CN104074949B - Elastic interlayer type vibration-reduction gear and the method reducing gear drive error - Google Patents
Elastic interlayer type vibration-reduction gear and the method reducing gear drive error Download PDFInfo
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- CN104074949B CN104074949B CN201410274458.6A CN201410274458A CN104074949B CN 104074949 B CN104074949 B CN 104074949B CN 201410274458 A CN201410274458 A CN 201410274458A CN 104074949 B CN104074949 B CN 104074949B
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Classifications
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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
- F16H55/14—Construction providing resilience or vibration-damping
- F16H55/16—Construction providing resilience or vibration-damping relating to teeth only
-
- 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
- F16H55/12—Toothed members; Worms with body or rim assembled out of detachable parts
-
- 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
- F16H55/17—Toothed wheels
Abstract
The present invention provides a kind of elastic interlayer type vibration-reduction gear and uses the method reducing gear drive error of this gear.Described elastic interlayer type vibration-reduction gear includes: gear matrix, described gear matrix includes circular body and the equally distributed multiple gear teeth base portions of circumferencial direction along circular body;Involute contour body, the both sides of each in multiple gear teeth base portions are respectively arranged with described involute contour body;With elastic interlayer, described elastic interlayer is arranged between gear teeth base portion and involute contour body in a sealing fashion so that each gear teeth base portion forms gear teeth with the involute contour body of both sides and elastic interlayer.The vibration-reduction gear of the present invention can reduce even eliminate vibration by arranging elastic interlayer, and then reduces the driving error of gear.Additionally, the gear of the present invention is owing to using fabricated structure, if some gear teeth serious wear or infringement, the most only need to change an involute contour body, thus provide cost savings, easy and simple to handle and shortening maintenance time.
Description
Technical field
The present invention relates to gear drive field, more particularly, to a kind of elasticity for reducing gear drive error every
Laminar vibration-reduction gear and method.
Background technology
Vibration, noise and comfortableness (NVH) are each big car load manufacture of international automobile industry and parts enterprises concern
One of problem.Gear, as the important drive disk assembly of modern automobile industry, is the main vibration source in car running process and noise
One of source, the dynamic behavior of gear and service behaviour have important impact to car load.A pair actual meshed gears, can not
There is various error with avoiding, such as profile error, base pitch error, central moment error etc., thus make actual engagement process become
Different.These variations will make involute gear produce the biggest vibration, dynamic loading and noise, the most seriously shadow in transmission process
Ring the transmission quality of gear.The vibration of gear not only affects the failure mode of internal gear, such as: breaking off gear teeth, the flank of tooth
Spot corrosion and peeling, tooth face agglutination and tooth root crackle etc., but also the resonance of other system of automobile can be caused, such as brakes
And steering, thus the reliability of these systems and the safety of car load are had influence on.The prior art indicate that, car load probably has
The failure problems of 40% is the vibration by change speed gear box and noise causes, and each major company has the research and development expense of nearly 30% to consume to exist
Solve in the problem of this aspect.
The produced vibration of pinion rotation can directly reflect pinion rotation inhomogeneities, and the transmission to drive system misses
Difference, noise important.Therefore, the vibration how reducing gear train is an up gear drive quality, reduces transmission by mistake
Difference and an effective way of noise, this also becomes those skilled in the art's urgency technical issues that need to address.
Chinese patent ZL200720185373.6 provides a kind of vibration and noise reducing gear, and this gear is by gear mass, teeth group
Becoming, the wheel abdomen between tooth root and fixing hole cylindrical is uniformly distributed and arranges multiple through hole, in through hole, interference fit is equipped with foam
Aluminum casting resin.The structure of the vibration and noise reducing gear disclosed in this patent documentation is only suitable for discoid flat gear, and
This vibration and noise reducing structure processed complex, effect of vibration and noise reduction is undesirable.
Additionally, existing gear is overall structure.If some gear teeth serious wear or infringement, then need to change
Whole gear, thus increase cost and maintenance time is long.In view of the problems referred to above of the prior art, need one processing simple
And can more effectively reduce gear and the gear error computational methods of gear drive error.
