CN111553039A - Cosine line tooth profile non-circular gear pair three-dimensional solid modeling method - Google Patents

Cosine line tooth profile non-circular gear pair three-dimensional solid modeling method Download PDF

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CN111553039A
CN111553039A CN202010562463.2A CN202010562463A CN111553039A CN 111553039 A CN111553039 A CN 111553039A CN 202010562463 A CN202010562463 A CN 202010562463A CN 111553039 A CN111553039 A CN 111553039A
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gear
driving wheel
driven wheel
blank
tooth
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CN111553039B (en
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史诺
刘琼
张雪宁
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Xian Aeronautical University
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    • 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
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H2057/0087—Computer aided design [CAD] specially adapted for gearing features ; Analysis of gear systems
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/08—Profiling
    • F16H55/084—Non-circular rigid toothed member, e.g. elliptic gear
    • 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
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    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/30—Computing systems specially adapted for manufacturing

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Abstract

The invention discloses a three-dimensional solid modeling method of a non-circular gear pair with a cosine line tooth profile, which comprises the steps of obtaining point coordinate values on pitch curves of a driving wheel and a driven wheel in the non-circular gear pair in an EXCEL table according to a transmission ratio function and a center distance, leading the point coordinate values into UGNX software to obtain pitch curves of the driving wheel and the driven wheel, creating a gear blank on the basis, obtaining a solid model of the non-circular gear by defining the initial position and the relative motion of the gear blank and a slotting cutter model and adopting a motion simulation means, wherein the transmission precision of the obtained three-dimensional model is superior to that of a reduced tooth profile method; the modeling process is simple, no complex calculation process is needed, and the calculated amount is small; the three-dimensional model of the non-circular gear pair is obtained by adopting the UG NX motion simulation technology, programming is not required to be performed by a design algorithm, and development difficulty is low.

Description

Cosine line tooth profile non-circular gear pair three-dimensional solid modeling method
Technical Field
The invention belongs to the field of mechanical design, and relates to a cosine line tooth profile non-circular gear pair three-dimensional solid modeling method.
Background
The non-circular gear is a special mechanical transmission part and can realize non-linear motion and power transmission. The non-circular gear has a complex structure, the difficulty in creating a three-dimensional solid model of a non-circular gear pair is high, and the existing non-circular gear three-dimensional modeling methods comprise the following steps:
(1) a reduced tooth profile method: the core idea of the conversion tooth profile method is to convert each gear tooth of the non-circular gear into the tooth profile of the equivalent circular gear, and the method is an approximate design method and is difficult to meet the requirement of high-precision transmission ratio.
(2) Tooth profile normal method: the tooth profile normal method is a drawing method, and in order to obtain an accurate tooth profile, a sufficient number of tooth profile normals need to be made, so that the modeling process is too complicated.
(3) An analytical method: the analytic method is that according to the gear meshing principle, a tooth profile equation is constructed, the data point coordinates of the tooth profile are obtained through calculation, a tooth profile curve is established in three-dimensional modeling software according to the data point coordinates, and stretching forming is carried out on the basis of the tooth profile curve.
(4) A cutter enveloping method: the tool enveloping method comprises two methods, wherein one method is to carry out secondary development in three-dimensional design software and generate a non-circular gear three-dimensional model through a generating method principle; and the other method is to program to obtain a machining process track envelope graph, and design an algorithm to extract tooth profile points of the non-circular gear, wherein the method has higher requirements on programming.
In summary, the existing design method needs complicated calculation and drawing, and the application of the non-circular gear is limited to a great extent.
