a positive intersection angle and a small intersection angle, in order to solve the problems of single application range, complex meshing characteristic reverse adjustment, and low calculation efficiency of the existing hypoid gear pair original design method.
In order to achieve the purpose, the invention provides a general design method of a hypoid gear pair considering the working conditions of a positive shaft intersection angle and a small shaft intersection angle, which comprises the following steps:
step S1: aiming at the working conditions of space crossed axis orthogonality or small axis angle of intersection, under the condition of known axis angle of intersection sigma, offset E and transmission ratio i12And the diameter d of the outer end of the bull wheelae2In the case of (1), the solution satisfies the geometric parameters that the two sections of cones are tangent to the known tangent point M in space: obtaining the parameters of hypoid gear pitch cone under target working condition, namely the large and small pitch cone angles gammam2、γm1Large and small wheel installation distance Am2、Am1And a large and small wheel helix angle betam2、βm1；
Step S2: according to the basic geometric parameters of the hypoid gear pitch cone meeting the conditions, selecting a shrinkage tooth system aiming at the working condition, and calculating the basic parameters of the hypoid gear blank meeting the requirements of the working condition;
step S3: after all gear geometric parameters meeting the working condition are determined, the hypoid gear large wheel machining parameters can be solved based on the large wheel machining principle of a face milling forming method, and the hypoid gear large wheel machining parameters comprise: horizontal tool position H2Radial tool position V2Machine tool root angle Mr2Horizontal wheel position DeltaXB2And bed position DeltaXA2Selecting a contact reference point F, and calculating first and second principal curvatures of the contact reference point F based on the Rogeries formula
Figure BDA0002817297400000021
And the first and second main directions
Figure BDA0002817297400000022
According to the partial synthesis method, the small wheel and the large wheel are completely conjugated at the point, so that the hypoid gear meshing characteristic parameters are set at the point, and the method comprises the following steps: the contact trace forms an angle theta with the first principal direction of the tooth surfacecrLength L of semi-major axis of contact ellipseceFirst derivative of the transmission error m12. The first and second principal curvatures of the small wheel at the point satisfying the engagement characteristic condition are calculated
Figure BDA0002817297400000023
And the first and second main directions
Figure BDA0002817297400000024
Based on the small wheel machining principle of the surface milling generating method, the machining parameters of the only hypoid gear small wheel meeting the meshing characteristic condition are solved, and the parameters comprise a radial tool position Sr1Angular tool position Qr1Machine tool root angle Mr1Horizontal wheel position DeltaXB1Bed position delta XA1Angle of inclination of knife I1Corner J of knife1Roll ratio C12And vertical wheel position Em1；
Step S4: after the derivation of the hypoid gear geometric parameters, the tooth blank basic parameters and the processing parameters aiming at the working conditions is completed, a three-dimensional model of the hypoid gear pair can be established based on the tooth surface reverse engineering, the characteristic that the geometric characteristics of the hypoid gear tooth surfaces with orthogonal and small-axis intersection angles are complex is considered, the geometric characteristic index inspection needs to be carried out on the tooth surfaces of the gear pair, and the accuracy of the tooth surfaces of the gear under the parameters is ensured. The index detection of the three large tooth surfaces comprises root undercut analysis, tooth top tip inspection and tooth root smooth transition analysis, and the precision and the quality of the tooth surfaces are guaranteed.
Further, in step S1, according to the known intersection angle Σ, offset E, and outer end diameter d of the large wheelae2Space contact point M three-dimensional coordinate (X)m，Ym，Zm) The following three geometric relations can be obtained:
Figure BDA0002817297400000025
Figure BDA0002817297400000026
Figure BDA0002817297400000031
in the formula i12Representing gear ratio, betam12The difference value of the helix angles of the large wheel and the small wheel.
Based on the forming principle and the generating principle of the hypoid gear tooth surface, two limiting conditions of the geometric characteristic constraint of the hypoid gear pair are obtained:
Figure BDA0002817297400000032
Figure BDA0002817297400000033
in the formula,
Figure BDA0002817297400000034
and alphanlimThe ultimate pressure angle and the ultimate method curvature are indicated, respectively.
Based on the working conditions of the space staggered axis orthogonality or the small axis angle orthogonality, according to three large geometrical relations and two large limiting conditions of the gear, an iteration mode taking the helical angle of the large wheel and the auxiliary angle of the small wheel as iteration variables and taking the offset distance and the curvature of the limit method as judging conditions is provided. Wherein, the inner loop is an offset loop, and the judgment condition is as follows:
|E-E*|<0.001
in the formula, E*Representing the offset of the hypoid gear after each iteration of the inner loop.
When the inner circulation judgment condition is met, the inner circulation is ended, the outer circulation is carried out, and the judgment condition is as follows:
Figure BDA0002817297400000035
in the formula,
Figure BDA0002817297400000036
indicating the radius of the cutter head selected,
Figure BDA0002817297400000037
representing the limit method curvature of the tooth surface of the hypoid gear after each iteration of the outer loop.
And when the external circulation judgment condition is met, ending the circulation and outputting the unique hypoid gear pitch cone parameter meeting the target working condition.
Further, the general formula of the surface milling hypoid gear shrinking mode in the step S2 is as follows:
Figure BDA0002817297400000038
in the formula, metIs the gear face module, Re2Large end cone distance of bull wheel, Rm2The large wheel reference point cone distance.
Further, the calculation formula of the hypoid gear large wheel machining parameters in the step S3 is as follows:
Figure BDA0002817297400000039
based on the relationship between the basic parameters of the local synthesis method, the following equation can be obtained:
Figure BDA00028172974000000310
wherein,
Figure BDA0002817297400000041
in the formula, the included angle of the first main direction of the meshing tooth surface of the small wheel and the large wheel is sigma12，a11，a12And a22Is the coefficient of the basic equation of the local synthesis method.
Figure BDA0002817297400000042
The equation for looking at three unknown coefficients is as follows:
Figure BDA0002817297400000043
wherein,
Figure BDA0002817297400000044
according to the local synthesis method, the following expression can be obtained:
Figure BDA0002817297400000045
wherein,
Figure BDA0002817297400000046
