CN109002654A - A kind of design method moving synchronously driving error curve and the spiral bevel gear using driving error curve - Google Patents
A kind of design method moving synchronously driving error curve and the spiral bevel gear using driving error curve Download PDFInfo
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- CN109002654A CN109002654A CN201810969141.2A CN201810969141A CN109002654A CN 109002654 A CN109002654 A CN 109002654A CN 201810969141 A CN201810969141 A CN 201810969141A CN 109002654 A CN109002654 A CN 109002654A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
Abstract
The present invention proposes a kind of design method for moving synchronously driving error curve and the spiral bevel gear using driving error curve.There are two change tooth point to the driving error curve tool that moves synchronously of the invention, it is meant that the number for changing tooth impact is few；Adjacent drive error curve is very close in the slope for changing tooth point, it is meant that the intimate indifference of angular speed when changing tooth；It is engaging-in and nibble out a little close driving error point of inflexion on a curve, second dervative zero, it is meant that inertia dynamic loading is almost nil when changing tooth；Adjacent drive error curve that is engaging-in and nibbling out between a little moves synchronously, it is meant that load distribution among teeth nonuniformity coefficient reaches minimum.These characteristics will greatly reduce load on wheel tooth and change vibration and impact brought by tooth, improve load distribution among teeth, further increase the transmission performance of spiral bevel gear.
Description
Technical field
The present invention relates to gear transmission technology field, specially a kind of design method for moving synchronously driving error curve and
Using the spiral bevel gear of driving error curve.
Background technique
Spiral bevel gear is highly important driving parts in machine driving, in aircraft, naval vessel and other accurate machines
Using very extensive in tool.The transmission performance of spiral bevel gear is related with driving error curve and teeth contact, wherein passing
Dynamic error curve vibrates again to it and noise has bigger influence.It is said from kinematics angle, gear drive error is driven wheel reality
The difference of border corner and nominal corner, it is the function of driving wheel corner or time, and slope indicates relatively fast in gear drive
Degree variation.Said from aerodynamic point, vibration be due to ohject displacement or (and) speed generating period variation caused by；Impact
Caused by being velocity jump, vibration and impact generate noise.Gear-driven vibration, impact and noise are mainly derived from the gear teeth and nibble
Close vibration and impact.Intermeshing a pair of gear, the cyclically-varying of relative displacement and speed at gear teeth meshing generate tooth
Take turns mesh vibration；Relative velocity mutation when the gear teeth are engaging-in generates gear engagement impact.Driving error curve can indicate gear
Displacement and velocity variations in transmission process, adjacent drive error curve change the speed difference at tooth point can indicate gear impact
Degree, adjacent drive error curve can indicate the size of inertia force, adjacent drive error changing the angular acceleration at tooth point
Gap between curve can indicate the degree of irregularity of load distribution among teeth.Therefore, transmission is commonly used in Gear system dynamic
Error curve measures the severe degree of gear train mesh vibration and impact.
In order to improve the stationarity of Spiral Bevel Gear Transmission, reduces vibration and noise, researcher propose a variety of transmissions
Error curve.Litvin is in document " Methods of Synthesis and Analysis for Hypoid Gear-
Drives of"Formate"and"HeIixform".Journal of Mechanical Design,1981,103(1):83
The parabolic type driving error curve proposed in~110 " is conducive to linear impact caused by absorbing installation error.The U.S.
The engineer Stadtfeld of Gleason company has found after carefully studying symmetrical parabolic type driving error curve, Ci Zhongchuan
Although dynamic error curve adjacent teeth pair in transmission process, which is only undergone, is once changed tooth, change at tooth point that there are biggish speed ranks
Jump, the shock and vibration for changing tooth are larger.For this purpose, he is in document " The Ultimate Motion Graph.Journal of
Mechanical Design, 2000,122 (9): 317~322 " propose quadravalence driving error curve.
Quadravalence driving error is the biquadratic function about driving wheel corner, it has recorded the driving wheel gear teeth and is engaged to from entrance
Exit in engagement process, the corner undulate quantity of driven wheel with driving wheel corner changing rule.The engagement of a pair of of gear teeth generates one
Driving error curve.As soon as gear pair often turns over a tooth pitch, quadravalence driving error curve repeats once.Spiral bevel gear
Quadravalence driving error curve determined by following element:
1, there are two maximum point and a minimum points, maximum point to be located at pole for independent quadravalence driving error curve
Small value point two sides.