Disclosure of Invention
The invention aims to provide a simple three-dimensional solid modeling method for a non-circular gear pair with a cosine tooth profile, which has the advantages of simple process, small calculated amount and high transmission precision of the obtained three-dimensional model.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a three-dimensional solid modeling method for a non-circular gear pair with a cosine line tooth profile comprises the following steps:
(1) setting a center distance and a transmission ratio function between a driving wheel and a driven wheel of the non-circular gear pair, and listing equations of a driving wheel pitch curve and a driven wheel pitch curve under a polar coordinate system;
(2) coordinate conversion is carried out, and equations of the driving wheel pitch curve and the driven wheel pitch curve under a polar coordinate system are converted into equations under a Cartesian coordinate system;
(3) make the driving wheel turn angle phi1In the range of 0-2 piPerforming linear interpolation, and calculating point coordinate values on a driving wheel pitch curve and a driven wheel pitch curve corresponding to different rotation angle values in an EXCEL table;
(4) respectively storing the point coordinate values on the driving wheel pitch curve and the driven wheel pitch curve obtained by calculation in a note file, and modifying the suffix name of the note file from txt to dat;
(5) opening UG NX software, importing the dat note file obtained in the step (4), and respectively generating a driving wheel pitch curve and a driven wheel pitch curve in a point-to-line mode;
(6) creating a tooth blank
Measuring pitch curve length L of the driving wheel or the driven wheel in UG NX, setting the tooth number of a cylindrical gear shaper cutter conjugated with the driving wheel and the driven wheel as z, and then determining the modulus of the gear shaper cutter
Figure BDA0002545184780000021
Selecting a driving wheel pitch curve to carry out curve offset, and setting the crest height coefficient ha*The offset distance is ha-ha*× M, obtaining the tooth top curve of drive wheel, stretching it along the negative direction of Z axis to obtain the tooth blank of drive wheel, and choosing the curve of driven wheel segment as object by the same method and with offset distance ha-ha*× M, obtaining a driven wheel tooth crest curve, stretching the driven wheel tooth crest curve along the Z-axis negative direction, wherein the stretching distance is the same as that of the driving wheel tooth blank, and obtaining a driven wheel tooth blank;
(7) creating a three-dimensional model of a slotting cutter
Creating a model file in UG NX software, creating a cylindrical gear shaper cutter solid model with a tooth profile being a cosine line, calculating the reference circle diameter D of the gear shaper cutter to be M multiplied by z, and drawing a reference circle sketch on one end face of the gear shaper cutter by taking the center of the end face as the center of a circle and D as the diameter;
(8) assembling the gear blank and the gear shaper cutter
Newly building an assembly file in UG NX software, assembling a driving wheel gear blank and a gear shaper cutter together, wherein a pitch curve of a driving wheel is tangent to a pitch circle of the gear shaper cutter, an intersection point of an X-axis negative half shaft and the pitch curve is taken as an object on the driving wheel gear blank, a central point of any gear tooth on the pitch circle is taken as an object on the gear shaper cutter, and the two points are overlapped to obtain the assembly file of the driving wheel gear blank and the gear shaper cutter;
when the driven wheel tooth blank is assembled with the gear shaper cutter, the pitch curve of the driven wheel is tangent to the reference circle of the gear shaper cutter, besides, the intersection point of the X-axis negative half shaft and the pitch curve is taken as a starting point on the driven wheel tooth blank, and the arc length from the starting point is taken as
Figure BDA0002545184780000031
The point of (2) is taken as an object, the central point of any gear tooth on the reference circle is taken as an object on the gear shaper cutter, and the two points are superposed to obtain an assembly file of a driven wheel tooth blank and the gear shaper cutter;
(9) motion simulation
Opening an assembly file of a driving wheel gear blank and a slotting cutter in UG NX, switching to a motion simulation module, performing motion simulation according to the steps of setting a connecting rod, setting a motion pair, setting a drive, setting a constraint, setting a tracking, setting a resolving scheme and solving calculation, and storing the position and the model of the slotting cutter in each calculating step in the solving process of the motion simulation;
in the same way, the motion simulation process of an assembly model of the driven wheel gear blank and the gear shaper cutter is carried out;
(10) solid model extraction
After the motion simulation solving of the driving wheel tooth blank and the pinion cutter assembly model is completed, clicking a geometric body-lifting body to operate, selecting the driving wheel tooth blank as a lifting target object in a dialog box of the lifting body, and clicking to confirm to complete the setting of the lifting body; selecting a lifting body in a part navigator as a target to obtain a three-dimensional model of a driving wheel;
the extraction mode and the steps of the three-dimensional solid model of the driven wheel are the same as those of the driving wheel, and the three-dimensional model of the driven wheel is obtained;
(11) creation of non-circular gear pairs
And newly building an assembly file in UG NX to complete the assembly of the driving wheel and the driven wheel, and ensuring that the tooth grooves of the driving wheel are just meshed with the gear teeth of the driven wheel at a zero line to obtain a non-circular gear pair three-dimensional model.
Further, the step (8) of assembling the gear blank and the pinion cutter is as follows:
newly building an assembly file in UG NX software, assembling a driving wheel gear blank and a gear shaper cutter together, wherein a pitch curve of a driving wheel is tangent to a pitch circle of the gear shaper cutter, an intersection point of an X-axis negative half shaft and the pitch curve is taken as an object on the driving wheel gear blank, a central point of any gear tooth on the pitch circle is taken as an object on the gear shaper cutter, and the two points are overlapped to obtain the assembly file of the driving wheel gear blank and the gear shaper cutter;
when the driven wheel tooth blank is assembled with the gear shaper cutter, the pitch curve of the driven wheel is tangent to the reference circle of the gear shaper cutter, besides, the intersection point of the X-axis negative half shaft and the pitch curve is taken as a starting point on the driven wheel tooth blank, and the arc length from the starting point is taken as
Figure BDA0002545184780000041
The center point of any gear tooth on the reference circle is used as an object on the gear shaping cutter, and the two points are superposed to obtain an assembly file of a driven wheel tooth blank and the gear shaping cutter.
The invention has the following advantages:
according to the invention, point coordinate values on pitch curves of a driving wheel and a driven wheel in a non-circular gear pair are obtained in an EXCEL table according to a transmission ratio function and a center distance, UG NX software is introduced to obtain the pitch curves of the driving wheel and the driven wheel, a gear blank is created on the basis, the initial position and the relative motion of the gear blank and a gear shaper cutter model are defined, and a physical model of the non-circular gear is obtained by adopting a motion simulation means. The three-dimensional model obtained by the method is superior to a conversion tooth form method in transmission precision; the method has relatively simple drawing process in three-dimensional software, and is convenient and fast to draw compared with a tooth profile normal method; the method has no complex calculation process, can complete all calculations in the EXCEL, and has small calculation amount compared with an analytical method; the method adopts UG NX motion simulation technology to obtain the three-dimensional model of the non-circular gear pair, does not need to design an algorithm for programming, and has small development difficulty compared with a cutter enveloping method.
The three-dimensional solid modeling method of the non-circular gear pair with the residual chord line tooth profile provides a foundation and a support for theoretical analysis, processing and manufacturing and engineering application of the non-circular gear pair, and the obtained accurate three-dimensional digital model of the non-circular gear pair can be directly applied to analysis and manufacturing.
Drawings
FIG. 1 is a flow chart of the modeling process of the present invention
FIG. 2a Driving track Curve
FIG. 2b driven wheel pitch curve
Figure 3a drive wheel tooth blank
FIG. 3b driven wheel tooth blank
Figure 4 slotting cutter and reference circle thereof
FIG. 5 Assembly of the driver gear blank and the pinion cutter
FIG. 6 Assembly of driven wheel tooth blank and pinion cutter
FIG. 7 shows the result of the simulation of the motion of the gear blank of the driving wheel and the pinion cutter
FIG. 8 shows the result of the simulation of the movement of the driven wheel gear blank and the gear shaper cutter
FIG. 9 three-dimensional model of driving wheel
FIG. 10 three-dimensional model of driven wheel
FIG. 11 non-circular gear pair
Detailed Description
The present invention will be described in further detail with reference to the following examples, which are not intended to limit the invention thereto.
As shown in FIG. 1, the three-dimensional solid modeling method of the non-circular gear pair with the cosine-line tooth profile comprises the following steps:
(1) setting the center distance and transmission ratio function between the driving wheel and the driven wheel, and listing the equations of the driving wheel and the driven wheel under a polar coordinate system
For example, the center distance is set to a value of 50mm
Function of transmission ratio of i21＝1-0.5cosφ1，φ1∈[0,2π]
Wherein phi is1Is a corner of the driving wheel
Under the polar coordinate system, the pitch curve equation of the driving wheel is as follows:
Figure BDA0002545184780000051
wherein r is1Is radial of a driving wheel
The pitch curve equation of the driven wheel is:
Figure BDA0002545184780000061
wherein r is2Is directed radially from the driven wheel2For turning the driven wheel
(2) Coordinate conversion is carried out, and the equation of the driving wheel and the driven wheel under a polar coordinate system is converted into the equation under a Cartesian coordinate system
The equation of the driving wheel pitch curve in a Cartesian coordinate system is as follows:
Figure BDA0002545184780000062
wherein x is1、y1、z1Is the coordinate value of the point on the driving wheel pitch curve in a Cartesian coordinate system
The equation of the driven wheel pitch curve in the Cartesian coordinate system is
Figure BDA0002545184780000063
Wherein x is2、y2、z2As a coordinate value of a point on the slave wheel pitch curve in a Cartesian coordinate system
(3) Make the driving wheel turn angle phi1And performing linear interpolation between 0 and 2 pi, and calculating point coordinate values on the driving wheel pitch curve and the driven wheel pitch curve corresponding to different rotation angle values in the EXCEL.
TABLE 1 active wheelset curve data
Figure BDA0002545184780000071
φ1(°) is the angle of rotation of the driving wheel
φ1(rad) is the angle of rotation (radian) of the driving wheel
r1Is radial of a driving wheel
x1、y1、z1Is the coordinate value of the point on the driving wheel pitch curve in a Cartesian coordinate system
TABLE 2 driven wheel pitch curve data
Figure BDA0002545184780000072
φ2(rad) for the driven wheel corner (radian)
r2Radial direction for driven wheel
x2、y2、z2As a coordinate value of a point on the slave wheel pitch curve in a Cartesian coordinate system
(4) And respectively storing the point coordinate values on the driving wheel pitch curve and the driven wheel pitch curve obtained by calculation in a note file, and modifying the suffix name of the note file from txt to dat.
(5) And (3) opening UG NX software, selecting the dat file generated in the step (4) by clicking splines, points in the file, and after clicking is determined, respectively generating a driving wheel pitch curve and a driven wheel pitch curve in a point-to-line mode, wherein the driving wheel pitch curve and the driven wheel pitch curve are as shown in a figure 2a and a figure 2b, and storing the files.
(6) Creating a tooth blank
Measuring the pitch curve length of the driving wheel or the driven wheel in UG NX, and obtaining the length L of the two pitch curves which is 155.0814mm
The number of teeth of a cylindrical gear shaping cutter conjugated with a driving wheel and a driven wheel is set to be z-20
Modulus of the pinion cutter
Figure BDA0002545184780000081
Selecting a driving wheel pitch curve to carry out curve offset, and setting the crest height coefficient ha*When the offset distance is 1, ha is the offset distance*× M is 2.4694mm, the addendum curve of the capstan is obtained, the capstan is stretched, the stretching direction is the Z-axis negative direction, the stretching distance is 20mm, the capstan tooth blank is obtained as shown in figure 3a, and the document is stored.
By the same method, a driven wheel pitch curve is selected as an object, the offset distance is 2.4694mm, a driven wheel tooth top curve is obtained, the driven wheel tooth top curve is stretched, the stretching direction is a Z-axis negative direction, the stretching distance is 20mm, a driven wheel tooth blank is obtained, and a file is stored as shown in figure 3 b.
(7) Creating a three-dimensional model of a slotting cutter
Creating a model file in UG NX software, creating a cosine tooth profile sketch map, wherein the cosine tooth profile equation is
Figure BDA0002545184780000082
xt, yt, zt are coordinate values of points on the tooth profile of the cosine line in a Cartesian coordinate system
M is the modulus of the pinion cutter
z is the number of teeth of the slotting cutter
H is the tooth crest height of the pinion cutter, and the value of the tooth crest height is offset distance H from the pitch curve in the step (6)aAre identical to each other
t is an expression variable in UG NX, and the variation range is 0-1
Substituting the parameter values into calculation to obtain a cosine line tooth profile equation of the gear shaper cutter as
Figure BDA0002545184780000091
And stretching the cosine line tooth profile sketch of the slotting cutter, wherein the stretching direction is the Z-axis negative direction, and the stretching distance is 20mm, so as to generate a solid model of the slotting cutter.
Calculating the reference circle diameter D of the gear shaper cutter M multiplied by z 49.3880mm
On one end face of the pinion cutter, a reference circle sketch is drawn by taking the center of the end face as the center of a circle and taking 49.3880mm as the diameter, and a file is stored as shown in figure 4.
(8) Assembling the gear blank and the gear shaper cutter
In addition, the intersection point of the X-axis negative half shaft and the pitch curve is taken as an object on the driving wheel tooth blank, the central point of any one gear tooth on the pitch circle is taken as an object on the gear shaper cutter, the two points are superposed as shown in figure 5, and the file is saved.
When the driven wheel tooth blank is assembled with the gear shaper cutter, the pitch curve of the driven wheel is tangent to the reference circle of the gear shaper cutter, besides, the intersection point (point A) of the negative half shaft of the X axis and the pitch curve is taken as a starting point on the driven wheel tooth blank, and the arc length from the starting point is taken as
Figure BDA0002545184780000092
The point (point B) of (a) is an object, the center point of any gear tooth on the pitch circle is an object on the slotting cutter, and the two points are overlapped as shown in fig. 6, and a file is stored.
(9) Motion simulation
Opening an assembly file of a driving wheel gear blank and a gear shaper cutter in UG NX, switching to a motion simulation module, and performing motion simulation according to the steps of setting a connecting rod, setting a kinematic pair, setting a drive, setting a constraint, setting a tracking, setting a solution scheme and solving calculation.
Setting a connecting rod: setting a driving wheel gear blank and a pitch curve as a fixed connecting rod L001, setting a connecting rod L002 as a connecting line of an original point of the driving wheel gear blank and the circle center of the gear slotting cutter, and setting a gear slotting cutter and a reference circle as a connecting rod L003;
setting a kinematic pair: a rotating pair J001 is arranged on the connecting rod L002, and the rotating center of the rotating pair J001 is the origin of the gear blank of the driving wheel;
drive setting: a constant drive is arranged on the rotating pair J001, and the rotating speed is 360 DEG/s;
and (3) setting constraints: selecting the center of a reference circle of the connecting rod L003 as a target point, and defining a point on-line pair by taking a connecting line of the origin of the driving wheel gear blank and the center of the gear shaper cutter as a target line; selecting a pitch curve on a driving wheel tooth blank as a first target curve, selecting a reference circle of a pinion cutter as a second target curve, and setting locking sliding to define an on-line pair;
setting and tracking: selecting a pinion cutter as a tracking object;
setting a resolving scheme: setting the simulation time to be 1s and the step number to be 200;
solving and calculating: and (4) solving the motion simulation, wherein the position and the model of the slotting cutter are automatically backed up in each calculation step.
The motion simulation result of the driving wheel gear blank and the gear shaper cutter is shown in figure 7, and a file is saved.
The motion simulation creation mode and the steps of the assembly model of the driven wheel gear blank and the gear shaper cutter are the same as those described above. The motion simulation result of the driven wheel gear blank and the gear shaper cutter is shown in figure 8, and a file is saved.
(10) Solid model extraction
And after the motion simulation solving of the driving wheel tooth blank and the pinion cutter assembly model is completed, clicking the geometric body-lifting body to operate, selecting the driving wheel tooth blank as a lifting target object in a dialog box of the lifting body, and clicking to confirm to complete the setting of the lifting body.
Clicking a geometry, merging and subtracting, entering a difference dialog box, selecting a lifting body in the part navigator as a target, selecting a feature group in the part navigator as a tool, clicking to determine that a driving wheel and a slotting cutter appear in a view window. The three-dimensional model of the capstan is selected in the view window as shown in fig. 9 and saved as a separate file.
The extraction method and steps of the three-dimensional entity model of the driven wheel are the same as those of the driving wheel, and the three-dimensional entity model of the driven wheel is obtained and stored as an independent file as shown in figure 10.
(11) Creation of non-circular gear pairs
And newly building an assembly file in UG NX to complete the assembly of the driving wheel and the driven wheel, ensuring that the tooth grooves of the driving wheel are just meshed with the gear teeth of the driven wheel at a zero line, and obtaining the assembled non-circular gear pair as shown in figure 11.
The present invention is described in detail with reference to the above embodiments, and those skilled in the art will understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (2)

1. A three-dimensional solid modeling method for a non-circular gear pair with a cosine line tooth profile is characterized by comprising the following steps:
(1) setting a center distance and a transmission ratio function between a driving wheel and a driven wheel of the non-circular gear pair, and listing equations of a driving wheel pitch curve and a driven wheel pitch curve under a polar coordinate system;
(2) coordinate conversion is carried out, and equations of the driving wheel pitch curve and the driven wheel pitch curve under a polar coordinate system are converted into equations under a Cartesian coordinate system;
(3) make the driving wheel turn angle phi1Performing linear interpolation between 0 pi and 2 pi, and calculating point coordinate values on a driving wheel pitch curve and a driven wheel pitch curve corresponding to different rotation angle values in an EXCEL table;
(4) respectively storing the point coordinate values on the driving wheel pitch curve and the driven wheel pitch curve obtained by calculation in a note file, and modifying the suffix name of the note file from txt to dat;
(5) opening UG NX software, importing the dat note file obtained in the step (4), and respectively generating a driving wheel pitch curve and a driven wheel pitch curve in a point-to-line mode;
(6) creating a tooth blank
Measuring pitch curve length L of the driving wheel or the driven wheel in UG NX, setting the tooth number of a cylindrical gear shaper cutter conjugated with the driving wheel and the driven wheel as z, and then determining the modulus of the gear shaper cutter
Figure FDA0002545184770000011
Selecting a driving wheel pitch curve to carry out curve offset, and setting the crest height coefficient ha*The offset distance is ha-ha*× M, obtaining the tooth top curve of drive wheel, stretching it along the negative direction of Z axis to obtain the tooth blank of drive wheel, and choosing the curve of driven wheel segment as object by the same method and with offset distance ha-ha*× M, obtaining a driven wheel tooth crest curve, stretching the driven wheel tooth crest curve along the Z-axis negative direction, wherein the stretching distance is the same as that of the driving wheel tooth blank, and obtaining a driven wheel tooth blank;
(7) creating a three-dimensional model of a slotting cutter
Creating a model file in UG NX software, creating a cylindrical gear shaper cutter solid model with a tooth profile being a cosine line, calculating the reference circle diameter D of the gear shaper cutter to be M multiplied by z, and drawing a reference circle sketch on one end face of the gear shaper cutter by taking the center of the end face as the center of a circle and D as the diameter;
(8) assembling the gear blank and the gear shaper cutter
Newly building an assembly file in UG NX software, assembling a driving wheel gear blank and a gear shaper cutter together, wherein a pitch curve of a driving wheel is tangent to a pitch circle of the gear shaper cutter, an intersection point of an X-axis negative half shaft and the pitch curve is taken as an object on the driving wheel gear blank, a central point of any gear tooth on the pitch circle is taken as an object on the gear shaper cutter, and the two points are overlapped to obtain the assembly file of the driving wheel gear blank and the gear shaper cutter;
when the driven wheel tooth blank is assembled with the gear shaper cutter, the pitch curve of the driven wheel is tangent to the reference circle of the gear shaper cutter, besides, the intersection point of the X-axis negative half shaft and the pitch curve is taken as a starting point on the driven wheel tooth blank, and the arc length from the starting point is taken as
Figure FDA0002545184770000021
The point of (2) is taken as an object, the central point of any gear tooth on the reference circle is taken as an object on the gear shaper cutter, and the two points are superposed to obtain an assembly file of a driven wheel tooth blank and the gear shaper cutter;
(9) motion simulation
Opening an assembly file of a driving wheel gear blank and a slotting cutter in UG NX, switching to a motion simulation module, performing motion simulation according to the steps of setting a connecting rod, setting a motion pair, setting a drive, setting a constraint, setting a tracking, setting a resolving scheme and solving calculation, and storing the position and the model of the slotting cutter in each calculating step in the solving process of the motion simulation;
in the same way, the motion simulation process of an assembly model of the driven wheel gear blank and the gear shaper cutter is carried out;
(10) non-circular gear solid model extraction
After the motion simulation solving of the driving wheel tooth blank and the pinion cutter assembly model is completed, clicking a geometric body-lifting body to operate, selecting the driving wheel tooth blank as a lifting target object in a dialog box of the lifting body, and clicking to confirm to complete the setting of the lifting body; selecting a lifting body in a part navigator as a target to obtain a three-dimensional model of a driving wheel;
the extraction mode and the steps of the three-dimensional solid model of the driven wheel are the same as those of the driving wheel, and the three-dimensional model of the driven wheel is obtained;
(11) creation of non-circular gear pairs
And newly building an assembly file in UG NX to complete the assembly of the driving wheel and the driven wheel, and ensuring that the tooth grooves of the driving wheel are just meshed with the gear teeth of the driven wheel at a zero line to obtain a non-circular gear pair three-dimensional model.
2. The method of claim 1 for three-dimensional solid modeling of a non-circular gear pair having a cosine profile, wherein: and (8) assembling the gear blank and the gear shaper cutter specifically as follows:
newly building an assembly file in UG NX software, assembling a driving wheel gear blank and a gear shaper cutter together, wherein a pitch curve of a driving wheel is tangent to a pitch circle of the gear shaper cutter, an intersection point of an X-axis negative half shaft and the pitch curve is taken as an object on the driving wheel gear blank, a central point of any gear tooth on the pitch circle is taken as an object on the gear shaper cutter, and the two points are overlapped to obtain the assembly file of the driving wheel gear blank and the gear shaper cutter;
when the driven wheel tooth blank is assembled with the gear shaper cutter, the pitch curve of the driven wheel is tangent to the reference circle of the gear shaper cutter, besides, the intersection point of the X-axis negative half shaft and the pitch curve is taken as a starting point on the driven wheel tooth blank, and the arc length from the starting point is taken as
Figure FDA0002545184770000031
The center point of any gear tooth on the reference circle is used as an object on the gear shaping cutter, and the two points are superposed to obtain an assembly file of a driven wheel tooth blank and the gear shaping cutter.
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CN113192180A (en) * 2021-04-28 2021-07-30 山东科技大学 Elliptic gear parameterization accurate modeling method based on gear shaping machining principle
CN113836665A (en) * 2021-09-28 2021-12-24 西安航空学院 Non-circular gear pitch curve design method for driving sine mechanism to do uniform reciprocating motion
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