CN108120596A - 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
- Publication number
- CN108120596A CN108120596A CN201711332595.0A CN201711332595A CN108120596A CN 108120596 A CN108120596 A CN 108120596A CN 201711332595 A CN201711332595 A CN 201711332595A CN 108120596 A CN108120596 A CN 108120596A
- Authority
- CN
- China
- Prior art keywords
- tooth
- line
- root
- wheel
- interference
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
- G01M13/02—Gearings; Transmission mechanisms
- G01M13/021—Gearings
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 position relationship of each geometric element；The lathe adjusting parameter and cutter parameters of given gear pair, determine actual dedendum line and actual 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 steamboat corner a little, 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, repeat the above process to obtain root interference area.This method can verify that out the root interference generated due to cutter fillet is excessive or lathe parameter sets unreasonable, determine actual fillet surface and the line of demarcation of working flank and root interference region.
Description
Technical Field
The invention belongs to the technical field of gear transmission, and particularly relates to a method for inspecting tooth root interference of a spiral bevel gear.
Background
In the transmission process of the spiral bevel gear pair, due to the factors of unreasonable tooth root design, gear tooth degeneration, installation error and the like, the abnormal meshing phenomenon of a small gear tooth top and a large gear tooth root or the abnormal meshing phenomenon of the large gear tooth top and the small gear tooth root is caused, and is called tooth root interference; the gear pair is a design defect, is often accompanied by strong vibration and impact, is easy to generate adverse phenomena such as tooth breakage, fatigue failure and the like at the tooth root, and affects the stability and the service life of gear transmission, so that inspection and elimination must be carried out when the gear pair is designed, processed, installed and adjusted.
Root fillet design and process parameter set irrational are the primary factors that cause root interference. In the traditional spiral bevel gear geometric design, the maximum radius of a cutter fillet is deduced according to the geometric relation that an equivalent gear of the spiral bevel gear is meshed with a rack cutter, the method is a simplified approximate method, the calculation process of the method relates to a large number of complex numerical formulas, and even if the numerical formula is adopted, the root interference phenomenon often occurs. In fact, the tooth root interference is closely related to the topological structure of the working tooth surface and the transition curved surface of the gear tooth, and the shape of the tooth surface is completely determined by machining parameters, so that the spiral bevel gear machining parameter setting has an important influence on the tooth root interference. In summary, both root fillet and machining parameters are interrelated root interference effects that must be considered simultaneously.
In the document of 'square, yang bin, duncao et al, root transition curved surface and interference of a gear tooth, undercut inspection and mechanical transmission 2002, 26 (1): 38-40', machining parameter design is optimized by considering a tooth root interference condition, and when a contact trajectory line does not exceed an intersection line of a working tooth surface and the transition curved surface, tooth root interference does not exist.
Disclosure of Invention
The invention aims to solve the problem of tooth root interference of the spiral bevel gear, and provides a method for detecting the tooth root interference of the spiral bevel gear, which can detect the tooth root interference generated by overlarge cutter fillet or unreasonable machine tool parameter setting, and determine the boundary of an actual transition curved surface and a working tooth surface and a tooth root interference area.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
a method for checking root interference of a spiral bevel gear comprises the following steps:
(1) The basic parameters of helical bevel gear pair are used to calculate the internal cone tooth top height, internal cone tooth root height and designed tooth root line gamma of gear pair f And design boundary gamma c (ii) a The outline elements are expressed on a rotary projection surface of the gear teeth, and the relative position relation of each geometric element is determined;
(2) According to the machine tool adjustment parameters and the cutter parameters of the bevel gear pair, by means of the gear space meshing principle and coordinate transformation, a tooth root transition surface equation is deduced, and an actual tooth root line L is determined f And the actual boundary line L c And is shown on the rotating projection plane of the gear teeth;
(3) Determining the small wheel angle of the engagement point by means of a wheel tooth contact analysis model on the basis of the geometric conditions of the contact on the large wheel tooth headSimilarly, the angle of rotation of the small wheel at the point of engagement is determined from the geometric conditions of the contact at the small wheel tooth tip and from the wheel tooth contact analysis model
(4) The whole meshing process of the gear pairIs dispersed intoi =1,2,3, \8230;, n; tooth surface contact analysis is carried out on a certain instantaneous small wheel corner, and the addendum line of the current gear tooth is converted into L a To the mating gear and shown on the rotary projection plane to obtain the tooth top projection line L a ′；
(5) Projection line L to tooth top a Discretizing, namely if a discrete point is below an actual boundary, determining the point as a potential point of root interference, and needing further judgment; if above the actual boundary, no root interference will occur at that point;
(6) Establishing a tooth root interference model, and if the normal distance from the potential point to a tooth root is greater than zero, avoiding the occurrence of tooth root interference; if the normal distance is less than zero, the normal distance is a tooth root interference point; in the fixed coordinate system, the position vector of the addendum line is represented as r ha The position vector and normal vector of the tooth root transition curved surface are respectively r hf And n hf Solving a non-linear equation r ha -r hf -λn hf Value of λ in = 0; if λ<, 0, indicating that interference occurs if λ> 0 means no interference;
(7) Discrete turning angle for each small wheelAnd (4) performing tooth surface contact analysis, and obtaining all interference points according to the steps (4) to (6), so that a series of interference points form a tooth root interference area, and further, the interference degree can be judged according to the size of lambda.
