CN108120596B - A kind of spiral bevel gear root interference method of inspection - Google Patents
A kind of spiral bevel gear root interference method of inspection Download PDFInfo
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Abstract
The present invention discloses a kind of method of inspection of spiral bevel gear root interference, and inner cone height of teeth top, inner cone height of teeth root, design dedendum line and the design line of demarcation of the gear teeth are calculated by geometric parameter, determines the positional relationship of each geometric element；The lathe adjusting parameter and cutter parameters of given gear pair, determine practical dedendum line and practical line of demarcation.The geometrical condition engaged according to gear pair in bull wheel, steamboat tooth top, it acquires engaging-in point and nibbles out the steamboat corner put, by entire engagement process discretization, Tooth Contact Analysis is carried out to all steamboat corners, the addendum line of current cog is transformed on coupling gear, obtain tooth top projection line, discretization is carried out to tooth top projection line, the potential point of root interference is obtained, further establishes root interference model, judge whether to interfere by normal distance, repeats the above process to obtain root interference area.This method can verify the root interference generated due to cutter fillet is excessive or lathe parameter is arranged unreasonable, determine the line of demarcation and root interference region of actual fillet surface and working flank.
Description
Technical field
The invention belongs to gear transmission technology field, in particular to a kind of spiral bevel gear root interference method of inspection.
Background technique
Spiral bevel gear pair in transmission process, due to tooth root design unreasonable or gear teeth denaturation, installation error etc. because
Element causes the improper meshing phenomena of steamboat tooth top and bull wheel tooth root or bull wheel tooth top and steamboat tooth root, referred to as root interference；
It is a kind of design defect, is often accompanied by strong vibration and impact, and it is unfavorable to be easy generation broken teeth, fatigue failure etc. at tooth root
Phenomenon influences gear-driven stationarity and service life, therefore must give in the design of gear pair, processing and installation adjustment
It gives inspection and and eliminates.
It is the principal element for causing root interference that root fillet design and machined parameters, which are arranged unreasonable,.Conventional helical bores tooth
It takes turns in geometry designs, the maximum radius of cutter fillet is the geometry being meshed according to spiral bevel gear virtual gear with rack cutter
What relation derivation came out, be a kind of simplified approximation method, calculating process is related to the numerical expression of large amount of complex, nonetheless
Also often there is root interference phenomenon.In fact, the close phase of the topological structure of root interference and gear teeth working flank, fillet surface
It closes, and the shape of the flank of tooth is entirely to be determined by machined parameters, therefore Machining Spiral Bevel Gear parameter setting is for root interference
It is to have important influence.To sum up, both root fillet and machined parameters are to be mutually related on root interference influence, it is necessary to simultaneously
It takes in.
Document " cut by the fillet and interference, root of the .HFT hypoid gear such as Fang Zongde, Yang Hongbin, Deng Xiaozhong
Machine driving is examined, 2002,26 (1): by considering root interference condition, optimization machined parameters design, when connecing in 38-40. "
When rail-engaging trace is no more than the boundary line of working flank and fillet surface, root interference just is not present, this method is more traditional
Design method makes moderate progress, but due to the spiral bevel gear flank of tooth be it is extremely complex, merely ensuring that working flank normally contacts is not
No more, it is necessary to consider the contact situation of fillet surface.
Summary of the invention
For goal of the invention in order to solve the problems, such as spiral bevel gear root interference, it is dry that the present invention provides a kind of spiral bevel gear tooth root
The method of inspection related to can verify the root interference generated due to cutter fillet is excessive or lathe parameter is arranged unreasonable,
Determine the line of demarcation and root interference region of actual fillet surface and working flank.
