CN107742054A - A kind of RV decelerators flank profil optimization correction method based on genetic algorithm - Google Patents
A kind of RV decelerators flank profil optimization correction method based on genetic algorithm Download PDFInfo
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Abstract
The invention discloses a kind of RV decelerators flank profil based on genetic algorithm to optimize correction method, according to three kinds of traditional profiling modes of Cycloidal Wheel, determines the contact range when tooth profile equation of Cycloidal Wheel and real work after correction of the flank shape；By the engagement normal gap of flank profil after correction of the flank shape, corresponding object function and constraints are established.And compensate back the profiling quantity after optimization in RV Key Part of Cycloid Cam Planetary Speed Reducer flank profils, so as to obtain the Optimization Model of Genetic Algorithm of Cycloid tooth profile.Using optimal modification of equidistance amount and modification of moved distance amount as target variable, minimum flank profil gap after two kinds of optimization corrections of the flank shape is object function, constraints during optimization is used as using Cycloidal Wheel node to the back lash between meshing point, the mixed penalty function for introducing 2 heterodynes simultaneously improves the iteration speed of optimized algorithm, finally give it is optimal it is equidistant with move away from profiling quantity.This method can fast and effectively determine to optimize calculating parameter, greatly improve computational efficiency and optimize precision.
Description
Technical field
The present invention relates to the design of RV Key Part of Cycloid Cam Planetary Speed Reducer and manufacturing technology field, is calculated more particularly to one kind based on heredity
The RV decelerators flank profil optimization correction method of method.
Background technology
RV decelerators are mainly made up of components such as planet carrier, centre wheel, Cycloidal Wheels, it have very high fatigue strength,
Rigidity and life-span, and return difference stable accuracy.Therefore many national high precision machines people are driven frequently with RV decelerators in the world.
Simultaneously because the Cycloidal pin-wheel drive applied in RV decelerators have small volume, gear range big, efficiency high, reliable operation,
Low noise advantages, this kind of drive are also widely used in many industries.
Theoretical standard cyclo drive belongs to tight mesh, and the wheel between cog for participating in engagement does not have back lash.But in reality
In the application of border, in order to compensate foozle, it is easy to assemble and disassemble and ensures lubrication, there must be engagement side between cycloidal gear teeth and pinwheel tooth
Gap.Therefore, actual Cycloidal Wheel can not use standard tooth form, it is necessary to correction of the flank shape.
The common profiling mode of Cycloidal Wheel has three kinds, is respectively：Modification of moved distance, modification of equidistance, three kinds of modification of rotated angle.Corner
The Cycloidal Wheel and the tooth root of standard pinwheel and tip portion that correction of the flank shape is ground can not individually make there will be intimate contact
With.Different correction methods and profiling quantity, there is completely different influence to RV decelerators.Document [1] propose shuffle away from
With just equidistantly combining correction method, although this method can obtain approaching the tooth form for gripping flank profil altogether, but gap is difficult to
The small requirement of return difference.And if the method ensure that radial clearance, new sideshake will be increased.Document [2] design uses
Matlab GUI methods, it is desirable to optimal equidistant modification of moved distance amount is found by maximum efficiency, but is not considered
Stress and deformation after correction of the flank shape in engagement process.Existing No. 201710537335.0 " Cycloid tooth profile correction of the flank shape of Chinese registered patent
Method and Cycloidal Wheel, RV decelerators ", the patent are repaiied using a kind of processing method of high-order parabola to Cycloid tooth profile
Shape, but this method can introduce larger mismachining tolerance, while do not account for the abrasion between the flank of tooth of workspace yet.
Above-mentioned document [1] and [2] are specially：
[1] the combination correcting mode of Jiang Tao, Sun Limin, Liu Kai the form of cycloidal gear tooth and its industry of optimization design [J] Zhengzhou
College journal, 1999, (03):54-56.
[2] bar figure cycloid hydraulic motor Cycloid tooth profile profile correction of the flank shape optimizing research [D] Nanjing Aero-Space University,
2016。
The content of the invention
Present invention aims at proposing a kind of RV decelerators flank profil based on genetic algorithm to optimize correction method, by this
Method can fast and effectively determine to optimize calculating parameter X, improve computational efficiency and optimize precision.
To achieve the above object, the technical solution adopted by the present invention is：
A kind of RV decelerators flank profil optimization correction method based on genetic algorithm, this method comprise the following steps：
Step 1: according to the three of RV Key Part of Cycloid Cam Planetary Speed Reducer kinds of conventional profiling modes, it is determined that equidistant plus shifting is away from combination correction of the flank shape side
Flank profil math equation after method correction of the flank shape.
Step 2：The foundation of Genetic Algorithm Model.
