CN109773279A - A kind of arc tooth line gear working method - Google Patents
A kind of arc tooth line gear working method Download PDFInfo
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- CN109773279A CN109773279A CN201910245476.4A CN201910245476A CN109773279A CN 109773279 A CN109773279 A CN 109773279A CN 201910245476 A CN201910245476 A CN 201910245476A CN 109773279 A CN109773279 A CN 109773279A
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Abstract
The present invention discloses a kind of arc tooth line gear working method.Using arc cutter disk to arc tooth line Gear Processing, keep arc cutter disk axis vertical with gear blank axis, and be located on the middle section of gear blank width direction, to process the symmetrical gear teeth；The cutter tooth of arc cutter disk rotates to form cutting cone face around the cutterhead with inclination angle, which is the main motion of cutting；While rotating, cutter head center also rotates around production shape wheel axis facing cutter, while workpiece is swung according to rolling than relationship, and the swing of milling cutter disk center and workpiece rotate to form generating motion；Cutterhead rotating forward cuts a complete tooth socket, and main shaft allow knife, and indexing mechanism rotates a tooth pitch, and facing cutter and workpiece carry out return and transform into, and next tooth socket are cut again, until processing all gear teeth.Gear-tooth strength can be improved in the arc tooth line gear that this method processes, and is transformed by Double-surfaces Method and is cut twice with facing cutter roundtrip, substantially increases processing efficiency.
Description
Technical field
The invention belongs to gear transmission technology field, in particular to a kind of arc tooth line gear working method.
Background technique
Modern Gear transmission just develops towards the direction of high-speed overload, proposes to the intensity of gear pair, vibration and noise
More stringent requirement.Arc tooth line gear is a kind of parallel-axes gears transmission along the contact of arc tooth line bumps, middle section tooth
Shape is standard involute, and transverse tooth thickness is gradually reduced from the middle to both ends, has overlap coefficient big, high, curved without axial force, transmission efficiency
The advantages that Qu Qiangdu is big, contact strength is good；Compared with involute gear, contact strength of tooth surface and teeth bending strength are improved about
20% and 10%, it is a kind of gear-driven form for having much potentiality, can satisfy that stable drive, vibration noise are low, the service life is long, low
The requirement such as installation accuracy, has broad application prospects.
The processing method of arc tooth line gear has: semi shield oil cylinder circle draw cut tooth method, Double-surfaces Method, single side method, Double-cutter method etc..It adopts
The new gear is processed with these methods, there are apparent differences in terms of production efficiency, Meshing engagement.In U.S.'s lattice
Using semi shield oil cylinder circle draw cut tooth method Machining Arc tooth trace gear, processing efficiency and precision obtain significant raising for gloomy company.Using
When Double-surfaces Method, gear teeth bumps two sides are cut out simultaneously, high in machining efficiency, but teeth directional relative curvature difference is big, and contact zone is small, bearing capacity
Difference；Single side method is first to process bull wheel with Double-surfaces Method, then adjust separately cutter radius processing pairing steamboat, and its essence is pass through knife
Disk semidiameter reaches that reduce teeth directional relative curvature poor along axial modification, even the purpose of total conjugated；But due to using two
Cutterhead, increased costs, processing efficiency is low, and mounting and adjusting is cumbersome.It is proposed in patent of invention CN101293288A using with knife
The straight line blade milling cutter disk to incline, by the method for imaginary produced gear come Machining Arc tooth trace gear, this method being capable of mesh control
The amount of mismatch of the flank of tooth, but there are two aspects:
1) cutting edge is straight line, and using imaginary produced gear processing, inevitably generates driving error, and with imagination
It produces the reduction of shape tooth number and increases.
2) because it uses master blade, the transverse tooth thickness for being processed gear is unable to get accurate control.
Summary of the invention
In order to solve arc tooth line gear there is the radius of curvature difference of concave and convex surface is larger, contact area is small and the flank of tooth
The problems such as contact strength is poor, the present invention provides a kind of arc tooth line gear working method, based on the concept of imaginary produced gear,
Using the two-sided curvature difference for transforming into circle-arc tooth line gear, reducing between mesh tooth face, meshing performance is improved.The circle that this method processes
Gear-tooth strength can be improved in curved tooth line gear, is transformed by Double-surfaces Method and is cut twice with facing cutter roundtrip, substantially increases processing
Efficiency.