The technical proposal for solving the technical problem of the invention the following steps are included:
A kind of method of inspection of spiral bevel gear root interference, comprising the following steps:
(1) by the basic parameter of spiral bevel gear pair, inner cone height of teeth top, inner cone height of teeth root, the design of gear pair are calculated
Dedendum line ΓfWith design line of demarcation Γc；And indicate these outline elements on the rotation perspective plane of the gear teeth, determine that each geometry is wanted
The relative positional relationship of element；
(2) according to the lathe adjusting parameter of bevel gear pair and cutter parameters, become by the gear space theory of engagement and coordinate
It changes, derives fillet equation, determine practical dedendum line LfWith practical line of demarcation Lc, and indicate to throw in the rotation of the gear teeth
On shadow face；
(3) the small of engaging-in point is acquired by tooth contact analysis model according to the geometrical condition contacted on bull wheel tooth top
Take turns cornerEqually, by the geometrical condition and tooth contact analysis model that are contacted on steamboat tooth top, acquire nibble out put it is small
Take turns corner
(4) by the entire engagement process of gear pairIt is discrete to beI=1,2,3 ..., n；To a certain instantaneous
Steamboat corner carries out Tooth Contact Analysis, and the addendum line of current cog is converted LaOnto coupling gear, and indicate to throw in rotation
On shadow face, tooth top projection line L is obtaineda′；
(5) to tooth top projection line La' discretization is carried out, if discrete point, under practical line of demarcation, the point is dry for tooth root
The potential point related to needs further to judge；If root interference will not occur for the point on practical line of demarcation；
(6) root interference model is established, if the normal distance of potential point to tooth root is greater than zero, it is dry that tooth root will not occur
It relates to；If normal distance is less than zero, for root interference point；In fixed coordinate system, the position vector of addendum line is expressed as rha, tooth
The position vector and normal vector of root fillet surface are respectively rhfAnd nhf, solve nonlinear equation rha-rhf-λnhfλ in=0
Value；If λ<0, explanation is interfered, if the explanation of λ>0 does not interfere；
(7) to the discrete corner of each steamboatTooth Contact Analysis is carried out, is found out according to step (4)-(6) all
Interference point, then a series of interference point just forms root interference area, further can judge interference degrees according to the size of λ.
As a further improvement of the present invention, in step (2), determine that specific step is as follows in the large and small practical line of demarcation of wheel:
By Principles of Gear Connection and homogeneous coordinate transformation, the position vector of steamboat working flank is derivedAnd normal vectorAnd the position vector of steamboat filletAnd normal vectorAs small flywheel rotor location parameter λ1=0 indicates knife tip circle
Angle minimum point cuts the practical dedendum line of steamboat, is projected on steamboat rotation perspective plane, obtains the practical dedendum line of steamboat
Lf1；Work as λ1=0.5 π-α1It indicates knife tip circle angle highest point, cuts the line of demarcation of working flank and fillet surface, projected
Onto rotation steamboat rotation perspective plane, the practical line of demarcation L of steamboat is obtainedc1；
Similarly, by Principles of Gear Connection and homogeneous coordinate transformation, the position vector of bull wheel working flank is derivedAnd normal vectorAnd the position vector of bull wheel filletAnd normal vectorWhen big flywheel rotor parameter lambda2=0 indicates knife tip circle angle most
Low spot cuts the practical dedendum line L of bull wheelf2；Work as λ2=π-α2It indicates knife tip circle angle highest point, just obtains bull wheel working flank
With the line of demarcation L of fillet surfacec2。
As a further improvement of the present invention, in step (3), determine that steamboat is engaging-in, nibbling out corner, specific step is as follows:
It is contact point on bull wheel addendum line that bull wheel tooth top, which enters the geometrical condition of engagement, needs to meet:
v2-ha2-tgθa2(h2-Re2)=0 (1)
In formula,
After coordinate transform, the position vector of steamboat and normal vector are indicated in engagement coordinate system ShIn, respectivelySimilarly, in engagement coordinate system ShIn, the position vector and method of bull wheel
It is respectively to vectorTangent item is continuously contacted with according to two flank of tooth
Part:
The equation group being made of formula (1) and (2) is solved, the engaging-in corner of steamboat is obtainedEqually, steamboat tooth top exits
The geometrical condition of engagement is contact point on steamboat tooth top, needs to meet:
v1-ha1-tgθa1(h1-Re1)=0 (3)
In formula,
The equation group being made of (2) and (3) is solved, obtain steamboat nibbles out corner
As a further improvement of the present invention, in step (4), determine that specific step is as follows for large and small wheel tooth top projection line:
By entire engagement processDiscrete is the n position of engagement(i=1,2,3 ..., n)；According to formula (2)
Tooth Contact Analysis carried out to a certain instantaneous steamboat corner, then by steamboat addendum line La1: ra1(xa1,ya1,za1) indicate big
Take turns coordinate system S2In, coordinate ra'1(x'a1,y'a1,z'a1), and indicate to obtain steamboat tooth top on bull wheel rotation perspective plane
The projection line L' of linea1, as shown in Figure 3；Similarly, by bull wheel addendum line La2: ra2(xa2,ya2,za2) indicate in steamboat coordinate system S1
In, coordinate ra'2(x'a2,y'a2,z'a2), and indicate to obtain the projection line of bull wheel addendum line on steamboat rotation perspective plane
L'a2。
As a further improvement of the present invention, in step (5), determine that specific step is as follows for root interference potential point:
On bull wheel rotation perspective plane, if steamboat addendum line La1' and bull wheel line of demarcation Lc2Meet:
Illustrate that two curved sections have intersection point G2, the point is by steamboat addendum line La1' it is divided into G1G2 and G2G3, the part G2G3 exists
Bull wheel lower part there is the potential position that root interference occurs, and root interference will not occur for G1G2；Similarly, it is rotated in steamboat
On perspective plane, if bull wheel addendum line La2' and steamboat line of demarcation Lc1Meet:
Illustrate that two curved sections have intersection point P2, the point is by bull wheel addendum line La2' it is divided into P1P2 and P2P3, the part P2P3 exists
Bull wheel lower part there is potentially possible generation root interference position, and root interference will not occur for P1P2.
As a further improvement of the present invention, in step (6), determine that specific step is as follows for root interference point:
Discrete for the potential steamboat addendum line G2G3 and bull wheel addendum line P2P3 that root interference occurs is n1And n2A point minute
It Wei not Pi(i=4,5 ..., n1+ 3) and Gi(i=4,5 ..., n2+ 3), to each discrete point Pi、 GiIt needs according to root interference mould
Type judges whether it is real interference point；By the position vector of steamboat fillet surfaceAnd normal vectorIt transforms to solid
Position fixing system ShIn, it is expressed asWithSimilarly, in fixed coordinate system
ShIn, the position vector and normal vector of bull wheel fillet surface are respectivelyWithWhen judging bull wheel root interference, equation is solvedAcquire λ2If λ2
< 0, illustrate that the discrete point interferes at bull wheel tooth root, if λ2> 0 illustrates that root interference does not occur for the point；Equally, for small
Wheel root interference is by solving equationIn λ1, illustrate that the discrete point occurs at steamboat tooth root
Interference, if λ1> 0 illustrates that root interference does not occur for the point.
As a further improvement of the present invention, in step (1), the basic parameter of spiral bevel gear pair includes outer end tooth top
Height, outer end height of teeth root, root angle, pitch cone angle, face cone angle, bottom clearance, the facewidth, outer cone distance and inner cone distance.
