CN103870663A - Gear transmission system design method based on particle swarm two-level optimization - Google Patents

Abstract

The invention provides a gear transmission system design method based on particle swarm two-level optimization. The method comprises the following steps that an optimal objective function is set, an optimal variable to be optimized is set, an optimal constraint is set, and an optimal solution gbest of the optimal variable is acquired through the particle swarm two-level optimization. According to the method, the optimal variable of a gear transmission system is acquired by the adoption of the particle swarm two-level optimization, the first level optimization is focused on meeting the requirement that the standard deviation of safety coefficients of contact fatigue strength of all external gears is small, and acquiring a feasible scheme of the number of gear teeth; and the second level optimization is focused on meeting the requirement that the standard deviation of safety coefficients of bending fatigue strength of all the external gears is small, and acquiring a refinement configuration scheme including all design variables. All strength indexes of the optimal gear transmission system are met, meanwhile, the difference of service lives of all the external gears is relatively small, the problem that short board effect often occurs in the gear transmission system can be avoided effectively, and reliability of the gear transmission system is improved.

Description

A kind of Design of Gear Drive System method based on population bilevel optimization

Technical field

The present invention relates to a kind of method for designing of the gear train assembly based on population bilevel optimization, especially relate to a kind of method for designing of aerogenerator planetary drive gear-box of the MW class based on Particle Swarm Optimization.

Background technology

The main-gear box of wind power generating set is a very important mechanical part in unit, and the kinematic train ratio of gear in it is large, and transmitted power is high.Wind turbine gearbox is often installed on the ground such as remote wilderness, high mountain, marine site, is difficult to arrive; The cabin space at gear case place is very narrow and small, keep in repair very difficult, and as gear case hung oneself from blower fan be filled to ground maintenance, expense is difficult to bear; This just forces gear case of blower to have higher fiduciary level requirement than full depth tooth roller box.And the damage of gear case of blower approximately 90% is due to some gear failures, but its loss causing substantially exceeds the value of this gear itself, the normal short-board effect occurring in Here it is wind turbine gearbox, the life-span gap therefore just shortening between each gear at the optimization initial stage is very necessary.

Traditional pass through artificial calculating and contrast one by one and select the gear train assembly optimization method of scheme, efficiency is lower and cannot assured plan optimum.

Summary of the invention

In order to address the above problem, the object of the invention is: a kind of robotization, the accurate Design of Gear Drive System method based on population bilevel optimization are provided.

For achieving the above object, the invention provides a kind of Design of Gear Drive System method based on population bilevel optimization, wherein said gear train assembly comprises 2 and above planet wheel pair or parallel teeth wheel set, or the combination of at least 1 planet wheel pair and at least 1 parallel teeth wheel set; Obtain the optimum solution g of the optimized variable X of described gear train assembly by population dual-layer optimization ^best; Described optimized variable X comprises: ratio of gear i, number of teeth z, modulus m, helixangleβ, and coefficient of facewidth

described coefficient of facewidth

for the ratio of the reference diameter of the work facewidth and driving gear,

Described Design of Gear Drive System method comprises the following steps:

A, setting the objective function of optimizing is f=a ₁f _h+ a ₂f _f, in formula, f _hfor the standard deviation of contact fatigue strength safety coefficient, f _ffor the standard deviation of bending fatigue strength safety coefficient, a ₁, a ₂weight factor, a ₁+ a ₂=1;

B, sets optimized variable to be optimized and is

in formula,

for all ratio of gear optimized variables, for all number of teeth optimized variables,

for all modulus optimized variables,

for all helix angle optimized variables,

for all coefficient of facewidth optimized variables;

C, sets the constraint condition of optimizing;

D, based on aforesaid objective function and constraint condition, obtains the optimum solution g of optimized variable by population bilevel optimization ^best:

First set population scale n; Ground floor is k from scale ₁* the population of n starts to optimize;

Set the iterations g of ground floor particle group optimizing ₁;

Set the inertia weight ω of ground floor particle group optimizing ₁, study factor c ₁₁and c ₁₂; Set the objective function weight factor a of ground floor particle group optimizing ₁₁, a ₁₂, wherein a ₁₁+ a ₁₂=1;

Set the iterations g of second layer particle group optimizing ₂;

Set the inertia weight ω of second layer particle group optimizing ₂, study factor c ₂₁and c ₂₂; Set the objective function weight factor a of second layer particle group optimizing ₂₁, a ₂₂, wherein a ₂₁+ a ₂₂=1;

Wherein, a ₁₁> a ₁₂, a ₂₁< a ₂₂, ω ₁> ω ₂, c ₁₁< c ₂₁, c ₁₂< c ₂₂;

The objective function of setting ground floor particle group optimizing is f=a ₁₁f _h+ a ₁₂f _f, and the optimized variable of ground floor particle group optimizing is

after ground floor particle group optimizing, select and meet the population that the scale of each constraint condition is n, and obtain feasible number of teeth allocation plan;

Reset the new objective function f=a of second layer particle group optimizing ₂₁f _h+ a ₂₂f _f, when second layer particle group optimizing by number of teeth optimized variable

with ratio of gear optimized variable

solidify, the optimized variable of second layer particle group optimizing is

E, rounding g ^bestin modulus, calculate and the rounding facewidth, thereby obtain the final numerical value of whole described optimized variable X.