Step 3：By the engagement normal gap of flank profil after correction of the flank shape, corresponding object function and constraints are established.And will be excellent
Profiling quantity after change is compensated back in RV Key Part of Cycloid Cam Planetary Speed Reducer flank profils, so as to obtain the Optimization Model of Genetic Algorithm of Cycloid tooth profile.
The technical solution used in the present invention is：
The step 1 is specially：
Standard flank profil parametric equation before RV Key Part of Cycloid Cam Planetary Speed Reducer corrections of the flank shape is
xc、ycFor the x of standard flank profil, y-coordinate value under cartesian coordinate system；S be curtate ratio expression formula, S=(1+k2-
2kcosθ)-0.5, k=azp/rp, θ ∈ (0, π)；
In formula, rp--- centre circle of gear pins radius；
rrp--- pin tooth radius；
iH--- the gearratio of Cycloidal Wheel and pinwheel；
K --- curtate ratio；
θ --- phase angle of meshing；
A --- eccentric throw；
zp--- the pinwheel number of teeth；
Three kinds of correction methods of Cycloidal Wheel include modification of equidistance method, modification of moved distance method, modification of rotated angle method.After correction of the flank shape
RV gear reducer mechanism stable drives, and processing technology is simple during practicing Buddhism or Taoism, using absolute value it is big just equidistantly and absolute value
Small negative shifting is away from combination correction method.
Add modification of equidistance is with the Cycloid tooth profile equation after modification of moved distance
Wherein xc1、yc1X, y-coordinate value away from flank profil after combination correction of the flank shape are moved to be equidistant under cartesian coordinate system；S1After correction of the flank shape
The expression formula of curtate ratio, S1=(1+k1 2-2k1cosθ)-0.5, k1To add the curtate ratio after correction of the flank shape, k1=azp/(rp-
Δrp), θ ∈ (0, π)
In formula, Δ rp--- modification of equidistance amount；
Δrrp--- modification of moved distance amount；
The step 2 is specially：
Genetic algorithm is a kind of iterative searching algorithm with high robustness.In solution procedure, genetic algorithm from
One initializaing variable colony starts, and finds the optimal solution of problem from generation to generation, until meeting convergence criterion or set in advance
Untill iterations.Then the RV decelerators profile modification based on genetic algorithm includes following steps：
1) encode
The object function and variable of problem are determined first, then variable is encoded, that is, determine the ginseng during correction of the flank shape
Number variable, correction method using it is equidistant plus move away from combination correction of the flank shape, then specification of variables is Δ rpWith Δ rrp；
2) setting of initial population
The original string structured data that a quantity is N is randomly generated, each string structure data are referred to as an individual, and this is N number of
Individual constitutes a colony.Genetic algorithm starts iteration using this individual as initial point, and N takes the integer between 20~1000.
When optimizing to the correction of the flank shape of RV decelerators, compare after N takes 20,50,100,200,500 several initial population quantity, it is very fast from efficiency
And the 50 conduct initial population quantity that precision is higher.
3) individual adaptation degree is assessed
Fitness function guides the iteration direction of optimization problem, and it shows individual or the superiority-inferiority of solution.Set fitness
Function is f, then, it is f' after linear transformation, and f'=af+b, wherein a and b selection are determined by formula：
In formula,For fitness function f average value, fmaxFor fitness function f maximum.To Cycloid tooth profile
When optimizing, in order to ensure that tooth root and the conjugation of the back lash at tooth top and face part are continuous, therefore by flank profil
The distance in gap is with engaging optimal solution of the normal gap distance as optimization direction, i.e., by Cycloidal Wheel node between meshing point
Distance, delta L and normal gap be d's and as fitness function f.
4) genetic manipulation
If the scale of population is N, the fitness of i-th of individual is fi, then the selected probability P of i-th bodysiFor：
SnTo add up fitness value,Initial population N is taken as 50, and the fitness of i-th of individual is i-th of tooth
The fitness function of wide correction of the flank shape point is fi.When then being optimized with genetic algorithm to Cycloid tooth profile correction of the flank shape, i-th of optimization point is taken to be chosen
In probability be
5) intersect
In the two parental chromosomes strings chosen at random, a crosspoint is randomly selected, two chromosomes are in the point
Front or rear progress part exchange, exchanges the coding of both sides, produces new individual；
For RV decelerator profile modifications, each profiling quantity is encoded using binary system, then can be by two when intersecting
The coding 0/1 of individual profiling quantity exchanges, by 0 → 1, or by 1 → 0；After modification of equidistance and modification of moved distance amount are carried out into cross exchanged,
The two new individuals are in optimized selection again.