Compared with the existing technology, the invention has the following advantages:
The method of inspection of the invention is calculated inner cone height of teeth top, the inner cone height of teeth root, design tooth root of the gear teeth by geometric parameter
Line and design line of demarcation, determine the positional relationship of each geometric element；The lathe adjusting parameter and cutter parameters of given gear pair, really
Fixed practical dedendum line and practical line of demarcation.According to gear pair bull wheel, steamboat tooth top engage geometrical condition, acquire engaging-in point and
The steamboat corner put is nibbled out, by entire engagement process discretization, Tooth Contact Analysis is carried out to all steamboat corners, front-wheel will be worked as
The addendum line of tooth transforms on coupling gear, obtains tooth top projection line, carries out discretization to tooth top projection line, obtains root interference
Potential point, further establish root interference model, judge whether to interfere by normal distance, repeat the above process to obtain tooth
Root interference region.This method is a kind of to obtain the practical dedendum line of spiral bevel gear and reality according to actual cutter parameters and machined parameters
The method in border line of demarcation has higher consistency with the gear teeth of actual processing, further the practical root circle of analysis and theoretical tooth root
The overproof amount in the high and theoretical tooth of circle, practical tooth high, practical line of demarcation and theoretical line of demarcation, can be used for accuracy of gear detection.In conjunction with
Tooth contact analysis and root interference model, check the root interference in entire engagement process comprehensively.In addition, of the invention
It can determine the specific location and interference region interfered, judge the degree of root interference.
Detailed description of the invention
Fig. 1 is spiral bevel gear root interference method flow diagram of the invention；
Fig. 2 is steamboat outline element of the invention and practical tooth root, practical boundary line chart；
Fig. 3 is bull wheel outline element of the invention and practical tooth root, practical boundary line chart；
Fig. 4 is Tooth Contact Analysis coordinate system of the invention；
Fig. 5 is root interference illustraton of model of the invention；
Fig. 6 is bull wheel root interference administrative division map of the invention.
Specific embodiment
As shown in Figure 1, the method for inspection of spiral bevel gear root interference of the invention, specific steps:
(1) basic parameter of spiral bevel gear pair includes outer end height of teeth top, outer end height of teeth root, root angle, pitch cone angle, face cone
Angle, bottom clearance, the facewidth, outer cone distance and inner cone distance calculate inner cone height of teeth top, the inner cone tooth root of gear pair according to above-mentioned geometric parameter
High, design dedendum line ΓfWith design line of demarcation Γc, and these outline elements are indicated on the rotation perspective plane of the gear teeth, it determines
The relative positional relationship of each geometric element.
(2) according to the lathe adjusting parameter of bevel gear pair and cutter parameters, especially cutter fillet parameter, by gear sky
Between the theory of engagement and coordinate transform, derive fillet equation, determine practical dedendum line LfWith practical line of demarcation Lc, and
It indicates on the rotation perspective plane of the gear teeth.
(3) the small of engaging-in point is acquired by tooth contact analysis model according to the geometrical condition contacted on bull wheel tooth top
Take turns cornerEqually, by the geometrical condition and tooth contact analysis model that are contacted on steamboat tooth top, acquire nibble out put it is small
Take turns corner
(4) by entire engagement processIt is discrete to be(i=1,2,3 ..., n).To a certain instantaneous small rotation
Angle carries out Tooth Contact Analysis, and the addendum line of current cog is converted LaOnto coupling gear, and indicate on rotation perspective plane,
Obtain tooth top projection line La′。
(5) to tooth top projection line La' discretization is carried out, if discrete point, under practical line of demarcation, the point is dry for tooth root
The potential point related to needs further to judge；If root interference will not occur for the point on practical line of demarcation.
(6) root interference model is established, if the normal distance of potential point to tooth root is greater than zero, it is dry that tooth root will not occur
It relates to；If normal distance is less than zero, for root interference point.In fixed coordinate system, the position vector of addendum line is expressed as rha, tooth
The position vector and normal vector of root fillet surface are respectively rhfAnd nhf, solve nonlinear equation rha-rhf-λnhfλ in=0
Value.If λ<0, explanation is interfered, if the explanation of λ>0 does not interfere.
(7) to the discrete corner of each steamboatTooth Contact Analysis is carried out, is found out according to step (4)-(6) all
Interference point, then a series of interference point just forms root interference area, further can judge interference degrees according to the size of λ.
Below by taking spiral bevel gear as an example, in conjunction with attached drawing, the present invention is described in further detail, and described is to this hair
Bright explanation rather than limit.