2, the slope in independent quadravalence driving error curve left maximum point left side and right maximum point right side graph.
3, the number of adjacent two quadravalences driving error intersections of complex curve.
4, the slope differences of the location of adjacent two quadravalences driving error intersections of complex curve and two curves in point of intersection.
The characteristics of quadravalence driving error curve is the impact generated when will change tooth, by the one of parabolic type driving error curve
Secondary large impact becomes the impact small three times of quadravalence driving error curve, it is desirable to the damage that the gear teeth are subject to by impact is reduced with this,
To be conducive to improve transmission stability and gear life.However, Stadtfeld proposes quadravalence driving error curve although reducing
The intensity of every Secondary Shocks, but increase the number of impact.It to be undergone when adjacent teeth exchanges tooth and change tooth three times.With regard to same tooth pair
For, it actually to be undergone six times in the engagement process from tooth root to tooth top and change tooth, wherein preceding occur three times when nipper and elder generation
Between guide tooth, after occur three times when between nipper and subsequent tooth.The quadravalence driving error curve for scrutinizing Stadtfeld type can also
Biggish relative velocity step is still had when it was found that changing tooth, change tooth be formed by impact be not well solved, so
Stadtfeld is changing tooth number and this pair of relative velocity step is conflicting, fails sufficiently in parameter designing that mutually restrict
Play the superiority of quadravalence driving error curve.
Summary of the invention
In order to solve the problems existing in the prior art, it is greatly reduced and changes tooth impact strength, further decrease spiral bevel gear biography
Vibration, impact and noise in dynamic improve load distribution among teeth, improve gear life, the present invention is on the basis of Stadtfeld
On, propose it is a kind of it is more excellent performance of move synchronously driving error curve, and give and move synchronously driving error curve
Design method, for improve spiral bevel gear transmission performance new thinking is provided.
The driving error curve tool proposed by the present invention that moves synchronously is there are two changing tooth point, it is meant that changes the number of tooth impact
It is few；Adjacent drive error curve is very close in the slope for changing tooth point, it is meant that the intimate indifference of angular speed when changing tooth；It is engaging-in
With nibble out a little close to driving error point of inflexion on a curve, second dervative zero, it is meant that inertia dynamic loading is almost nil when changing tooth；It nibbles
The adjacent drive error curve for entering and nibbling out between a little moves synchronously, it is meant that load distribution among teeth nonuniformity coefficient reaches most
It is small.These characteristics will greatly reduce load on wheel tooth and change vibration and impact brought by tooth, improve Transverse Load point
Match, further increases the transmission performance of spiral bevel gear.
The description of driving error curve is moved synchronously in the present invention:
In order to improve transmission properties, it is desirable to reduce change tooth number, reduce change tooth impact strength and Transverse Load
The degree of irregularity of distribution.Synchronous Transmission error curve proposed by the invention can be good at meeting these requirements.It has
Following features:
(1) intersection point of adjacent drive error curve is close to inflection point
Synchronous Transmission error curve designed by the present invention is made of the curved section that several convex-concaves connect.Convex-concave curved section
Joining place be inflection point.Angular acceleration at inflection point is zero.The intersection point of adjacent drive error curve is engaging-in with adjacent teeth pair
It puts and nibbles out and a little correspond to.The present invention makes engaging-in point and nibbles out a little almost to fall in inflection point, steadily changes tooth to the greatest extent to realize.
This is one of innovative point of the invention.
(2) slope differences of adjacent drive error curve point of intersection are minimum
Making the slope jack per line of adjacent drive error curve point of intersection, i.e., the trend of two driving error curves is consistent, and
Guarantee the angle at this between driving error curve near tangent close to 180 °, this will greatly reduce adjacent rodent population at this
Practical opposite angular velocity difference, be effectively reduced the shock and vibration for changing tooth generation.This is second innovative point of the invention.