As a further improvement of the invention, in the step (2), the specific steps of determining the actual boundary between the large wheel and the small wheel are as follows:
deducing the position vector of the working tooth surface of the small wheel by means of the gear meshing principle and homogeneous coordinate transformationAnd normal vectorAnd position vector of root transition surface of pinionAnd normal vectorWhen the position parameter lambda of the small wheel cutter head 1 And (= 0) cutting the actual tooth root line of the small wheel by representing the lowest point of the cutter top fillet, projecting the actual tooth root line of the small wheel onto a rotating projection plane of the small wheel to obtain the actual tooth root line L of the small wheel f1 (ii) a When lambda is 1 ＝0.5π-α 1 The highest point of the cutter top fillet is represented, the boundary of the working tooth surface and the transition curved surface is cut and projected onto the rotary projection surface of the small rotary wheel, and the actual boundary L of the small rotary wheel is obtained c1 ；
In the same way, the position vector of the working tooth surface of the large wheel is deduced by means of the gear meshing principle and homogeneous coordinate transformationAnd normal vectorAnd position vector of transition curved surface of large gear tooth rootAnd normal vectorWhen the bull wheel cutter parameters lambda 2 =0 denotes the lowest point of the cutter top fillet, the actual tooth root line L of the big wheel is cut f2 (ii) a When lambda is 2 ＝π-α 2 The highest point of the cutter top fillet is shown, and the boundary L of the working tooth surface of the bull wheel and the transition curved surface is obtained c2 。
As a further improvement of the present invention, in the step (3), the specific steps of determining the engaging-in and engaging-out rotation angle of the small wheel are as follows:
the geometrical condition that the top of the big gear enters the meshing is that the contact point is on the top line of the big gear tooth, and the requirements are met:
v 2 -h a2 -tgθ a2 (h 2 -R e2 )＝0 (1)
in the formula (I), the compound is shown in the specification, after coordinate transformation, the position vector and the normal vector of the small wheel are expressed in a meshing coordinate system S h In each case areIn a similar manner, in the meshing coordinate system S h The position vector and the normal vector of the large wheel are respectivelyAccording to the condition that two tooth surfaces are in continuous contact with tangency:
solving an equation set consisting of the formulas (1) and (2) to obtain the engagement rotation angle of the small wheelSimilarly, the geometrical condition that the small wheel tooth crest is disengaged is that the contact point is on the small wheel tooth crest, and the following requirements are met:
v 1 -h a1 -tgθ a1 (h 1 -R e1 )＝0 (3)
in the formula (I), the compound is shown in the specification, solving the equation set composed of (2) and (3) to obtain the engagement rotation angle of the small wheel
As a further improvement of the invention, in the step (4), the specific steps of determining the tooth top projection lines of the large wheel and the small wheel are as follows:
the whole engaging processDiscrete as n engagement positions(i =1,2,3, \8230;, n); according to the formula (2), the tooth surface contact analysis is carried out on a certain instantaneous small wheel corner, and then the addendum line L of the small wheel is measured a1 ：r a1 (x a1 ,y a1 ,z a1 ) Expressed in a large wheel coordinate system S 2 In, its coordinate is r a ' 1 (x' a1 ,y' a1 ,z' a1 ) And a projection line L 'for obtaining a tip line of the small wheel on the large wheel rotation projection plane' a1 As shown in fig. 3; in the same way, the top line L of the big gear teeth a2 ：r a2 (x a2 ,y a2 ,z a2 ) Expressed in a small wheel coordinate system S 1 In, its coordinate is r a ' 2 (x' a2 ,y' a2 ,z' a2 ) And shows a projection line L 'for obtaining a top line of the large gear on the projection plane of the small wheel rotation' a2 。
As a further improvement of the invention, in the step (5), the specific steps of determining the root interference potential point are as follows:
on the projection plane of the big wheel, if the addendum line L of the small wheel a1 ' line L with the bull wheel c2 Satisfies the following conditions:
it is shown that the two curve segments have an intersection point G2, which is the point of the addendum line L of the small wheel a1 ' division into G1G2 and G2G3, the G2G3 portion below the large wheel dividing line is where root interference is potentially occurring, while G1G2 does not occur; similarly, on the projection plane of the small wheel rotation, if the top line L of the big wheel tooth is a2 ' line L of demarcation with small wheel c1 Satisfies the following conditions:
it is shown that the two curve segments have an intersection point P2, which is the top line L of the big gear tooth a2 ' split into P1P2 and P2P3, with the P2P3 portion below the large wheel dividing line being a potential location for root interference, and P1P2 not.
