CN109063326B - Gear accurate modeling method considering microscopic shape correction and actual machining errors - Google Patents
Gear accurate modeling method considering microscopic shape correction and actual machining errors Download PDFInfo
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Abstract
The invention provides a gear accurate modeling method considering microscopic shape modification and actual machining errors, which firstly deduces necessary parameters of a gear and a cutter required in the modeling process; obtaining an average tooth profile trace line and an average spiral line trace line of the gear according to the actual detected tooth profile and the actual detected spiral line of the gear; obtaining the tooth profile shape deviation and the spiral line shape deviation according to the actually detected tooth profile and the waviness of the actually detected spiral line; and obtaining the eccentricity of the gear and the offset of the actual tooth profile according to the radial runout and the tooth pitch deviation detection result of the gear. In three-dimensional software, drawing an actual involute, an actual base circle spiral line and a tooth root transition curve, and performing tooth profile deviation array; and finally, carrying out curved surface scanning, trimming and combining in software, carrying out materialized tooth space cutting, and obtaining an accurate three-dimensional model after array deviation. The gear model established by the method can simulate the meshing state of an actually machined gear, and predict the failure form and the service life of the gear.
Description
Technical Field
The invention relates to a gear accurate modeling method, in particular to a gear accurate modeling method considering microscopic modification and actual machining errors, and belongs to the field of gear modeling and machining.
Background
At present, the strength checking calculation method of the gear is generally carried out according to the ISO6336 standard, and when the influence of factors such as micro-modification and machining error of the gear on the strength of the gear is considered, the calculation result is corrected through various coefficients. The purpose of micro-modification of the gear is to effectively improve the meshing state of the gear, and machining errors of the gear can cause the problems of uneven tooth direction and tooth space load distribution of the gear, interference between a tooth root and a tooth top, increase of gear transmission errors and the like.
Due to the diversity and randomness of gear machining errors, in engineering practice, the phenomenon that the actual failure mode and failure time of a gear are inconsistent with calculation and checking often occurs. In order to research the root cause of the gear failure problem, predict and evaluate the influence of various machining errors of the gear on the gear meshing, effectively avoid various failure risks of the gear and the like, a gear model containing microscopic modification and actual machining errors needs to be established, and a finite element simulation technology is utilized to carry out accurate analysis and calculation.
However, in the existing gear modeling methods, only one aspect of micro-modification or machining errors is considered, and the micro-modification and the actual machining errors are not considered comprehensively.
Therefore, it is highly desirable to provide a precise gear modeling method that comprehensively considers microscopic modification and actual machining errors.
Disclosure of Invention
Aiming at the technical problems, the invention provides a gear accurate modeling method considering microscopic modification and actual machining errors. The gear three-dimensional model established by the method can be used for simulation calculation of finite elements and the like, the meshing state of the actually processed gear is simulated, and the failure form and failure time of the gear are predicted more accurately, so that the processing precision of the gear is controlled in a targeted manner.
The technical scheme adopted by the invention is as follows:
the embodiment of the invention provides a gear accurate modeling method considering microscopic modification and actual machining errors, which comprises the following steps:
the method comprises the following steps: determining a relevant parameter relational expression required in a modeling process according to design parameters of a gear and cutter parameters, wherein the design parameters comprise tooth number, modulus, pressure angle, helix angle, deflection coefficient, addendum circle diameter, dedendum circle diameter and tooth width, the cutter parameters comprise addendum height, tooth thickness, fillet radius and raised head quantity, and the relevant parameter relational expression comprises a gear end surface parameter calculation formula and a cutter auxiliary parameter calculation formula;
step two: determining an average tooth profile trace and an average spiral line trace according to an actual detected tooth profile and an actual detected spiral line of the gear, wherein the average tooth profile trace comprises tooth profile modification and tooth profile inclination deviation, and the average spiral line trace comprises spiral line modification and spiral line inclination deviation;
step three: determining the shape deviation of the tooth profile and the shape deviation of the spiral line according to the actually detected tooth profile of the gear and the waviness of the actually detected spiral line;
step four: drawing an actual involute, an actual spiral line and a tooth root transition curve, wherein the actual involute comprises tooth profile modification, tooth profile inclination deviation and tooth profile shape deviation, and the actual spiral line comprises spiral line modification, spiral line inclination deviation and spiral line shape deviation;
step five: determining the eccentricity of the gear and the offset of the tooth profile according to the radial runout detection result and the tooth pitch deviation detection result;
step six: respectively scanning the actual involute and the tooth root transition curve drawn in the fourth step along the actual spiral line and the theoretical spiral line, synthesizing the tooth profile curved surface and the tooth root curved surface obtained by scanning, and performing materialization on the synthesized curved surface to cut off the tooth socket; and performing offset array on the tooth grooves according to the gear eccentricity and the tooth pitch deviation obtained in the step five to obtain a gear accurate model considering the microscopic modification and the actual machining error.
Optionally, in the second step, the mean profile trace includes a parabolic portion and a linear portion, wherein the expression of the parabolic portion equation is:
in the formula:
Δ1-mean tooth profile trace offset in μm;
the involute roll angle, as a variable in this equation, is given in rad; a is1、b1、c1-the expression coefficients, determined from the actual gear measurements;
the expression for the linear portion equation of the mean profile trace is:
in the formula:
Δ2-mean tooth profile trace offset in μm;
the involute roll angle, as a variable in this equation, is given in rad; b2、c2-the expression coefficients are determined from the actual gear measurements.
Optionally, in the second step, the equation of the average spiral trace is expressed as:
Δ3＝a3Z2+b3Z+c3
in the formula: delta3-average spiral trace offset in μm; z-the tooth direction variable, in mm; a is3、b3、c3-the expression coefficients are determined from the actual gear measurements.
Optionally, in the third step:
determining the tooth profile shape deviation according to the following formula:
in the formula: delta4-tooth profile shape deviation in μm;
the involute roll angle, as a variable in this equation, is given in rad; a. the1、k1-the expression coefficients, determined from the actual gear measurements;
determining the helical line shape deviation according to the following formula:
Δ5＝A2sin(k2Z)
in the formula:
Δ5-helical shape deviation in μm; z-the tooth direction variable, in mm; a. the2、k2-the expression coefficients are determined from the actual gear measurements.
Optionally, in the fourth step, on the basis of the theoretical involute, an average tooth profile trace is obtained by removing material, and a tooth profile shape deviation is added to the average tooth profile trace to obtain an actual involute, wherein the material removal amount direction is a normal direction of the theoretical involute.
Optionally, in the fourth step, on the basis of the theoretical base circle helix, an average base circle helix is obtained by removing the material, and a helix shape deviation is added on the average base circle helix to obtain an actual base circle helix, wherein the material removal amount direction is the base circle tangential direction, and the drum shape directions of the base circle helices of the left tooth surface and the right tooth surface are opposite.
Optionally, in the fourth step, in the hobbing process, the root transition curve is an equidistant curve of an extended involute cut by a radius portion of the tool.
Optionally, in the step six:
the method for scanning the tooth profile curved surface comprises the following steps: establishing a base circular cylindrical surface in three-dimensional modeling software, and trimming the base circular cylindrical surface by using an actual base circular spiral line to obtain a trimming edge as a scanning track; projecting the actual involute in the step four to obtain a scanning section, and controlling a command 'section plane' in software to be a 'constant normal direction and be vertical to the curved surface' during scanning;
the method for scanning the curved surface of the tooth root comprises the following steps: trimming the base circle cylindrical surface by using a theoretical base circle spiral line, and taking the obtained trimmed edge as a scanning track; projecting the tooth root transition curve drawn in the fourth step to obtain a scanning section, and controlling a command 'cutting plane' in software to be 'constant normal and perpendicular to the curved surface' during scanning;
and trimming and combining the scanned tooth profile curved surface and the scanned tooth root curved surface, performing materialized cutting of the tooth socket, and offsetting the array to obtain a gear three-dimensional model considering microscopic modification and actual processing errors.
According to the accurate gear modeling method provided by the embodiment of the invention, the microscopic modification and the actual machining error of the gear are comprehensively considered, and the actual detection items of the gear are analyzed one by one and added into an ideal gear model. Deducing necessary parameters of the gear and the cutter required in the modeling process according to the basic principle of involute gear engagement and a machining process (hobbing); fitting according to the actual detected tooth profile and the actual detected spiral line of the gear to obtain an average tooth profile trace line and an average spiral line trace line of the gear; according to the actually detected tooth profile and the actually detected waviness of the spiral line, obtaining tooth profile shape deviation and spiral line shape deviation which accord with a sine function rule; and obtaining the eccentric amount of the gear and the offset of the actual tooth profile according to the radial runout and the tooth pitch deviation detection result of the gear. In three-dimensional software (Creo software), drawing an actual involute, an actual base circle spiral line and a tooth root transition curve, and performing tooth profile deviation array according to the eccentricity and the tooth pitch deviation of the gear; and finally, carrying out surface scanning, trimming and merging in three-dimensional modeling software (Creo software), carrying out materialized cutting of the tooth socket, and carrying out array offset to obtain an accurate three-dimensional model of the micro-modification gear.
The gear model established by the method provided by the embodiment of the invention can be used for finite element simulation calculation, simulating the meshing state of the actually processed gear, and predicting the failure form and the service life of the gear. The method is based on modeling, and can be used for analyzing the influence degree of different types of machining errors on the stress state of the gear, so that the machining precision of the gear is controlled more pertinently.
Drawings
FIG. 1 is a schematic flow chart of a method for accurately modeling a gear according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the structural parameters of the tool;
FIG. 3 is a schematic diagram of a detected gear mean profile trace;
FIG. 4 is a schematic diagram of a test gear mean spiral trace;
FIG. 5 is a schematic diagram of an actual tooth profile trace of a test gear;
FIG. 6 is a schematic diagram of an actual helical trace of a test gear;
FIG. 7 is a schematic diagram of an actual involute;
FIG. 8 is a schematic view of the true base circle helix of a right-hand gear;
FIG. 9 is a schematic view of the true base circle helix of a left-hand gear;
FIG. 10 is a schematic view of a tooth root transition curve;
FIG. 11 is a schematic diagram of the end face structural parameters of a bevel gear cutter;
FIG. 12 is a graph showing the results of gear run-out detection;
FIG. 13 is a schematic view of an eccentric gear;
FIG. 14 is a schematic diagram showing the detection results of the single pitch deviation of the gear;
FIG. 15 is a schematic illustration of a single pitch deviation caused by gear eccentricity;
FIG. 16 is a schematic representation of actual tooth profile offset;
FIG. 17 is a schematic view of a scanning surface;
FIG. 18 is a schematic illustration of an exemplary ablation gullet;
FIG. 19 is a schematic view of a three-dimensional model of a gear taking into account microscopic contouring and actual machining errors.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a schematic flow chart of a method for accurately modeling a gear according to an embodiment of the present invention; FIG. 2 is a schematic diagram of the structural parameters of the tool; FIG. 3 is a schematic diagram of a detected gear mean profile trace; FIG. 4 is a schematic diagram of a test gear mean spiral trace; FIG. 5 is a schematic diagram of an actual tooth profile trace of a test gear; FIG. 6 is a schematic diagram of an actual spiral trace of a test gear; FIG. 7 is a schematic diagram of an actual involute; FIG. 8 is a schematic view of the true base circle helix of a right-hand gear; FIG. 9 is a schematic view of the true base circle helix of a left-hand gear; FIG. 10 is a schematic view of a tooth root transition curve; FIG. 11 is a schematic diagram of the end face structural parameters of a bevel gear cutter; FIG. 12 is a graph showing the results of gear run-out detection; FIG. 13 is a schematic view of an eccentric gear; FIG. 14 is a schematic diagram showing the detection results of the single pitch deviation of the gear; FIG. 15 is a schematic illustration of a single pitch deviation caused by gear eccentricity; FIG. 16 is a schematic representation of actual tooth profile offset; FIG. 17 is a schematic view of a scanning surface; FIG. 18 is a schematic illustration of an exemplary ablation gullet; FIG. 19 is a schematic view of a three-dimensional model of a gear taking into account microscopic contouring and actual machining errors.
As shown in FIG. 1, the precise modeling method for the gear considering the microscopic modification and the actual machining error provided by the invention comprises the following steps:
the method comprises the following steps: determining a relevant parameter relational expression required in a modeling process according to design parameters of a gear and cutter parameters, wherein the design parameters comprise tooth number, modulus, pressure angle, helix angle, deflection coefficient, addendum circle diameter, dedendum circle diameter and tooth width, the cutter parameters comprise addendum height, tooth thickness, fillet radius and raised head quantity, and the relevant parameter relational expression comprises a gear end surface parameter calculation formula and a cutter auxiliary parameter calculation formula;
step two: determining an average tooth profile trace and an average spiral line trace according to an actual detected tooth profile and an actual detected spiral line of the gear, wherein the average tooth profile trace comprises tooth profile modification and tooth profile inclination deviation, and the average spiral line trace comprises spiral line modification and spiral line inclination deviation;
step three: determining the shape deviation of the tooth profile and the shape deviation of the spiral line according to the actually detected tooth profile of the gear and the waviness of the actually detected spiral line;
step four: drawing an actual involute, an actual spiral line and a tooth root transition curve, wherein the actual involute comprises tooth profile modification, tooth profile inclination deviation and tooth profile shape deviation, and the actual spiral line comprises spiral line modification, spiral line inclination deviation and spiral line shape deviation;
step five: determining the eccentricity of the gear and the offset of the tooth profile according to the radial runout detection result and the tooth pitch deviation detection result;
step six: respectively scanning the actual involute and the tooth root transition curve drawn in the fourth step along the actual spiral line and the theoretical spiral line, synthesizing the tooth profile curved surface and the tooth root curved surface obtained by scanning, and performing materialization on the synthesized curved surface to cut off the tooth socket; and performing offset array on the tooth grooves according to the gear eccentricity and the tooth pitch deviation obtained in the step five to obtain a gear accurate model considering the microscopic modification and the actual machining error.
In the second step, the average tooth profile trace comprises a parabolic part and a linear part, wherein the expression of the equation of the parabolic part is as follows:
in the formula:
Δ1-mean tooth profile trace offset in μm;
the involute roll angle, as a variable in this equation, is given in rad; a is1、b1、c1-expression coefficients, determined from the actual gear measurements, i.e. the coordinates of the three points on the parabola:
the expression for the linear portion equation of the mean profile trace is:
in the formula:
Δ2-mean tooth profile trace offset in μm;
the involute roll angle, as a variable in this equation, is given in rad; b is a mixture of2、c2-expression coefficients, determined by the actual gear measurements, i.e. coordinates of two points on a straight line:
in addition, in the second step, the equation expression of the average spiral trace is:
Δ3＝a3Z2+b3Z+c3
in the formula: delta3-average spiral trace offset in μm; z-the tooth direction variable, in mm; a is3、b3、c3-the expression coefficient is determined by the actual detection result of the gear, namely the three-point coordinates of the spiral trace: b is1(Z1，－Cβ1)，B2(Z2，0)，B3(Z3，－Cβ2). From this equation, it can be found that the axial modification amount is C when Z is 0 and Z is b on the front and rear end faces of the gear, respectivelyβ3And Cβ4。
Further, in the third step, the tooth profile waviness (tooth profile shape deviation) may be determined according to the actually detected tooth profile trace diagram, so as to determine the tooth profile shape deviation conforming to the sine function law, and specifically, the tooth profile shape deviation may be determined according to the following formula:
in the formula: delta4-tooth profile shape deviation in μm;
the involute roll angle, as a variable in this equation, is given in rad; a. the1、k1-the expression coefficients, determined from the actual gear measurements;
in addition, in step three, the spiral waviness (spiral shape deviation) can be determined according to the actually detected spiral line trace diagram, so as to determine the spiral shape deviation conforming to the sine function law, and specifically, the spiral shape deviation can be determined according to the following formula:
Δ5＝A2sin(k2Z)
in the formula:
Δ5-helical shape deviation in μm; z-the tooth direction variable, in mm; a. the2、k2-the expression coefficients are determined from the actual gear measurements.
Further, in the fourth step, on the basis of the theoretical involute, an average tooth profile trace is obtained by removing material, a tooth profile shape deviation is added to the average tooth profile trace to obtain an actual involute, and the material removal amount direction is the normal direction of the theoretical involute. The curve equation of the actual involute is in the form of a piecewise function (drum profile section and tooth crest edge section).
In a default coordinate system of three-dimensional modeling software (Creo software), a curve equation of a drum-shaped modification part of the actual involute is as follows:
the curve equation of the addendum trimming part of the actual involute is as follows:
in the formula:
αk1-the width of the base circular tooth space corresponds to half of the central angle;
-representing the variation of the actual involute at the start of the base circle; alpha is alphakThe argument, the involute pressure angle (°), of the preceding equation is
The latter range of independent variables is
rb-base circle radius; delta1、Δ2-mean tooth profile trace offset (μm); delta4-tooth profile shape deviation.
In addition, in the fourth step, on the basis of the theoretical base circle helix, an average base circle helix is obtained by removing materials, and a helix shape deviation is added on the average base circle helix to obtain an actual base circle helix, wherein the material removal amount direction is the base circle tangential direction, and the drum shape directions of the base circle helices of the left tooth surface and the right tooth surface are opposite.
In a default coordinate system of three-dimensional modeling software (Creo software), the actual base circle spiral equation of the right tooth surface is as follows:
the actual base circle spiral equation of the left tooth surface is as follows:
in the formula:
t-independent variable, range is [0, 1](ii) a b-gear tooth width; beta is a betab-base circle helix angle; delta3-average spiral trace offset; delta5-deviations in the shape of the helix; the plus or minus direction and the plus or minus direction indicate that the rotation direction of the gear is right; the "+ -" middle "-" indicates that the gear rotation direction is left-handed.
In the fourth step, in the hobbing process, the tooth root transition curve is an equidistant curve of an extended involute curve formed by cutting a corner portion of the tool.
In three-dimensional modeling software (Creo software), a Cartesian coordinate system is established by taking the circle center of a gear as an origin and the tooth thickness central line of the gear as an axis Y, and a tooth root transition curve equation is as follows:
in the formula:
r-gear reference circle radius; a is1-a tool assistance parameter; rc-tool fillet radius; α' -argument, range (α, 90);
-a tool-assistance parameter which is,
in step five, determining the eccentricity f of the gear according to the detection result of the radial runout of the geare. The eccentricity of the gear not only affects the radial runout of the gear, but also affects the tooth pitch deviation of the gear, and the actual tooth profile offset can be obtained by comparing the actually measured tooth pitch deviation with the tooth pitch deviation caused by the eccentricity and subtracting the actually measured tooth pitch deviation from the actually measured tooth pitch deviation.
In the sixth step, the method for scanning the tooth profile curved surface comprises the following steps: establishing a base circular cylindrical surface in three-dimensional modeling software, and trimming the base circular cylindrical surface by using an actual base circular spiral line to obtain a trimming edge as a scanning track; and projecting the actual involute in the step four to obtain a scanning section, and controlling a command 'section plane' in software to be a constant normal direction and be vertical to the curved surface during scanning.
In addition, in the sixth step, the root surface scanning method is as follows: trimming the base circle cylindrical surface by using a theoretical base circle spiral line, and taking the obtained trimmed edge as a scanning track; and (4) projecting the tooth root transition curve drawn in the fourth step to obtain a scanning section, and controlling a command 'section plane' in software to be a constant normal direction and be vertical to the curved surface during scanning.
And trimming and combining the scanned tooth profile curved surface and the scanned tooth root curved surface, performing materialized cutting of the tooth socket, and offsetting the array to obtain a gear three-dimensional model considering microscopic modification and actual processing errors.
[ examples ] A method for producing a compound
Hereinafter, the precise modeling method of the gear according to the present invention will be described in detail with reference to examples.
1. Determining design parameters and cutter parameters of the gear, and inputting a related parameter relational expression:
(1) inputting design parameters and tool parameters of the gear in three-dimensional modeling software (Creo software in the embodiment), and adjusting the model precision to 10-6mm。
Design parameters of the gear include:
number of teeth z
Modulus (mm) mn
Pressure angle (°) alphan
Helix angle (°) β
Coefficient of variation xn
Diameter of addendum circle (mm) da
Root circle diameter (mm) df
Tooth width (mm) b
The cutter parameters of the gear include:
radius of cutter fillet (mm) Rc
Nose amount (mm) p of cutterr
(2) The gear face parameters can be deduced according to the design parameters of the gear, including the face module m of the geartEnd face pressure angle αtCoefficient of end face displacement xtCircle of reference being straightDiameter d, reference circle radius r, base circle diameter dbBase radius rbAnd base circle helix angle betabThe above parameters can be calculated by the gear basic calculation formula.
Parameters related to the starting position of the theoretical involute of the gear can be deduced according to the design parameters of the gear, including the gear reference circle spread angle thetak(°) half of the central angle of base circle tooth thicknesskThe parameters are all gear end face parameters.
According to the design parameters of the gear and the cutter parameters, other relevant parameters of the cutter can be deduced, including the addendum height h of the cuttercTooth thickness S of cutting toolNAnd an auxiliary parameter a as shown in FIG. 21，b1，ftwThe above parameters are all tool normal parameters.
Inputting the relation of each parameter in three-dimensional modeling software (Creo software):
mt＝mn/cosβ
αt＝arctan(tanαn/cosβ)
xt＝xncosβ
d＝mtz
r＝d/2
db＝dcosαt
rb＝d/2
θk＝180tanαt/π-αt
αk＝180(π/2-2xttanαt)/(πz)-θk
βb＝arctan(tanβcosαt)
hc＝(d-df)/2
a1＝hc-rc
SN＝(π/2-2xntanαn)mn
ftw＝2(SN/2+pr/cosαn-a1tanαn-rc/cosαn)
b1＝(πmn-ftw)/2
2. determining an average tooth profile trace and an average spiral trace according to actual detection parameters of the gear:
(1) determining an average tooth profile trace:
a coordinate system as shown in fig. 3 was established, where the abscissa is the roll angle (rad) of the profile involute and the ordinate is the distance (μm) by which the mean profile trace was shifted from the theoretical involute. According to three-point coordinates in the range of the tooth profile drum shape modification on the actually detected tooth profile trace diagram:
the parabolic portion of the mean profile trace may be expressed as:
according to coordinates of two points in the tooth top trimming edge range on the tooth profile trace diagram:
the straight portion of the mean profile trace can be represented as:
(2) determine the average spiral trace:
a coordinate system is established as shown in fig. 4, where the abscissa is the gear tooth width (mm) and the ordinate is the distance (μm) by which the mean helix trace is offset from the theoretical helix. According to the coordinates of three points on the spiral line: b is1(Z1，－Cβ1)，B2(Z2，0)，B3(Z3，－Cβ2) Mean helical stitchThe line can be represented as:
Δ3＝a3Z2+b3Z+c3
from this equation, it can be found that the axial relief amount is C when Z is 0 and Z is b on the front and rear end faces of the gear, respectivelyβ3And Cβ4。
3. Determining the tooth profile shape deviation and the spiral line shape deviation according to the actual detection parameters of the gear:
as shown in fig. 5, the tooth profile shape deviation and waviness of the gear are determined according to the actually detected tooth profile trace diagram of the gear, so as to determine the tooth profile shape deviation according with the sine law:
in the formula:
Δ4-tooth profile shape deviation (μm);
-the involute roll angle (rad), as a variable in this formula; a. the1、k1-expressing the coefficients.
As shown in fig. 6, according to the actually detected spiral line trace diagram of the gear, the spiral line shape deviation and waviness of the gear are determined, so that the spiral line shape deviation conforming to the sine law is determined:
Δ5＝A2sin(k2Z)
in the formula:
Δ5-deviation of the shape of the spiral (μm); z-tooth direction variation (mm); a. the2、k2-expressing the coefficients.
4. The actual involute, actual helix and root transition curves are plotted in three-dimensional modeling software (Creo software):
(1) and (3) drawing an actual involute:
in the three-dimensional modeling software (Creo software), the actual involute is drawn through an equation, as shown in fig. 7, the equation coordinate system is selected as the software default coordinate system CS, the type of the coordinate system is selected as the cylindrical coordinate, and then the curve equation of the actual involute drum shape modification part is:
the curve equation of the actual involute tooth crest edge trimming part is as follows:
in the formula:
αk1-the base circle tooth space width corresponds to half of the central angle;
-representing the variation of the actual involute at the start of the base circle; alpha is alphakThe argument, the involute pressure angle (°), of the preceding equation is
The latter range of independent variables is
rb-base circle radius; delta of1、Δ2-mean tooth profile trace offset (μm); delta4-deviation of tooth profile shape.
(2) Drawing of real spiral line
In the three-dimensional modeling software (Creo software), an actual base circle spiral line is drawn by an equation. Because the drum shape directions of the left and right tooth surfaces are opposite when the tooth direction drum shape modification is carried out, the actual base circle spiral lines of the left and right tooth surfaces need to be drawn separately for distinguishing. The equation coordinate system is selected as a software default coordinate system CS, the type of the coordinate system is selected as a cylindrical coordinate, and then the curve equation of the actual base circle spiral line of the right tooth surface is as follows:
the actual base circle spiral equation of the left tooth surface is as follows:
in the formula:
t-independent variable, range is [0, 1 ]](ii) a b-gear tooth width; beta is a betab-base circle helix angle; delta3-average spiral trace offset; delta5-deviations in the shape of the helix; the plus or minus part and the plus or minus part indicate that the rotation direction of the gear is right; the "+ -" middle "-" indicates that the gear rotation direction is left-handed.
The right and left tooth surface base circle drum-shaped modification spiral lines in right rotation are shown in fig. 8, and the right and left tooth surface base circle drum-shaped modification spiral lines in left rotation are shown in fig. 9.
(3) Plotting root transition curves
In the hobbing process, the tooth root transition curve is an equidistant curve of an extended involute formed by cutting a round corner part of a cutter, and the principle and equation derivation are not repeated. In three-dimensional modeling software (Creo software), a Cartesian coordinate system CS0 is established by taking the circle center of a gear as an origin and the tooth thickness central line of the gear as an axis Y, and the tooth root transition curve equation is as follows:
in the formula:
r-gear reference circle radius; a is1-a tool assistance parameter; r isc-tool fillet radius; α' -argument, range (α, 90);
-a tool-assistance parameter which is,
modeling curves such asAs shown in fig. 10.
The key point of the invention lies in the derivation of the tooth root transition curve of the bevel gear, the end surface parameter of the cutter is shown in figure 11, the parameter of the cutter in the tooth height direction is unchanged, and the parameter of the tooth width direction and the fillet parameter are converted according to the following formula.
b1t＝b1/cosβ
5. Determining the eccentricity and tooth profile offset of the gear:
the results of detecting the radial runout of the gear are shown in FIG. 12, where the radial runout of the gear is FrEccentricity of feThe two corresponding relations are as follows:
Fr＝2fe
drawing the motion axis of the gear, wherein the offset of the motion axis of the gear relative to the gear tooth axis of the gear is feThe eccentric gear is shown in fig. 13.
The actually measured pitch deviation of the gear is shown in fig. 14, the influence of the eccentricity of the gear on the single pitch deviation is shown in fig. 15, and the deviation amount delta f of the actual tooth profile can be obtained by subtracting the actual tooth profile and the eccentric gearptAs shown in fig. 16.
6. Carrying out curved surface scanning, curved surface synthesis, tooth space cutting and offset array to obtain a gear model considering microscopic modification and actual machining errors:
(1) creating a scan trajectory
Respectively trimming the base circle cylindrical surfaces by using the actual base circle spiral lines of the left tooth surface and the right tooth surface in three-dimensional modeling software (Creo software) to obtain scanning tracks of the left tooth surface and the right tooth surface; and (4) trimming the base circle cylindrical surface by using a theoretical base circle spiral line to obtain a tooth root transition curve scanning track.
(2) Performing curved surface scanning to obtain transition curved surfaces of left and right tooth surfaces and tooth roots
In three-dimensional modeling software (Creo software), the scanning methods of the left tooth surface and the right tooth surface are the same as those of the tooth root transition curved surface, the scanning track created in the step (1) is selected, the 'section plane control' is selected as a 'constant normal', the plane where the front end surface of the gear is located is selected as a 'direction reference', and the 'horizontal/vertical control' is selected as a 'vertical curved surface'; and (3) creating a scanning cross section, wherein the tooth surface scanning cross section is an actual involute, the tooth root curved surface scanning cross section comprises a tooth root transition curve and a tooth root circle, scanning is performed by selecting 'the sketched cross section is unchanged in the scanning process', and the curved surface scanning result is shown in fig. 17.
(3) Performing tooth space cutting and array deviation to obtain a precise model of the modified gear
In the three-dimensional modeling software (Creo software), the addendum cylinder is drawn with the CS origin of coordinates as the center, the left and right tooth flanks and the dedendum transition curved surfaces scanned in (2) are trimmed and synthesized, the curved surface group is materialized, and "material removal" is selected, as shown in fig. 18. The features are subjected to an offset array with an offset of Δ fptThereby obtaining a three-dimensional model of the gear considering the microscopic modification and the actual machining error, which is shown in fig. 19.
In summary, the precise modeling method for the gear provided by the embodiment of the invention comprehensively considers the microscopic modification and the actual machining error of the gear, and analyzes the actual detection items of the gear one by one and adds the actual detection items into an ideal gear model. Deducing necessary parameters of the gear and the cutter required in the modeling process according to the basic principle of involute gear engagement and a machining process (hobbing); fitting according to the actual detected tooth profile and the actual detected spiral line of the gear to obtain an average tooth profile trace line and an average spiral line trace line of the gear; according to the actually detected tooth profile and the actually detected waviness of the spiral line, obtaining tooth profile shape deviation and spiral line shape deviation which accord with a sine function rule; and obtaining the eccentric amount of the gear and the offset of the actual tooth profile according to the radial runout and the tooth pitch deviation detection result of the gear. In three-dimensional software (Creo software), drawing an actual involute, an actual base circle spiral line and a tooth root transition curve, and performing tooth profile deviation array according to tooth pitch deviation; and finally, carrying out surface scanning, trimming and merging in three-dimensional modeling software (Creo software), carrying out materialized cutting of the tooth socket, and carrying out array offset to obtain an accurate three-dimensional model of the micro-modification gear. The gear model established by the method can be used for finite element simulation calculation, simulating the meshing state of an actually machined gear, and predicting the failure mode and the service life of the gear. The method is based on modeling, and can be used for analyzing the influence degree of different types of machining errors on the stress state of the gear, so that the machining precision of the gear is controlled more pertinently.
The above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (8)
1. A gear accurate modeling method considering microscopic modification and actual machining errors is characterized by comprising the following steps:
the method comprises the following steps: determining a relevant parameter relational expression required in a modeling process according to design parameters of a gear and cutter parameters, wherein the design parameters comprise tooth number, modulus, pressure angle, helix angle, deflection coefficient, addendum circle diameter, dedendum circle diameter and tooth width, the cutter parameters comprise addendum height, tooth thickness, fillet radius and raised head quantity, and the relevant parameter relational expression comprises a gear end surface parameter calculation formula and a cutter auxiliary parameter calculation formula;
step two: determining an average tooth profile trace and an average spiral trace according to an actual detected tooth profile and an actual detected spiral of the gear, wherein the average tooth profile trace comprises tooth profile modification and tooth profile inclination deviation, and the average spiral trace comprises spiral modification and spiral inclination deviation;
step three: determining the shape deviation of the tooth profile and the shape deviation of the spiral line according to the actually detected tooth profile of the gear and the waviness of the actually detected spiral line;
step four: drawing an actual involute, an actual spiral line and a tooth root transition curve, wherein the actual involute comprises tooth profile modification, tooth profile inclination deviation and tooth profile shape deviation, and the actual spiral line comprises spiral line modification, spiral line inclination deviation and spiral line shape deviation;
step five: determining the eccentricity of the gear and the offset of the tooth profile according to the radial runout detection result and the tooth pitch deviation detection result;
step six: respectively scanning the actual involute and the tooth root transition curve drawn in the fourth step along the actual spiral line and the theoretical spiral line, synthesizing the tooth profile curved surface and the tooth root curved surface obtained by scanning, and performing materialization on the synthesized curved surface to cut off the tooth socket; and performing offset array on the tooth grooves according to the gear eccentricity and the tooth pitch deviation obtained in the step five to obtain a gear accurate model considering the microscopic modification and the actual machining error.
2. The method according to claim 1, wherein in step two, the mean profile trace comprises a parabolic portion and a linear portion, wherein the equation for the parabolic portion is expressed as:
in the formula:
Δ1-mean tooth profile trace offset in μm;
the involute roll angle, as a variable in this equation, in rad; a is1、b1、c1-the expression coefficients, determined from the actual gear measurements;
the expression for the linear portion equation of the mean profile trace is:
in the formula:
Δ2-mean tooth profile trace offset in μm;
the involute roll angle, as a variable in this equation, in rad; b2、c2-the expression coefficients, determined from the actual gear detection results.
3. The method according to claim 1, wherein in the second step, the equation of the average spiral trace is expressed as:
Δ3＝a3Z2+b3Z+c3
in the formula: delta3-average spiral trace offset in μm; z-tooth direction variable, unit is mm; a is a3、b3、c3-the expression coefficients are determined from the actual gear measurements.
4. The method according to claim 1, characterized in that in the third step:
determining the tooth profile shape deviation according to the following formula:
in the formula: delta4-tooth profile shape deviation in μm;
gradually advancingThe open line roll angle is used as a variable in the equation and the unit is rad; a. the1、k1-the expression coefficients, determined from the actual detection of the gear;
determining the helical line shape deviation according to the following formula:
Δ5＝A2sin(k2Z)
in the formula:
Δ5-helical shape deviation in μm; z-the tooth direction variable, in mm; a. the2、k2-the expression coefficients are determined from the actual gear measurements.
5. The method according to claim 1, wherein in the fourth step, an average profile trace is obtained by removing material on the basis of a theoretical involute, and a profile shape deviation is added to the average profile trace to obtain an actual involute, wherein the material removal amount direction is a normal direction of the theoretical involute.
6. The method as claimed in claim 1, wherein in the fourth step, on the basis of the theoretical base circle helix, an average base circle helix is obtained by removing material, and an actual base circle helix is obtained by adding helix shape deviation to the average base circle helix, wherein the material removal amount direction is a base circle tangential direction, and the base circle helix drum shapes of the left and right tooth surfaces are opposite.
7. The method of claim 1 wherein in said fourth step, in the hobbing process, the root transition curve is an equidistant curve of an extended involute cut from a radiused portion of the tool.
8. The method according to claim 1, characterized in that in said step six:
the method for scanning the tooth profile curved surface comprises the following steps: establishing a base circular cylindrical surface in three-dimensional modeling software, and trimming the base circular cylindrical surface by using an actual base circular spiral line to obtain a trimming edge as a scanning track; projecting the actual involute in the step four to obtain a scanning section, and controlling a command 'section plane' in software to be a 'constant normal direction and be vertical to the curved surface' during scanning;
the method for scanning the curved surface of the tooth root comprises the following steps: trimming the base circle cylindrical surface by using a theoretical base circle spiral line, and taking the obtained trimmed edge as a scanning track; projecting the tooth root transition curve drawn in the fourth step to obtain a scanning section, and controlling a command 'cutting plane' in software to be 'constant normal and perpendicular to the curved surface' during scanning;
and trimming and combining the scanned tooth profile curved surface and the scanned tooth root curved surface, performing materialized cutting of the tooth socket, and offsetting the array to obtain a gear three-dimensional model considering microscopic modification and actual processing errors.
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