(3) curved section between adjacent drive error curve intersection point is almost overlapped
The either first guide tooth of original Stadtfeld driving error curve to curve, when nipper is to curve or subsequent tooth
Larger to the gap between curve, this means that the load that adjacent two pairs of gear teeth are respectively shared also can be extremely uneven in actual motion
Weighing apparatus.And Synchronous Transmission error curve in engaging-in point and is nibbled out the adjacent drive error curve between a little and is almost overlapped after improving, this
Mean that in actual motion, no matter the size of plus load, adjacent two pairs of gear teeth can all engage simultaneously, this will greatly be dropped
The degree of irregularity of low load distribution among teeth.This is third innovative point of the invention.
Three above inventive point overcomes the deficiency of Stadtfeld driving error curve, improves Spiral Bevel Gear Transmission
Performance.
The implementation method of driving error curve is moved synchronously in the present invention
The driven wheel corner of spiral bevel gear is defined as driving error relative to the difference of its nominal corner.At the uniform velocity depending on driving wheel
Rotation, then the driving error of driven wheel forms driving error curve in company with the variation course of driving wheel corner.By driven wheel
After actual rotational angle presses Taylor series expansion at flank of tooth reference point, the first rank of Taylor series is moved on to the equation left side, equation
Right side is the expression formula of driving error.The item number that the series is included and the coefficient of each single item determine the shape of driving error curve
State.In general, driving error curve is made of several convex-concaves towards different curved sections.
Realize that the technical method of target of the present invention is made of following steps:
Step 1: using flank of tooth reference point as symmetric points, there are three the letters in period for construction tool in driving error curvilinear coordinate system
Humorous driving error curve；Its mathematic(al) representation is
Wherein a is the amplitude of driving error curve；T is the angular pitch of driving wheel,For the actual rotational angle of driving wheel,For
When the flank of tooth refers to point gearing, the actual rotational angle of driving wheel；
It sequentially takes 13 control points from left to right on simple harmonic quantity driving error curve, is four maximum point A respectively1、
A5、A9And A13, three minimum point A3、A7And A11Inflection point A on axis of abscissas is fallen in six2、A4、A6、A8、A10And A12；Wherein
Minimum point A7It is point corresponding with flank of tooth reference point；
Step 2: using the horizontal line where minimum point as symmetry axis, by three starting control point A1、A2And A3With three ends
Control point and three end of a period control points are symmetric to the lower section of symmetry axis, obtain A1’、A2’、A3’、A11’、A12' and A13', it obtains
The simple harmonic quantity type driving error curve of variation；
Step 3: to A1’、A2’、A3’、A4、A5、A6、A7、A8、A9、A10、A11’、A12' and A13' Cubic Spline Fitting is carried out,
And the driving error curve obtained after fitting is translated into a/2 to the negative direction of ordinate, it obtains initial when nipper is to single biography
Dynamic error curve；
Step 4: the initial nipper of working as that step 3 is obtained respectively translates one to single driving error curve to the left and to the right
Angular pitch respectively obtains first guide tooth to the driving error curve with subsequent tooth pair；
Step 5: with three control point A of starting1’、A2’、A3' and end three control point A11’、A12' and A13' seat
Mark is set to optimization design variable, establishes following multi-objective optimization design of power model and optimizes, obtains moving synchronously biography
Dynamic error curve:
WhereinIt indicates when nipper is in single driving error curve, control point AjThe second dervative at place；
It indicates when nipper is in single driving error curve, control point AjThe first derivative at place,Indicate first guide tooth to driving error
In curve, control point AjThe first derivative at place；It indicates when nipper is in single driving error curve, control point Aj’That locates is small
Corner is taken turns,Indicate first guide tooth in driving error curve, control point Aj’The steamboat corner at place.
Beneficial effect
The quadravalence driving error curve that Stadtfeld is proposed changes tooth frequency height, and the relative velocity step for changing tooth point is still inclined
Greatly, load distribution among teeth is not uniform enough, and transmission performance is to be improved.The present invention can improve curved-tooth bevel gear in terms of following three
The transmission performance of wheel:
(1) for adjacent drive error curve only there are two intersection point, tooth number of shocks is changed in reduction.