Summary of the invention
In order to solve the problems referred to above, the present invention provides a kind of elastic interlayer type vibration-reduction gear and uses this gear to reduce tooth
The method of wheel driving error.The elastic interlayer type vibration-reduction gear of the present invention can reduce even to eliminate shake by arranging elastic interlayer
Dynamic, and then reduce the driving error of gear.
According to an aspect of the present invention, a kind of elastic interlayer type vibration-reduction gear includes: gear matrix, described gear matrix
The equally distributed multiple gear teeth base portions of circumferencial direction including circular body with along circular body;Involute contour body, multiple
The both sides of each in gear teeth base portion are respectively arranged with described involute contour body and elastic interlayer, and described elastic interlayer is with close
Envelope mode is arranged between gear teeth base portion and involute contour body so that each gear teeth base portion and the involute contour body of both sides
Gear teeth are formed with elastic interlayer.
Elastic interlayer can be between gear teeth base portion and involute contour body.
Further, elastic interlayer can pass through acrylate AB glue, QN-906AB glue, QN-505AB glue or KEYDAK
(KD-340) anoxia glue is between gear teeth base portion and involute contour body.
Alternatively, elastic interlayer can be welded between gear teeth base portion and involute contour body.
Further, during described welding includes laser welding, argon arc welding, plasma weldering, the weldering of infrared wire bonding, vacuum electric bundle
Any welding.
Elastic interlayer is made up of elastomeric material.
The rigidity of elastomeric material is in the range of 10E3~10E8N/m.
Elastomeric material can be chliorinated polyvinyl chloride, polymer rubber alloy, aluminium alloy or copper alloy.
Elastic interlayer is sized such that width is transverse tooth thickness 0.01~0.3 times of elastic interlayer, elastic interlayer
An a length of fully teeth height.
According to another aspect of the present invention, the above-mentioned elastic interlayer type vibration-reduction gear of a kind of use reduces gear drive error
Method comprise the following steps: S1: derive only with the gear drive error computing formula of oscillating component;S2: derive only with
The two-freedom kinetics equation of the elastic interlayer type vibration damping driving gear of oscillating component, and obtain driving gear matrix steady state solution
Amplitude;S3: by the elastic interlayer material chosen, the amplitude of driving gear matrix steady state solution is reduced and trend towards null value;With
S4: set up the two-freedom kinetics equation of elastic interlayer type vibration damping driven gear according to S2 step and S3 step, choose elasticity
The steady state solution of elastic interlayer type vibration damping driven gear matrix is reduced and trends towards null value by interlayer material, thus makes according to S1 step
Driving error with flexible interlayer type vibration-reduction gear system reduces and trends towards null value.
Step S1 farther includes:
The driving error of elastic interlayer type vibration-reduction gear represents with following formula:
X (t)=Rppθ1(t)-Rpgθ3(t) (1)
Wherein, RppAnd RpgIt is respectively the driving gear in the most intermeshing a pair elastic interlayer type vibration-reduction gear and driven
The pitch radius of gear, θ1(t) and θ3T () is respectively the angular displacement of the matrix of driving gear and driven gear;
The angular displacement of the matrix of driving gear and driven gear includes the position, angle that the angular displacement at the uniform velocity changed and vibration cause
Move, following formula represent:
Wherein,The angular displacement at the uniform velocity changed for elastic interlayer type vibration damping driving gear and driven gear,For elasticity
The angular displacement that interlayer type vibration damping driving gear and driven gear cause due to vibration, ω1,3Angular velocity and ω for vibration1,3=2 π
n1,3/ 60, n1,3For elastic interlayer type vibration damping driving gear and the rotating speed of the matrix of driven gear;
For a pair normal meshed gears there is below equation:
Equation (3) is substituted in formula (1) and obtains gear drive error computing formula (4):
S2 step farther includes:
According to the kinetics equation that dAlembert principle acquisition is following:
Wherein, θ1And θ2It is respectively angular displacement and the angle of involute contour body of elastic interlayer type vibration damping driving gear matrix
Displacement;k1Torsional rigidity for gear matrix;k2Torsional rigidity for elastic interlayer;TmAnd TpIt is respectively pair of engaged gears
The moment of resistance that the meshing resistance square at the uniform velocity changed and vibration cause;ToFor the engagement moment of gear, To=Fo×RPp,Wherein FoFor
Engagement force;I1Rotary inertia for driving gear;I2For involute contour body relative to the rotary inertia of gear centre, this rotation
The value of inertia is determined by formula for translation of axis (7):
I2=mL2+I20 (7)
Wherein, m is the quality of involute contour body, and L is the center of mass point o ' length to gear centre of the involute of profile body
Degree, I20For the involute contour body rotary inertia relative to self center of mass point o '.