As a further improvement of the invention, in the step (6), the specific steps of determining the root interference point are as follows:
for small gear addendum line G2G3 and large gear addendum line P2P3 with potential root interference discretization of n 1 And n 2 The points are respectively P i (i＝4,5,…,n 1 + 3) and G i (i＝4,5,…,n 2 + 3), for each discrete point P i 、 G i Judging whether the interference point is a real interference point or not according to the tooth root interference model; position vector of small wheel transition curved surfaceAnd normal vectorTransformation to a fixed coordinate system S h In are respectively represented asAndin a similar way, in a fixed coordinate system S h The position vector and the normal vector of the transition curved surface of the middle wheel and the large wheel are respectivelyAndwhen judging the interference of the big gear tooth root, solving the equationFind lambda 2 If λ is 2 <, 0, which shows that the discrete points interfere at the root of the big gear, if lambda 2 &0 indicates that no root interference occurs at this point; also, root interference is solved for the pinion by solving equationsλ in 1 It is stated that the discrete points interfere at the roots of the pinions if λ 1 >, 0 indicates that root interference does not occur at this point.
As a further improvement of the invention, in the step (1), the basic parameters of the helical bevel gear pair comprise external end tooth crest height, external end tooth root height, root cone angle, pitch cone angle, face cone angle, tip clearance, tooth width, external cone distance and internal cone distance.
Compared with the prior art, the invention has the following beneficial effects:
the inspection method of the invention calculates the height of the inner cone tooth top, the height of the inner cone tooth root, a designed tooth root line and a designed boundary line of the gear teeth according to the geometric parameters, and determines the position relation of each geometric element; and (4) given machine tool adjustment parameters and tool parameters of the gear pair, and determining an actual tooth root line and an actual dividing line. According to the geometrical condition that the gear pair is engaged with at bull wheel, bull wheel addendum, steamboat corner of the little gear tooth, try to get the engagement point and nibble the steamboat corner of the point, with whole meshing process discretization, carry out flank of tooth contact analysis to all steamboat corners, with the addendum line of the present teeth of a cogwheel transform to mating gears on, obtain the tooth top projection line, carry out the discretization to the tooth top projection line, obtain the latent point that the tooth root is interfered, further establish the tooth root and interfere the model, judge whether take place to interfere by normal distance, repeat above-mentioned process and obtain the tooth root and interfere the district. The method is a method for obtaining the actual tooth root line and the actual boundary line of the spiral bevel gear according to the actual cutter parameters and the machining parameters, has higher consistency with the actually machined gear teeth, further analyzes the overlength quantity of the actual tooth root circle and the theoretical tooth root circle, the actual tooth height and the theoretical tooth height, and the actual boundary line and the theoretical boundary line, and can be used for gear precision detection. The tooth root interference during the entire meshing process is fully checked in conjunction with the tooth contact analysis and the tooth root interference model. In addition, the invention can determine the specific position and interference area where interference occurs and judge the degree of tooth root interference.
Drawings
FIG. 1 is a flow chart of a helical bevel gear root interference method of the present invention;
FIG. 2 is a plot of the small wheel profile elements and the actual roots, actual demarcation line for the present invention;
FIG. 3 is a plot of the contour elements of the bull wheel and the actual roots, actual demarcation line for the present invention;
FIG. 4 is a tooth surface contact analysis coordinate system of the present invention;
FIG. 5 is a diagram of a root interference model of the present invention;
FIG. 6 is a diagram of the large tooth root interference area of the present invention.
Detailed Description
As shown in FIG. 1, the method for inspecting the tooth root interference of the spiral bevel gear comprises the following specific steps:
(1) The basic parameters of the helical bevel gear pair include external end tooth top height, external end tooth root height, root cone angle, pitch cone angle, face cone angle, tip clearance, tooth width, external cone distance and internal cone distance, and according to the above-mentioned geometric parameters the internal cone tooth top height, internal cone tooth root height and designed tooth root line gamma of the gear pair can be calculated f And design boundary gamma c And representing the outline elements on a rotating projection plane of the gear teeth, and determining the relative position relation of the geometric elements.
(2) According to the machine tool adjustment parameters and the cutter parameters of the bevel gear pair, particularly the cutter fillet parameters, the tooth root transition surface equation is deduced by means of the gear space meshing principle and coordinate transformation, and the actual tooth root line L is determined f And the actual boundary line L c And is shown on the plane of projection of the rotation of the gear teeth.
(3) Determining the small wheel angle of the engagement point by means of a wheel tooth contact analysis model on the basis of the geometric conditions of the contact on the large wheel tooth headSimilarly, the angle of rotation of the small wheel at the engagement point is determined from the geometric conditions of the contact at the tooth tip of the small wheel and from the model for analyzing the contact of the teeth
(4) The whole engaging processIs dispersed into(i =1,2,3, \8230;, n). Tooth surface contact analysis is carried out on a certain instantaneous small wheel corner, and the addendum line of the current gear tooth is converted into L a To the mating gear and shown on the rotary projection plane to obtain tooth top projection line L a ′。
(5) Projection line L to tooth top a If the discrete point is below the actual boundary, the point is a potential point of tooth root interference, and further judgment is needed; above the actual boundary line, no root interference occurs at this point.