To achieve the above object, the present invention adopts the following technical scheme:
A kind of arc tooth line gear working method, comprising the following steps:
Using arc cutter disk to arc tooth line Gear Processing, keep arc cutter disk axis vertical with gear blank axis, and position
In on the middle section of gear blank width direction, to process the symmetrical gear teeth；The cutter tooth of arc cutter disk is around the cutterhead with inclination angle
Rotation forms cutting cone face, which is the main motion of cutting；While rotating, cutter head center is also around production shape wheel for facing cutter
Axis rotates, while workpiece is swung according to rolling than relationship, and the swing of milling cutter disk center and workpiece rotate to be formed and transform into fortune
It is dynamic；After cutterhead rotating forward cuts a complete tooth socket, cutter spindle allow knife, and gear blank is rotated a tooth by indexing mechanism
Away from facing cutter and workpiece carry out return and transform into, and next tooth socket are cut again, until processing all gear teeth.
Preferably, the tooth form of the arc cutter disk is made of curve sword and knife tip circle arc, curve sword it is basic
Tooth form is involute, is the involute profile transformed by rack cutter, further progress profile modification；Knife tip circle arc is connection work
Make flank profil and knife top sword, the center location and radius of circular arc are calculated according to the continuous Tangent Condition of knife tip circle arc and involute；
After cutter tilt, improve the pressure angle of the inside and outside cutter tooth shape of facing cutter at node.
Preferably, the reference frame of the rack gear is Sc(xc,yc,zc), left side straight line sword coordinate system is Spl(xpl,
ypl,zpl) and right side straight line sword coordinate system be Spl(xpr,ypr,zpr)；
In ScIn coordinate system, the position vector of rack cutter is expressed as
Normal vector is expressed as
In formula, αnFor rack cutter normal pressure angle, usFor the location parameter on linear cutting edge, apFor parabola correction of the flank shape system
Number, am=0.25mnFor the half of space width, mnFor gear normal module.
Preferably, the generating motion relationship of the cutter tooth flank profil of the arc cutter disk are as follows:
Sd(xd,yd,zd) it is to be processed reference gear coordinate system, Ss(xs, ys, zs) it is to be processed gear coordinate, with involute
The generating principle of gear is identical, rack cutter coordinate ScIt is mobileWhile, it is processed gear rotationrpsFor imaginary gear shaping
The pitch radius of cutter tooth wheel；According to plane engagement theory, in xcycArbitrary point (x on plane inner rack knifec, yc) and instantaneous company
Line is parallel with the method for rack cutter arrow；In ScIn, the mesh equation of rack cutter and processed gear indicates are as follows:
In formula, xc,ycFor the component of rack cutter position vector, nxc, nycFor two components of rack cutter normal vector, thus
Obtain the processing corner for being processed gear:
Cutter tooth-profile position vector is transformed into SsIn coordinate system, the position equation and unit normal direction arrow of cutter tooth flank profil are obtained
Amount are as follows:
In formula,rpsFor the pitch circle half for being processed gear
Diameter,For the processing corner of imaginary gear shaping cutter tooth wheel.
Preferably, the flank profil of the cutter is dimerous by work flank profil and knife tip circle angle, and work flank profil is
For the working flank of Generating gear, and knife tip circle angle is processing fillet surface；The knife tip circle angle of cutter is designed as single circular arc
Shape, so that knife tip circle angular radius is maximum；Center of arc E0In the symmetrical centre of the two sides facewidth, knife tip circle arc and work flank profil
Intersection point be E1, circular arc highest point is E2, the parameter at knife tip circle angle is determined according to the following conditions:
1) two curves are in E1Point is continuous tangent；
2)E2For the highest point of cutter fillet, pinion cutter radius of addendum ras=rps+1.25mn, rpsFor imaginary pinion cutter section
Radius of circle, mnFor gear normal module；Obtain following equation group:
In formula, θfFor the angle parameter of Circular Nose Cutting Edge, XfFor the location parameter of center of arc, r0For arc radius；First arrow
Measuring equation indicates in E1Point is continuous, and second equation is indicated in E1The method arrow of point is equal, and third equation is knife tip circle arc highest point
Condition, there are four nonlinear equations altogether for above-mentioned equation group, and unknown number is θf,Xf,r0, us, thus equation has solution, to obtain
The parameter of knife tip circle arc.
Preferably, the facing cutter has cutter tilt, the radius of curvature at interior knife node are as follows:
ri'=(rc/cosγ-0.25πmn)/cos(αn+ γ),
Radius of curvature at outer knife node are as follows: ro'=(rc/cosγ+0.25πmn)/cos(αn- γ), in formula, rcFor cutterhead
Diameter is defined as cutter tooth center to the distance of rotary shaft, and γ is cutter tilt.