Further, formula (5) and (6) are carried out following coordinate transform, to eliminate the at the uniform velocity change in formula (5) and (6)
Change part:
Coordinate (8) is substituted in formula (5) and (6) and obtains below equation:
The general solution of equation group is expressed as:
Formula (11) is substituted into formula (9) and (10) and obtains following driving gear matrix and involute contour body steady state solution
Amplitude:
Wherein, It is respectively elastic interlayer type vibration damping driving gear and the amplitude of driven gear.
S3 step farther includes: according to known involute contour body relative to the rotary inertia I of gear centre2And bullet
Property interlayer type vibration damping driving gear angular velocity of vibration ω1Choose elastic interlayer material k2, make the rigidity of elastic interlayer material meet with
Lower equation:
By equation (14) substitution (13) acquisition below equation:
Now, elastic interlayer type vibration damping driving gear is by moment produced by elastomeric materialWith elastic interlayer type
Oscillating component moment T of vibration damping driving gear matrixpEquivalence is reversely cancelled out each other so that according to formula (12), elastic interlayer
The oscillating component amplitude of formula vibration damping driving gear matrix is
In step s 4, by the angular displacement of the matrix of elastic interlayer type vibration damping driven gear3, angular velocity of vibration ω3And base
Torsional rigidity k of body3Replace θ1、ω1And k1Substitute into formula and equation (5)-(15), thus it is driven to obtain elastic interlayer type vibration damping
The oscillating component amplitude of gear matrix is
When meeting formula (16) and (17), obtain the driving error of gear according to gear drive error computing formula (4)
For:
Accompanying drawing explanation
The explanation of embodiment will be clearly appeared from by above and other aspect and the feature of the present invention from below in conjunction with accompanying drawing, its
In:
Fig. 1 is the mesh schematic representation of the elastic interlayer type vibration-reduction gear of a pair according to the present invention;
Fig. 2 is the signal of the structure of the gear matrix showing elastic interlayer type vibration-reduction gear according to embodiments of the present invention
Figure;
Fig. 3 is the enlarged diagram of the involute contour body of elastic interlayer type vibration-reduction gear according to embodiments of the present invention;
And
Fig. 4 is the schematic diagram of the elastic interlayer of elastic interlayer type vibration-reduction gear according to embodiments of the present invention.
Detailed description of the invention
Describe illustrative, the non-limiting example of the present invention with reference to the accompanying drawings in detail, carry out according to the present invention
Further illustrate.
Fig. 1 shows the mesh schematic representation of the elastic interlayer type vibration-reduction gear of a pair according to the present invention, wherein driving gear 1
It is meshed with driven gear 2.Here, as a example by driving gear 1, describe the elastic interlayer according to the present invention in detail with reference to Fig. 1-4
The structure of formula vibration-reduction gear.
Gear 1 includes gear matrix 10, involute contour body 11 and elastic interlayer 12.Gear matrix 10 includes circular body
13 and equally distributed multiple gear teeth base portions 14 of circumferencial direction along circular body 13.See Fig. 3, in multiple gear teeth base portions 14
The both sides of each be respectively arranged with involute contour body 11.Elastic interlayer 12 be arranged in a sealing fashion gear teeth base portion 14 with
Between involute contour body 11 so that each gear teeth base portion 14 is formed with the involute contour body 11 of both sides and elastic interlayer 12
One gear teeth of gear.