Figure BDA0002817297400000047
from this, it can be derived that the expression for the first principal direction angle of the engaging flanks of the small and large wheels is:
Figure BDA0002817297400000048
wherein the small wheel has a first principal curvature K at the point F of the tooth surfaceIpAnd a second principal curvature KIIpThe expression is as follows:
Figure BDA0002817297400000049
the expressions of the first principal direction and the second principal direction of the tooth surface of the small wheel at the tooth surface F point can be obtained according to the equation as follows:
Figure BDA00028172974000000410
three meshing characteristic parameters are jointly preset on the basis of the principal curvature and the principal direction of the small gear tooth surface at the tooth surface F point: the contact trace forms an angle theta with the first principal direction of the tooth surfacecrLength L of semi-major axis of contact ellipseceFirst derivative of the transmission error m12Solving the processing parameters of the hypoid gear pair small wheel by the surface milling generating method: radial tool position Sr1Angular tool position Qr1Machine tool root angle Mr1Horizontal wheel position DeltaXB1Bed position delta XA1Angle of inclination of knife I1Corner J of knife1Roll ratio C12And vertical wheel position Em1。
The beneficial effect of this scheme lies in:
1. the invention discloses a general design method of a hypoid gear pair considering working conditions of positive axis intersection angle and small axis intersection angle, which is based on the working conditions of space staggered axis orthogonality or small axis intersection angle, and provides an iteration mode with a large wheel helical angle and a small wheel auxiliary angle as iteration variables and offset distance and limit method curvature as judgment conditions according to three large geometric relations and two large limiting conditions of a gear.
2. The invention discloses a general design method of a hypoid gear pair considering the working conditions of a positive axis intersection angle and a small axis intersection angle, which determines a general design flow of the hypoid gear pair considering the working conditions of the positive axis intersection angle and the small axis intersection angle based on the known working conditions of a space staggered axis, and can efficiently solve the unique gear geometry and processing parameters meeting the working conditions, the preset meshing characteristic parameters and the tooth surface shrinkage tooth system. The method avoids the defects that the traditional design method is poor in convergence, complex in design, and only aims at a single orthogonal working condition, and multiple times of inverse adjustment are needed; the method has high integration and high calculation efficiency, can cope with any target working condition, and realizes the integrated design and calculation of the geometric parameters of the gear, the basic parameters of the gear blank and the gear tooth processing parameters.
3. The invention discloses a general design method of a hypoid gear pair considering working conditions of a positive axis intersection angle and a small axis intersection angle, which is based on a space pitch cone contact theory, a local synthesis method and a surface milling hypoid gear processing principle, and obtains geometric parameters and processing parameters of the hypoid gear pair meeting orthogonal working conditions and extreme working conditions. The method overcomes the defects of single object and complex reverse adjustment in the prior art, not only can be used for a gear pair under the conventional working condition, but also can be applied to hypoid gear transmission under the small-axis intersection angle and the limit working condition; meanwhile, the characteristic that the inverse adjustment is needed for multiple times to achieve the target contact characteristic in the prior art is improved, the machining parameters of the machine tool are inversely calculated through the preset contact characteristic, the calculation efficiency and the calculation precision are high, the target contact characteristic is met at one time, multiple inverse adjustment is not needed, and the requirement on the experience of technical personnel is not high. This method greatly improves the drawbacks of the prior art.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
FIG. 1 is a flow chart of the calculation of the basic geometric design parameters of a hypoid gear pair with a positive shaft intersection angle and a small shaft intersection angle;
FIG. 2 is a tooth blank geometry parameter definition diagram for a hypoid gear set in accordance with the present invention;
FIG. 3 is a flow chart of the calculation of machining parameters for a hypoid gear pair having a positive axis intersection angle and a small axis intersection angle in accordance with the present invention;
FIG. 4(a) is a first schematic view of a hypoid gear set tooth surface defect in accordance with the present invention;
FIG. 4(b) is a schematic view of a hypoid gear set tooth surface defect of the present invention;
FIG. 5(a) is a first schematic view of the hypoid gear pair root smooth transition detection of the present invention;
FIG. 5(b) is a schematic view of a hypoid gear pair tooth root smooth transition detection of the present invention;
FIG. 5(c) is a third schematic view of the hypoid gear pair tooth root smooth transition detection of the present invention;
FIG. 6 is a schematic view of the hypoid gear pair tooth root and tip width measurement of the present invention;
FIG. 7 is a hypoid gear set mesh model in an orthogonal state according to the present invention;
FIG. 8 is a hypoid gear pair mesh model in a small-axis angular state according to the present invention;
FIG. 9 is a detail of the hypoid gear tooth flank geometry and meshing characteristics in an orthogonal condition according to the present invention;
FIG. 10 is a graph showing details of the tooth flank geometry and the meshing characteristics of a hypoid gear set according to the present invention in a small crossed-axis angular state.
Detailed Description
The following is further detailed by way of specific embodiments:
a general design method of a hypoid gear pair considering working conditions of positive shaft intersection angle and small shaft intersection angle comprises the following steps:
step S1: aiming at the working conditions of space crossed axis orthogonality or small axis angle of intersection, under the condition of known axis angle of intersection sigma, offset E and transmission ratio i12And the diameter d of the outer end of the bull wheelae2In the case of (1), solving the geometric parameters that satisfy the known tangency point M of the two sections of cones in space: obtaining the parameters of hypoid gear pitch cone under target working condition, namely the large and small pitch cone angles gammam2、γm1Large and small wheel installation distance Am2、Am1And a large and small wheel helix angle betam2、βm1；
According to the characteristic that the space staggered shaft pitch cone is tangent to a space known point M, three geometric relational expressions of any crossed-angle pitch cone hypoid gear can be deduced: 1) the geometric relationship of the center distance, 2) the geometric relationship of the offset angle, 3) the geometric relationship of the transmission ratio, and the three relationships have direct geometric relationship with the basic parameters of the pitch cone.