6) make a variation
For each genic value of caused offspring individuals in crossover operation, the puppet between one [0,1] is randomly generated
Random number rand, if rand ＜ Pm, with regard to carrying out mutation operation, corresponding genic value is negated, i.e., 0, which becomes 1 or 1, is changed into 0.
Wherein, PmFor random variation probability.During the correction of the flank shape to RV decelerators, the requirement to precision is higher, therefore
Relatively low random variation probability is taken, randomness is reduced, takes PmFor 0.001.
7) iterative query
Into iteration optimizing, repeat step 3)~6), and judge whether to reach and preset required precision, if reaching requirement
Or then jump out iteration after no obvious Optimal improvements.Iterations is set as 500 times, i.e., is jumped out after 500 iteration optimizations
Circulation, now the profile accuracy of RV decelerators reaches requirement.
The step 3 is specially：
Because the correction of the flank shape carried out to RV decelerators cycloidal-pin wheel includes modification of equidistance and modification of moved distance, therefore fix remaining ginseng
Number, two variables of design are respectively modification of equidistance amount Δ rpWith modification of moved distance amount Δ rrp.Then variable X is：
The result X of calculating be it is optimal equidistantly with modification of moved distance amount.
During the correction of the flank shape of Cycloidal Wheel, take it is just equidistant plus it is negative move away from combination correction method come to the tooth in working range
Exterior feature is approached.Corresponding to the design variable X in iterative process, at generation circle center with angle variable quantityFor abscissa, normal direction
Variable quantity L is that ordinate establishes coordinate system, and rightInterval division n etc. divides sampling interval.Along ent is sampled at n+1
On, the coordinate of modification of equidistance and two kinds of correction of the flank shape flank profil normal direction variation curves of modification of moved distance is respectively For abscissa, L1i、L2iOrdinate after respectively two kinds of corrections of the flank shape.
Then object function is set as two curve T1、T2The minimum value of Diff N, i.e.,：
In RV decelerators, the stator pinwheel number for participating in being driven in mesh regional is more, the stress of cycloidal-pin wheel mechanism
State is better, and motion is more steady.Cycloidal Wheel node is to the distance between meshing point Δ L
In formula,--- gap；
rs--- pinwheel is distributed radius of circle；
For Cycloidal Wheel correction of the flank shape constraint requirements, in order to prevent interfering phenomenon, it is necessary to protect in RV decelerator operation process
Demonstrate,prove certain normal gap d, this method using just it is equidistant+negative move away from correction method, i.e.,：
In order to meet the wear-resisting condition of the flank of tooth and between cog lubricating requirement, it is also necessary to ensure certain engagement normal gap.Cause
Bound for objective function can be set as by this：
In order to carry out optimization to above-mentioned model, the penalties of 2 extrapolations is introduced to be solved.Pass through
A series of penalty factor ci, the optimum point of former restricted problem is approached by seeking the minimal point of penalty.Penalty is：
Determine target variable X, object function f (x) with after two constraintss, introducing corresponding penalty to improve
Algorithm iteration speed, you can the genetic algorithm set by step 2 is iterated optimization, obtains optimal modification of equidistance amount Δ
rpWith modification of moved distance amount Δ rrp。
The invention has the advantages that：The present invention equidistantly adds tooth profile equation and something lost after migrating by analyzing Cycloidal Wheel
Pass iterative algorithm and propose a kind of RV decelerators flank profil optimization correction method based on genetic algorithm.With optimal modification of equidistance amount
It is target variable with modification of moved distance amount, the minimum flank profil gap after two kinds of optimization corrections of the flank shape is object function, is arrived with Cycloidal Wheel node
Constraints when back lash between meshing point is as optimization, while the mixed penalty functions of 2 heterodynes is introduced to improve
The iteration speed of optimized algorithm, finally give it is optimal it is equidistant with move away from profiling quantity.The algorithm can be determined fast and effectively
Optimize calculating parameter X, computational efficiency and optimization precision are greatly improved, so as to provide a kind of cycloid of new RV decelerators
Take turns correction method.
Brief description of the drawings
Fig. 1 is the FB(flow block) of genetic algorithm.
Fig. 2 is the Cycloid tooth profile schematic diagram after correction of the flank shape.
Fig. 3 is the tooth curve and flank profil gap schematic diagram of partial enlargement.
Fig. 4 is the design sketch of the present invention.