1, geometric element calculates
The basic parameter of spiral bevel gear pair is respectively small tooth number z1=34, big tooth number z2=116, crossed axis angle γ=
79.2833 °, steamboat is left-handed, bull wheel dextrorotation.The geometric parameter of steamboat includes outer end height of teeth top ha1=4.71mm, outer end height of teeth root
hf1=2.77mm, addendum angle θa1=1.2167 °, pitch cone angle δ1=15.2833 °, bottom clearance c1=0.75mm, facewidth b1=
26.4mm, outer cone distance Re1=255.71mm；The geometric parameter of steamboat includes outer end height of teeth top ha1=4.71mm, outer end height of teeth root
hf1=2.77mm, addendum angle θa1=1.2167 °, pitch cone angle δ1=15.2833 °, bottom clearance c1=0.75mm, facewidth b1=
26.4mm, outer cone distance Re1=255.71mm；Inner cone height of teeth top, the inner cone tooth of the gear teeth are calculated according to the geometrical relationship of above-mentioned parameter
Root is high, designs dedendum line and design line of demarcation, and these profile geometric elements are indicated on the rotation perspective plane of the gear teeth, determines
Each element relative position, as shown in Fig. 2 and Fig. 3.
2, the large and small practical line of demarcation of wheel
The lathe adjusting parameter of steamboat concave surface: radial 243.6674mm, workhead offset 0.0mm, wheel blank established angle
14.65 °, horizontal wheels position 30.9137mm, bed -7.8209mm, ratio, angular knife position 4.221567 are rolled, coefficient is compared in second order rolling
0.18238,.The parameter of the outer knife of steamboat: 20 ° of profile angle, radius of corner 0.762mm.By Principles of Gear Connection and homogeneous coordinates
Transformation, derives the position vector of steamboat working flankAnd normal vector
And the position vector of steamboat filletAnd normal vectorWhen
Small flywheel rotor location parameter λ1=0 indicates knife tip circle angle minimum point, cuts the practical dedendum line of steamboat, is projected into steamboat
It rotates on perspective plane, obtains the practical dedendum line L of steamboatf1；Work as λ1=0.5 π-α1It indicates knife tip circle angle highest point, cuts work
The line of demarcation of the flank of tooth and fillet surface is projected on rotation steamboat rotation perspective plane, obtains the practical line of demarcation L of steamboatc1, such as
Shown in Fig. 2.
The lathe adjusting parameter on bull wheel convex surface: nose radius 227.2665mm, radial 218.13789mm, vertical wheel
Position 0.0mm, rolls ratio 1.112217,59.14 ° of angular knife position by 62.79 ° of wheel blank established angle.The parameter of knife in bull wheel: profile angle
20 °, radius of corner 1.524mm.Similarly, by Principles of Gear Connection and homogeneous coordinate transformation, bull wheel working flank is derived
Position vectorAnd normal vectorAnd the position of bull wheel fillet
Set vectorAnd normal vectorWhen big flywheel rotor parameter lambda2=0 indicates knife top
Fillet minimum point cuts the practical dedendum line L of bull wheelf2；Work as λ2=π-α2It indicates knife tip circle angle highest point, just obtains bull wheel work
Make the line of demarcation L of the flank of tooth and fillet surfacec2, as shown in Figure 3.