According to the known shaft intersection angle sigma, the offset E and the outer end diameter d of the large wheelae2Space contact point M three-dimensional coordinate (X)m，Ym，Zm) The following three main relations can be obtained:
Figure BDA0002817297400000061
Figure BDA0002817297400000062
Figure BDA0002817297400000063
in the formula i12Representing gear ratio, betam12The difference value of the helix angles of the large wheel and the small wheel.
Based on the forming principle and the generating principle of the hypoid gear tooth surface, two limiting conditions of the geometric characteristic constraint of the hypoid gear pair are obtained:
Figure BDA0002817297400000064
Figure BDA0002817297400000065
in the formula,
Figure BDA0002817297400000066
and alphanlimThe ultimate pressure angle and the ultimate method curvature are indicated, respectively.
Ultimate pressure angle alphanlimThe method is a unique index for measuring the forming property of the concave-convex tooth surface of the hypoid gear, namely the pressure angle alpha of the concave-convex tooth surfaceccAnd alphacvAngle alpha to extreme pressurenlimThere is a direct geometric relationship-ultimate pressure angle alphanlimAnd (3) defining conditions, wherein if the pressure angle of the concave-convex tooth surface does not meet the defined conditions, the tooth surface generates singular points, a meshing equation cannot be solved, the tooth surface is distorted, and undercuts are generated. Meanwhile, based on the processing characteristics of the face milling generating method, the radius of the cutter head and the tooth direction radian of the gear have unique geometric relationship, namely the curvature of the extreme method
Figure BDA0002817297400000071
The limit condition is that the tooth camber of the gear can pass the limit method curvature
Figure BDA0002817297400000072
And (4) measuring. Therefore, solving the hypoid gear not only satisfies three geometric relations, but also satisfies two limiting conditions: limiting pressure angle limiting conditions and limiting method curvature limiting conditions;
based on the working conditions of the space staggered axis orthogonality or the small axis angle orthogonality, according to three large geometrical relations and two large limiting conditions of the gear, an iteration mode taking the helical angle of the large wheel and the auxiliary angle of the small wheel as iteration variables and taking the offset distance and the curvature of the limit method as judging conditions is provided. Wherein, the inner loop is an offset loop, and the judgment condition is as follows:
|E-E*|<0.001
in the formula, E*Representing the offset of the hypoid gear after each iteration of the inner loop.
When the inner circulation judgment condition is met, the inner circulation is ended, the outer circulation is carried out, and the judgment condition is as follows:
Figure BDA0002817297400000073
in the formula,
Figure BDA0002817297400000074
indicating the radius of the cutter head selected,
Figure BDA0002817297400000075
representing the limit method curvature of the tooth surface of the hypoid gear after each iteration of the outer loop.
And when the external circulation judgment condition is met, ending the circulation and outputting the hypoid gear pitch cone parameters aiming at the target working condition.
Step S2: according to the basic geometric parameters of the hypoid gear pair pitch cone meeting the conditions, selecting a shrinkage gear system aiming at the working condition, and calculating the geometric parameters of the hypoid gear meeting the requirements of the working condition; the gear tooth surface contraction mode is an important geometric index of the arc-tooth hypoid gear, and different from the existing standard, the invention considers the influence of different intersecting angles on the pitch cone distance and deduces the hypoid gear contraction mode suitable for all the intersecting angles.
Step B2: the four parameters of the hypoid gear pair assembly relation are respectively as follows: offset E, axle angle Σ, large wheel mounting distance Am2Mounting distance A of small wheelm1The four parameters described above completely constrain the hypoid gear assembly characteristics. The parameters of the geometric morphology of the fully constrained tooth surface mainly comprise: pitch cone angle gammamiAngle of taper gammaaiRoot angle gammafiDistance Z from apex of cone to intersection of axismiDistance Z from the vertex of the face cone to the intersection of the axesaiDistance Z from apex of root cone to intersection of axesfi. Wherein, when i is 1, it represents a small wheel, and when i is 2, it represents a large wheel. The above parameters are derived from the alternate axis hypoid gear pair geometry.
The general formula of the surface milling hypoid gear shrinkage mode is as follows:
Figure BDA0002817297400000076
in the formula, metIs the gear face module, Re2Large end cone distance of bull wheel, Rm2The large wheel reference point cone distance.
Step S3: after all gear parameters meeting the working condition are determined, based on a large wheel machining principle of a face milling forming method, the large wheel machining parameters of the hypoid gear can be solved, and the method comprises the following steps: horizontal tool position H2Radial tool position V2Machine tool root angle Mr2Horizontal wheel position DeltaXB2And bed position DeltaXA2Selecting a contact reference point F, and calculating first and second principal curvatures of the contact reference point F based on the Rogeries formula
Figure BDA0002817297400000081
And the first and second main directions
Figure BDA0002817297400000082
According to the partial synthesis method, the small wheel and the large wheel are completely conjugated at the point, so that the hypoid gear meshing characteristic parameters are set at the point, and the method comprises the following steps: the contact trace forms an angle theta with the first principal direction of the tooth surfacecrLength L of semi-major axis of contact ellipseceFirst derivative of the transmission error m12. The first and second principal curvatures of the small wheel at the point satisfying the engagement characteristic condition are calculated
Figure BDA0002817297400000083
And the first and second main directions
Figure BDA0002817297400000084
Based on the small wheel machining principle of the surface milling generating method, unique hypoid gear small wheel machining parameters including radial tool position S can be solvedr1Angular tool position Qr1Machine tool root angle Mr1Horizontal wheel position DeltaXB1Bed position delta XA1Angle of inclination of knife I1Corner J of knife1Roll ratio C12And vertical wheel position Em1；