Elastic interlayer 12 is made up of elastomeric material.In order to make gear obtain good effectiveness in vibration suppression, the rigidity of elastomeric material
Preferably in the range of 10E3~10E8N/m.Elastomeric material can be such as chliorinated polyvinyl chloride, polymer rubber alloy,
Aluminium alloy or the material of copper alloy, be merely illustrative at this.According to an example, elastic interlayer 12 is pasted onto gear teeth base portion
Between 14 and involute contour body 11.Elastic interlayer 12 can use various adhesive to paste, such as pass through acrylate AB glue,
QN-906AB glue, QN-505AB glue or KEYDAK (KD-340) anoxia glue are at described gear teeth base portion and described involute contour
Between body.It should be noted that the adhesive that elastic interlayer is used is not limited to this, and any glue commonly used in the art can be used
Stick.Alternatively, elastic interlayer 12 can also be welded between gear teeth base portion 14 and involute contour body 11.Such as, described
Welding includes that any one of laser welding, argon arc welding, plasma weldering, infrared wire bonding, vacuum electric bundle weldering are welded, and only makees at this
Do not represent for example enumerates and be limited to above-mentioned listed welding manner.But, elastic interlayer and gear teeth base portion and involute contour
The fit system of body is not limited to this, can use any sealing fit system commonly used in the art.
See Fig. 4, show schematically show the elastic interlayer of the elastic interlayer type vibration-reduction gear according to the present invention.A is bullet
Property interlayer width in a circumferential direction, b is the length of elastic interlayer, the length that i.e. elastic interlayer extends to tooth top from tooth root.
According to the present invention, being preferably sized so that 0.01~0.3 times that a is transverse tooth thickness of elastic interlayer, b is a fully teeth height.
The gear matrix of the elastic interlayer type vibration-reduction gear according to the present invention primarily serves transmission from the power on power transmission shaft
Square effect, and linked together with involute contour body by elastic interlayer, thus form elastic interlayer type vibration-reduction gear.One
Gear engages transmitting movement and power by involute contour body with the involute contour body conjugation of another gear.Elastic interlayer
It is arranged in a sealing fashion between gear matrix and involute contour body, by vibration isolation material by elastic vibration isolation gear matrix
Oscillating component is delivered on involute contour body, thus suppresses the mesh vibration of gear, reduces rotational noise, is particularly suited for height
The actuating device of precision.The elastic interlayer type vibration-reduction gear of the present invention uses fabricated structure, can be with material customary in the art
Material, processing mode and heat treatment method manufacture gear matrix and profile body.Additionally, due to this fabricated structure, if certain
One gear teeth serious wear or infringement, the most only need to change an involute contour body just, without changing whole tooth
Wheel, thus provide cost savings, easy and simple to handle and shorten maintenance time.Therefore, gear teeth processing technology is good, applies simple technique
Just can complete Hardened gear face and high-precision Gear Processing, thus improve the bearing capacity of actuating device, extend the use of gear pair
Life-span.
The elastic interlayer type vibration-reduction gear of the present invention can reduce even eliminate vibration by arranging elastic interlayer, and then fall
The driving error of low gear.It follows that explanation is reduced gear drive according to the use elasticity interlayer type vibration-reduction gear of the present invention
The method of error.
The method reducing gear drive error according to the present invention comprises the following steps:
S1: derive only with the gear drive error computing formula of oscillating component;
S2: the only two-freedom kinetics equation of elastic interlayer type vibration damping driving gear with oscillating component of deriving, and
Obtain the amplitude of driving gear matrix steady state solution;
S3: by the elastic interlayer material chosen, the amplitude of driving gear matrix steady state solution is reduced and trend towards null value;
With
S4: set up the two-freedom kinetics equation of elastic interlayer type vibration damping driven gear according to S2 step and S3 step,
Choose elastic interlayer material the steady state solution of elastic interlayer type vibration damping driven gear matrix to be reduced and trend towards null value, thus according to
S1 step makes the driving error of band flexible interlayer type vibration-reduction gear system reduce and trend towards null value.
It follows that will be explained in step S1.Generally, the driving error of elastic interlayer type vibration-reduction gear is with following formula table
Show:
X (t)=Rppθ1(t)-Rpgθ3(t) (1)
Wherein, RppAnd RpgIt is respectively the driving gear in the most intermeshing a pair elastic interlayer type vibration-reduction gear and driven
The pitch radius of gear, θ1(t) and θ3T () is respectively the angular displacement of the matrix of driving gear and driven gear.According to the present invention,
The angular displacement of the matrix of driving gear and driven gear includes the angular displacement that the angular displacement at the uniform velocity changed and vibration cause, by following
Formula represents:
Wherein,The angular displacement at the uniform velocity changed for elastic interlayer type vibration damping driving gear and driven gear,For bullet
Property interlayer type vibration damping driving gear and driven gear due to the angular displacement that causes of vibration, ω1,3Angular velocity and ω for vibration1,3=
2πn1,3/ 60, n1,3For elastic interlayer type vibration damping driving gear and the rotating speed of the matrix of driven gear.
For a pair normal meshed gears, there is below equation:
Equation (3) is substituted in formula (1) and obtains gear drive error computing formula (4):
According to one embodiment of present invention, in S2 step, kinetics equation can obtain according to dAlembert principle.
Described kinetics equation can be:
Wherein, θ1And θ2It is respectively angular displacement and the angular displacement of involute contour body of elastic interlayer type vibration damping driving gear;
k1Torsional rigidity for gear matrix;k2Torsional rigidity for elastic interlayer;TmAnd TpIt is respectively the at the uniform velocity change of pair of engaged gears
The moment of resistance that the meshing resistance square changed and vibration cause;ToFor the meshing resistance square of gear, To=Fo×Rpp, wherein FoFor engagement
Power;I1Rotary inertia for driving gear;I2It is used to relative to the rotary inertia of gear centre, described rotation for involute contour body
The value of amount is determined by formula for translation of axis (7):
I2=mL2+I20 (7)
Wherein, m is the quality of involute contour body, and L is the center of mass point o ' length to gear centre of the involute of profile body
Degree, I20For the involute contour body rotary inertia (as shown in Figure 3) relative to self center of mass point o '.
Formula (5) and (6) are carried out following coordinate transform, to eliminate the at the uniform velocity changing unit in formula (5) and (6):
Then, coordinate (8) is substituted into acquisition below equation in formula (5) and (6):
The general solution of equation group is expressed as:
Formula (11) is substituted in formula (9) and (10) and obtains following driving gear matrix and involute contour body stable state
The amplitude solved:
Wherein,KnowIt is respectively elastic interlayer type vibration damping driving gear and the amplitude of driven gear.
In S3 step, according to known involute contour body relative to the rotary inertia I of gear centre2With elastic interlayer
Formula vibration damping driving gear angular velocity of vibration ω1Choose elastic interlayer material k2, make the rigidity of elastic interlayer material meet such as the following
Formula:
k2=I2ω1 2 (14)。
Then, equation (14) is substituted into (13) acquisition below equation:
Now, elastic interlayer type vibration damping driving gear is by moment produced by elastomeric materialWith elastic interlayer type
Oscillating component moment T of vibration damping driving gear matrixpEquivalence is reversely cancelled out each other so that according to formula (12), elastic interlayer
The oscillating component amplitude of formula vibration damping driving gear matrix is
Further, in step s 4, by the angular displacement of the matrix of elastic interlayer type vibration damping driven gear3, angle of throw speed
Degree ω3Torsional rigidity k with matrix3Replace θ1、ω1And k1Substitute into formula and equation (5)-(15), the most permissible
The oscillating component amplitude obtaining elastic interlayer type vibration damping driven gear matrix is
The derivation of driven gear is identical with the derivation of driving gear, will not be described in great detail at this.
When meeting formula (16) and when (17) zero, obtain the transmission of gear by mistake according to gear drive error computing formula (4)
Difference is:
The method reducing gear drive error according to the present invention uses elastic interlayer type vibration-reduction gear, is had by selection
The elastomeric material of certain rigidity forms elastic interlayer so that the amplitude of the oscillating component of driving gear matrix and driven gear matrix
Reduce and trend towards null value, and then gear-driven error can be reduced, gear drive error can be reduced the most ideally
To zero.
Although the exemplary embodiments of the present invention is illustrated, but it is clear that it will be understood by those skilled in the art that
Can be changed without departing substantially from the case of spirit and principles of the present invention, its scope is in claims and its equivalent
It is defined.
Claims (16)
1. an elastic interlayer type vibration-reduction gear, including:
Gear matrix, described gear matrix includes circular body and equally distributed many along the circumferencial direction of described circular body
Individual gear teeth base portion;
Involute contour body, the both sides of each in the plurality of gear teeth base portion are respectively arranged with described involute contour body;
With
Elastic interlayer, described elastic interlayer is arranged between described gear teeth base portion and described involute contour body in a sealing fashion,
Each described gear teeth base portion is made to form gear teeth with the involute contour body of both sides and elastic interlayer.
Elastic interlayer type vibration-reduction gear the most according to claim 1, wherein, described elastic interlayer is pasted onto described gear teeth base
Between portion and described involute contour body.
Elastic interlayer type vibration-reduction gear the most according to claim 2, wherein, described elastic interlayer is by acrylate AB
Glue, QN-906AB glue, QN-505AB glue or KEYDAK (KD-340) anoxia glue are at described gear teeth base portion and described involute
Between profile body.
Elastic interlayer type vibration-reduction gear the most according to claim 1, wherein, described elastic interlayer is welded on the described gear teeth
Between base portion and described involute contour body.
Elastic interlayer type vibration-reduction gear the most according to claim 4, wherein, described welding include laser welding, argon arc welding,
Any one of plasma weldering, infrared wire bonding, vacuum electric bundle weldering are welded.
Elastic interlayer type vibration-reduction gear the most according to claim 1, wherein, described elastic interlayer is made up of elastomeric material.
Elastic interlayer type vibration-reduction gear the most according to claim 6, wherein, the rigidity of described elastomeric material at 10E3~
In the range of 10E8N/m.
Elastic interlayer type vibration-reduction gear the most according to claim 6, wherein, described elastomeric material be chliorinated polyvinyl chloride,
Polymer rubber alloy, aluminium alloy or copper alloy.
Elastic interlayer type vibration-reduction gear the most according to claim 1, wherein, described elastic interlayer is sized such that
Width is transverse tooth thickness 0.01~0.3 times of described elastic interlayer, an a length of fully teeth height of described elastic interlayer.
10. the method reducing gear drive error, described method uses elastic interlayer type according to claim 1 to subtract
Shake gear, said method comprising the steps of:
S1: derive only with the gear drive error computing formula of oscillating component;
S2: the only two-freedom kinetics equation of elastic interlayer type vibration damping driving gear with oscillating component of deriving, and obtain
The amplitude of driving gear matrix steady state solution;
S3: by the elastic interlayer material chosen, the amplitude of described driving gear matrix steady state solution is reduced and trend towards null value;
With
S4: set up the two-freedom kinetics side of elastic interlayer type vibration damping driven gear according to described S2 step and described S3 step
Journey, chooses elastic interlayer material and the steady state solution of elastic interlayer type vibration damping driven gear matrix is reduced and trend towards null value, thus
The driving error making band flexible interlayer type vibration-reduction gear system according to described S1 step reduces and trends towards null value.
11. methods according to claim 10, wherein, described S1 step farther includes:
The driving error of described elastic interlayer type vibration-reduction gear represents with following formula:
X (t)=Rppθ1(t)-Rpgθ3(t) (1)
Wherein, RppAnd RpgIt is respectively the driving gear in elastic interlayer type vibration-reduction gear described in intermeshing a pair and driven tooth
The pitch radius of wheel, θ1(t) and θ3T () is respectively the angular displacement of the matrix of described driving gear and described driven gear;
The angular displacement of the matrix of described driving gear and described driven gear includes what the angular displacement at the uniform velocity changed and vibration caused
Angular displacement, is represented by following formula:
Wherein,The angular displacement at the uniform velocity changed for described elastic interlayer type vibration damping driving gear and driven gear,For described
The angular displacement that elastic interlayer type vibration damping driving gear and driven gear cause due to vibration, ω1,3Angular velocity and ω for vibration1,3
=2 π n1,3/ 60, n1,3For described elastic interlayer type vibration damping driving gear and the rotating speed of the matrix of driven gear;
For a pair normal meshed gears, there is below equation:
Equation (3) is substituted in formula (1) and obtains described gear drive error computing formula (4):
12. methods according to claim 11, wherein, described S2 step farther includes:
According to the described kinetics equation that dAlembert principle acquisition is following:
Wherein, θ1And θ2It is respectively the angular displacement of described elastic interlayer type vibration damping driving gear matrix and described involute contour body
Angular displacement;k1Torsional rigidity for described gear matrix;k2Torsional rigidity for described elastic interlayer;TmAnd TpIt is respectively institute
State the moment of resistance at the uniform velocity changed of pair of engaged gears and vibrate the moment of resistance caused;ToFor the engagement moment of gear, To=Fo×
Rpp, wherein FoFor engagement force;I1Rotary inertia for described driving gear;I2For described involute contour body relative in gear
The rotary inertia of the heart, the value of described rotary inertia is determined by formula for translation of axis (7):
I2=mL2+I20 (7)
Wherein, m is the quality of involute contour body, and L is the center of mass point o ' length to gear centre of the involute of profile body, I20
For the involute contour body rotary inertia relative to self center of mass point o '.