(6) Establishing a tooth root interference model, and if the normal distance from the potential point to a tooth root is greater than zero, avoiding the occurrence of tooth root interference; and if the normal distance is less than zero, the normal distance is a tooth root interference point. In the fixed coordinate system, the position vector of the addendum line is represented as r ha The position vector and normal vector of the tooth root transition surface are r hf And n hf Solving a non-linear equation r ha -r hf -λn hf Value of λ in =0. If λ<, 0, indicating that interference occurs if λ>, 0 means no interference.
(7) Discrete turning angle for each small wheelAnd (4) performing tooth surface contact analysis, and obtaining all interference points according to the steps (4) to (6), so that a series of interference points form a tooth root interference area, and further, the interference degree can be judged according to the size of lambda.
The present invention will be described in further detail below by taking a spiral bevel gear as an example and combining with the accompanying drawings, which are used for explanation and not limitation.
1. Geometric element calculation
The basic parameter of the spiral bevel gear pair is the number of teeth z of the small gear 1 =34, large gear tooth number z 2 =116, angle of intersection γ =79.2833 °, small wheel left hand, large wheel right hand. The geometric parameters of the small wheel include the external end tooth crest height h a1 =4.71mm, outer end tooth root height h f1 =2.77mm, crest angle θ a1 =1.2167 ° and pitch angle δ 1 =15.2833 °, tip clearance c 1 =0.75mm, tooth width b 1 =26.4mm, outer cone distance R e1 =255.71mm; the geometric parameters of the small wheel comprise the external end tooth crest height h a1 =4.71mm, outer end tooth root height h f1 =2.77mm, crest angle θ a1 =1.2167 ° and pitch angle δ 1 =15.2833 °, top clearance c 1 =0.75mm, tooth width b 1 =26.4mm, outer cone distance R e1 =255.71mm; calculating the inner cone crest height, the inner cone root height, the design root line and the design dividing line of the gear tooth according to the geometrical relationship of the parameters, representing the contour geometrical elements on the rotary projection plane of the gear tooth, and determining the relative positions of the elements, as shown in fig. 2 and 3.
2. Actual boundary line of large wheel and small wheel
Adjusting parameters of the machine tool for the concave surface of the small wheel: the radial cutter position is 243.6674mm, the vertical wheel position is 0.0mm, the wheel blank installation angle is 14.65 degrees, the horizontal wheel position is 30.9137mm, the bed position is-7.8209 mm, the rolling ratio is 4.221567, and the second-order rolling ratio coefficient is 0.18238. Parameters of the small wheel outer cutter: the tooth form angle is 20 degrees, and the fillet radius is 0.762mm. Deducing the position vector of the working tooth surface of the small wheel by means of the gear meshing principle and homogeneous coordinate transformationAnd normal vectorAnd position vector of root transition surface of pinionAnd normal vectorWhen the position parameter lambda of the small wheel cutter head 1 =0 represents the lowest point of a cutter top fillet, the actual tooth root line of the small wheel is cut, and the actual tooth root line of the small wheel is projected on the rotating projection plane of the small wheel to obtain the actual tooth root line L of the small wheel f1 (ii) a When lambda is 1 ＝0.5π-α 1 The highest point of the cutter top fillet is represented, the boundary of the working tooth surface and the transition curved surface is cut and projected onto the rotary projection surface of the small rotary wheel, and the actual boundary L of the small rotary wheel is obtained c1 As shown in fig. 2.
Adjusting parameters of the machine tool with the convex surface of the large wheel: the radius of the tool nose is 227.2665mm, the radial tool position is 218.13789mm, the vertical wheel position is 0.0mm, the wheel blank installation angle is 62.79 degrees, the rolling ratio is 1.112217, and the angular tool position is 59.14 degrees. Parameters of the bull wheel inner cutter: the tooth form angle is 20 degrees, and the fillet radius is 1.524mm. In the same way, the position vector of the working tooth surface of the large wheel is deduced by means of the gear meshing principle and homogeneous coordinate transformationAnd normal vectorAnd position vector of transition curved surface of large gear tooth rootAnd normal vectorWhen the bull wheel cutter parameters lambda 2 =0 denotes the lowest point of the cutter top fillet, the actual tooth root line L of the big wheel is cut f2 (ii) a When lambda is 2 ＝π-α 2 The highest point of the cutter top fillet is represented, and the boundary L between the working tooth surface of the bull wheel and the transition curved surface is obtained c2 As shown in fig. 3.