The machining parameters of the large wheel machine of the hypoid gear by the surface milling generating method can be derived based on the machining process of the hypoid gear by the surface milling generating method; (2) the axial and radial spacing between the preset contact reference point F and the cutting contact point M can be represented by Δ X and Δ Y, respectively. The distance can be defined as an offset, which represents the deviation between the preset contact position center and the contact point; (3) according to the local comprehensive theory, the hypoid gear pair has a unique complete conjugate contact reference point F, and the major and minor gear flanks have the same principal direction and principal curvature at the point. Based on this propertyThree parameters of meshing characteristics: the contact trace forms an angle theta with the first principal direction of the tooth surfacecrLength L of semi-major axis of contact ellipseceFirst derivative of the transmission error m12The purpose of completely controlling the meshing characteristic is achieved. The three parameters respectively control the width, the direction and the transfer error of the contact patch; (4) based on the preset parameters and the main direction and the main curvature of the large wheel under the global coordinate system, the main direction and the main curvature of the hypoid gear pair small wheel can be solved, and based on the main direction and the main curvature of the small wheel, the hypoid gear small wheel processing parameters are solved by considering the hypoid gear processing principle of a surface milling and generating method.
The hypoid gear large wheel machining parameter calculation formula is as follows:
Figure BDA0002817297400000085
based on the relationship between the basic parameters of the local synthesis method, the following equation can be obtained:
Figure BDA0002817297400000086
wherein,
Figure BDA0002817297400000087
in the formula, the included angle of the first main direction of the meshing tooth surface of the small wheel and the large wheel is sigma12，a11，a12And a22Is the coefficient of the basic equation of the local synthesis method.
Figure BDA0002817297400000091
The equation for looking at three unknown coefficients is as follows:
Figure BDA0002817297400000092
wherein,
Figure BDA0002817297400000093
according to the local synthesis method, the following expression can be obtained:
Figure BDA0002817297400000094
wherein,
Figure BDA0002817297400000095
Figure BDA0002817297400000096
from this, it can be derived that the expression for the first principal direction angle of the engaging flanks of the small and large wheels is:
Figure BDA0002817297400000097
wherein the small wheel has a first principal curvature K at the point F of the tooth surfaceIpAnd a second principal curvature KIIpThe expression is as follows:
Figure BDA0002817297400000098
the expressions of the first principal direction and the second principal direction of the tooth surface of the small wheel at the tooth surface F point can be obtained according to the equation as follows:
Figure BDA0002817297400000099
based on principal curvature and principal of small wheel tooth surface at tooth surface F pointAnd (3) direction, jointly presetting three meshing characteristic parameters: the contact trace forms an angle theta with the first principal direction of the tooth surfacecrLength L of semi-major axis of contact ellipseceFirst derivative of the transmission error m12And the processing parameters of the hypoid gear pair small wheel by the surface milling generating method can be solved: radial tool position Sr1Angular tool position Qr1Machine tool root angle Mr1Horizontal wheel position DeltaXB1Bed position delta XA1Angle of inclination of knife I1Corner J of knife1Roll ratio C12And vertical wheel position Em1。
Step S4: after the derivation of the hypoid gear geometric parameters, the tooth blank basic parameters and the processing parameters aiming at the working conditions is completed, a three-dimensional model of a hypoid gear pair can be established based on tooth surface reverse engineering, the characteristic that the hypoid gear tooth surface geometric characteristics are complex in orthogonal and small-axis intersection angles is considered, the tooth surface of the gear needs to be subjected to geometric characteristic index inspection, and the accuracy of the tooth surface of the gear under the parameters is ensured. The index detection of the three large tooth surfaces comprises root undercut analysis, tooth top tip inspection and tooth root smooth transition analysis, and the precision and the quality of the tooth surfaces are guaranteed.
The hypoid gear tooth surface is extremely sensitive to geometric design parameters, slight parameter change can cause change of tooth surface geometric characteristics to cause change of tooth surface singular point tooth profile critical value, and based on the characteristic, undercut inspection is provided to ensure the tooth surface quality; (2) hypoid gear tooth surfaces usually adopt high-low deflection, which also causes tooth top width to become sharp and influences geometric characteristics, and tooth top tapering inspection can avoid the problem; (3) the tooth root part of the tooth surface of the hypoid gear has a unique direct relation with the root angle of the machine tool, and the hypoid gear root section smoothness transition machine tool root angle unique parameter is iteratively met based on the space projection relation.
As shown in fig. 1, a flow chart for calculating basic geometric design parameters of a hypoid gear pair for positive and small intersecting axes is provided, and in order to facilitate understanding of the present invention, the essence of the technical route is as follows: and based on the given input parameters, solving basic geometric parameters of the gear pair suitable for the given working condition by iterating the key geometric variables.
To be explainedThe method comprises the following steps: the input parameters of the hypoid gear with the small intersection angle are divided into two types: the input parameters are given and the input parameters are calculated. Wherein the given input parameters include: the angle of intersection sigma of the axis and the offset E, the nominal radius r of the cutter headcoA transmission ratio i12And the outer end pitch diameter d of the bull wheelae2The five parameters are determined by the design conditions and cannot be changed once the design conditions are determined.
In addition, calculating the output parameters includes: number of teeth of small gear N1Number of teeth of large gear N2Width of bull gear teeth b2And big wheel helix angle betam2(the value is a given parameter, detailed solving process is described later). The design flow includes two iteration variables: helix angle gamma of bull wheelm2And large wheel auxiliary offset angle epsilonm2. Helix angle gamma of bull wheelm2The initial value calculation formula is as follows:
Figure BDA0002817297400000101
auxiliary bias angle epsilon of bull wheelm2The initial value is calculated as follows
Figure BDA0002817297400000102
Loop a represents the initial value calculation process for the two iteration variables, and the purpose of this loop is to provide initial values for the entire design calculation flow, so it is used only once throughout the loop. Based on the two iteration initial variables and the geometric relationship in fig. 1, the basic geometric parameters of the pitch cone can be solved: small wheel pitch cone angle gammam1Helix angle beta of small wheelm1And small wheel reference point pitch cone radius rm1. The offset E under the iterative parameter can be obtained through the third geometric relation of the parameters and the small-axis angle hypoid gear*Thus, the determination condition is as follows:
|E-E*|≤AE(3) in the formula, AEIndicating the accuracy of the first judgment condition, when the difference between the calculated offset distance and the given offset distance is smaller than the judgment accuracy, performing the next calculation, and if not, iteratingBig wheel auxiliary offset angle epsilon'm2The specific iterative equation is as follows:
Figure BDA0002817297400000103
further, when the first determination condition is satisfied, the limit method curvature and the pressure angle of the large gear tooth surface can be obtained according to the limit method curvature equation and the limit pressure angle formula, and the second determination condition is as follows:
Figure BDA0002817297400000111
in the formula, ARAnd expressing the precision of the second judgment condition, when the curvature of the limit method is calculated and the nominal radius of the cutter head is selected to meet the judgment precision, obtaining the final values of all iteration variables simultaneously meeting the two judgment conditions, and if the final values of all iteration variables do not meet the judgment condition, iterating the large wheel pitch cone angle under the condition that the large wheel auxiliary offset angle meeting the first judgment condition is not changed, wherein a specific iteration equation is as follows:
γ′m2＝′m2+Δγm2 (6)
in the formula, Δ γm2Are iterative variables. Through the iteration, all the basic geometrical parameters of the pitch cone can be solved, including: small wheel pitch cone angle gammam1Helix angle beta of small wheelm1Small wheel pitch cone distance rm1Small wheel pitch cone angle gammam2Helix angle beta of small wheelm2Small pitch cone distance rm2. The iteration precision and the judgment precision can be freely controlled, theoretically, the higher the iteration precision and the judgment precision is, the more accurate the iteration final value is, and meanwhile, the calculation time of the whole cycle is longer, wherein the recommended iteration precision and the judgment precision are 10-3mm。
Fig. 2 and 3 are respectively a tooth blank geometric parameter definition diagram of the hypoid gear pair according to the invention and a hypoid gear pair machining parameter calculation flow diagram of the hypoid gear pair according to the invention, wherein the hypoid gear pair is aimed at a positive shaft intersection angle and a small shaft intersection angle.
In order to facilitate the understanding of the invention, the essence of the technical route is as follows: and (3) presetting theoretical contact points and meshing characteristic parameters based on the conical reference point of the large wheel section, and solving the only small wheel machining parameter meeting the meshing condition. The whole tooth surface is completely conjugated only at the theoretical contact point, and the aim of completely controlling the contact characteristic is achieved by presetting contact characteristic parameters.
Based on a hypoid gear machining flow, a partial synthesis method and a tooth root traversal cycle model, a small-axis intersection angle hypoid gear machining parameter calculation and meshing characteristic design flow is provided, and is specifically shown in fig. 3.
Specifically, the tooth surface basic geometric parameters can be obtained by solving the pitch cone model and the tooth surface basic parameters of the small-axis intersection angle hypoid gear, and the unique large gear machining parameters and the unique tool parameters are solved based on the forming method hypoid gear machining process. And a unique bull wheel mathematical model can be established through the cutter parameters and the machining parameters. By establishing a preset tooth flank engagement point, a first cyclic variable is proposed to control the position of the contact patch, taking into account the distance to the tooth flank reference point. And solving the main curvature and the main direction at the reference point of the large wheel according to the Rodriguez space curvature theorem. Based on the process, a second cycle variable is provided, and the machine tool root cone angle of the concave surface and the convex surface of the gear is controlled, so that the smooth transition condition at the tooth root of the concave-convex surface is controlled. And the three cyclic variables, i.e. the third, fourth and fifth, are basic input variables of the local synthesis method, including the length of the long axis of the contact patch, the included angle between the contact track and the main direction of the tooth surface and the preset peak-to-peak value of the transmission error, and the size, the direction and the transmission error of the contact patch are controlled through the three variables.
Further, based on the local synthesis method parameters and the small-intersection-angle hypoid gear assembly mathematical model, the main curvature and the main direction of the small wheel tooth surface at the meshing point can be obtained, the small wheel machine tool machining parameters and cutter parameters are solved by adopting a method for simulating small wheel machining by a generating method, and the small wheel tooth surface is established according to the gear mathematical model of the small wheel by the generating method.
Based on the established large and small gear tooth surfaces, the invention simulates the gear meshing process through tooth surface contact analysis to obtain the meshing characteristic of the gear pair with the small shaft angle and the hypoid surface, and the meshing characteristic comprises the following steps: contact patch, transfer error. The meshing characteristic fine adjustment is considered, a closed-loop tooth surface contact characteristic design flow is established, and a method for fine adjusting corresponding circulation variables and reversely solving machining parameters of large and small wheel machine tools is provided aiming at different meshing characteristic indexes.
On the other hand, for the hypoid gear pair with a small intersection angle, undercut is particularly easy to occur at the tooth root of the small gear tooth surface, that is, the working tooth surface section and the transition arc section cannot be smoothly transited, as shown in fig. 4(a) and 4 (b). It can be known from the figure that when the undercut occurs, the tooth surface can not smoothly reach the tooth root section, the convergence of the tooth root section is reduced after the meshing equation is solved, and a high-quality solution can not be found. According to the gear meshing principle, points which cannot be solved by a meshing equation are defined as singular points, and the singular points can be expressed as the following equation in the tooth surface generating process:
Figure BDA0002817297400000121
in the formula, r1Representing a position vector of any point on the face of the pinion.
Based on the principle of gear engagement, the above equation can be converted into four matrices:
Figure BDA0002817297400000122
Figure BDA0002817297400000123
Figure BDA0002817297400000124
based on the gear meshing principle, the critical conditions of singular points on the tooth surface of the small wheel are as follows:
Figure BDA0002817297400000125
the singular point set of the pinion tooth surface can be represented by the following equation:
Figure BDA0002817297400000126
in the formula,
Figure BDA0002817297400000127