During gear drive, adjacent teeth pair changes tooth generation in the point of intersection of adjacent drive error curve.At each
Change tooth point, generally all can that there are speed of related movement is poor between engaging-in tooth pair, so as to cause meshing impact；Tooth is being nibbled out to it
Between generate to nibble out and impact because of the driving error of adjacent teeth pair and the elastic potential energy of release gear teeth accumulation.Frequency of impact and transmission miss
The number of hits of poor curve is directly proportional.Reduce number of hits, it is meant that reduce the number that mesh impact occurs for the gear teeth, accordingly decrease and nibble
The damage caused by the gear teeth is hit in syzygies.
(2) engaging-in and nibble out a little close inflection point, the slope of adjacent drive error curve point of intersection is almost equal, so that changing tooth
Inertia force and relative angle Velocity Step Technique all very littles at point change tooth bring shock and vibration to reduce.
Driving error slope of a curve represents the difference of driven wheel actual angular speed and its theoretical angular speed, changes phase at tooth point
Adjacent driving error slope of a curve difference then represents the difference for changing the practical relative velocity of tooth point.The practical relative speed difference of tooth point is changed to get over
Greatly, it is more violent to change tooth impact.In symmetrical parabolic type driving error curve, a driving error curve at tooth point is changed
Slope is positive, and another driving error slope of a curve is negative, and the difference for changing the practical speed of related movement of tooth point is very big, therefore changes tooth punching
It hits also very big.Stadtfeld exactly sees that symmetrical parabolic type driving error curve in this disadvantage for changing tooth point, proposes four
Rank driving error curve, and point out in order to reduce the impact for changing the generation of tooth point, at this between tangent line of adjacent drive error curve
Angle more preferably greater than 135 °, and this is only when changing the tangent line of tooth point adjacent drive error curve while being positive or being negative simultaneously
Just it is able to achieve.From in driving error curve graph, this requirement, which is equivalent to change tooth point, is located at adjacent two driving error curves
Ascent stage or descending branch.In the quadravalence driving error curve that Stadtfeld is proposed, there are three change adjacent drive error curve
Tooth point, wherein ascent stage and the descending branch changing tooth point and be located at adjacent drive error curve on the left side and the right, but ascent stage
With there is a curve just developing towards inflection point direction in descending branch, it is meant that this changes the angle between the tangent slope of tooth point at two
It is difficult to effectively expand；And tooth point is changed in remaining centre, but be ascent stage and the adjacent drive error of a driving error curve
It is bigger will to increase the angle difficulty changed at tooth point between driving error curve near tangent for the intersection point of curve descending branch.Namely
Say, three of the quadravalence driving error curve of Stadtfeld type change tooth point be all difficult to be effectively reduced change tooth bring impact.This
Outside, there are angular acceleration changing at tooth point for the quadravalence driving error curve that Stadtfeld is proposed, this necessarily brings inertia force, from
And aggravate to change the shock and vibration of tooth generation.Although the quadravalence driving error curve that Stadtfeld is proposed is driven parabolic type
Error curve has certain improvement, but it is clear that being also extremely improved space.
(3) the distance between adjacent drive error curve is very close, and effectively symmetrical load is between adjacent teeth pair
Distribution.
Gap between adjacent drive error curve indicates the load that two pairs of gear teeth in bi-tooth gearing section are undertaken
There are difference, and this difference can expand with the increase of the gap between driving error curve.This gap is reduced, is meaned
Reduce load distribution among teeth degree of irregularity.Original no matter first guide tooth of Stadtfeld driving error curve is to curve
With when nipper is between curve, or when nipper pair and subsequent tooth are between curve, there is larger gap, this means that
After gear teeth load, the small tooth of driving error to first contacting and can undertake biggish load, the big tooth of driving error to rear contact and
Lesser load can be undertaken, resulting adverse effect includes but is not limited to: the big leading generation of Contact Stress of Gear is glued
With spot corrosion, contact area it is big be easy to produce EDGE CONTACT etc..And the difference between improved driving error curve becomes smaller, very
To being almost overlapped, this is meant that in actual loaded operation, no matter the size of plus load, two pairs of gear teeth can all occurs simultaneously
Engagement, two pairs of gear teeth institutes are loaded almost equal, this is extremely advantageous to Contact Stress of Gear, balanced load distribution among teeth is improved.
Above 3 points are changed tooth number of shocks from reduction respectively, reduce and change tooth impact and dynamic loading and balanced Transverse Load minute
With three aspects, the transmission performance of spiral bevel gear is improved.