3, steamboat is engaging-in, nibbles out corner
It is contact point on bull wheel addendum line that bull wheel tooth top, which enters the geometrical condition of engagement, needs to meet:
v2-ha2-tgθa2(h2-Re2)=0 (1)
In formula,
After coordinate transform, the position vector of steamboat and normal vector are indicated in engagement coordinate system ShIn, respectivelySimilarly, in engagement coordinate system ShIn, the position vector and method of bull wheel
It is respectively to vectorTangent item is continuously contacted with according to two flank of tooth
Part:
The equation group being made of formula (1) and (2) is solved, the engaging-in corner of steamboat is obtainedEqually, steamboat tooth top exits
The geometrical condition of engagement is contact point on steamboat tooth top, needs to meet:
v1-ha1-tgθa1(h1-Re1)=0 (3)
In formula,
The equation group being made of (2) and (3) is solved, obtain steamboat nibbles out corner
4, large and small wheel tooth top projection line
By entire engagement processDiscrete is the n position of engagement(i=1,2,3 ..., n).According to formula (2)
Tooth Contact Analysis carried out to a certain instantaneous steamboat corner, then by steamboat addendum line La1: ra1(xa1,ya1,za1) indicate big
Take turns coordinate system S2In, coordinate ra'1(x'a1,y'a1,z'a1), and indicate to obtain steamboat tooth top on bull wheel rotation perspective plane
The projection line L' of linea1, as shown in Figure 3.Similarly, by bull wheel addendum line La2: ra2(xa2,ya2,za2) indicate in steamboat coordinate system S1
In, coordinate ra'2(x'a2,y'a2,z'a2), and indicate to obtain the projection line of bull wheel addendum line on steamboat rotation perspective plane
L'a2。
5, root interference potential point
On bull wheel rotation perspective plane, if steamboat addendum line La1' and bull wheel line of demarcation Lc2Meet:
Illustrate that two curved sections have intersection point G2, the point is by steamboat addendum line La1' it is divided into G1G2 and G2G3, the part G2G3 exists
Bull wheel lower part there is the potential position that root interference occurs, and root interference will not occur for G1G2.Similarly, it is rotated in steamboat
On perspective plane, if bull wheel addendum line La2' and steamboat line of demarcation Lc1Meet
Illustrate that two curved sections have intersection point P2, the point is by bull wheel addendum line La2' it is divided into P1P2 and P2P3, the part P2P3 exists
Bull wheel lower part there is potentially possible generation root interference position, and root interference will not occur for P1P2.
6, root interference point
Discrete for the potential steamboat addendum line G2G3 and bull wheel addendum line P2P3 that root interference occurs is n1And n2A point minute
It Wei not Pi(i=4,5 ..., n1+ 3) and Gi(i=4,5 ..., n2+ 3), to each discrete point Pi、 GiIt needs according to root interference mould
Type judges whether it is real interference point.By the position vector of steamboat fillet surfaceAnd normal vectorIt transforms to solid
Position fixing system ShIn, it is expressed asWithSimilarly, in fixed coordinate system
ShIn, the position vector and normal vector of bull wheel fillet surface are respectivelyWithWhen judging bull wheel root interference, equation is solvedAcquire λ2If λ2
< 0, illustrate that the discrete point interferes at bull wheel tooth root, if λ2> 0 illustrates that root interference does not occur for the point.Equally, for small
Wheel root interference is by solving equationIn λ1, illustrate that the discrete point occurs at steamboat tooth root
Interference, if λ1> 0 illustrates that root interference does not occur for the point.
7, root interference area
Corner is engaged with steamboat in step (4)To input parameter, to gear pair from engaging-in point to nibbling out the entire model put
Interior carry out Tooth Contact Analysis is enclosed, finds out all discrete points interfered further according to step (4)-(6), then by a series of dry
It relates to and a little forms root interference area, according to λ1And λ2Size judgement occur root interference severity.
Finally, it should be noted that above-described embodiment is merely illustrative of the technical solution of the present invention, and not to embodiment party
The restriction of formula.It for those of ordinary skill in the art, without departing from the spirit and scope of the present invention, can be
Other various forms of changes and improvements are carried out on the basis of above description, these changes and improvements should be still in the invention
Protection scope among.The scope of the present invention is defined by the appended claims and its equivalents.
Claims (7)
1. a kind of method of inspection of spiral bevel gear root interference, which comprises the following steps:
(1) by the basic parameter of spiral bevel gear pair, inner cone height of teeth top, the inner cone height of teeth root, design tooth root of gear pair are calculated
Line ΓfWith design line of demarcation Γc；And indicate these outline elements on the rotation perspective plane of the gear teeth, determine each geometric element
Relative positional relationship；
(2) it is pushed away according to the lathe adjusting parameter of bevel gear pair and cutter parameters by the gear space theory of engagement and coordinate transform
Fillet equation is exported, determines practical dedendum line LfWith practical line of demarcation Lc, and indicate on the rotation perspective plane of the gear teeth
On；
(3) the small rotation of engaging-in point is acquired by tooth contact analysis model according to the geometrical condition contacted on bull wheel tooth top
AngleEqually, by the geometrical condition and tooth contact analysis model that contact on steamboat tooth top, the small rotation nibbled out and put is acquired
Angle
(4) by the entire engagement process of gear pairIt is discrete to beTo a certain instantaneous small rotation
Angle carries out Tooth Contact Analysis, and the addendum line of current cog is converted LaOnto coupling gear, and indicate on rotation perspective plane,
Obtain tooth top projection line La′；
(5) to tooth top projection line La' discretization is carried out, if discrete point, under practical line of demarcation, which is the latent of root interference
In point, need further to judge；If root interference will not occur for the point on practical line of demarcation；
(6) root interference model is established, if the normal distance of potential point to tooth root is greater than zero, root interference will not occur；If
Normal distance is then root interference point less than zero；In fixed coordinate system, the position vector of addendum line is expressed as rha, tooth root mistake
The position vector and normal vector for crossing curved surface are respectively rhfAnd nhf, solve nonlinear equation rha-rhf-λnhfThe value of λ in=0；If
λ<0, explanation interfere, if the explanation of λ>0 does not interfere；
(7) to the discrete corner of each steamboatTooth Contact Analysis is carried out, finds out all interference according to step (4)-(6)
Point, then a series of interference point just forms root interference area, further can judge interference degrees according to the size of λ.
2. a kind of method of inspection of spiral bevel gear root interference according to claim 1, which is characterized in that step (2)
In, determine that specific step is as follows in the large and small practical line of demarcation of wheel:
By Principles of Gear Connection and homogeneous coordinate transformation, the position vector of steamboat working flank is derivedAnd normal vectorAnd the position vector of steamboat filletAnd normal vectorAs small flywheel rotor location parameter λ1=0 indicates knife tip circle
Angle minimum point cuts the practical dedendum line of steamboat, is projected on steamboat rotation perspective plane, obtains the practical dedendum line of steamboat
Lf1；Work as λ1=0.5 π-α1It indicates knife tip circle angle highest point, cuts the line of demarcation of working flank and fillet surface, projected
Onto rotation steamboat rotation perspective plane, the practical line of demarcation L of steamboat is obtainedc1；
Similarly, by Principles of Gear Connection and homogeneous coordinate transformation, the position vector of bull wheel working flank is derivedAnd normal vectorAnd the position vector of bull wheel filletAnd normal vectorWhen big flywheel rotor parameter lambda2=0 indicates knife tip circle angle most
Low spot cuts the practical dedendum line L of bull wheelf2；Work as λ2=π-α2It indicates knife tip circle angle highest point, just obtains bull wheel working flank
With the line of demarcation L of fillet surfacec2。
3. a kind of method of inspection of spiral bevel gear root interference according to claim 1, which is characterized in that step (3)
In, determine that steamboat is engaging-in, nibbling out corner, specific step is as follows:
It is contact point on bull wheel addendum line that bull wheel tooth top, which enters the geometrical condition of engagement, needs to meet:
v2-ha2-tgθa2(h2-Re2)=0 (1)
In formula,Through
After crossing coordinate transform, the position vector of steamboat and normal vector are indicated in fixed coordinate system ShIn, respectivelySimilarly, in fixed coordinate system ShIn, the position vector and method of bull wheel