represents a tooth surface meshing equation, u and beta respectively represent a tooth surface tooth profile parameter and a tooth direction parameter of the small wheel,
Figure BDA0002817297400000128
indicating the rotational angle during gear generating. The boundary u of the singular point can be solved by the equation systemlim。
Based on the contact characteristics of the tooth surface, the minimum value u of the tooth profile of the working tooth surface can be knownminThe expression is as follows:
Figure BDA0002817297400000131
in the formula, RFiIn order to transition the radius of the circular arc segment,
Figure BDA0002817297400000132
the cutter head pressure angle is represented, where i ═ cc represents a concave surface, and i ═ cv represents a convex surface. The condition that the hypoid gear tooth surface with the small intersection angle does not generate undercut is as follows:
ulim<umin (14)
it should be noted that when the minimum profile parameter is greater than the minimum u value that produces an undercut, no undercut is produced. Meanwhile, the parameters influencing the tooth surface undercut are very many, and almost all the tooth surface basic design parameters influence the tooth surface undercut, so that the small-axis intersection angle gear tooth surface basic design parameters need to be discussed.
Based on the goal of hypoid gear root smoothness, an iterative approach is proposed, as shown in particular in fig. 5(a), 5(b) and 5 (c). The hypoid gear with small crossed angle is discretized into m × n gearsAnd points, wherein m represents a tooth surface tooth profile direction discrete point, and n represents a tooth surface tooth direction discrete point. RAvkAnd RAckDenotes the kth point of the root segment, where k ranges from 1 to n. The projection of the concave surface and the convex surface on the plane Q is shown in the figure, and the point on the convex surface and the concave surface of the tooth surface is at RAvkAnd RAckThe projection points on the projection surface are respectively CkAnd VkLine segment
Figure BDA0002817297400000133
And
Figure BDA0002817297400000134
is defined as B, and the coordinate expression of B in the plane Q is:
Figure BDA0002817297400000135
Figure BDA0002817297400000136
in the formula, xbAnd ybRepresents the abscissa and ordinate values of B in the plane Q, B1And b2Is the root line segment
Figure BDA0002817297400000137
And
Figure BDA0002817297400000138
auxiliary parameter of k1And k2Is a line segment
Figure BDA0002817297400000139
And
Figure BDA00028172974000001310
the four parameters are expressed as follows:
Figure BDA00028172974000001311
Figure BDA00028172974000001312
Figure BDA00028172974000001313
Figure BDA00028172974000001314
in the formula (x)c1，yc1，zc1)，(xcn，ycn，zcn)，(xv1，yc1，zc1) And (x)vn，yvn，zvn) Respectively represent a point RAc1，RAv1，RAcnAnd RAvnCoordinate values in the coordinate system of the large wheel, after projection, line segments
Figure BDA00028172974000001315
And
Figure BDA00028172974000001316
angle of (a) of1The expression is as follows:
Figure BDA00028172974000001317
line segment
Figure BDA00028172974000001318
And
Figure BDA00028172974000001319
angle of (a) ofnThe expression is as follows:
Figure BDA00028172974000001320
the sum of the two angles is:
Σσ＝σ1+σn (23)
as the sum of the two angles approaches 0, the flank transition is also smoother. As shown in fig. 5(B), when the intersection point B is not within the tooth surface range, although the included angle between the concave surface and the convex surface is close to or even equal to 0 degree, the tooth root still cannot be smoothly transited, so that the coordinate axis of the point B needs to be limited, specifically as follows:
xn<xb<x1 (24)
yn<yb<y1 (25)
the above condition limits the intersection point B within the range of the tooth surface, avoiding the above situation.
Further, the geometrical morphology of the small-axis cross-angle hypoid gear pair is extremely sensitive to almost all gear parameters, and based on the above, a method for detecting tooth surface tooth crest sharpening of the small-axis cross-angle hypoid gear is provided, as shown in fig. 6. In the figure, the tooth surface is discretized into a plurality of points, where m denotes a tooth surface tooth profile direction discretization point and n denotes a tooth surface tooth direction discretization. As shown, the first point near the tip of the small end is defined as (1,1), the first point near the root of the small end is defined as (m,1), the first point near the tip of the large end is defined as (1, n), and the first point near the root of the large end is defined as (m, n). Defining the gear tip as TACjAnd TAVj，TACjIs a concave crest point, TAVjIs convex addendum point, and addendum width is defined as DTCVjWhere j represents the number of discrete points of the hypoid gear tooth tip, ranging from 1 to n. The tooth tip width expression is as follows:
Figure BDA0002817297400000141
in the formula (x)cj，ycj，zcj) And (x)vj，yvj，zvj) Respectively representing the cartesian coordinate systems of the addendum points and addendum points.
Here, in order to ensure sufficient tooth surface contact strength, the tooth tip width needs to satisfy the following condition based on the gear manual:
DTCVj>0.3mn (27)
in the formula, mnRepresenting the gear normal module.
The embodiment 1 is a hypoid gear pair meshing model with a positive shaft intersection angle, and the embodiment 2 is a hypoid gear pair meshing model with a small shaft intersection angle.
TABLE 1 hypoid gear set pitch cone design parameters
Figure BDA0002817297400000142
Figure BDA0002817297400000151
TABLE 2 hypoid tooth flank geometry basic parameters of gear pairs
Figure BDA0002817297400000152
TABLE 3 hypoid gear pair bull wheel processing parameter table
Figure BDA0002817297400000153
TABLE 4 hypoid gear set Preset contact characteristic parameters
Figure BDA0002817297400000154
TABLE 5 hypoid small gear machining parameters
Figure BDA0002817297400000161
Based on the data in tables 1 to 5 above, an orthogonal angle and small axis orthogonal angle hypoid gear pair mesh model can be established, as shown in fig. 7 and 8 in particular.
Fig. 9 and 10 show details of geometric features and meshing characteristics of the orthorhombic and hypoid gear pair models established after geometric checking, respectively, and the contact patch and the transmission error are close to preset parameters, and the reliability of the method is verified through the above example and the tooth surface contact analysis.
In conclusion, compared with the existing method, the implementation method of the invention has the advantages of target diversity, high calculation efficiency and accuracy. Meanwhile, the meshing characteristic parameters can be designed in advance in a preset mode without reverse adjustment. The effectiveness and the practicability of the method are verified by the examples, so that the method has higher practical significance and popularization value in the field of the industry.
The foregoing is merely an example of the present invention and common general knowledge of known specific structures and features of the embodiments is not described herein in any greater detail. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several changes and modifications can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicability of the present invention.