Applicant formerly also proposed that the quadravalence driving error curve of two kinds of spiral bevel gears was Chinese patent respectively
CN102661381A and Chinese patent CN103438186A, this two patents from adjacent teeth to engagement when change tooth number, adjacent
Two aspects of slope differences at driving error intersections of complex curve improve the transmission performance of spiral bevel gear, and the present invention is basic herein
On, further improvement has been done in terms of following three:
(1) the engaging-in point and nibbling out of being staggered is put to mitigate and change tooth impact.
During gear drive, adjacent teeth pair changes tooth generation in the intersection of adjacent drive error curve.Each
It is a to change tooth point, generally all can that there are speed of related movement is poor between engaging-in tooth pair, there are elastic potential energys nibbling out between tooth pair
Release, thus leads to gear angular velocity fluctuation.Tooth points are changed in reduction, inevitably facilitate the stationarity for improving gear operation.Two
The driving error curve that first patent proposes only has one and changes tooth point, it will change tooth points and reduce to minimum, but it is phase
The crosspoint of adjacent driving error curve, it means that it is both the previous engaging-in point for nibbling out point and latter tooth pair to tooth, i.e.,
It engaging-in point and nibbles out and a little coincides with the intersection.And driving error curve proposed by the present invention is seemed there are two intersection points, it is real
It is then equivalent to a crosspoint, this is almost to be overlapped to bring by the driving error curve between two intersection points to move synchronously characteristic
It is determined.It is latter that engagement is entered to tooth in first point of intersection, then tooth is moved synchronously with previous, is handed over until second
It is previous at point that engagement is exited to tooth.Therefore, first intersection point is the latter engaging-in point to tooth, and second intersection point is previous to tooth
Point is nibbled out, primary engaging-in plus primary nibble out is equivalent to once change tooth, and substantially there is no increases to change tooth number.Moreover, will
Engaging-in point and a distance that is a little staggered is nibbled out, avoids engaging-in flank of tooth slap and nibble out the release of point elasticity potential energy and coincide at one
Thus brought synergistic effect can further decrease and change tooth impact bring angular velocity fluctuation.
(2) it engaging-in point and nibbles out a little close to inflection point, slope of the adjacent drive error curve at this is almost equal, relative angle
Velocity Step Technique is minimum, changes tooth bring shock and vibration to reduce.
The quadravalence driving error curve that two first patents propose, adjacent drive error curve intersection point fall in the vertex of curve
At (maximum point), the impact for changing tooth generation is reduced.But the connection between driving error curve is smooth not enough, and when transmission changes
Tooth is not stable enough, relative velocity step and between cog movement can discontinuously generate shock and vibration.The present invention misses adjacent drive
The intersection point of poor curve is close to inflection point, in engaging-in point and the slope for nibbling out adjacent drive error curve at point because moving synchronously more
Close, it is engaging-in and nibble out and impact that this will greatly reduce the flank of tooth.
(3) first guide tooth pair with work as driving error curve between nipper pair or when the driving error between nipper pair and subsequent tooth pair
The difference of the distance between curve reduces.
The distance between slightly higher driving error curve and lower driving error curve difference are bright on driving error curve
It is aobvious to reduce.There are certain gaps between adjacent teeth pair for the quadravalence driving error curve of two first patents, this just represents
After the gear teeth load work, necessarily lead to the difference in load distribution among teeth.And improved driving error curve in engaging-in point and
It nibbles out between a little and is almost overlapped, this means that after actual motion load, it may appear that two pairs of gear teeth engage simultaneously, alleviate every
Loaded, the improvement teeth contact situation of one gear teeth.
Above 3 points put respectively from the engaging-in point and nibbling out of being staggered with reduce change tooth impact, reduce engaging-in point or nibble out put it is oblique
Rate and them is allowed to change that tooth impact, adjacent drive error curve is almost overlapped to reduce load distribution among teeth close to inflection point to reduce
These three aspects of degree of irregularity, illustrate this invention relative to improvement brought by two first patents.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures
Obviously and it is readily appreciated that, in which:
Fig. 1 is Stadtfeld driving error curve:
The type driving error curve is as shown in Figure 1.In figure, left-most curve (dotted line), intermediate curve (solid line) and the right are bent
Line (chain-dotted line) respectively indicate first guide tooth to, when nipper to subsequent tooth pair.Wherein, first guide tooth pair with when nipper to there are three friendships
Point (three, left side solid dot), when nipper pair and it is subsequent to tooth also there are three intersection point (three, the right hollow dots), leftmost friendship
The intersection point (hollow dots) of point (solid dot) and rightmost bilateral symmetry substantially centered on coordinate origin.These intersection points be all for
The position of tooth is changed between expression adjacent teeth pair.