3. Angle of rotation for engaging small wheel
The geometrical condition that the top of the big gear enters the meshing is that the contact point is on the top line of the big gear tooth, and the requirements are met:
v 2 -h a2 -tgθ a2 (h 2 -R e2 )＝0(1)
in the formula (I), the compound is shown in the specification, after coordinate transformation, the position vector and the normal vector of the small wheel are expressed in a meshing coordinate system S h In each case areIn a similar manner, in the meshing coordinate system S h The position vector and the normal vector of the large wheel are respectivelyAccording to the condition that two tooth surfaces are in continuous contact with tangency:
solving an equation set consisting of the formulas (1) and (2) to obtain the engagement rotation angle of the small wheelSimilarly, the geometrical condition that the small wheel tooth crest is disengaged is that the contact point is on the small wheel tooth crest, and the following requirements are met:
v 1 -h a1 -tgθ a1 (h 1 -R e1 )＝0 (3)
in the formula (I), the compound is shown in the specification, solving the equation set composed of (2) and (3) to obtain the engagement rotation angle of the small wheel
4. Projection line of big and small wheel tooth top
The whole engaging processDiscrete as n engagement positions(i =1,2,3, \8230;, n). According to the formula (2), the tooth surface contact analysis is carried out on a certain instantaneous small wheel corner, and then the addendum line L of the small wheel is measured a1 ：r a1 (x a1 ,y a1 ,z a1 ) Expressed in a large wheel coordinate system S 2 In, its coordinate is r a ' 1 (x' a1 ,y' a1 ,z' a1 ) And shows a projection line L 'for obtaining a tip line of the small wheel on the projection plane of the large wheel rotation' a1 As shown in fig. 3. In the same way, the top line L of the big gear teeth a2 ：r a2 (x a2 ,y a2 ,z a2 ) Expressed in a small wheel coordinate system S 1 In, its coordinate is r a ' 2 (x' a2 ,y' a2 ,z' a2 ) And shows a projection line L 'for obtaining a top line of the large gear on the projection plane of the small wheel rotation' a2 。
5. Root interference potential
On the rotary projection plane of the big wheel, if the addendum line L of the small wheel a1 ' line L of demarcation with the bull wheel c2 Satisfies the following conditions:
it is illustrated that the two curve segments have an intersection point G2, which is the point at which the tip line L of the small wheel is located a1 ' division into G1G2 and G2G3, the G2G3 portion is below the large wheel dividing line where root interference is potentially occurring, while G1G2 does not. Similarly, on the projection plane of the small wheel rotation, if the top line L of the big wheel tooth is L a2 ' line L of demarcation with small wheel c1 Satisfy the requirements of
It is shown that the two curve segments have an intersection point P2, which is the top line L of the big gear tooth a2 ' split into P1P2 and P2P3, with the P2P3 portion below the large wheel dividing line being a potential location for root interference, and P1P2 not.
6. Root interference point
For small gear addendum line G2G3 and large gear addendum line P2P3 with potential root interference discretization of n 1 And n 2 The points are respectively P i (i＝4,5,…,n 1 + 3) and G i (i＝4,5,…,n 2 + 3), for each discrete point P i 、 G i Whether the interference point is a real interference point needs to be judged according to the tooth root interference model. Position vector of small wheel transition curved surfaceAnd normal vectorTransformation to a fixed coordinate system S h In are respectively represented asAndin a similar way, in a fixed coordinate system S h The position vector and the normal vector of the transition curved surface of the middle wheel and the large wheel are respectivelyAndwhen the interference of the big gear tooth root is judged, the equation is solvedFind lambda 2 If λ 2 <, 0, which shows that the discrete points interfere at the root of the big gear, if lambda 2 >, 0 indicates that no root interference occurs at this point. Also, root interference is solved for the pinion by solving equationsλ of (2) 1 It is stated that the discrete points interfere at the roots of the pinions if 1 >, 0 indicates that no root interference occurs at this point.
7. Root interference zone
Using the engaging angle of the small wheel in the step (4)Performing tooth surface contact analysis on the gear pair in the whole range from a meshing point to a meshing point for inputting parameters, then obtaining all discrete points where interference occurs according to the steps (4) to (6), forming a tooth root interference area by a series of interference points, and forming a tooth root interference area according to lambda 1 And λ 2 Determines the severity of the occurrence of root interference.
Finally, it should be noted that the above examples are only for illustrating the technical solutions of the present invention, and are not intended to limit the embodiments. It will be apparent to those skilled in the art that various other changes and modifications can be made in the invention without departing from the spirit and scope of the invention, and it is intended that all such changes and modifications fall within the scope of the invention as defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A method for checking root interference of a spiral bevel gear is characterized by comprising the following steps:
(1) The basic parameters of helical bevel gear pair are used to calculate the internal cone tooth top height, internal cone tooth root height and designed tooth root line gamma of gear pair f And designing a parting line gamma c (ii) a Representing the outline elements on a rotary projection surface of the gear teeth, and determining the relative position relation of the geometric elements;
(2) According to the machine tool adjustment parameters and the cutter parameters of the bevel gear pair, by means of the gear space meshing principle and coordinate transformation, a tooth root transition surface equation is deduced, and an actual tooth root line L is determined f And the actual boundary line L c And is shown on the plane of projection of the rotation of the gear teeth;
(3) Determining the small wheel angle of the engagement point by means of a wheel tooth contact analysis model on the basis of the geometric conditions of the contact on the large wheel tooth headSimilarly, the angle of rotation of the small wheel at the engagement point is determined from the geometric conditions of the contact at the tooth tip of the small wheel and from the model for analyzing the contact of the teeth
(4) The whole meshing process of the gear pairIs dispersed intoTooth surface contact analysis is carried out on a certain instantaneous small wheel corner, and the addendum line of the current gear tooth is converted into L a To the mating gear and shown on the rotary projection plane to obtain tooth top projection line L a ′；
(5) Projection line L to tooth top a If the discrete point is below the actual boundary, the point is a potential point of tooth root interference, and further judgment is needed; if above the actual boundary line, no root interference occurs at that point;
(6) Establishing a tooth root interference model, and if the normal distance from the potential point to the tooth root is greater than zero, avoiding the occurrence of tooth root interference; if the normal distance is less than zero, the normal distance is a tooth root interference point; in the fixed coordinate system, the position vector of the addendum line is represented as r ha The position vector and normal vector of the tooth root transition surface are r hf And n hf Solving the nonlinear equation r ha -r hf -λn hf Value of λ in = 0; if λ<, 0, indicating that interference occurs if λ>, 0 means no interference;
(7) Discrete turning angle for each small wheelAnd (4) performing tooth surface contact analysis, and obtaining all interference points according to the steps (4) to (6), so that a series of interference points form a tooth root interference area, and further, the interference degree can be judged according to the size of lambda.
2. The method for inspecting the root interference of the spiral bevel gear according to claim 1, wherein in the step (2), the specific steps of determining the actual boundary between the large wheel and the small wheel are as follows:
deducing the position vector of the working tooth surface of the small wheel by means of the gear meshing principle and homogeneous coordinate transformationAnd normal vectorAnd position vector of root transition surface of pinionAnd normal vectorWhen the position parameter lambda of the small wheel cutter head 1 And (= 0) cutting the actual tooth root line of the small wheel by representing the lowest point of the cutter top fillet, projecting the actual tooth root line of the small wheel onto a rotating projection plane of the small wheel to obtain the actual tooth root line L of the small wheel f1 (ii) a When lambda is 1 ＝0.5π-α 1 The highest point of the cutter top fillet is represented, the boundary between the working tooth surface and the transition curved surface is cut and projected on the rotary projection surface of the small rotary wheel, and the actual boundary L of the small rotary wheel is obtained c1 ；
In the same way, the position of the working tooth surface of the large wheel is deduced by means of the gear meshing principle and homogeneous coordinate transformationPosition vectorAnd normal vectorAnd position vector of transition curved surface of large gear tooth rootAnd normal vectorWhen the bull wheel cutter head parameter lambda 2 =0 represents the lowest rounded point of the cutter top, and the actual tooth root line L of the large wheel is cut f2 (ii) a When lambda is 2 ＝π-α 2 The highest point of the cutter top fillet is shown, and the boundary L of the working tooth surface of the bull wheel and the transition curved surface is obtained c2 。
3. The method for detecting the tooth root interference of the spiral bevel gear according to claim 1, wherein in the step (3), the specific steps of determining the engaging-in and engaging-out rotation angles of the small wheels are as follows:
the geometrical condition that the top of the big gear enters the meshing is that the contact point is on the top line of the big gear tooth, and the requirements are met:
v 2 -h a2 -tgθ a2 (h 2 -R e2 )＝0 (1)
in the formula (I), the compound is shown in the specification,after coordinate transformation, the position vector and the normal vector of the small wheel are expressed in a meshing coordinate system S h In each case areIn the same way, in the meshing coordinate system S h The position vector and the normal vector of the large wheel are respectivelyAccording to the condition that two tooth surfaces are in continuous contact with tangency:
solving an equation set consisting of the formulas (1) and (2) to obtain the engagement rotation angle of the small wheelSimilarly, the geometrical condition that the small wheel tooth crest is disengaged is that the contact point is on the small wheel tooth crest, and the following requirements are met:
v 1 -h a1 -tgθ a1 (h 1 -R e1 )＝0 (3)
in the formula (I), the compound is shown in the specification,solving the equation set composed of (2) and (3) to obtain the engagement rotation angle of the small wheel
4. The method for inspecting the root interference of the spiral bevel gear according to claim 3, wherein in the step (4), the specific steps of determining the tooth top projection lines of the big wheel and the small wheel are as follows:
the whole meshing process of the gear pairDiscrete as n engagement positionsAccording to the formula (2), performing tooth surface contact analysis on a certain instantaneous small wheel corner, and then performing addendum line L on the small wheel a1 ：r a1 (x a1 ,y a1 ,z a1 ) Expressed in a large wheel coordinate system S 2 Wherein the coordinate is r' a1 (x' a1 ,y' a1 ,z' a1 ) And shows a projection line L 'for obtaining a tip line of the small wheel on the projection plane of the large wheel rotation' a1 As shown in fig. 3; in the same way, the top line L of the big gear is arranged a2 ：r a2 (x a2 ,y a2 ,z a2 ) Expressed in a small wheel coordinate system S 1 Wherein the coordinate is r' a2 (x' a2 ,y' a2 ,z' a2 ) And a projection line L 'for obtaining a top line of the large gear tooth on the small wheel rotation projection plane' a2 。
5. The method for checking the root interference of the spiral bevel gear according to claim 1, wherein in the step (5), the specific step of determining the root interference potential point is as follows:
on the large wheel rotation projection plane, if the small wheel addendum line L' a1 Line L with the bull wheel c2 Satisfies the following conditions:
it is illustrated that the two curve segments have an intersection point G2, which is the point at which the tip line L of the small wheel is located a1 ' division into G1G2 and G2G3, the G2G3 portion below the large wheel dividing line is where root interference is potentially occurring, while G1G2 does not occur; similarly, on the projection plane of the small wheel rotation, if the top line L of the big wheel tooth is a2 ' line L of demarcation with small wheel c1 Satisfies the following conditions:
it is shown that the two curve segments have an intersection point P2, which is the top line L of the big gear tooth a2 ' split into P1P2 and P2P3, with the P2P3 portion below the large wheel dividing line being a potential location for root interference, and P1P2 not.