Claims (4)

1. A general design method for hypoid gear pair is characterized in that: the method comprises the following steps:
step S1: aiming at the working conditions of space crossed axis orthogonality or small axis angle of intersection, under the condition of known axis angle of intersection sigma, offset E and transmission ratio i12And the diameter d of the outer end of the bull wheelae2In the case of (1), the solution satisfies the geometric parameters that the two sections of cones are tangent to the known tangent point M in space: obtaining the parameters of hypoid gear pitch cone under target working condition, namely the large and small pitch cone angles gammam2、γm1Large and small wheel installation distance Am2、Am1And a large and small wheel helix angle betam2、βm1；
Step S2: according to the basic geometric parameters of the hypoid gear pitch cone meeting the conditions, selecting a shrinkage tooth system aiming at the working condition, and calculating the basic parameters of the hypoid gear blank meeting the requirements of the working condition;
step S3: after all gear geometric parameters meeting the working condition are determined, solving hypoid gear large wheel machining parameters based on a large wheel machining principle of a face milling forming method, wherein the hypoid gear large wheel machining parameters comprise: horizontal tool position H2Radial tool position V2Machine tool root angle Mr2Horizontal wheel position DeltaXB2And bed position DeltaXA2Selecting a contact reference point F, and calculating first and second principal curvatures of the contact reference point F based on the Rogeries formula
Figure FDA0002817297390000011
And the first and second main directions
Figure FDA0002817297390000012
According to the partial synthesis method, the small wheel and the large wheel are completely conjugated at the point, so that the hypoid gear meshing characteristic parameters are set at the point, and the method comprises the following steps: the contact trace forms an angle theta with the first principal direction of the tooth surfacecrLength L of semi-major axis of contact ellipseceFirst derivative of the transmission error m12(ii) a The first and second principal curvatures of the small wheel at the point satisfying the engagement characteristic condition are calculated
Figure FDA0002817297390000013
And the first and second main directions
Figure FDA0002817297390000014
Based on the small wheel machining principle of the surface milling generating method, the machining parameters of the only hypoid gear small wheel meeting the meshing characteristic condition are solved, and the parameters comprise a radial tool position Sr1Angular tool position Qr1Machine tool root angle Mr1Horizontal wheel position DeltaXB1Bed position delta XA1Angle of inclination of knife I1Corner J of knife1Roll ratio C12And vertical wheel position Em1；
Step S4: after the derivation of the geometric parameters, basic parameters and processing parameters of the hypoid gear aiming at the working conditions is completed, a three-dimensional model of the hypoid gear pair is established based on a tooth surface reverse engineering, the characteristic that the geometric characteristics of the tooth surface of the hypoid gear with orthogonal and small-axis crossed angles are complex is considered, the geometric characteristic index inspection needs to be carried out on the tooth surface of the gear pair, and the accuracy of the tooth surface of the gear under the parameters is ensured; the index detection of the three large tooth surfaces comprises root undercut analysis, tooth top tip inspection and tooth root smooth transition analysis, and the precision and the quality of the tooth surfaces are guaranteed.
2. The hypoid gear set universal design method of claim 1, wherein: in step S1, according to the known shaft intersection angle sigma, the offset E and the outer end diameter d of the bull wheelae2Space contact point M three-dimensional coordinate (X)m，Ym，Zm) The following three geometric relations can be obtained:
Figure FDA0002817297390000015
Figure FDA0002817297390000021
Figure FDA0002817297390000022
in the formula i12Representing gear ratio, betam12The difference value of the helix angles of the big wheel and the small wheel is obtained;
based on the forming principle and the generating principle of the hypoid gear tooth surface, two limiting conditions of the geometric characteristic constraint of the hypoid gear pair are obtained:
Figure FDA0002817297390000023
Figure FDA0002817297390000024
in the formula,
Figure FDA0002817297390000025
and alphanlimRespectively representing the ultimate pressure angle and the ultimate method curvature;
based on the working conditions of space staggered axis orthogonality or small axis angle of intersection, according to three major geometrical relations and two major limiting conditions of the gear, an iteration mode taking a helical angle of a large wheel and an auxiliary angle of a small wheel as iteration variables and taking a bias distance and a curvature of a limit method as judging conditions is provided;
wherein, the inner loop is an offset loop, and the judgment condition is as follows:
|E-E*|＜0.001
in the formula, E*Representing the offset of the hypoid gear after each iteration of the internal loop;
when the inner circulation judgment condition is met, the inner circulation is ended, the outer circulation is carried out, and the judgment condition is as follows:
Figure FDA0002817297390000026
in the formula,
Figure FDA0002817297390000027
indicating the radius of the cutter head selected,
Figure FDA0002817297390000028
representing the limit method curvature of the tooth surface of the hypoid gear after each iteration of the external cycle;
and when the external circulation judgment condition is met, ending the circulation and outputting the unique hypoid gear pitch cone parameter meeting the target working condition.
3. The hypoid gear set universal design method of claim 2, wherein: the general formula of the surface milling hypoid gear shrinking mode in the step S2 is as follows:
Figure FDA0002817297390000029
in the formula, metIs the gear face module, Re2Large end cone distance of bull wheel, Rm2The large wheel reference point cone distance.
4. The hypoid gear set universal design method of claim 3, wherein: the calculation formula of the hypoid gear large wheel machining parameters in the step S3 is as follows:
Figure FDA0002817297390000031
based on the relationship between the basic parameters of the local synthesis method, the following equation is obtained:
Figure FDA0002817297390000032
wherein,
Figure FDA0002817297390000033
in the formula, the included angle of the first main direction of the meshing tooth surface of the small wheel and the large wheel is sigma12，a11，a12And a22Is the local synthesis method basic equation coefficient;
Figure FDA0002817297390000034
the equation for looking at three unknown coefficients is as follows:
Figure FDA0002817297390000035
wherein,
Figure FDA0002817297390000036
according to the local synthesis method, the following expression is obtained:
Figure FDA0002817297390000037
wherein,
Figure FDA0002817297390000038
Figure FDA0002817297390000039
therefore, the expression of the first main direction included angle of the meshing tooth surfaces of the small wheel and the large wheel is derived as follows:
Figure FDA00028172973900000310
wherein the small wheel has a first principal curvature K at the point F of the tooth surfaceIpAnd a second principal curvature KIIpThe expression is as follows:
Figure FDA00028172973900000311
the expressions of the first principal direction and the second principal direction of the tooth surface of the small wheel at the tooth surface F point are obtained according to the equation as follows:
Figure FDA00028172973900000312
based on the tooth surface of the small wheelAnd (3) jointly presetting three meshing characteristic parameters of the principal curvature and the principal direction of the surface F point: the contact trace forms an angle theta with the first principal direction of the tooth surfacecrLength L of semi-major axis of contact ellipseceFirst derivative of the transmission error m12Solving the processing parameters of the hypoid gear pair small wheel by the surface milling generating method: radial tool position Sr1Angular tool position Qr1Machine tool root angle Mr1Horizontal wheel position DeltaXB1Bed position delta XA1Angle of inclination of knife I1Corner J of knife1Roll ratio C12And vertical wheel position Em1。
CN202011410805.5A 2020-12-04 2020-12-04 Universal design method for hypoid gear pair Active CN112541235B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011410805.5A CN112541235B (en) 2020-12-04 2020-12-04 Universal design method for hypoid gear pair