13. methods according to claim 12, wherein:
Formula (5) and (6) are carried out following coordinate transform, to eliminate the at the uniform velocity changing unit in formula (5) and (6):
Coordinate (8) is substituted in formula (5) and (6) and obtains below equation:
The general solution of equation group is expressed as:
And
Formula (11) is substituted into formula (9) and (10) and obtains following described driving gear matrix and involute contour body steady state solution
Amplitude:
Wherein,WithIt is respectively described elastic interlayer type vibration damping driving gear and the amplitude of driven gear.
14. methods according to claim 13, wherein, described S3 step farther includes:
According to known described involute contour body relative to the rotary inertia I of gear centre2With elastic interlayer type vibration damping driving tooth
Wheel angular velocity of vibration ω1Choose elastic interlayer material k2, make the rigidity of described elastic interlayer material meet below equation:
Equation (14) is brought in formula (13), it is thus achieved that below equation:
Now, described elastic interlayer type vibration damping driving gear leads to moment produced by described elastomeric materialWith described elasticity every
Oscillating component moment T of laminar vibration damping driving gear matrixpEquivalence is reversely cancelled out each other so that according to formula (12), described
The oscillating component amplitude of elastic interlayer type vibration damping driving gear matrix is
15. methods according to claim 14, wherein, in described step S4, by elasticity interlayer type vibration damping driven gear
The angular displacement of matrix3, angular velocity of vibration ω3Torsional rigidity k with matrix3Replace θ1、ω1And k1Substitute into formula and equation
(5)-(15), thus the oscillating component amplitude obtaining described elastic interlayer type vibration damping driven gear matrix is
16. methods according to claim 15, wherein, when meeting formula (16) and (17), according to described gear drive
Error calculation formula (4) obtains the driving error of gear:
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CN104502096B (en) * | 2015-01-05 | 2016-10-19 | 盐城工学院 | Dynamic transmission error of gear computational methods |
CN112579965B (en) * | 2020-12-04 | 2024-01-30 | 武汉理工大学 | Involute cylindrical spur gear rotational inertia calculation method |
CN113124116B (en) * | 2021-04-09 | 2023-03-28 | 江西增鑫科技股份有限公司 | Material line power box |
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CN102966721A (en) * | 2012-11-29 | 2013-03-13 | 四川大学 | Filtering gear with high reliability and precision |
CN103438183A (en) * | 2013-04-19 | 2013-12-11 | 四川大学 | Intelligent gear |
CN203585266U (en) * | 2013-12-12 | 2014-05-07 | 嵊州市特种链轮有限公司 | Wear-resistant and noise-reducing chain wheel |
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JP4919154B2 (en) * | 2006-12-19 | 2012-04-18 | スズキ株式会社 | Resin gear |
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CN1051613A (en) * | 1989-11-07 | 1991-05-22 | 张梅村 | Thermoplastics wrapped-cored reinforced gear |
CN102966721A (en) * | 2012-11-29 | 2013-03-13 | 四川大学 | Filtering gear with high reliability and precision |
CN103438183A (en) * | 2013-04-19 | 2013-12-11 | 四川大学 | Intelligent gear |
CN203585266U (en) * | 2013-12-12 | 2014-05-07 | 嵊州市特种链轮有限公司 | Wear-resistant and noise-reducing chain wheel |
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