6. The method for inspecting root interference of a spiral bevel gear according to claim 5, wherein in the step (6), the specific steps for determining the root interference point are as follows:
for small gear addendum line G2G3 and large gear addendum line P2P3 with potential root interference discretization of n 1 And n 2 The points are respectively P i (i＝4,5,…,n 1 + 3) and G i (i＝4,5,…,n 2 + 3), for each discrete point P i 、G i Judging whether the interference point is a real interference point or not according to the tooth root interference model; position vector of small wheel transition curved surfaceAnd normal vectorTransformation to a fixed coordinate system S h In each case are represented byAndin a similar manner, in a fixed coordinate system S h The position vector and the normal vector of the transition curved surface of the middle wheel and the large wheel are respectivelyAndwhen the interference of the big gear tooth root is judged, the equation is solvedFind lambda 2 If λ 2 <, 0, which shows that the discrete point interferes at the root of the big gear, if lambda 2 &0 indicates that no root interference occurs at this point; also, root interference is solved for the pinion by solving equationsλ of (2) 1 Description of the inventionThe discrete points interfere at the roots of the pinions if lambda 1 >, 0 indicates that no root interference occurs at this point.
7. The method for inspecting interference at roots of helical bevel gears according to claim 1, wherein in step (1), the basic parameters of the helical bevel gear pair include external end tooth top height, external end tooth bottom height, root cone angle, pitch cone angle, face cone angle, tip clearance, tooth width, external cone distance and internal cone distance.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711332595.0A CN108120596B (en) | 2017-12-13 | 2017-12-13 | A kind of spiral bevel gear root interference method of inspection |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711332595.0A CN108120596B (en) | 2017-12-13 | 2017-12-13 | A kind of spiral bevel gear root interference method of inspection |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108120596A true CN108120596A (en) | 2018-06-05 |
| CN108120596B CN108120596B (en) | 2019-07-30 |
Family
ID=62229873
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201711332595.0A Expired - Fee Related CN108120596B (en) | 2017-12-13 | 2017-12-13 | A kind of spiral bevel gear root interference method of inspection |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108120596B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108533686A (en) * | 2018-06-12 | 2018-09-14 | 中国地质大学（武汉） | Concave-convex engagement pure rolling bevel gear mechanism for intersecting axle transmission |
| CN109238200A (en) * | 2018-09-12 | 2019-01-18 | 中国航发哈尔滨东安发动机有限公司 | A method of detection bevel gear root bores parameter |
| CN109241613A (en) * | 2018-08-31 | 2019-01-18 | 西安交通大学 | A kind of cutter root relief parameter determination method of spiral bevel gear |
| CN111666641A (en) * | 2020-05-25 | 2020-09-15 | 重庆青山工业有限责任公司 | Method for calculating tooth surface parameters of straight bevel gear |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002005654A (en) * | 2000-06-20 | 2002-01-09 | Akira Yoshida | Measuring method for error in tooth plane of bevel bear |
| CN101025384A (en) * | 2006-02-18 | 2007-08-29 | 山东理工大学 | Tooth-face contact-area quantized testing method |
| CN104112038A (en) * | 2014-06-25 | 2014-10-22 | 陕西高华知本化工科技有限公司 | Method for designing linear conjugate inner gearing pump tooth profile |
| CN104330065A (en) * | 2014-07-28 | 2015-02-04 | 河南科技大学 | Spiral bevel gear tooth surface curvature interference detection method |
| CN105156637A (en) * | 2015-09-18 | 2015-12-16 | 长安大学 | Skew line tooth surface gear transmission pair and tooth width geometric design method |
| CN106015516A (en) * | 2016-05-24 | 2016-10-12 | 北京航空航天大学 | Inside engaged gear tooth form design method based on B-spline engaging line |
| CN106767606A (en) * | 2017-03-21 | 2017-05-31 | 重庆大学 | Quimby pump rotor interference detection method based on rigging error |
| CN106958643A (en) * | 2017-05-11 | 2017-07-18 | 河南科技大学 | Gear tooth contact performance analysis method |
-
2017
- 2017-12-13 CN CN201711332595.0A patent/CN108120596B/en not_active Expired - Fee Related
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002005654A (en) * | 2000-06-20 | 2002-01-09 | Akira Yoshida | Measuring method for error in tooth plane of bevel bear |
| CN101025384A (en) * | 2006-02-18 | 2007-08-29 | 山东理工大学 | Tooth-face contact-area quantized testing method |