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011410805.5A CN112541235B (en) 2020-12-04 2020-12-04 Universal design method for hypoid gear pair

Publications (2)

Publication Number Publication Date
CN112541235A true CN112541235A (en) 2021-03-23
CN112541235B CN112541235B (en) 2022-09-02

Family

ID=75016100

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011410805.5A Active CN112541235B (en) 2020-12-04 2020-12-04 Universal design method for hypoid gear pair

Country Status (1)

Country Link
CN (1) CN112541235B (en)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113361031A (en) * 2021-06-03 2021-09-07 重庆大学 Three-dimensional tooth shape design method for flexible gear of harmonic reducer
CN113486476A (en) * 2021-08-11 2021-10-08 重庆大学 Grinding wheel tooth profile design method for grinding double-arc harmonic reducer rigid wheel slotting tool
CN114004036A (en) * 2021-12-29 2022-02-01 天津德科智控股份有限公司 Gear rack reverse design method for steering gear
CN114492118A (en) * 2022-01-10 2022-05-13 安徽农业大学 Method for adjusting machining parameters of hypoid gear of tractor main reducer
CN117235938A (en) * 2023-11-15 2023-12-15 湖南中大创远数控装备有限公司 Method and system for adjusting contact area of spiral bevel gear

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20150147129A1 (en) * 2012-06-22 2015-05-28 Aisin Seiki Kabushiki Kaisha Device and method for manufacturing crown gear
JP2016008682A (en) * 2014-06-25 2016-01-18 大竹技研株式会社 Hypoid gear
JP2018112206A (en) * 2017-01-07 2018-07-19 大竹技研株式会社 Skewed shaft gear and intersecting shaft gear
CN109993464A (en) * 2019-04-24 2019-07-09 合肥工业大学 Reduce the machining parameters optimization method of hypoid gear installation error susceptibility
CN109992877A (en) * 2019-03-28 2019-07-09 长安大学 A kind of method of gear pair geometrical contact analysis
CN110966374A (en) * 2019-11-25 2020-04-07 金华新天齿轮有限公司 Design method of hypoid gear with large reduction ratio for high-precision robot
CN111687493A (en) * 2020-06-08 2020-09-22 西安交通大学 Variable tool path machining method for cycloidal-tooth bevel gear based on integral cutter head

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20150147129A1 (en) * 2012-06-22 2015-05-28 Aisin Seiki Kabushiki Kaisha Device and method for manufacturing crown gear
JP2016008682A (en) * 2014-06-25 2016-01-18 大竹技研株式会社 Hypoid gear
JP2018112206A (en) * 2017-01-07 2018-07-19 大竹技研株式会社 Skewed shaft gear and intersecting shaft gear
CN109992877A (en) * 2019-03-28 2019-07-09 长安大学 A kind of method of gear pair geometrical contact analysis
CN109993464A (en) * 2019-04-24 2019-07-09 合肥工业大学 Reduce the machining parameters optimization method of hypoid gear installation error susceptibility
CN110966374A (en) * 2019-11-25 2020-04-07 金华新天齿轮有限公司 Design method of hypoid gear with large reduction ratio for high-precision robot
CN111687493A (en) * 2020-06-08 2020-09-22 西安交通大学 Variable tool path machining method for cycloidal-tooth bevel gear based on integral cutter head

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
SIYUAN LIU: "computerized determination of the qualified region of main design parameters of face-milled hypoid gears with low shaft angle", 《MECHANISM AND MACHINE THEORY》 *
卓耀彬 等: "准双曲面齿轮副节锥参数新算法", 《机床与液压》 *
宋朝省 等: "小角度空间交错轴变厚齿轮传动啮合动态特性研究", 《震动与冲击》 *
梁成成 等: "基于刀具法向基准的奥利康准双曲面齿轮精确建模与验证", 《重庆大学学报》 *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113361031A (en) * 2021-06-03 2021-09-07 重庆大学 Three-dimensional tooth shape design method for flexible gear of harmonic reducer
CN113486476A (en) * 2021-08-11 2021-10-08 重庆大学 Grinding wheel tooth profile design method for grinding double-arc harmonic reducer rigid wheel slotting tool
CN114004036A (en) * 2021-12-29 2022-02-01 天津德科智控股份有限公司 Gear rack reverse design method for steering gear
CN114004036B (en) * 2021-12-29 2022-03-18 天津德科智控股份有限公司 Gear rack reverse design method for steering gear
CN114492118A (en) * 2022-01-10 2022-05-13 安徽农业大学 Method for adjusting machining parameters of hypoid gear of tractor main reducer
CN114492118B (en) * 2022-01-10 2024-04-09 安徽农业大学 Method for adjusting processing parameters of hypoid gear of main speed reducer of tractor
CN117235938A (en) * 2023-11-15 2023-12-15 湖南中大创远数控装备有限公司 Method and system for adjusting contact area of spiral bevel gear
CN117235938B (en) * 2023-11-15 2024-02-13 湖南中大创远数控装备有限公司 Method and system for adjusting contact area of spiral bevel gear

Also Published As

Publication number Publication date
CN112541235B (en) 2022-09-02

Similar Documents

Publication Publication Date Title
CN112541235B (en) Universal design method for hypoid gear pair
CN108446524B (en) Modeling method of spiral bevel gear for numerical control machining
CN109482983B (en) method for grinding generating cycloidal-tooth bevel gear
CN110008594B (en) Automatic modeling and assembling method for finite element grid of planetary transmission herringbone gear
CN109241683B (en) Design method for free tooth surface of helical gear
CN109063326B (en) Gear accurate modeling method considering microscopic shape correction and actual machining errors
CN109992877B (en) Method for analyzing geometric contact of gear pair
CN109993464B (en) Machining parameter optimization method for reducing mounting error sensitivity of hypoid gear
CN108730480B (en) Cycloidal gear of RV reducer and tooth profile reverse active modification method thereof
Zhou et al. A grinding method of face gear mating with a conical spur involute pinion
CN111666643B (en) Method for determining contact performance of complex tooth surface
CN113868901A (en) Finite element-based full-parametric gear meshing analysis method
CN112705794A (en) Tooth cutting tool for machining cycloid gear and design method thereof
CN109977579B (en) Machine tool machining parameter optimization method for improving hypoid gear meshing quality
CN109396567B (en) Digital envelope method for determining profile of worm grinding wheel in generating grinding of shape-modified cycloid gear
CN108120596A (en) A kind of spiral bevel gear root interference method of inspection
CN111219473B (en) Design method of spiral bevel gear with large contact ratio
CN110508879B (en) Numerical control turning flash and chamfering method for involute surface enveloping ring surface worm
CN109033669B (en) Spiral bevel gear simulation machining modeling method based on universal motion parameter driving
CN113192180B (en) Elliptic gear parameterization accurate modeling method based on gear shaping machining principle
CN110802280A (en) Involute spiral bevel gear tooth surface design method
Połowniak et al. Double enveloping worm gear modelling using CAD environment
CN113446960B (en) Tooth surface point cloud theoretical distribution modeling method and measuring method
CN109116803B (en) Split type equal-base bevel gear cutting motion trajectory calculation method
Tsay et al. Novel profile modification methodology for moulded face-gear drives

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant