CN109063326A - A kind of gear Precise modeling considering microcosmic correction of the flank shape and actual processing error - Google Patents
A kind of gear Precise modeling considering microcosmic correction of the flank shape and actual processing error Download PDFInfo
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Abstract
The present invention provides a kind of gear Precise modeling for considering microcosmic correction of the flank shape and actual processing error, this method derives the call parameter of gear and cutter needed for modeling process first；According to the actually detected flank profil of gear and actually detected helix, the average flank profil trace and average helix trace of gear are obtained；According to the waviness of actually detected flank profil and actually detected helix, profile geometry deviation and helix shape deviation are obtained；According to the circular runout of gear and circular pitch deviation testing result, the eccentricity of gear and the offset of practical tooth are obtained.In three-dimensional software, practical involute, practical base helix and fillet curve are drawn, and carry out flank profil offset array；Curved surface scanning, trimming are finally carried out in software and is merged, and are carried out hypostazation and are cut off tooth socket, obtain accurate three-dimensional model after offset array.The model of gear established using this method, the meshing state of analog actual processing gear predict the failure mode and service life of gear.
Description
Technical field
The present invention relates to a kind of gear Precise modelings, and in particular to a kind of to consider microcosmic correction of the flank shape and actual processing error
Gear Precise modeling, belong to gear modeling and manufacture field.
Background technique
Currently, the strength check method of gear is carried out generally according to ISO6336 standard, the microcosmic correction of the flank shape of gear is being considered
It is to be modified by each term coefficient to calculated result and when influence of the factors such as mismachining tolerance to the strength of gear teeth.Gear
The purpose of microcosmic correction of the flank shape is to be able to be effectively improved the meshing state of gear, and the mismachining tolerance of gear can then cause gear teeth
It is uneven to, load distribution among gear teeth, the problems such as tooth root, tooth top interference and gear transmission error increase, and in a standard to items
The selection of coefficient, usually empirically chart or empirical equation carry out.
Due to the diversity and randomness of Errors in Gear Processing, in engineering practice, often there is the considered repealed of gear
Inconsistent phenomenon is checked in mode and out-of-service time and calculating.In order to study the basic reason of gear failure problem generation, prediction
The influence generated with evaluation gear items mismachining tolerance to gear engagement, effectively evades various failure risks of gear etc., needs
The model of gear comprising microcosmic correction of the flank shape and actual processing error is established, carries out accurately analysis meter using finite element simulation technology
It calculates.
However, the one aspect of microcosmic correction of the flank shape or mismachining tolerance is only accounted in existing gear modeling method, and
Microcosmic correction of the flank shape and actual processing error are not comprehensively considered.
It would therefore be highly desirable to need to provide a kind of gear Accurate Model side for comprehensively considering microcosmic correction of the flank shape and actual processing error
Method.
Summary of the invention
In view of the above technical problems, the present invention, which provides, a kind of considers that microcosmic correction of the flank shape and the gear of actual processing error are accurately built
Mould method, this method not only allow for the microcosmic profile modifying parameters of reality of gear, have also comprehensively considered total profile deviation, the spiral of gear
The actual processings error such as line deviation, circular runout and circular pitch deviation.The gears ' three-dimensional model established using this method, can be used for having
The simulation calculations such as member are limited, the meshing state of actual processing gear is simulated, when more accurately predicting the failure mode and failure of gear
Between, to be targetedly controlled to the machining accuracy of gear.
The technical solution adopted by the present invention are as follows:
The embodiment of the present invention provides a kind of gear Precise modeling for considering microcosmic correction of the flank shape and actual processing error, packet
It includes:
Step 1: according to the design parameter and cutter parameters of gear, relevant parameter relationship needed for modeling process is determined
Formula, the design parameter include the number of teeth, modulus, pressure angle, helical angle, modification coefficient, tip diameter, root diameter and tooth
Width, the cutter parameters include height of teeth top, transverse tooth thickness, radius of corner and plush copper amount, and the relevant parameter relational expression includes gear end
Face parameter calculation formula and cutter auxiliary parameter calculation formula；
Step 2: average flank profil trace and average spiral shell are determined according to the actually detected flank profil of gear and actually detected helix
Spin line trace, the average flank profil trace includes profile modification and flank profil dip deviation, and the average helical stitching line includes spiral shell
Spin line correction of the flank shape and helix dip deviation；
Step 3: according to the waviness of the actually detected flank profil of gear and actually detected helix determine profile geometry deviation and
Helix shape deviation；
Step 4: practical involute, practical helix and fillet curve are drawn, the practical involute includes flank profil
Correction of the flank shape, flank profil dip deviation and profile geometry deviation, the practical helix include helix correction of the flank shape, helix dip deviation and
Helix shape deviation；
Step 5: it according to circular runout testing result and circular pitch deviation testing result, determines gear eccentricity amount and determines tooth
Wide offset；
Step 6: the practical involute and fillet curve drawn in step 4 are prolonged into practical helix and theory respectively
Helix is scanned, and tooth profile and root surface that scanning obtains are synthesized, and the curved surface of synthesis is carried out hypostazation
Cut off tooth socket；And gear eccentricity amount and circular pitch deviation according to obtained in step 5, tooth socket is subjected to offset array, is examined
Consider the exactly modeling of gear tooth of microcosmic correction of the flank shape and actual processing error.
Optionally, in the step 2, average flank profil trace includes parabola branch and straight line portion, wherein parabolic
The expression formula of line Duffing equation are as follows:
In formula:
Δ1- averagely flank profil trace offset, unit is μm；- involute roll angle is used as variable in the equation, single
Position is rad；a1、b1、c1- expression formula coefficient is determined by the actually detected result of gear；
The expression formula of the straight line portion equation of average flank profil trace are as follows:
In formula:
Δ2- averagely flank profil trace offset, unit is μm；- involute roll angle is used as variable in the equation, single
Position is rad；b2、c2- expression formula coefficient is determined by the actually detected result of gear.
Optionally, in the step 2, the equation expression formula of average helical stitching line are as follows:
Δ3=a3Z2+b3Z+c3
In formula: Δ3- average helical stitching line deviation, unit are μm；Z-teeth directional direction variable, unit mm；a3、
b3、c3- expression formula coefficient is determined by the actually detected result of gear.
Optionally, in the step 3:
The profile geometry deviation is determined according to following formula:
In formula: Δ4- profile geometry deviation, unit are μm；- involute roll angle is used as variable, unit in the equation
For rad；A1、k1- expression formula coefficient is determined by the actually detected result of gear；
The helix shape deviation is determined according to following formula:
Δ5=A2sin(k2Z)
In formula:
Δ5- helix shape deviation, unit are μm；Z-teeth directional direction variable, unit mm；A2、k2- expression formula system
Number, is determined by the actually detected result of gear.
Optionally, in the step 4, on the basis of theoretical involute, average flank profil mark is obtained by removing material
Line adds profile geometry deviation on average flank profil trace and obtains practical involute, and material removal amount direction is theoretical involute
Normal direction.
Optionally, in the step 4, on the basis of theoretical base helix, average base is obtained by removing material
Circle helix adds helix shape deviation on average base helix and obtains practical base helix, wherein material removal
Amount direction is basic circle tangential direction, and the base helix cydariform of the left and right flank of tooth is contrary.
Optionally, in the step 4, in gear hobbing process technique, fillet curve is the fillet part by cutter
The equidistant curve for the prolate involute that cutting is formed.
Optionally, in the step 6:
The method of tooth profile scanning are as follows: basic circle cylindrical surface is established in 3 d modeling software, with practical base helix
The basic circle cylindrical surface is trimmed, is scanning track with the trimming side of acquisition；By practical involute described in step 4 project with
Scanning cross-section is obtained, " cutting plane " will be ordered to control in software when scanning for " constant normal direction and perpendicular to curved surface "；
The method of root surface scanning are as follows: trim basic circle cylindrical surface with theoretical base helix, be with the trimming side of acquisition
Scan track；Fillet curve will be drawn in step 4 to project to obtain scanning cross-section, when scanning will order in software
" cutting plane " control is " constant normal direction and perpendicular to curved surface "；
The tooth profile scanned is trimmed and merged with root surface, carries out hypostazation and cuts off tooth socket, deviate battle array
Obtain considering the gears ' three-dimensional model of microcosmic correction of the flank shape and actual processing error after column.
Gear Precise modeling provided in an embodiment of the present invention has comprehensively considered the microcosmic correction of the flank shape and actual processing of gear
The actually detected project of gear is analyzed one by one and is added in the ideal model of gear by error.It is engaged according to involute gear
Basic principle and processing technology (gear hobbing process) derive the call parameter of gear and cutter needed for modeling process；According to tooth
The actually detected flank profil of wheel and actually detected helix, obtain the average flank profil trace and average helix of gear after being fitted
Trace；According to the waviness of actually detected flank profil and actually detected helix, the profile geometry for obtaining meeting SIN function rule is inclined
Difference and helix shape deviation；According to the circular runout of gear and circular pitch deviation testing result, the eccentricity and reality of gear are obtained
The offset of border flank profil.In three-dimensional software (Creo software), practical involute, practical base helix and tooth root transition are drawn
Curve carries out flank profil offset array according to the eccentricity of gear and circular pitch deviation；Finally at 3 d modeling software (Creo software)
Middle progress curved surface scanning, trimming and merge, carries out hypostazation and cut off tooth socket, obtain the accurate of microcosmic profile modifying gear after offset array
Threedimensional model.
The model of gear established using method provided in an embodiment of the present invention, can be used for finite element stimulation, and simulation is real
Border processes the meshing state of gear, predicts the failure mode and service life of gear.It is modeled based on this method, can be used for analyzing not
Same type mismachining tolerance is to the influence degree of strength of gear state, so that more targeted control Gear Processing precision
System.
Detailed description of the invention
Fig. 1 is the flow diagram of gear Precise modeling provided in an embodiment of the present invention；
Fig. 2 is tool structure parameter schematic diagram；
Fig. 3 is that detection gear is averaged flank profil trace schematic diagram；
Fig. 4 is detection gear average helical stitching line schematic diagram；
Fig. 5 is the practical tooth trace schematic diagram for detecting gear；
Fig. 6 is the practical helix trace schematic diagram for detecting gear；
Fig. 7 is practical involute schematic diagram；
Fig. 8 is the practical base helix schematic diagram of dextrorotation gear；
Fig. 9 is the practical base helix schematic diagram of left-handed gear；
Figure 10 is fillet curve schematic diagram；
Figure 11 is bevel gear cutter end face structure parameter schematic diagram；
Figure 12 is gear circular runout testing result schematic diagram；
Figure 13 is eccentric gear schematic diagram；
Figure 14 is gear individual circular pitch error testing result schematic diagram；
Figure 15 is the individual circular pitch error schematic diagram as caused by gear eccentricity；
Figure 16 is practical tooth side-play amount schematic diagram；
Figure 17 is sweep surface schematic diagram；
Figure 18 hypostazation cuts off tooth socket schematic diagram；
Figure 19 is the gears ' three-dimensional model schematic diagram for considering microcosmic correction of the flank shape and actual processing error.
Specific embodiment
To keep the technical problem to be solved in the present invention, technical solution and advantage clearer, below in conjunction with attached drawing and tool
Body embodiment is described in detail.
Fig. 1 is the flow diagram of gear Precise modeling provided in an embodiment of the present invention；Fig. 2 is tool structure parameter
Schematic diagram；Fig. 3 is that detection gear is averaged flank profil trace schematic diagram；Fig. 4 is detection gear average helical stitching line schematic diagram；Fig. 5
It is the practical tooth trace schematic diagram for detecting gear；Fig. 6 is the practical helix trace schematic diagram for detecting gear；Fig. 7 is practical
Involute schematic diagram；Fig. 8 is the practical base helix schematic diagram of dextrorotation gear；Fig. 9 is that the practical base helix of left-handed gear shows
It is intended to；Figure 10 is fillet curve schematic diagram；Figure 11 is bevel gear cutter end face structure parameter schematic diagram；Figure 12 is gear diameter
To glitch detection result schematic diagram；Figure 13 is eccentric gear schematic diagram；Figure 14 is the signal of gear individual circular pitch error testing result
Figure；Figure 15 is the individual circular pitch error schematic diagram as caused by gear eccentricity；Figure 16 is practical tooth side-play amount schematic diagram；Figure 17 is
Sweep surface schematic diagram；Figure 18 hypostazation cuts off tooth socket schematic diagram；Figure 19 is the tooth for considering microcosmic correction of the flank shape and actual processing error
Take turns threedimensional model schematic diagram.
As shown in Figure 1, the gear Precise modeling provided by the invention for considering microcosmic correction of the flank shape and actual processing error, packet
Include following steps:
Step 1: according to the design parameter and cutter parameters of gear, relevant parameter relationship needed for modeling process is determined
Formula, the design parameter include the number of teeth, modulus, pressure angle, helical angle, modification coefficient, tip diameter, root diameter and tooth
Width, the cutter parameters include height of teeth top, transverse tooth thickness, radius of corner and plush copper amount, and the relevant parameter relational expression includes gear end
Face parameter calculation formula and cutter auxiliary parameter calculation formula；
Step 2: average flank profil trace and average spiral shell are determined according to the actually detected flank profil of gear and actually detected helix
Spin line trace, the average flank profil trace includes profile modification and flank profil dip deviation, and the average helical stitching line includes spiral shell
Spin line correction of the flank shape and helix dip deviation；
Step 3: according to the waviness of the actually detected flank profil of gear and actually detected helix determine profile geometry deviation and
Helix shape deviation；
Step 4: practical involute, practical helix and fillet curve are drawn, the practical involute includes flank profil
Correction of the flank shape, flank profil dip deviation and profile geometry deviation, the practical helix include helix correction of the flank shape, helix dip deviation and
Helix shape deviation；
Step 5: it according to circular runout testing result and circular pitch deviation testing result, determines gear eccentricity amount and determines tooth
Wide offset；
Step 6: the practical involute and fillet curve drawn in step 4 are prolonged into practical helix and theory respectively
Helix is scanned, and tooth profile and root surface that scanning obtains are synthesized, and the curved surface of synthesis is carried out hypostazation
Cut off tooth socket；And gear eccentricity amount and circular pitch deviation according to obtained in step 5, tooth socket is subjected to offset array, is examined
Consider the exactly modeling of gear tooth of microcosmic correction of the flank shape and actual processing error.
Wherein, in the step 2, average flank profil trace includes parabola branch and straight line portion, wherein parabola
The expression formula of Duffing equation are as follows:
In formula:
Δ1- averagely flank profil trace offset, unit is μm；- involute roll angle is used as variable in the equation, single
Position is rad；a1、b1、c1- expression formula coefficient determines 3 coordinates on i.e. parabola by the actually detected result of gear:
The expression formula of the straight line portion equation of average flank profil trace are as follows:
In formula:
Δ2- averagely flank profil trace offset, unit is μm；- involute roll angle is used as variable in the equation, single
Position is rad；b2、c2- expression formula coefficient determines by the actually detected result of gear, i.e., two o'clock coordinate on straight line:
In addition, in the step 2, the equation expression formula of average helical stitching line are as follows:
Δ3=a3Z2+b3Z+c3
In formula: Δ3- average helical stitching line deviation, unit are μm；Z-teeth directional direction variable, unit mm；a3、
b3、c3- expression formula coefficient determines by the actually detected result of gear, i.e. 3 coordinates of helix trace: B1(Z1,-Cβ1), B2
(Z2, 0), B3(Z3,-Cβ2).Axial modification amount is respectively C when can obtain i.e. Z=0 and Z=b on gear front/rear end by the equationβ3
And Cβ4。
Further, in the step 3, flank profil waviness (tooth can be determined according to actually detected flank profil trace diagram
Wide form variations), so that it is determined that meet the profile geometry deviation of SIN function rule, it specifically can be according to the determination of following formula
Profile geometry deviation:
In formula: Δ4- profile geometry deviation, unit are μm；- involute roll angle is used as variable, unit in the equation
For rad；A1、k1- expression formula coefficient is determined by the actually detected result of gear；
In addition, can determine helix waviness (helix according to actually detected helix trace diagram in step 3
Form variations), so that it is determined that meet the helix shape deviation of SIN function rule, it specifically can be according to the determination of following formula
Helix shape deviation:
Δ5=A2sin(k2Z)
In formula:
Δ5- helix shape deviation, unit are μm；Z-teeth directional direction variable, unit mm；A2、k2- expression formula system
Number, is determined by the actually detected result of gear.
Further, in the step 4, on the basis of theoretical involute, average flank profil is obtained by removing material
Trace adds profile geometry deviation on average flank profil trace and obtains practical involute, and material removal amount direction is that theory is gradually opened
The normal direction of line.The curvilinear equation of the practical involute is piecewise function form (cydariform correction of the flank shape part and tooth top tip relief portion
Point).
In 3 d modeling software (Creo software) default coordinate system, the song of the cydariform correction of the flank shape part of the practical involute
Line equation are as follows:
The curvilinear equation of the tooth top tip relief part of the practical involute are as follows:
In formula:
αk1- basic circle space width corresponds to the half of central angle；- indicate practical involute in basic circle initial position
Variable quantity；αk- independent variable, pressure angle of involute (°), previous equation independent variable range are Latter equation
Independent variable range isrb- base radius；Δ1、Δ2- be averaged flank profil trace offset (μm)；Δ4Tooth
Wide form variations.
In addition, on the basis of theoretical base helix, obtaining average basic circle by removing material in the step 4
Helix adds helix shape deviation on average base helix and obtains practical base helix, wherein material removal amount
Direction is basic circle tangential direction, and the base helix cydariform of the left and right flank of tooth is contrary.
In 3 d modeling software (Creo software) default coordinate system, the right practical base helix equation of the flank of tooth are as follows:
The left practical base helix equation of the flank of tooth are as follows:
In formula:
T-independent variable, range are [0,1]；B-gear tooth width；βb- Base spiral angle；Δ3- average helical stitching line is inclined
Shifting amount；Δ5- helix shape deviation；"+" indicates that gear rotation direction is dextrorotation in " ± "；"-" indicates that gear rotation direction is in " ± "
It is left-handed.
In addition, in gear hobbing process technique, fillet curve is to be cut by the fillet part of cutter in the step 4
Make the equidistant curve of the prolate involute formed.
In 3 d modeling software (Creo software), using the gear center of circle as origin, gear teeth transverse tooth thickness middle line is that Y-axis establishes flute card
That coordinate system, fillet curve equation are as follows:
In formula:
R-gear compound graduation radius of circle；a1- cutter auxiliary parameter；Rc- cutter radius of corner；α '-independent variable, range are
(α, 90)；- cutter auxiliary parameter,
In step 5, according to gear circular runout testing result, determine that the eccentricity of gear is fe.The eccentricity of gear
The circular runout of gear is not only influenced, while will affect the circular pitch deviation of gear, compares the circular pitch deviation of actual measurement and by eccentricity
The offset of practical tooth can be obtained in caused circular pitch deviation after subtracting each other.
In the step 6, the method for tooth profile scanning are as follows: establish basic circle cylindrical surface in 3 d modeling software, use
Practical base helix trims the basic circle cylindrical surface, is scanning track with the trimming side of acquisition；Gradually by reality described in step 4
Burst at the seams and projected to obtain scanning cross-section, when scanning " cutting plane " will be ordered to control in software for " constant normal direction and perpendicular to
Curved surface ".
In addition, in the step 6, the method for root surface scanning are as follows: trim basic circle cylinder with theoretical base helix
Face is scanning track with the trimming side of acquisition；It projects fillet curve is drawn in step 4 to obtain scanning cross-section,
" cutting plane " will be ordered to control as " constant normal direction and perpendicular to curved surface " in software when scanning.
The tooth profile scanned is trimmed and merged with root surface, carries out hypostazation and cuts off tooth socket, deviate battle array
Obtain considering the gears ' three-dimensional model of microcosmic correction of the flank shape and actual processing error after column.
[embodiment]
Hereinafter, gear Precise modeling provided by the invention is described in detail in conjunction with the embodiments.
1. determining the design parameter and cutter parameters of gear, relevant parameter relational expression is inputted:
(1) design parameter and cutter parameters of gear are carried out in 3 d modeling software (the present embodiment is Creo software)
Input, model accuracy are adjusted to 10-6mm。
The design parameter of gear includes:
Number of teeth z
Modulus (mm) mn
Pressure angle (°) αn
Helical angle (°) β
Modification coefficient xn
Tip diameter (mm) da
Root diameter (mm) df
The facewidth (mm) b
The cutter parameters of gear include:
Cutter radius of corner (mm) Rc
Cutter plush copper amount (mm) pr
(2) gear face parameter can be derived according to the design parameter of said gear, the transverse module m including geart, end
Surface pressure angle αt, end face modification coefficient xt, reference diameter d, reference radius r, base circle diameter (BCD) db, base radius rbAnd base
Circle helixangleβb, above each parameter can calculate by gear basic calculating formula.
Parameter relevant to the initial position of gear theory involute can be derived according to the design parameter of said gear, wrapped
Include gear compound graduation circle exhibition angle θk(°), the half α of base circular thickness central anglek(°), the above parameter are gear face parameter.
Other relevant parameters of cutter, including cutter teeth can be derived according to the design parameter of said gear and cutter parameters
Rise hc, cutter transverse tooth thickness SNAnd auxiliary parameter a as shown in Figure 21, b1, ftw, the above parameter is cutter normal dimensions.
The input of each parameter relationship formula is carried out in 3 d modeling software (Creo software):
mt=mn/cosβ
αt=arctan (tan αn/cosβ)
xt=xncosβ
D=mtz
R=d/2
db=dcos αt
rb=d/2
θk=180tan αt/π-αt
αk=180 (pi/2-2xttanαt)/(πz)-θk
βb=arctan (tan β cos αt)
hc=(d-df)/2
a1=hc-rc
SN=(pi/2-2xntanαn)mn
Ftw=2 (SN/2+pr/cosαn-a1tanαn-rc/cosαn)
b1=(π mn-ftw)/2
2. determining average flank profil trace and average helix trace according to the actually detected parameter of gear:
(1) average flank profil trace is determined:
Establish coordinate system as shown in Figure 3, wherein abscissa is the roll angle (rad) of flank profil involute, and ordinate is average
Flank profil trace deviates the distance (μm) of theoretical involute.According in actually detected flank profil trace diagram within the scope of flank profil cydariform correction of the flank shape
3 coordinates: The parabola of average flank profil trace
Part may be expressed as:
According to the two o'clock coordinate in flank profil trace diagram within the scope of tooth top tip relief: The straight line portion of average flank profil trace may be expressed as:
(2) average helical stitching line is determined:
Establish coordinate system as shown in Figure 4, wherein abscissa is gear tooth width (mm), and ordinate is average helical stitching
The distance (μm) of line offset theory helix.According to 3 coordinates on helix trace: B1(Z1,-Cβ1), B2(Z2, 0), B3
(Z3,-Cβ2), average helical stitching line may be expressed as:
Δ3=a3Z2+b3Z+c3
It can be obtained according to the equation, axial modification amount is respectively C when being Z=0 and Z=b on gear front/rear endβ3And Cβ4。
3. the actually detected parameter according to gear determines profile geometry deviation and helix shape deviation:
As shown in figure 5, the profile geometry deviation and waviness of gear are determined according to the actually detected flank profil trace diagram of gear,
So that it is determined that meeting the profile geometry deviation of sinusoidal rule:
In formula:
Δ4- profile geometry deviation (μm)；- involute roll angle (rad) is used as variable in the formula；A1、k1- expression
Formula coefficient.
As shown in fig. 6, determining the helix shape deviation and wave of gear according to the actually detected helix trace diagram of gear
Degree, so that it is determined that meeting the helix shape deviation of sinusoidal rule:
Δ5=A2sin(k2Z)
In formula:
Δ5- helix shape deviation (μm)；Z-teeth directional direction variable (mm)；A2、k2- expression formula coefficient.
4. drawing practical involute, practical helix and fillet curve in 3 d modeling software (Creo software):
(1) practical involute is drawn:
In 3 d modeling software (Creo software), practical involute is drawn by equation, as shown in fig. 7, equation coordinate
System is selected as software default coordinate system CS, and coordinate set type is selected as cylindrical coordinates, then the song of practical involute cydariform correction of the flank shape part
Line equation are as follows:
The curvilinear equation of practical involute tooth top tip relief part are as follows:
In formula:
αk1- basic circle space width corresponds to the half of central angle；- indicate practical involute in basic circle initial position
Variable quantity；αk- independent variable, pressure angle of involute (°), previous equation independent variable range are Latter equation
Independent variable range isrb- base radius；Δ1、Δ2- be averaged flank profil trace offset (μm)；Δ4—
Profile geometry deviation.
(2) practical helix is drawn
In 3 d modeling software (Creo software), practical base helix is drawn by equation.Due to the left and right flank of tooth into
When row teeth directional cydariform correction of the flank shape, cydariform is contrary, therefore the practical base helix of the left and right flank of tooth needs separately to draw, and is subject to
Difference.Equation coordinate system is selected as software default coordinate system CS, and coordinate set type is selected as cylindrical coordinates, then the practical basic circle of the right flank of tooth
The curvilinear equation of helix are as follows:
The left practical base helix equation of the flank of tooth are as follows:
In formula:
T-independent variable, range are [0,1]；B-gear tooth width；βb- Base spiral angle；Δ3- average helical stitching line is inclined
Shifting amount；Δ5- helix shape deviation；"+" indicates that gear rotation direction is dextrorotation in " ± "；"-" indicates that gear rotation direction is in " ± "
It is left-handed.
Flank of tooth basic circle cydariform correction of the flank shape helix when dextrorotation or so is as shown in figure 8, flank of tooth basic circle cydariform correction of the flank shape when left-handed or so
Helix is as shown in Figure 9.
(3) fillet curve is drawn
In gear hobbing process technique, fillet curve is the prolate involute formed by the fillet part cutting system of cutter
Equidistant curve, principle and equation inference do not repeat.It is original with the gear center of circle in 3 d modeling software (Creo software)
Point, gear teeth transverse tooth thickness middle line are that Y-axis establishes cartesian coordinate system CS0, fillet curve equation are as follows:
In formula:
R-gear compound graduation radius of circle；a1- cutter auxiliary parameter；Rc- cutter radius of corner；α '-independent variable, range are
(α, 90)；- cutter auxiliary parameter,Its model curve is as shown in Figure 10.
Key of the invention is the derivation of helical gear fillet curve, and cutter transverse parameters are as shown in figure 11, knife
Has the parameter constant in the high direction of tooth, the parameter and fillet parameter in facewidth direction convert as follows.
b1t=b1/cosβ
5. determining the eccentricity and flank profil offset of gear:
The circular runout testing result of gear is as shown in figure 12, and the circular runout of gear is Fr, eccentricity fe, the two is right
It should be related to are as follows:
Fr=2fe
The movement axle center of gear is drawn, the offset in the gear teeth axle center relative to gear is fe, the eccentric gear such as Figure 13
It is shown.
The actual measurement circular pitch deviation of gear is as shown in figure 14, influence such as Figure 15 institute of the eccentricity of gear to individual circular pitch error
Show, the two subtracts each other the offset Δ f that practical tooth can be obtainedpt, as shown in figure 16.
6. carrying out curved surface scanning, curved surface synthesis, tooth socket excision and offset array, obtain considering microcosmic correction of the flank shape and actual processing
The model of gear of error:
(1) creation scanning track
Basic circle cylinder is trimmed with the practical base helix of the left and right flank of tooth respectively in 3 d modeling software (Creo software)
Face obtains left and right flank of tooth scanning track；Basic circle cylindrical surface is trimmed with theoretical base helix, obtains fillet curve scanning
Track.
(2) curved surface scanning is carried out, the left and right flank of tooth and fillet are obtained
In 3 d modeling software (Creo software), the left and right flank of tooth is identical as the scan method of fillet, selection
Scanning track is created in step (1), and " cutting plane control " is selected as " constant normal direction ", it is flat where selection gear front end face
Face is used as " direction reference ", and " horizontal/vertical control " is selected as " perpendicular to curved surface "；Scanning cross-section is created, flank of tooth scanning is cut
Face is practical involute, and root surface surface sweeping section includes fillet curve and root circle, and " grass draws section scanned for selection
It is constant in journey " it is scanned, curved surface scanning result is as shown in figure 17.
(3) tooth socket excision is carried out, obtains profile modifying gear accurate model after offset array
In 3 d modeling software (Creo software), outside circle cylinder is drawn centered on CS coordinate origin, by institute in (2)
The left and right flank of tooth and fillet of scanning are trimmed and are synthesized, which are carried out hypostazation processing, selection " is gone
Except material ", as shown in figure 18.This feature is subjected to offset array, offset is Δ fpt, to obtain considering microcosmic correction of the flank shape and reality
The gears ' three-dimensional model of border mismachining tolerance, the threedimensional model are as shown in figure 19.
To sum up, gear Precise modeling provided in an embodiment of the present invention has comprehensively considered the microcosmic correction of the flank shape and reality of gear
The actually detected project of gear is analyzed one by one and is added in the ideal model of gear by border mismachining tolerance.According to involute teeth
Wheel engagement basic principle and processing technology (gear hobbing process) derive the call parameter of gear and cutter needed for modeling process；
According to the actually detected flank profil of gear and actually detected helix, the average flank profil trace of gear is obtained after being fitted and is averaged
Helix trace；According to the waviness of actually detected flank profil and actually detected helix, the flank profil for meeting SIN function rule is obtained
Form variations and helix shape deviation；According to the circular runout of gear and circular pitch deviation testing result, the bias of gear is obtained
The offset of amount and practical tooth.In three-dimensional software (Creo software), practical involute, practical base helix and tooth are drawn
Root easement curve carries out flank profil offset array according to circular pitch deviation；The finally march in 3 d modeling software (Creo software)
Surface scan, trimming and merge, carries out hypostazation and cut off tooth socket, obtain the accurate three-dimensional mould of microcosmic profile modifying gear after offset array
Type.The model of gear established using this method can be used for finite element stimulation, simulate the meshing state of actual processing gear,
Predict the failure mode and service life of gear.It is modeled based on this method, can be used for analyzing different type mismachining tolerance to gear
The influence degree of stress, so that more targeted control Gear Processing precision.
Embodiment described above, only a specific embodiment of the invention, to illustrate technical solution of the present invention, rather than
It is limited, scope of protection of the present invention is not limited thereto, although having carried out with reference to the foregoing embodiments to the present invention detailed
Illustrate, those skilled in the art should understand that: anyone skilled in the art the invention discloses
In technical scope, it can still modify to technical solution documented by previous embodiment or variation can be readily occurred in, or
Person's equivalent replacement of some of the technical features；And these modifications, variation or replacement, do not make corresponding technical solution
Essence is detached from the spirit and scope of technical solution of the embodiment of the present invention, should be covered by the protection scope of the present invention.Therefore,
The protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (8)
1. a kind of gear Precise modeling for considering microcosmic correction of the flank shape and actual processing error characterized by comprising
Step 1: according to the design parameter and cutter parameters of gear, relevant parameter relational expression needed for modeling process, institute are determined
Stating design parameter includes the number of teeth, modulus, pressure angle, helical angle, modification coefficient, tip diameter, root diameter and the facewidth, institute
Stating cutter parameters includes height of teeth top, transverse tooth thickness, radius of corner and plush copper amount, and the relevant parameter relational expression includes gear face parameter
Calculation formula and cutter auxiliary parameter calculation formula；
Step 2: average flank profil trace and average helix are determined according to the actually detected flank profil of gear and actually detected helix
Trace, the average flank profil trace includes profile modification and flank profil dip deviation, and the average helical stitching line includes helix
Correction of the flank shape and helix dip deviation；
Step 3: profile geometry deviation and spiral are determined according to the waviness of the actually detected flank profil of gear and actually detected helix
Wire shaped deviation；
Step 4: drawing practical involute, practical helix and fillet curve, the practical involute includes that flank profil is repaired
Shape, flank profil dip deviation and profile geometry deviation, the practical helix include helix correction of the flank shape, helix dip deviation and spiral shell
Spin line form variations；
Step 5: it according to circular runout testing result and circular pitch deviation testing result, determines gear eccentricity amount and determines that flank profil is inclined
Shifting amount；
Step 6: the practical involute and fillet curve drawn in step 4 are prolonged into practical helix and theoretical spiral respectively
Line is scanned, and tooth profile and root surface that scanning obtains are synthesized, and the curved surface of synthesis is carried out hypostazation excision
Tooth socket；And gear eccentricity amount and circular pitch deviation according to obtained in step 5, tooth socket is subjected to offset array, obtains considering micro-
See the exactly modeling of gear tooth of correction of the flank shape and actual processing error.
2. the method according to claim 1, wherein in the step 2, average flank profil trace includes parabolic
Line part and straight line portion, wherein the expression formula of parabola branch equation are as follows:
In formula:
Δ1Average flank profil trace offset, unit are μm；Involute roll angle, is used as variable in the equation, and unit is
rad；a1、b1、c1Expression formula coefficient is determined by the actually detected result of gear；
The expression formula of the straight line portion equation of average flank profil trace are as follows:
In formula:
Δ2Average flank profil trace offset, unit are μm；Involute roll angle, is used as variable in the equation, and unit is
rad；b2、c2Expression formula coefficient is determined by the actually detected result of gear.
3. the method according to claim 1, wherein in the step 2, the equation of average helical stitching line
Expression formula are as follows:
Δ3=a3Z2+b3Z+c3
In formula: Δ3Average helical stitching line deviation, unit are μm；Z- teeth directional direction variable, unit mm；a3、b3、c3- table
Up to formula coefficient, determined by the actually detected result of gear.
4. the method according to claim 1, wherein in the step 3:
The profile geometry deviation is determined according to following formula:
In formula: Δ4- profile geometry deviation, unit are μm；- involute roll angle, is used as variable in the equation, and unit is
rad；A1、k1- expression formula coefficient is determined by the actually detected result of gear；
The helix shape deviation is determined according to following formula:
Δ5=A2sin(k2Z)
In formula:
Δ5- helix shape deviation, unit are μm；Z-teeth directional direction variable, unit mm；A2、k2- expression formula coefficient, by
The actually detected result of gear determines.
5. the method according to claim 1, wherein in the step 4, on the basis of theoretical involute,
Average flank profil trace is obtained by removing material, profile geometry deviation is added on average flank profil trace and obtains practical involute,
Material removal amount direction is the normal direction of theoretical involute.
6. the method according to claim 1, wherein in the step 4, in the base of theoretical base helix
On plinth, average base helix is obtained by removing material, helix shape deviation is added on average base helix and is obtained
Practical base helix, wherein material removal amount direction is basic circle tangential direction, and the base helix cydariform side of the left and right flank of tooth
To opposite.
7. the method according to claim 1, wherein in the step 4, in gear hobbing process technique, tooth root
Easement curve is the equidistant curve of the prolate involute formed by the fillet part cutting system of cutter.
8. the method according to claim 1, wherein in the step 6:
The method of tooth profile scanning are as follows: establish basic circle cylindrical surface in 3 d modeling software, trimmed with practical base helix
The basic circle cylindrical surface is scanning track with the trimming side of acquisition；Practical involute described in step 4 is projected to obtain
Scanning cross-section will order " cutting plane " to control when scanning for " constant normal direction and perpendicular to curved surface " in software；
The method of root surface scanning are as follows: trim basic circle cylindrical surface with theoretical base helix, be scanning with the trimming side of acquisition
Track；Fillet curve will be drawn in step 4 to project to obtain scanning cross-section, when scanning will order " truncated in software
Face " control is " constant normal direction and perpendicular to curved surface "；
The tooth profile scanned is trimmed and merged with root surface, carries out hypostazation and cuts off tooth socket, after offset array
Obtain considering the gears ' three-dimensional model of microcosmic correction of the flank shape and actual processing error.
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