Preferably, the normal section of the cutter tooth forms the cutting conical surface, θ after rotary shaft rotationcTurn for facing cutter
Angle, SsFor the moving coordinate system of imaginary pinion cutter, SgFor pinion cutter reference frame, θsFor gear shaping swivel angle；SfFor reference gear seat
Mark system, S1For gear moving coordinate system, θ1For gear corner, the position vector and normal vector for being processed gear can pass through coordinate
Transformation obtains:
Mesh equation during Gear Shaping are as follows:
f(us,θs,θf)=n1·v1f
Wherein, in S1The relative velocity of pinion cutter and processed gear in coordinate system:
v1f=V1-Vg=ω1×r1-ωg×(r1-O1Og),
Wherein, ω1=[0 0-m1s], ωg=[0 0 1], O1Og=[rps+rp10 0], rp1To be processed pitch circle
Radius, θ1=m1sθs, m1sFor the inverse of gear pair transmission ratio, the above-mentioned two equation group of simultaneous obtains the tooth of arc tooth line gear
Face mathematical model.
Compared with prior art, the present invention has following technical effect that
The present invention is using the processing method of the arc cutter disk Machining Arc tooth trace gear with cutter tilt, arc cutter
The basic tooth form of dise knife tooth is involute, and knife top is calculated specific circular arc by geometry constraint conditions and set using single designed arc-shaped appearance
Count parameter.The tooth form of the obtained gear teeth is involute on each normal section, is conducive to give full play of the excellent of involute profile
Gesture；The radius of curvature for reducing concave and convex surface by cutterhead cutter tilt is poor, increases face area, improves gear-tooth strength；By
A gear teeth of arc tooth line gear are equivalent in round tool itself, and are processed using generating, guarantee the essence of gear teeth transverse tooth thickness
Degree.By the inclination angle of cutter axis, reduce the curvature difference of inside and outside knife.Facing cutter is rotated around own axes, is formed imagination and is produced shape
One tool gear teeth of gear, while cutter head center produces the axis oscillating of shape wheel around imagination, imaginary pinion cutter is formed, to add
Work gear；Gear-tooth strength can be improved in the arc tooth line gear that this method processes, and is transformed into and facing cutter roundtrip by Double-surfaces Method
It cuts twice, substantially increases processing efficiency.
Detailed description of the invention
Fig. 1 is rack cutter normal section schematic diagram of the invention；
Fig. 2 is that cutter tooth of the invention transforms into coordinate system schematic diagram；
Fig. 3 is knife tip circle arc schematic diagram of the invention；
Fig. 4 is tilt facing cutter schematic diagram of the invention；
Fig. 5 is Cutter coordinate system schematic diagram of the invention；
Fig. 6 is flank of tooth mark schematic diagram of the invention；
Fig. 7 is the gear pair physical model schematic diagram of the embodiment of the present invention processing.
Wherein, 1 is nodel line, and 2 be flank of tooth trace, and 3 be bull wheel, and 4 be involute gear, and 5 be steamboat.
Specific embodiment
To keep the features and advantages of the present invention more obvious and easy to understand, with reference to the accompanying drawings and detailed description to this
Invention is described in further detail.
As shown in Figures 1 to 6, a kind of arc tooth line gear working method of the present invention, used technical solution include with
Lower step:
(1) tooth form of arc cutter disk is made of curve sword and knife tip circle arc.The basic tooth form of curve sword is standard
Involute is the involute profile transformed by basic rack knife, further considers profile modification, improves meshing performance；Knife top
Circular arc is connection work flank profil and knife top sword, and the center of circle of circular arc is calculated according to the continuous Tangent Condition of knife tip circle arc and involute
Position and radius.After cutter tilt certain angle, improve the pressure angle of the inside and outside cutter tooth shape of facing cutter at node, reduces recessed
The curvature difference on convex surface increases contact area.
(2) arc tooth line gear shaping process.Cutter axis is vertical with gear blank axis, and is located in gear blank width direction
On section, to process the symmetrical gear teeth.Cutter tooth rotates to form cutting cone face around the cutterhead with certain inclination angle, which is to cut
The main motion cut；While rotating, cutter head center also rotates around production shape wheel axis facing cutter, while workpiece is according to rolling ratio
Relationship is swung, and the swing of milling cutter disk center and workpiece rotate to form generating motion.Cutterhead rotating forward cuts complete one
After tooth socket, cutter spindle allow knife, and gear blank is rotated a tooth pitch by indexing mechanism, and facing cutter and workpiece carry out return and transform into,
Next tooth socket is cut again, until processing all gear teeth.