Fig. 2 is the quadravalence driving error curve based on spiral bevel gear in Chinese patent CN102661381A:
Only one intersection point of adjacent two curves of the quadravalence driving error curve, reduces and changes the number of teeth, reduce impact and
Vibration frequency, and adjacent two curves are very close in the slope of point of intersection, so that vibration and impact very little when changing tooth, into one
Step improves the transmission performance of spiral bevel gear.Left-most curve (dotted line), intermediate curve (solid line) and the right curve (chain-dotted line) point
Not Biao Shi first guide tooth to, when nipper to subsequent tooth pair.Wherein, to there is an intersection point, (left side is solid with nipper is worked as first guide tooth pair
Point), when nipper pair and it is subsequent also have to tooth an intersection point (the right hollow dots), two o'clock centered on coordinate origin bilateral symmetry.
These intersection points are all used to indicate that the position that tooth is changed between adjacent teeth pair.Wherein, Fig. 2 (a) and Fig. 2 (b) is respectively to rise
Section and descending branch change tooth.
Fig. 3 is the modified quadravalence driving error curve based on spiral bevel gear in Chinese patent CN103438186A:
In figure left-most curve, intermediate curve and the right curve respectively indicate first guide tooth to, when nipper to subsequent tooth pair.Its
In, first guide tooth pair subsequent has when nipper pair and also one to tooth with when nipper is to there is an intersection point (convex peak vertex, green solid dot)
A intersection point (convex peak vertex, green solid dot), the intersection point on the left side and the intersection point on the right left and right pair substantially centered on coordinate origin
Claim.These intersection points are all used to indicate that the position that tooth is changed between adjacent teeth pair.For Fig. 2, further reduce
Slope differences of the adjacent drive error curve in point of intersection.
Fig. 4 is Synchronous Transmission error curve of the invention；
Fig. 5 is first guide tooth pair and the driving error curve partial enlarged view for working as nipper pair in the present invention；
Fig. 6 is the driving error curve partial enlarged view in the present invention when nipper pair and subsequent tooth pair；
Left-most curve (dotted line), intermediate curve (solid line) and the right curve (chain-dotted line) respectively indicate first guide tooth in Fig. 4~6
To, when nipper to subsequent tooth pair.Wherein:
1) first guide tooth pair and the first intersection point (first left solid dot) when nipper pair is when the engaging-in point of nipper pair, this
When second dervative close to zero, first guide tooth pair and the driving error curve slope here when nipper pair are almost equal, and
The first derivative jack per line of two curves.
2) first guide tooth pair nibbles out point with second intersection point (second left solid dot) when nipper pair for first guide tooth pair,
For second dervative at this time also close to zero, first guide tooth pair and the driving error curve slope here when nipper pair are same intimate
It is equal, and the first derivative jack per line of two curves.
3) working as the engaging-in point of nipper pair and nibbling out between a little for first guide tooth pair, when the transmission of nipper pair and first guide tooth pair misses
Poor curve is almost overlapped.
4) when the intersection point between nipper pair and subsequent tooth pair is also there are two (two hollow dots on the right), mutually turning therebetween
Change and motion conditions, with when nipper pair with elder generation guide tooth to identical.
Fig. 7 is simple harmonic quantity type driving error curve；
Fig. 8 is the simple harmonic quantity type driving error curve of variation；
Fig. 9 is the single driving error curve tentatively obtained；
Figure 10 is adjacent drive error curve.
Specific embodiment
The embodiment of the present invention is described below in detail, the embodiment is exemplary, it is intended to it is used to explain the present invention, and
It is not considered as limiting the invention.