In said method, ground floor particle group optimizing comprises the following steps:

11) initialization a group particle, population scale is the k of default population scale n ₁doubly, then each number of teeth in rounding particle

and whether checking meets each constraint condition;

12) select k ₁* in the population scale of n, choose n the particle that meets each constraint condition, calculate its target function value; And by the position mark of this n particle be

choose the particle that described target function value is minimum, be labeled as g ^best;

13) in initialization gained population, the speed of each particle is

0.25 < rand _i< 0.75;

14) enter iteration phase, setting flying speed is:

$V_i^{k+1}={\mathrm{\&omega;}}_1{V}_i^k+{\mathrm{<figure-callout\; id="11"\; label="c"\; filenames="HDA0000485447940000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_{11}*{\mathrm{rand}}_1*(p_i^{\mathrm{best}}-x_i)+{\mathrm{<figure-callout\; id="12"\; label="c"\; filenames="HDA0000485447940000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_{12}*{\mathrm{rand}}_2*(g^{\mathrm{best}}-x_i);$

In formula, ω ₁for inertia weight, reduce c with iterative process linearity between [0.9,0.4] ₁₁, c ₁₂for learning the factor, be two nonnegative constants, rand ₁, rand ₂it is the random number between [0,1];

Population reposition is: $x_i^k=x_i+V_i^{k+1};$

15) the rounding number of teeth, the ratio of gear of reruning, verifies whether each particle meets constraint condition, for ungratified particle, repeating step 14 regenerates reposition;

16) repeating step 14), 15) several times, if particle is still solution trivial, with

substitute solution trivial;

17) calculate the target function value of each particle, more each particle current goal functional value is corresponding with it

target function value, and will

be set as the position that target function value is relatively minimum; The optimal objective function value of all particles and g in more current population ^besttarget function value, and by g ^bestbe set as the position that target function value is relatively minimum;

18) repeating step 14)-17), until reach the iterations g of ground floor ₁; Acquisition meets the population that the scale of each constraint condition is n, and now, this population has obtained feasible number of teeth allocation plan, and g ^bestobtain the standard deviation of contact fatigue strength safety coefficient and the standard deviation of bending fatigue strength safety coefficient after ground floor particle group optimizing.

In said method, second layer particle group optimizing comprises the following steps:

21) reset objective function f=a ₂₁f _h+ a ₂₂f _f, for evaluate the population obtaining after ground floor particle group optimizing each particle and

g ^besttarget function value;

22) set

in

the speed of dimension is 0;

23) enter second layer iteration phase, setting flying speed is:

$V_i^{k+1}={\mathrm{\&omega;}}_2{V}_i^k+c_{21}*{\mathrm{rand}}_1*(p_i^{\mathrm{best}}-x_i)+c_{22}*{\mathrm{rand}}_2*(g^{\mathrm{best}}-x_i);$

In formula, ω ₂for inertia weight, reduce c with iterative process linearity between [0.9,0.4] ₂₁, c ₂₂for the study factor, be two nonnegative constants, rand ₁, rand ₂it is the random number between [0,1];

Population reposition is: $x_i^k=x_i+V_i^{k+1};$

24) calculate the target function value of each particle, more each particle current goal functional value is corresponding with it

target function value, and will

be set as the position that target function value is relatively minimum; The optimal objective function value of all particles and g in more current population ^besttarget function value, and by g ^bestbe set as the position that target function value is relatively minimum;

25) repeating step 23)-24), until reach end condition; The population that now scale is n meets each constraint condition, and g ^bestobtain contact fatigue strength safety coefficient standard deviation and bending fatigue strength safety coefficient standard deviation after second layer particle group optimizing.

Preferably, described step 25) in end condition be set as: reach maximum iteration time g ₁+ g ₂or meet precision conditions:

G ^bestthe variable quantity of j iteration of target function value f accumulative total be less than a predefined threshold value e, | f _n-f _n-j| < e;

Wherein f _nfor current g ^besttarget function value, f _n-jfor the g before j iteration ^besttarget function value.