Embodiment
In order to further appreciate that the invention, features and effects of the present invention, following examples are hereby enumerated, and coordinate accompanying drawing
Describe in detail：
A kind of RV decelerators flank profil optimization correction method based on genetic algorithm, is comprised the following steps that：
Standard flank profil parametric equation before step 1 RV Key Part of Cycloid Cam Planetary Speed Reducer corrections of the flank shape is
Wherein xc、ycFor the x of standard flank profil, y-coordinate value under cartesian coordinate system；S be curtate ratio expression formula, S=(1
+k2-2kcosθ)-0.5, k=azp/rp, θ ∈ (0, π)
In formula, rp--- centre circle of gear pins radius
rrp--- pin tooth radius
iH--- the gearratio of Cycloidal Wheel and pinwheel
K --- curtate ratio
θ --- phase angle of meshing
A --- eccentric throw
zp--- the pinwheel number of teeth
Three kinds of correction methods of Cycloidal Wheel include modification of equidistance method, modification of moved distance method, modification of rotated angle method.After correction of the flank shape
RV gear reducer mechanism stable drives, and processing technology is simple during practicing Buddhism or Taoism, using absolute value it is big just equidistantly and absolute value
Small negative shifting is away from combination correction method.
Add modification of equidistance is with the Cycloid tooth profile equation after modification of moved distance
Wherein xc1、yc1X, y-coordinate value away from flank profil after combination correction of the flank shape are moved to be equidistant under cartesian coordinate system；S1After correction of the flank shape
The expression formula of curtate ratio, S1=(1+k1 2-2k1cosθ)-0.5, k1To add the curtate ratio after correction of the flank shape, k1=azp/(rp-
Δrp), θ ∈ (0, π)
In formula, Δ rp--- modification of equidistance amount
Δrrp--- modification of moved distance amount
Step 2 genetic algorithm is a kind of iterative searching algorithm with high robustness.In solution procedure, heredity
Algorithm finds the optimal solution of problem from generation to generation since an initializaing variable colony, until meeting convergence criterion or advance
Untill the iterations of setting.The structure chart of genetic algorithm is as shown in figure 1, mainly include following steps：
1) encode
The object function and variable of problem are determined first, then variable is encoded, that is, determine the ginseng during correction of the flank shape
Number variable, correction method of the invention using it is equidistant plus move away from combination correction of the flank shape, then variable can be set as Δ rpWith Δ rrp；
2) setting of initial population
The original string structured data that a quantity is N is randomly generated, each string structure data are referred to as an individual, and this is N number of
Individual constitutes a colony.Genetic algorithm starts iteration using this individual as initial point, and N takes the integer between 20~1000.
When optimizing to the correction of the flank shape of RV decelerators, compare after N takes several initial population quantity such as 20,50,100,200,500, from efficiency
Very fast and higher precision 50 are used as initial population quantity.
3) individual adaptation degree is assessed
Fitness function guides the iteration direction of optimization problem, and it shows individual or the superiority-inferiority of solution.Set fitness
Function is f, then, it is f' after linear transformation, and f'=af+b, wherein a and b selection are determined by formula：
In formula,For fitness function f average value, fmaxFor fitness function f maximum.To Cycloid tooth profile
When optimizing, in order to ensure that tooth root and the conjugation of the back lash at tooth top and face part are continuous, therefore by flank profil
The distance in gap is with engaging optimal solution of the normal gap distance as optimization direction, i.e., by Cycloidal Wheel node between meshing point
Distance, delta L and normal gap be d's and as fitness function f.
4) genetic manipulation
If the scale of population is N, the fitness of i-th of individual is fi, then the selected probability P of i-th bodysiFor：
SnTo add up fitness value,Initial population N is taken as 50, and the fitness of i-th of individual is i-th of tooth
The fitness function of wide correction of the flank shape point is fi.When then being optimized with genetic algorithm to Cycloid tooth profile correction of the flank shape, i-th of optimization point can be taken
Selected probability is
5) intersect
In the two parental chromosomes strings chosen at random, a crosspoint is randomly selected, two chromosomes are in the point
Front or rear progress part exchange, exchanges the coding of both sides, produces new individual；
For RV decelerator profile modifications, each profiling quantity is encoded using binary system, then can be by two when intersecting
The coding 0/1 of individual profiling quantity exchanges, by 0 → 1, or by 1 → 0；After modification of equidistance and modification of moved distance amount are carried out into cross exchanged,
The two new individuals are in optimized selection again.
6) make a variation
For each genic value of caused offspring individuals in crossover operation, the puppet between one [0,1] is randomly generated
Random number rand, if rand ＜ Pm, with regard to carrying out mutation operation, corresponding genic value is negated, i.e., 0, which becomes 1 or 1, is changed into 0.
Wherein, PmFor random variation probability.During the correction of the flank shape to RV decelerators, the requirement to precision is higher, therefore
Relatively low random variation probability can be taken, randomness is reduced, takes PmFor 0.001.
7) iterative query
Into iteration optimizing, repeat step 3)~6), and judge whether to reach and preset required precision, if reaching requirement
Or then jump out iteration after no obvious Optimal improvements.The present invention sets iterations as 500 times, i.e., excellent by 500 iteration
Circulation is jumped out after change, now the profile accuracy of RV decelerators can reach requirement.
Step 3, therefore can be with because the correction of the flank shape carried out to RV decelerators cycloidal-pin wheel includes modification of equidistance and modification of moved distance
Remaining parameter is fixed, two variables of design are respectively modification of equidistance amount Δ rpWith modification of moved distance amount Δ rrp.Then variable X is：
The result X of calculating be it is optimal equidistantly with modification of moved distance amount.
During the correction of the flank shape of Cycloidal Wheel, take it is just equidistant plus it is negative move away from combination correction method come to the tooth in working range
Exterior feature is approached.Corresponding to the design variable X in iterative process, at generation circle center with angle variable quantityFor abscissa, normal direction
Variable quantity L is that ordinate establishes coordinate system, and rightInterval division n etc. divides sampling interval.Along ent is sampled at n+1
On, the coordinate of modification of equidistance and two kinds of correction of the flank shape flank profil normal direction variation curves of modification of moved distance is respectively
WhereinFor abscissa, L1i、L2iOrdinate after respectively two kinds of corrections of the flank shape.
Then object function can be set as two curve T1、T2The minimum value of Diff N, i.e.,：
In RV decelerators, the stator pinwheel number for participating in being driven in mesh regional is more, the stress of cycloidal-pin wheel mechanism
State is better, and motion is more steady.Cycloidal Wheel node is to the distance between meshing point Δ L
In formula,--- gap,
rs--- pinwheel is distributed radius of circle
For traditional Cycloidal Wheel correction of the flank shape constraint requirements, in order to prevent interfering phenomenon in RV decelerator operation process,
Need to ensure certain normal gap d, moved in the present invention using just equidistant+negative away from ground correction method, i.e.,：
In order to meet the wear-resisting condition of the flank of tooth and between cog lubricating requirement, it is also necessary to ensure certain engagement normal gap.Cause
Bound for objective function can be set as by this：
In order to carry out optimization to above-mentioned model, the penalties of 2 extrapolations is introduced to be solved.Pass through
A series of penalty factor ci, the optimum point of former restricted problem is approached by seeking the minimal point of penalty.Penalty is：
Determine target variable X, object function f (x) with after two constraintss, introducing corresponding penalty to improve
Algorithm iteration speed, you can the genetic algorithm set by step 2 is iterated optimization, obtains optimal modification of equidistance amount Δ
rpWith modification of moved distance amount Δ rrp.Fig. 2 and Fig. 3 is the cycloidal gear teeth after resulting correction of the flank shape after genetic algorithm iteration optimization
Wide schematic diagram and local tooth curve and flank profil gap schematic diagram.
As described above, the present invention can be better realized.
Embodiments of the present invention are simultaneously not restricted to the described embodiments, other any Spirit Essences for not running counter to the present invention
With made under principle change, modification, replacement, combine, simplification, should be equivalent substitute mode, be included in the present invention's
Within protection domain.
Claims (4)
1. a kind of RV decelerators flank profil optimization correction method based on genetic algorithm, it is characterised in that this method includes following step
Suddenly：
Step 1: according to the three of RV Key Part of Cycloid Cam Planetary Speed Reducer kinds of conventional profiling modes, it is determined that equidistant plus shifting is repaiied away from combination correction method
Flank profil math equation after shape；
Step 2：The foundation of Genetic Algorithm Model；
Step 3：By the engagement normal gap of flank profil after correction of the flank shape, corresponding object function and constraints are established；And after optimizing
Profiling quantity compensate back in RV Key Part of Cycloid Cam Planetary Speed Reducer flank profils, so as to obtain the Optimization Model of Genetic Algorithm of Cycloid tooth profile.
2. a kind of RV decelerators flank profil optimization correction method based on genetic algorithm according to claim 1, its feature exist
In step 1 is specially：
Standard flank profil parametric equation before RV Key Part of Cycloid Cam Planetary Speed Reducer corrections of the flank shape is
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xc、ycFor the x of standard flank profil, y-coordinate value under cartesian coordinate system；S be curtate ratio expression formula, S=(1+k2-
2kcosθ)-0.5, k=azp/rp, θ ∈ (0, π)；
In formula, rp--- centre circle of gear pins radius；
rrp--- pin tooth radius；
iH--- the gearratio of Cycloidal Wheel and pinwheel；
K --- curtate ratio；
θ --- phase angle of meshing；
A --- eccentric throw；
zp--- the pinwheel number of teeth；
Three kinds of correction methods of Cycloidal Wheel include modification of equidistance method, modification of moved distance method, modification of rotated angle method；In view of the RV after correction of the flank shape
Gear reducer mechanism stable drive, and processing technology is simple during practicing Buddhism or Taoism, using big just equidistantly small with absolute value of absolute value
It is negative to move away from combination correction method；
Add modification of equidistance is with the Cycloid tooth profile equation after modification of moved distance
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<mn>1</mn>
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</mrow>
<mi>cos</mi>
<mo>&lsqb;</mo>
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</msup>
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<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein xc1、yc1X, y-coordinate value away from flank profil after combination correction of the flank shape are moved to be equidistant under cartesian coordinate system；S1For short width after correction of the flank shape
The expression formula of coefficient, S1=(1+k1 2-2k1cosθ)-0.5, k1To add the curtate ratio after correction of the flank shape, k1=azp/(rp-Δ
rp), θ ∈ (0, π)
In formula, Δ rp--- modification of equidistance amount；
Δrrp--- modification of moved distance amount.
3. a kind of RV decelerators flank profil optimization correction method based on genetic algorithm according to claim 1, its feature exist
In the step 2 is specially：
Genetic algorithm is a kind of iterative searching algorithm with high robustness；In solution procedure, genetic algorithm is from one
Initializaing variable colony starts, and finds the optimal solution of problem from generation to generation, until meeting convergence criterion or iteration set in advance
Untill number；Then the RV decelerators profile modification based on genetic algorithm includes following steps：
1) encode
The object function and variable of problem are determined first, then variable is encoded, that is, determine that the parameter during correction of the flank shape becomes
Amount, correction method using it is equidistant plus move away from combination correction of the flank shape, then specification of variables is Δ rpWith Δ rrp；
2) setting of initial population
The original string structured data that a quantity is is randomly generated, each string structure data are referred to as an individual, this individual structure
Into a colony.Genetic algorithm starts iteration using this individual as initial point, takes the integer between 20~1000.RV is slowed down
When device correction of the flank shape optimizes, compare after taking 20,50,100,200,500 several initial population quantity, and precision very fast from efficiency is higher
50 be used as initial population quantity.
3) individual adaptation degree is assessed
Fitness function guides the iteration direction of optimization problem, and it shows individual or the superiority-inferiority of solution；Set fitness function
It is f, then, it is f' after linear transformation, and f'=af+b, wherein a and b selection are determined by formula：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>a</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>C</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
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<mi>f</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>-</mo>
<mover>
<mi>f</mi>
<mo>&OverBar;</mo>
</mover>
</mrow>
</mfrac>
<mover>
<mi>f</mi>
<mo>&OverBar;</mo>
</mover>
</mrow>
</mtd>
</mtr>
<mtr>
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<mrow>
<mi>b</mi>
<mo>=</mo>
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<mrow>
<msub>
<mi>f</mi>
<mi>max</mi>
</msub>
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<mi>C</mi>
<mover>
<mi>f</mi>
<mo>&OverBar;</mo>
</mover>
</mrow>
<mrow>
<msub>
<mi>f</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>-</mo>
<mover>
<mi>f</mi>
<mo>&OverBar;</mo>
</mover>
</mrow>
</mfrac>
<mover>
<mi>f</mi>
<mo>&OverBar;</mo>
</mover>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula,For fitness function f average value, fmaxFor fitness function f maximum；Excellent to Cycloid tooth profile progress
During change, in order to ensure that tooth root and the conjugation of the back lash at tooth top and face part are continuous, therefore by flank profil gap
Distance is with engaging optimal solution of the normal gap distance as optimization direction, i.e., by the distance between Cycloidal Wheel node to meshing point Δ
L and normal gap be d's and as fitness function f；
4) genetic manipulation
If the scale of population is N, the fitness of i-th of individual is fi, then the selected probability P of i-th bodysiFor：
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>f</mi>
<mi>i</mi>
</msub>
<msub>
<mi>S</mi>
<mi>n</mi>
</msub>
</mfrac>
</mrow>
SnTo add up fitness value,Initial population N is taken as 50, and the fitness of i-th of individual is i-th of profile modification
The fitness function of point is fi；When then being optimized with genetic algorithm to Cycloid tooth profile correction of the flank shape, i-th of optimization point is taken to be selected general
Rate is
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mi>i</mi>
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<mi>i</mi>
</msub>
<mo>/</mo>
<munderover>
<mo>&Sigma;</mo>
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<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>50</mn>
</munderover>
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<mi>i</mi>
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<mi>i</mi>
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<mo>&Sigma;</mo>
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<mn>50</mn>
</munderover>
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<mi>&Delta;L</mi>
<mi>i</mi>
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<msub>
<mi>d</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
5) intersect
In the two parental chromosomes strings chosen at random, randomly select a crosspoint, two chromosomes before the point or
Part exchange is carried out afterwards, is exchanged the coding of both sides, is produced new individual；
For RV decelerator profile modifications, each profiling quantity is encoded using binary system, then two can be repaiied when intersecting
The coding 0/1 of shape amount exchanges, by 0 → 1, or by 1 → 0；After modification of equidistance and modification of moved distance amount are carried out into cross exchanged, then it is right
The two new individuals are in optimized selection；
6) make a variation
For each genic value of caused offspring individuals in crossover operation, the pseudorandom between one [0,1] is randomly generated
Number rand, if rand ＜ Pm, with regard to carrying out mutation operation, corresponding genic value is negated, i.e., 0, which becomes 1 or 1, is changed into 0；
Wherein, PmFor random variation probability；During the correction of the flank shape to RV decelerators, the requirement to precision is higher, therefore takes relatively low
Random variation probability, reduce randomness, take PmFor 0.001；
7) iterative query
Into iteration optimizing, repeat step 3)~6), and judge whether to reach and preset required precision, if reaching requirement or not having
Iteration is then jumped out after there are obvious Optimal improvements；Iterations is set as 500 times, i.e., circulation is jumped out after 500 iteration optimizations,
Now the profile accuracy of RV decelerators reaches requirement.
4. a kind of RV decelerators flank profil optimization correction method based on genetic algorithm according to claim 1, its feature exist
In the step 3 is specially：
Because the correction of the flank shape carried out to RV decelerators cycloidal-pin wheel includes modification of equidistance and modification of moved distance, therefore remaining parameter is fixed,
It is respectively modification of equidistance amount Δ r to design two variablespWith modification of moved distance amount Δ rrp；Then variable X is：
<mrow>
<mi>X</mi>
<mo>=</mo>
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<mtd>
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<mi>&Delta;r</mi>
<mi>p</mi>
</msub>
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</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mrow>
<mi>r</mi>
<mi>p</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
The result X of calculating be it is optimal equidistantly with modification of moved distance amount；
During the correction of the flank shape of Cycloidal Wheel, take it is just equidistant plus it is negative move away from combination correction method come to the flank profil in working range
Approached；Corresponding to the design variable X in iterative process, at generation circle center with angle variable quantityFor abscissa, normal direction
Variable quantity L is that ordinate establishes coordinate system, and rightInterval division n etc. divides sampling interval；Along ent is sampled at n+1
On, the coordinate of modification of equidistance and two kinds of correction of the flank shape flank profil normal direction variation curves of modification of moved distance is respectively For abscissa, L1i、L2iOrdinate after respectively two kinds of corrections of the flank shape；
Then object function is set as two curve T1、T2The minimum value of Diff N, i.e.,：
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</munderover>
<mo>|</mo>
<mrow>
<msub>
<mi>L</mi>
<mrow>
<mn>1</mn>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>L</mi>
<mrow>
<mn>2</mn>
<mi>i</mi>
</mrow>
</msub>
</mrow>
<mo>|</mo>
</mrow>
In RV decelerators, the stator pinwheel number for participating in being driven in mesh regional is more, the stress of cycloidal-pin wheel mechanism
Better, motion is more steady；Cycloidal Wheel node is to the distance between meshing point Δ L
In formula,--- gap；
rs--- pinwheel is distributed radius of circle；
For Cycloidal Wheel correction of the flank shape constraint requirements, in order to prevent interfering phenomenon, it is necessary to ensure one in RV decelerator operation process
Fixed normal gap d, this method using just it is equidistant+negative move away from correction method, i.e.,：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>d</mi>
<mo>=</mo>
<msub>
<mi>&Delta;r</mi>
<mi>p</mi>
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<mo>+</mo>
<msub>
<mi>&Delta;r</mi>
<mrow>
<mi>r</mi>
<mi>p</mi>
</mrow>
</msub>
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<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;r</mi>
<mi>p</mi>
</msub>
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<mi>&Delta;r</mi>
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</mrow>
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</mtd>
</mtr>
</mtable>
</mfenced>
To meet the wear-resisting condition of the flank of tooth and between cog lubricating requirement, it is also necessary to ensure certain engagement normal gap；Therefore can incite somebody to action
Bound for objective function is set as：
In order to carry out optimization to above-mentioned model, the penalties of 2 extrapolations is introduced to be solved；Pass through a system
The penalty factor c of rowi, the optimum point of former restricted problem is approached by seeking the minimal point of penalty；Penalty is：
<mrow>
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<mrow>
<mi>l</mi>
<mi>i</mi>
<mi>m</mi>
</mrow>
<mrow>
<mi>x</mi>
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<mi>&infin;</mi>
</mrow>
</munder>
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<mn>2</mn>
</msub>
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<mo>(</mo>
<mi>x</mi>
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</mrow>
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<mn>0</mn>
</mrow>
Determine target variable X, object function f (x) with after two constraintss, introducing corresponding penalty to improve algorithm
Iteration speed, you can the genetic algorithm set by step 2 is iterated optimization, obtains optimal modification of equidistance amount Δ rpWith
Modification of moved distance amount Δ rrp。
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| CN108620691A (en) * | 2018-03-21 | 2018-10-09 | 湖北工业大学 | A kind of Cycloid tooth profile correction method and Cycloidal Wheel, RV retarders |
| CN108662115A (en) * | 2018-05-23 | 2018-10-16 | 湖北工业大学 | Cycloid tooth profile correction of the flank shape multi-objective optimization design of power method |
| CN108730480A (en) * | 2018-07-27 | 2018-11-02 | 河南科技大学 | A kind of Cycloidal Wheel and its reverse active correction method of flank profil of RV retarders |
| CN108920816A (en) * | 2018-06-29 | 2018-11-30 | 江苏国茂减速机股份有限公司 | A kind of method for solving of the two teeth difference cycloidal tooth profile equivalent substitution tooth form based on Matlab |
| CN109446709A (en) * | 2018-11-12 | 2019-03-08 | 温州大学 | A kind of the cycloidal profile curve emulation mode and system of speed reducer |
| CN109766562A (en) * | 2018-09-27 | 2019-05-17 | 中原工学院 | Cycloid tooth profile correction method based on genetic algorithm and population combinational algorithm |
| CN109828616A (en) * | 2019-01-21 | 2019-05-31 | 厦门大学 | A kind of parts mix selection method and system of RV retarder |
| CN110414056A (en) * | 2019-06-28 | 2019-11-05 | 湖北工业大学 | A kind of Cycloid tooth profile correction method compensating flexible deformation |
| CN111125898A (en) * | 2019-12-17 | 2020-05-08 | 之江实验室 | Rapid optimization method for profile modification coefficient of cycloidal gear tooth profile |
| CN111488659A (en) * | 2020-04-09 | 2020-08-04 | 北京理工大学 | Multi-parameter tooth profile modification optimization design method for bevel gear |
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| CN108620691A (en) * | 2018-03-21 | 2018-10-09 | 湖北工业大学 | A kind of Cycloid tooth profile correction method and Cycloidal Wheel, RV retarders |
| CN108662115A (en) * | 2018-05-23 | 2018-10-16 | 湖北工业大学 | Cycloid tooth profile correction of the flank shape multi-objective optimization design of power method |
| CN108662115B (en) * | 2018-05-23 | 2020-08-04 | 湖北工业大学 | Multi-objective optimization design method for profile modification of cycloidal gear tooth profile |
| CN108920816A (en) * | 2018-06-29 | 2018-11-30 | 江苏国茂减速机股份有限公司 | A kind of method for solving of the two teeth difference cycloidal tooth profile equivalent substitution tooth form based on Matlab |
| CN108730480A (en) * | 2018-07-27 | 2018-11-02 | 河南科技大学 | A kind of Cycloidal Wheel and its reverse active correction method of flank profil of RV retarders |
| CN109766562A (en) * | 2018-09-27 | 2019-05-17 | 中原工学院 | Cycloid tooth profile correction method based on genetic algorithm and population combinational algorithm |
| CN109446709A (en) * | 2018-11-12 | 2019-03-08 | 温州大学 | A kind of the cycloidal profile curve emulation mode and system of speed reducer |
| CN109828616A (en) * | 2019-01-21 | 2019-05-31 | 厦门大学 | A kind of parts mix selection method and system of RV retarder |
| CN110414056A (en) * | 2019-06-28 | 2019-11-05 | 湖北工业大学 | A kind of Cycloid tooth profile correction method compensating flexible deformation |
| CN111125898A (en) * | 2019-12-17 | 2020-05-08 | 之江实验室 | Rapid optimization method for profile modification coefficient of cycloidal gear tooth profile |
| CN111488659A (en) * | 2020-04-09 | 2020-08-04 | 北京理工大学 | Multi-parameter tooth profile modification optimization design method for bevel gear |
| CN111488657A (en) * | 2020-04-09 | 2020-08-04 | 北京理工大学 | Involute helical gear pair double-parameter tooth profile modification optimization design method |
| CN111488657B (en) * | 2020-04-09 | 2023-03-24 | 北京理工大学 | Involute helical gear pair double-parameter tooth profile modification optimization design method |
| CN113137935A (en) * | 2021-04-25 | 2021-07-20 | 四川大学 | RV reducer cycloid wheel wear testing system and method based on computer vision |
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