(1) formation basic theory of driving error
Spiral bevel gear is the transmission of point contact Local conjugation, and driving error is defined as
In formula--- the actual rotational angle of driving wheel, driven wheel
--- when the flank of tooth refers to point gearing, the actual rotational angle of driving wheel and driven wheel
z1、z2--- the number of teeth of driving wheel, driven wheel
First item in formula (1)Corner when for driven wheel relative to reference point gearing,For actively
Corner when taking turns relative to reference point gearing,For the driven wheel theory corner determined by nominal transmission ratio.Wherein,
Driven wheel relative rotationIt is driving wheel relative rotationFunction, can generally be written as
Its value is related with driving wheel axial modification mode and profiling quantity.
(2) progression form of driving error
Driven wheel actual rotational angle formula (2) is launched into Taylor series at reference point
The instantaneous transmission ratio at reference point is generally taken to be equal to nominal transmission ratio, then the driving error of progression form is
Or it is abbreviated as
A in formula --- the second dervative of driving error curve or the first derivative of instantaneous transmission ratio
B --- three order derivatives of driving error curve or the second dervative of instantaneous transmission ratio
The Fourth-Derivative of C --- driving error curve or three order derivatives of instantaneous transmission ratio
--- it is higher than the sum of five rank items
When the only first item of modus ponens (5) to get the second order driving error curve proposed to Litvin
When modus ponens (5) to Section 3 to get the quadravalence driving error curve proposed to Stadtfeld
(3) driving error curvilinear coordinate system
The coordinate system for describing driving error curve is cartesian cartesian coordinate system, and axis of abscissas is driving wheel corner, is indulged
Reference axis is driven wheel driving error.When the abscissa of the flank of tooth reference point of nipper pair is zero, the flank of tooth reference point of other teeth pair
Continuation is translated along abscissa axial sides according to angular pitch and is obtained.Define the fluctuating range in driving error curve practical function section
For driving error amplitude, value rotates angular acceleration and jerk according to driven wheel and substantially chooses in 2 "~20 " ranges.
(4) Synchronous Transmission error curve generation method
1) using flank of tooth reference point as symmetric points, there are three the simple harmonic quantity driving error curves in period for construction tool, as shown in Figure 7.
Its mathematic(al) representation is
In formula, a is the amplitude of driving error curve；T is the angular pitch of driving wheel, it is equal to 2 π/z1。
On simple harmonic quantity driving error curve, 13 control points are sequentially taken from left to right, they are four maximum respectively
Point (A1、A5、A9And A13), three minimum point (A3、A7And A11) and six fall in inflection point (A on axis of abscissas2、A4、A6、A8、A10
And A12).Wherein, minimum point A7It is exactly point corresponding with flank of tooth reference point.
2) by three starting control point (A in Fig. 71、A2And A3) and three end of a period control point (A11、A12And A13) be symmetric to
Using the horizontal line where minimum point as the lower section of symmetry axis, A is obtained1’、A2’、A3’、A11’、A12' and A13', to be formed such as
The simple harmonic quantity type driving error curve of variation shown in Fig. 8.
3) above-mentioned 13 control points of Cubic Spline Fitting are used, can allow three control points of starting in fit procedure
(A1’、A2' and A3') and end three control point (A11’、A12' and A13') drawn close slightly to axis of abscissas and axis of ordinates.So
Afterwards, driving error curve is translated into a/2 to the negative direction of ordinate, tentatively obtains single driving error curve, as shown in Figure 9.
4) it maintains to work as nipper to the constant of driving error curve, it is respectively translated to an angular pitch to the left and to the right, respectively
First guide tooth is obtained to the driving error curve with subsequent tooth pair, as shown in the chain-dotted line and dotted line in Figure 10.
5) with three pre-control point A of starting1'~A3' and end three pre-control point A11'~A13' coordinate position be it is excellent
Change design variable, constrains this six pre-control points and drawn close slightly towards axis of ordinates and axis of abscissas, with first guide tooth in A4And A6Place
Close to inflection point, first guide tooth pair and work as nipper in A4And A6The slope at place is equal, first guide tooth pair with when nipper is in A3'~A7It
Between driving error curve as close to for objective function, establish following multi-objective optimization design of power model:
In formula, superscript p and c respectively indicate first guide tooth to when nipper pair；Subscript i or iAjIndicate driving error curve
Discrete point serial number.The meaning of other symbols is the same.