| CN104112038A (en) * | 2014-06-25 | 2014-10-22 | 陕西高华知本化工科技有限公司 | Method for designing linear conjugate inner gearing pump tooth profile |
| CN104330065A (en) * | 2014-07-28 | 2015-02-04 | 河南科技大学 | Spiral bevel gear tooth surface curvature interference detection method |
| CN105156637A (en) * | 2015-09-18 | 2015-12-16 | 长安大学 | Skew line tooth surface gear transmission pair and tooth width geometric design method |
| CN106015516A (en) * | 2016-05-24 | 2016-10-12 | 北京航空航天大学 | Inside engaged gear tooth form design method based on B-spline engaging line |
| CN106767606A (en) * | 2017-03-21 | 2017-05-31 | 重庆大学 | Quimby pump rotor interference detection method based on rigging error |
| CN106958643A (en) * | 2017-05-11 | 2017-07-18 | 河南科技大学 | Gear tooth contact performance analysis method |
Non-Patent Citations (2)
| Title |
|---|
| 方宗德: "HFT准双曲面齿轮的齿根过渡曲面和干涉、根切检验", 《机械传动》 * |
| 王斌: "盘刀加工等基圆锥齿轮干涉检验的截面曲线法", 《组合机床与自动化加工技术》 * |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108533686A (en) * | 2018-06-12 | 2018-09-14 | 中国地质大学（武汉） | Concave-convex engagement pure rolling bevel gear mechanism for intersecting axle transmission |
| CN108533686B (en) * | 2018-06-12 | 2020-01-17 | 中国地质大学（武汉） | Concave-convex mesh pure rolling bevel gear mechanism for crossed shaft transmission |
| CN109241613A (en) * | 2018-08-31 | 2019-01-18 | 西安交通大学 | A kind of cutter root relief parameter determination method of spiral bevel gear |
| 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 |
| CN109238200A (en) * | 2018-09-12 | 2019-01-18 | 中国航发哈尔滨东安发动机有限公司 | A method of detection bevel gear root bores parameter |
| 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 |
| CN111666641A (en) * | 2020-05-25 | 2020-09-15 | 重庆青山工业有限责任公司 | Method for calculating tooth surface parameters of straight bevel gear |
| CN111666641B (en) * | 2020-05-25 | 2024-04-05 | 重庆青山工业有限责任公司 | Calculation method for tooth surface parameters of straight bevel gear |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108120596B (en) | 2019-07-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108120596A (en) | A kind of spiral bevel gear root interference method of inspection | |
| CN107992698B (en) | Tooth surface contact analysis method for spiral bevel gear | |
| JP4376938B2 (en) | Cornu helical gear | |
| CN108873809B (en) | High-order tooth surface error correction method for spiral bevel gear | |
| CN109707822B (en) | Design method of small-modulus harmonic transmission meshing tooth form applied to robot and detector | |
| CN105156637B (en) | A kind of oblique line flank of tooth gear driving pair and facewidth geometric design method | |
| CN112541235B (en) | Universal design method for hypoid gear pair | |
| CN103732340A (en) | Optimization of face cone element for spiral bevel and hypoid gears | |
| CN109993464B (en) | Machining parameter optimization method for reducing mounting error sensitivity of hypoid gear | |
| CN109992877A (en) | A kind of method of gear pair geometrical contact analysis | |
| CN110966374A (en) | Design method of hypoid gear with large reduction ratio for high-precision robot | |
| WO2020252842A1 (en) | Design method based on actual load for tooth surface contact spot of gear | |
| CN105127521B (en) | A kind of hobboing cutter and processing method for being used to process Double Involute Gear | |
| Iñurritegui et al. | Numerical-experimental analysis of highly crowned spherical gear couplings working at high misalignment angles | |
| CN109446667B (en) | Method for calculating dynamic backlash of helical bevel gear pair | |
| CN109977579B (en) | Machine tool machining parameter optimization method for improving hypoid gear meshing quality | |
| CN110039123B (en) | Method for processing inverted cone teeth by variable-pressure-angle hob | |
| CN109014440B (en) | Forming method of involute variable-thickness gear slotting cutter | |
| CN109033669B (en) | Spiral bevel gear simulation machining modeling method based on universal motion parameter driving | |
| CN115221655B (en) | Method for evaluating transmission precision of helical non-circular gear | |
| CN108562256B (en) | Tooth top height measuring method for incomplete circular arc end in middle of tooth profile | |
| CN115789207A (en) | Method for modifying tooth profile of cylindrical involute gear in tooth direction | |
| Koulin et al. | A new profile roughness measurement approach for involute helical gears | |
| CN109284544B (en) | Helical bevel gear shape cooperative manufacturing parameter driving mixing reverse regulation and control method | |
| Markowski et al. | Tooth contact analysis of Novikov convexo-concave gears |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20190730 Termination date: 20191213 |