In said method, the standard deviation f of described contact fatigue strength safety coefficient _hfor:

$f_H=\sqrt{\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(S_{\mathrm{Hj}}-{\stackrel{\&OverBar;}{S}}_H)}^2},$

${\stackrel{\&OverBar;}{S}}_H=\frac{1}{H}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{S}_{\mathrm{Hj}},$

The total quantity that wherein N is all outer rotors, S _hjfor the contact fatigue strength safety coefficient of each outer rotor,

for the mean value of the contact fatigue strength safety coefficient of each outer rotor;

The standard deviation f of described bending fatigue strength safety coefficient _ffor:

$f_F=\sqrt{\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(S_{\mathrm{Fj}}-{\stackrel{\&OverBar;}{S}}_F)}^2},$

${\stackrel{\&OverBar;}{S}}_F=\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{S}_{\mathrm{Fj}},$

The total quantity that wherein N is all outer rotors, S _fjfor the bending fatigue strength safety coefficient of each outer rotor,

for the mean value of the bending fatigue strength safety coefficient of each outer rotor.

Preferably, the constraint condition of described planet wheel pair or parallel teeth wheel set comprises the bound of number of teeth constraint condition, ratio error constraint condition, flank of tooth contact fatigue strength constraint condition, tooth root bending fatigue strength constraint condition, optimized variable.

Preferably, the constraint condition of described planet wheel pair also comprises in abutting connection with condition, concentric condition and assembled condition.

Preferably, described number of teeth constraint condition comprises: the number of teeth correspondence of two gears that are meshed meets highest common divisor said conditions gcd (z ₁, z ₂)≤k, k is less than or equal to 3 positive integer.

Preferably, described ratio error is constrained to:

${\mathrm{Err}}_{\min }<(\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{i}_j-i_0)/i_0<{\mathrm{Err}}_{\max },$

In formula: n is the progression of gear train assembly gear pair, i _jbe the ratio of gear of j level gear pair, i ₀for the ratio of gear requiring.

Described flank of tooth contact fatigue strength constraint condition, tooth root bending fatigue strength constraint condition are:

Cogged flank of tooth contact fatigue strength safety coefficient is all greater than minimal-contact fatigue strength safety coefficient, and cogged tooth root bending fatigue strength safety coefficient is all greater than minimum bend fatigue strength safety coefficient, that is:

$\&ForAll;S_{\mathrm{Hj}}>S_{H\min },$

In formula: S _hjfor the flank of tooth contact fatigue strength safety coefficient of each gear; S _fjfor the tooth root bending fatigue strength safety coefficient of each gear.

Being limited to up and down of described optimized variable:

Describedly in abutting connection with condition be:

L > d _ap, that is: $2a_{\mathrm{sp}}\sin \frac{\mathrm{\&pi;}}{n_p}>d_{\mathrm{ap}},$

In formula: L is the distance between adjacent two planetary gear centers, d _apfor maximum row star-wheel tip diameter, n _pfor number of planet gears, a _spfor sun gear and planetary gear centre distance.

Described concentric condition is:

$\frac{z_s+z_p}{\cos {\mathrm{\&alpha;}}_{\mathrm{sp}}}=\frac{z_r-z_p}{\cos {\mathrm{\&alpha;}}_{\mathrm{pr}}},$

In formula: α _prfor the actual engaging angle of planetary gear and ring gear Meshing Pair; z _s, z _p, z _rbe respectively sun gear, planetary gear, the ring gear number of teeth.

Described assembled condition is:

In formula: z _s, z _rbe respectively sun gear, the ring gear number of teeth, n _pfor number of planet gears.

In said method, in rounding, module is got 0.5 integral multiple.

Preferably, described gear train assembly is the gear train assembly in gear case of blower.

Than prior art, gear train assembly Optimization Design of the present invention can be carried out by computer auxiliaring means the iterative of multiple schemes, and finds the optimum solution obtaining in whole optimization space, and efficiency is higher; And can be by the setting of objective function, make the parameter of optimization close towards the direction of manual intervention, reduce the randomness of optimizing.Gear train assembly Optimization Design of the present invention is by the self-characteristic of combination gear case, use population bilevel optimization to obtain optimized variable, ground floor optimization lays particular emphasis on the less requirement of standard deviation that meets all outer rotor contact fatigue strength safety coefficient, and obtains feasible number of teeth scheme; Second layer optimization lays particular emphasis on the less requirement of bending fatigue strength safety coefficient standard deviation that meets all outer rotors, and draws the refinement allocation plan including all design variables.The invention enables the gear train assembly of optimization in meeting every intensity index, the life-span gap of each outer rotor is less, can effectively avoid the normal short-board effect occurring in gear train assembly, improves the reliability of gear train assembly.