Specific steps of the invention are illustrated below in conjunction with specific embodiment:
(1) the basic profile of the cutter tooth of facing cutter or grinding wheel is standard involute, considers profile modification on this basis.Flank profil
It is to be transformed by rack cutter, Fig. 1 is rack cutter normal section schematic diagram, rack gear reference frame Sc(xc,yc,zc), left side straight line sword
Coordinate system Spl(xpl,ypl,zpl) and right side straight line sword coordinate system Spl(xpr,ypr,zpr)。
In ScIn coordinate system, the position vector of rack cutter is expressed as
Normal vector is expressed as
In formula, αnFor rack cutter normal pressure angle, usFor the location parameter on linear cutting edge, apFor parabola correction of the flank shape system
Number, am=0.25mnFor the half of space width, mnFor gear normal module.
Fig. 2 is that cutter tooth transforms into coordinate system, Sd(xd,yd,zd) it is to be processed reference gear coordinate system, Ss(xs, ys, zs) it is quilt
Process gear coordinate, rack cutter coordinate S identical as the generating principle of involute gearcIt is mobileWhile, it is processed gear
RotationrpsFor the pitch radius of imaginary gear shaping cutter tooth wheel.According to plane engagement theory, in xcycIt is any on plane inner rack knife
Point (xc, yc) parallel with the method for rack cutter arrow with instantaneous line.In ScIn, the mesh equation table of rack cutter and processed gear
It is shown as
In formula, xc,ycFor the component of rack cutter position vector, nxc, nycFor two components of rack cutter normal vector, thus
Obtain the processing corner for being processed gear
Cutter tooth-profile position vector is transformed into SsIn coordinate system, the position equation and unit normal direction arrow of cutter tooth flank profil are obtained
Amount is
In formula,rpsFor the pitch circle half for being processed gear
Diameter,For the processing corner of imaginary gear shaping cutter tooth wheel
(2) Fig. 3 be knife tip circle arc schematic diagram, cutter tooth-profile be it is dimerous by work flank profil I and knife tip circle angle II,
Working portion is the working flank for Generating gear, and knife tip circle angle is for processing fillet surface, and usual cutter needs
Fillet is sharpened out to improve cutting wear.The knife tip circle angle of cutter is designed as single circular shape, so that knife tip circle angle half
Diameter is maximum, improves gear teeth dedendum strength.Center of arc E0In the symmetrical centre of the two sides facewidth, knife tip circle arc and the flank profil that works
Intersection point is E1, circular arc highest point is E2, the parameter at knife tip circle angle is determined according to the following conditions: 1) two curves are in E1Point company
Continue tangent；2)E2For the highest point of cutter fillet, pinion cutter radius of addendum ras=rps+1.25mn, rpsFor imaginary pinion cutter section
Radius of circle, mnFor gear normal module.Obtain following equation group:
In formula, θfFor the angle parameter of Circular Nose Cutting Edge, XfFor the location parameter of center of arc, r0For arc radius.First arrow
Measuring equation indicates in E1Point is continuous, and second equation is indicated in E1The method arrow of point is equal, and third equation is knife tip circle arc highest point
Condition, there are four nonlinear equations altogether for above-mentioned equation group, and unknown number is θf,Xf,r0, us, thus equation has solution, to obtain
The parameter of knife tip circle arc.
(3) Fig. 4 is the facing cutter with certain cutter tilt.If when without cutter tilt, the radius of curvature at interior knife node is ri
=(rc-0.25πmn)/cosαn, the radius of curvature at outer knife node is ro=(rc+0.25πmn)/cosαn, song between the two
Rate semidiameter isIf cutter tilt in consideration, the radius of curvature at interior knife node is ri'=(rc/cosγ-0.25π
m)/cos(αn+ γ), the radius of curvature at outer knife node are as follows:
ro'=(rc/cosγ+0.25πm)/cos(αn-γ)；It can find out apparently from figure, the cutterhead with cutter tilt
Interior knife radius of curvature increases, and outer knife radius of curvature reduces, thus cutter tilt can effectively reduce the curvature of concave and convex surface
Difference；Same method is for processing bull wheel, therefore the curvature difference between the concave surface of bull wheel and steamboat convex surface is also reduced therewith, so
It is capable of increasing contact area, improves gear-tooth strength.
(4) Fig. 5 is the coordinate relationship of imaginary produced gear Machining Arc tooth trace gear.The normal section of cutter tooth is around rotation
The cutting conical surface, θ are formed after axis rotationcFor facing cutter corner, γ is cutter tilt, SsFor the moving coordinate system of imaginary pinion cutter, SgIt is slotting
Serrated knife reference frame, θsFor gear shaping swivel angle；SfFor reference gear coordinate system, S1For gear moving coordinate system, θ1Turn for gear
Angle, the position vector and normal vector for being processed gear can be obtained by coordinate transform.
Mesh equation during Gear Shaping is
f(us,θs,θf)=n1·v1f
Wherein, in S1The relative velocity v of pinion cutter and processed gear in coordinate system1f=V1-Vg=ω1×r1-ωg×
(r1-O1Og),
Wherein, ω1=[0 0-m1s], ωg=[0 0 1], O1Og=[rps+rp10 0], rp1To be processed pitch circle
Radius, θ1=m1sθs, m1sFor the inverse of gear pair transmission ratio, arc tooth line gear is can be obtained in the above-mentioned two equation group of simultaneous
Mathematical Model of Teeth.
Embodiment:
Modulus 3.0mm, small tooth number 21, big tooth number 34, production shape tooth number 25,20 ° of normal pressure angle, facewidth 30mm,
Addendum coefficient 1.0, height of teeth root coefficient 1.25, cutter radius 60mm, 5 ° of cutter tilt, steamboat is left-handed (along rotary shaft negative direction
See arc tooth line to the left), bull wheel dextrorotation (sees arc tooth line to the right) along rotary shaft negative direction.Fig. 6 is flank of tooth mark, it is clear that ratio
The mark area of common arc tooth cylindrical gear is much greater, therefore gear-tooth strength can be improved.
The gear pair physical model that processing method through the invention obtains is as shown in Figure 7.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
A specific embodiment of the invention is only limitted to this, for those of ordinary skill in the art to which the present invention belongs, is not taking off
Under the premise of from present inventive concept, several simple deduction or replace can also be made, the present invention is all shall be regarded as belonging to and is mentioned
The scope of patent protection that claims of friendship determine.
Claims (7)
1. a kind of arc tooth line gear working method, which comprises the following steps:
Using arc cutter disk to arc tooth line Gear Processing, keep arc cutter disk axis vertical with gear blank axis, and is located at tooth
On the middle section of base width direction, to process the symmetrical gear teeth；The cutter tooth of arc cutter disk is rotated around the cutterhead with inclination angle
The cutting conical surface is formed, which is the main motion of cutting；While rotating, cutter head center is also around production shape wheel axis for facing cutter
It rotates, while workpiece is swung according to rolling than relationship, the swing of milling cutter disk center and workpiece rotate to form generating motion；Knife
After disk rotating forward cuts a complete tooth socket, cutter spindle allow knife, and gear blank is rotated a tooth pitch, milling cutter by indexing mechanism
Disk and workpiece carry out return and transform into, and next tooth socket are cut again, until processing all gear teeth.
2. a kind of arc tooth line gear working method as described in claim 1, which is characterized in that the arc cutter disk
Tooth form is made of curve sword and knife tip circle arc, and the basic tooth form of curve sword, which is involute, to be transformed into gradually by rack cutter
Burst at the seams tooth form, further progress profile modification；Knife tip circle arc is connection work flank profil and knife top sword, according to knife tip circle arc and is gradually opened
The continuous Tangent Condition of line calculates the center location and radius of circular arc；After cutter tilt, improve node at facing cutter it is interior,
The pressure angle of outer cutter tooth shape.
3. a kind of arc tooth line gear working method as claimed in claim 2, which is characterized in that the reference of the rack gear is sat
Mark system is Sc(xc,yc,zc), left side straight line sword coordinate system is Spl(xpl,ypl,zpl) and right side straight line sword coordinate system be Spl(xpr,
ypr,zpr)；
In ScIn coordinate system, the position vector of rack cutter is expressed as
Normal vector is expressed as
In formula, αnFor rack cutter normal pressure angle, usFor the location parameter on linear cutting edge, apFor parabola correction of the flank shape coefficient, am
=0.25mnFor the half of space width, mnFor gear normal module.
4. a kind of arc tooth line gear working method as described in claim 1, which is characterized in that the arc cutter disk
The generating motion relationship of cutter tooth flank profil are as follows:
Sd(xd,yd,zd) it is to be processed reference gear coordinate system, Ss(xs, ys, zs) it is to be processed gear coordinate, with involute gear
Generating principle it is identical, rack cutter coordinate ScIt is mobileWhile, it is processed gear rotationrpsFor imaginary gear shaping cutter tooth wheel
Pitch radius；According to plane engagement theory, in xcycArbitrary point (x on plane inner rack knifec, yc) and instantaneous line and tooth
The method arrow of knife is parallel；In ScIn, the mesh equation of rack cutter and processed gear indicates are as follows:
In formula, xc,ycFor the component of rack cutter position vector, nxc, nycFor two components of rack cutter normal vector, to obtain
It is processed the processing corner of gear:
Cutter tooth-profile position vector is transformed into SsIn coordinate system, the position equation and unit normal vector of cutter tooth flank profil are obtained are as follows:
In formula,rpsFor be processed gear pitch radius,For the processing corner of imaginary gear shaping cutter tooth wheel.
5. a kind of arc tooth line gear working method as described in claim 1, which is characterized in that the flank profil of the cutter is
Dimerous by work flank profil and knife tip circle angle, work flank profil is the working flank for Generating gear, and knife tip circle angle
It is processing fillet surface；The knife tip circle angle of cutter is designed as single circular shape, so that knife tip circle angular radius is maximum；Center of arc
E0In the symmetrical centre of the two sides facewidth, the intersection point of knife tip circle arc and work flank profil is E1, circular arc highest point is E2, knife tip circle angle
Parameter be to be determined according to the following conditions:
1) two curves are in E1Point is continuous tangent；
2)E2For the highest point of cutter fillet, pinion cutter radius of addendum ras=rps+1.25mn, rpsFor imaginary pinion cutter pitch circle half
Diameter, mnFor gear normal module；Obtain following equation group:
In formula, θfFor the angle parameter of Circular Nose Cutting Edge, XfFor the location parameter of center of arc, r0For arc radius；First vector side
Journey is indicated in E1Point is continuous, and second equation is indicated in E1The method arrow of point is equal, and third equation is knife tip circle arc highest point item
Part, there are four nonlinear equations altogether for above-mentioned equation group, and unknown number is θf,Xf,r0, us, thus equation has solution, to obtain knife
The parameter of tip circle arc.
6. a kind of arc tooth line gear working method as described in claim 1, which is characterized in that the facing cutter has knife
Inclination angle, the radius of curvature at interior knife node are as follows:
ri'=(rc/cosγ-0.25πmn)/cos(αn+ γ),
Radius of curvature at outer knife node are as follows: r 'o=(rc/cosγ+0.25πmn)/cos(αn- γ), in formula, rcIt is straight for cutterhead
Diameter is defined as cutter tooth center to the distance of rotary shaft, and γ is cutter tilt.
7. a kind of arc tooth line gear working method as described in claim 1, which is characterized in that the normal direction of the cutter tooth is cut
Face forms the cutting conical surface, θ after rotary shaft rotationcFor facing cutter corner, SsFor the moving coordinate system of imaginary pinion cutter, SgIt is slotting
Serrated knife reference frame, θsFor gear shaping swivel angle；SfFor reference gear coordinate system, S1For gear moving coordinate system, θ1Turn for gear
Angle, the position vector and normal vector for being processed gear can be obtained by coordinate transform:
Mesh equation during Gear Shaping are as follows:
f(us,θs,θf)=n1·v1f
Wherein, in S1The relative velocity of pinion cutter and processed gear in coordinate system:
v1f=V1-Vg=ω1×r1-ωg×(r1-O1Og),
Wherein, ω1=[0 0-m1s], ωg=[0 0 1], O1Og=[rps+rp10 0], rp1To be processed pitch circle half
Diameter, θ1=m1sθs, m1sFor the inverse of gear pair transmission ratio, the above-mentioned two equation group of simultaneous obtains the flank of tooth of arc tooth line gear
Mathematical model.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111322373A (en) * | 2020-03-12 | 2020-06-23 | 长安大学 | Gear pair design method based on claw helix rack knife |
| CN112122714A (en) * | 2020-10-14 | 2020-12-25 | 天津大学 | Fly cutter for machining curve face gear and machining and using method thereof |
| CN114985844A (en) * | 2022-06-28 | 2022-09-02 | 湖南中大创远数控装备有限公司 | Grinding method for spiral bevel gear |
| CN115889899A (en) * | 2023-03-08 | 2023-04-04 | 四川大学 | Machining machine tool and machining method for circular-arc tooth trace cylindrical internal gear |
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