It is respectively to vectorTangent item is continuously contacted with according to two flank of tooth
Part:
The equation group being made of formula (1) and (2) is solved, the engaging-in corner of steamboat is obtainedEqually, steamboat tooth top exits engagement
Geometrical condition is contact point on steamboat tooth top, needs to meet:
v1-ha1-tgθa1(h1-Re1)=0 (3)
In formula,It asks
The equation group that solution is made of (2) and (3), obtain steamboat nibbles out corner
4. a kind of method of inspection of spiral bevel gear root interference according to claim 3, which is characterized in that step (4)
In, determine that specific step is as follows for large and small wheel tooth top projection line:
By the entire engagement process of gear pairDiscrete is the n position of engagementAccording to formula (2)
Tooth Contact Analysis carried out to a certain instantaneous steamboat corner, then by steamboat addendum line La1: ra1(xa1,ya1,za1) indicate big
Take turns coordinate system S2In, coordinate is r 'a1(x'a1,y'a1,z'a1), and indicate to obtain steamboat tooth top on bull wheel rotation perspective plane
The projection line L' of linea1, as shown in Figure 3；Similarly, by bull wheel addendum line La2: ra2(xa2,ya2,za2) indicate in steamboat coordinate system S1
In, coordinate is r 'a2(x'a2,y'a2,z'a2), and indicate to obtain the projection line of bull wheel addendum line on steamboat rotation perspective plane
L'a2。
5. a kind of method of inspection of spiral bevel gear root interference according to claim 1, which is characterized in that step (5)
In, determine that specific step is as follows for root interference potential point:
On bull wheel rotation perspective plane, if steamboat addendum line L'a1With bull wheel line of demarcation Lc2Meet:
Illustrate that two curved sections have intersection point G2, the point is by steamboat addendum line La1' it is divided into G1G2 and G2G3, the part G2G3 is in bull wheel point
It is the potential position that root interference occurs below boundary line, and root interference will not occur for G1G2；Similarly, perspective plane is rotated in steamboat
On, if bull wheel addendum line La2' and steamboat line of demarcation Lc1Meet:
Illustrate that two curved sections have intersection point P2, the point is by bull wheel addendum line La2' it is divided into P1P2 and P2P3, the part P2P3 is in bull wheel point
It is potentially possible generation root interference position below boundary line, and root interference will not occur for P1P2.
6. a kind of method of inspection of spiral bevel gear root interference according to claim 5, which is characterized in that step (6)
In, determine that specific step is as follows for root interference point:
Discrete for the potential steamboat addendum line G2G3 and bull wheel addendum line P2P3 that root interference occurs is n1And n2A point is respectively
Pi(i=4,5 ..., n1+ 3) and Gi(i=4,5 ..., n2+ 3), to each discrete point Pi、GiIt needs to be sentenced according to root interference model
Whether disconnected is real interference point；By the position vector r of steamboat fillet surface1 (f)And normal vectorTransform to fixed coordinates
It is ShIn, it is expressed asWithSimilarly, in fixed coordinate system ShIn, greatly
Take turns fillet surface position vector and normal vector be respectivelyWithWhen sentencing
When disconnected bull wheel root interference, equation is solvedAcquire λ2If λ2< 0, illustrate the discrete point in the big gear teeth
It is interfered at root, if λ2> 0 illustrates that root interference does not occur for the point；It equally, is by solving equation for steamboat root interferenceIn λ1If λ1< 0, illustrate that the discrete point interferes at steamboat tooth root, if λ1> 0 explanation should
Root interference does not occur for point.
7. a kind of method of inspection of spiral bevel gear root interference according to claim 1, which is characterized in that step (1)
In, the basic parameter of spiral bevel gear pair include outer end height of teeth top, outer end height of teeth root, root angle, pitch cone angle, face cone angle, bottom clearance,
The facewidth, outer cone distance and inner cone distance.
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| CN109241613B (en) * | 2018-08-31 | 2020-07-28 | 西安交通大学 | Method for determining cutter root trimming parameters of spiral bevel gear |
| CN109238200B (en) * | 2018-09-12 | 2021-04-27 | 中国航发哈尔滨东安发动机有限公司 | Method for detecting bevel gear root cone parameters |
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