Driving error curve after optimization is as shown in Figure 4.
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective
In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.
Claims (2)
1. a kind of design method for moving synchronously driving error curve, it is characterised in that: the following steps are included:
Step 1: using flank of tooth reference point as symmetric points, there are three the simple harmonic quantities in period to pass for construction tool in driving error curvilinear coordinate system
Dynamic error curve；Its mathematic(al) representation is
Wherein a is the amplitude of driving error curve；T is the angular pitch of driving wheel,For the actual rotational angle of driving wheel,For the flank of tooth
When with reference to point gearing, the actual rotational angle of driving wheel；
It sequentially takes 13 control points from left to right on simple harmonic quantity driving error curve, is four maximum point A respectively1、A5、A9
And A13, three minimum point A3、A7And A11Inflection point A on axis of abscissas is fallen in six2、A4、A6、A8、A10And A12；It is wherein minimum
It is worth point A7It is point corresponding with flank of tooth reference point；
Step 2: using the horizontal line where minimum point as symmetry axis, by three starting control point A1、A2And A3It is controlled with three ends of a period
System point and three end of a period control points are symmetric to the lower section of symmetry axis, obtain A1’、A2’、A3’、A11’、A12' and A13', it is made a variation
Simple harmonic quantity type driving error curve；
Step 3: to A1’、A2’、A3’、A4、A5、A6、A7、A8、A9、A10、A11’、A12' and A13' Cubic Spline Fitting is carried out, and will
The driving error curve obtained after fitting translates a/2 to the negative direction of ordinate, obtains initial nipper of working as and misses to single transmission
Poor curve；
Step 4: the initial nipper of working as that step 3 is obtained respectively translates a tooth pitch to single driving error curve to the left and to the right
Angle respectively obtains first guide tooth to the driving error curve with subsequent tooth pair；
Step 5: with three control point A of starting1’、A2’、A3' and end three control point A11’、A12' and A13' coordinate bit
It is set to optimization design variable, establish following multi-objective optimization design of power model and is optimized, obtains moving synchronously transmission mistake
Poor curve:
WhereinIt indicates when nipper is in single driving error curve, control point AjThe second dervative at place；Expression is worked as
Nipper is in single driving error curve, control point AjThe first derivative at place,Indicate first guide tooth to driving error curve
In, control point AjThe first derivative at place；It indicates when nipper is in single driving error curve, control point Aj’The small rotation at place
Angle,Indicate first guide tooth in driving error curve, control point Aj’The steamboat corner at place.
2. a kind of using the spiral bevel gear for moving synchronously driving error curve, it is characterised in that: described to move synchronously transmission mistake
Poor curve is to move synchronously driving error curve using what step 1 method designed.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI672448B (en) * | 2019-01-07 | 2019-09-21 | 正修學校財團法人正修科技大學 | Design method of point contact cosine helical gear transmission mechanism of fourth-order transmission error |
| CN110285203A (en) * | 2019-06-12 | 2019-09-27 | 北京工业大学 | A kind of harmonic speed reducer multi-tooth meshing load distributed model design method |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103438186A (en) * | 2013-08-27 | 2013-12-11 | 西北工业大学 | Four-order transmission error curve design method based on spiral bevel gears |
-
2018
- 2018-08-23 CN CN201810969141.2A patent/CN109002654B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103438186A (en) * | 2013-08-27 | 2013-12-11 | 西北工业大学 | Four-order transmission error curve design method based on spiral bevel gears |
Non-Patent Citations (2)
| Title |
|---|
| YANMING MU等: "A novel tooth surface modification method for spiral bevel gears with higher-order transmission error", 《MECHANISM AND MACHINE THEORY》 * |
| 苏进展等: "弧齿锥齿轮四阶传动误差的设计", 《华南理工大学学报(自然科学版)》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI672448B (en) * | 2019-01-07 | 2019-09-21 | 正修學校財團法人正修科技大學 | Design method of point contact cosine helical gear transmission mechanism of fourth-order transmission error |
| CN110285203A (en) * | 2019-06-12 | 2019-09-27 | 北京工业大学 | A kind of harmonic speed reducer multi-tooth meshing load distributed model design method |
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