Brief description of the drawings

Fig. 1 is the module map of partly directly driving gear case of embodiments of the invention.

Fig. 2 is the cut-open view that partly directly drives gear case of embodiments of the invention.

Wherein:

1, input planet carrier	2, first order planet carrier upwind bearing
		3, front casing	4, first order ring gear
5, first order planetary gear	6, first order planetary bearing
		7, planet axis	8, first order sun gear
9, wind direction bearing under planet carrier	10, second level planet carrier
		11, second level planet carrier upwind bearing	12, wind direction bearing under the planet carrier of the second level
13, second level sun gear	14, output shaft
		15, second level planetary bearing	16, second level planet axis
17, second level planetary gear	18, rear box
		19, second level ring gear	20, middle casing

Embodiment

In order to make the object, technical solutions and advantages of the present invention clearer, describe the present invention below in conjunction with the drawings and specific embodiments.

The method for designing of the present embodiment is based on Particle Swarm Optimization, but is optimized on its basis and improves.The present embodiment is to be optimized by Matlab software.

Being described below of Particle Swarm Optimization:

Particle Swarm Optimization is a kind of random optimization method based on colony intelligence, instruct Optimizing Search by the swarm intelligence that in population, interparticle cooperation and competition produces, fast convergence rate, ability of searching optimum is strong, and need to, by the specific information of problem itself, can not solve most of optimization problem.

The ultimate principle of Particle Swarm Optimization is: potential solution is regarded as to a particle, in solution space, fly, when optimization, make multiple particles according to direction and the position of self and the individual experience adjustments flight that closes on, thereby reach the object of searching optimum solution from the overall situation.The dimension of solution space is the dimension of optimized variable.Suppose, in the target search space of a D dimension, to form group by m particle, i particle is expressed as x _i=(x _i1, x _i2..., x _iD) ^t, i=1,2 ... m, i particle is x in the position of the search volume of D dimension _i, the optimal location that i particle searches is up to now designated as the optimal location that all population search is up to now designated as g ^best, the flying speed of i particle is designated as V _i, each particle awing want simultaneously to oneself

with overall g ^best2 approach and regulate the speed and position.The speed of the k+1 time iteration of i particle is modified to:

$V_i^{k+1}={\mathrm{\&omega;}}_1{V}_i^k+c_1*{\mathrm{rand}}_1*(p_i^{\mathrm{best}}-x_i)+c_1*{\mathrm{rand}}_2*(g^{\mathrm{best}}-x_i)---\left(1\right);$

Position correction is:

$x_i^k=x_i+V_i^{k+1}---\left(2\right);$

In formula, ω is inertia weight, reduces c with iterative process linearity between [0.9,0.4] ₁, c ₂for the study factor, be two nonnegative constants, rand ₁, rand ₂it is the random number between [0,1].

Formula

the renewal of particle rapidity, formed by following 3 parts: Part I represents that particle present speed is subject to the impact of previous generation particle rapidity, Part II represents the degree of awareness of particle, the level of learning that is particle to self optimum solution, Part III is social part, represents the level of learning of particle to colony's globally optimal solution.

The step of particle group optimizing is:

1) position of each particle and speed in initialization population;

2) population is carried out to objective function evaluation;

3) obtain each particle

g with whole population ^best;

4), according to formula (1), (2), adjust position and the speed of each particle;

5), if meet end condition, stop calculating, otherwise return to 2.

The improvement of the Optimization Design in the present embodiment is embodied in:

The present embodiment provides a kind of method for designing of hierarchy optimization, and the method completes by bilevel optimization: ground floor optimization lays particular emphasis on the less requirement of standard deviation that meets all outer rotor contact fatigue strength safety coefficient, and obtains feasible number of teeth scheme; Second layer optimization lays particular emphasis on the less requirement of standard deviation that meets all outer rotor bending fatigue safety coefficient, and all Optimal Parameters of rounding; Every one deck optimization can complete by a whole conventional particle group optimizing process.

Propose optimization method of the present invention and have following reason:

The optimization of planetary transmission system possesses intrinsic feature itself, if its allocation plan is simply applied mechanically conventional Particle Swarm Optimization Model unreasonable.

Planetary transmission system can comprise multi-stage gear pair, and these gear pairs are likely planet wheel pair or parallel teeth wheel set, or both combinations.The optimization of planetary transmission system possesses following features:

Feature 1: every one-level planet pinion pair all needs to follow in abutting connection with multiple constraints such as condition, concentric condition, assembled conditions, and the overall ratio that gear pairs at different levels form should meet ratio error constraint; Below specifically introduce each constraint condition.

In abutting connection with condition (inapplicable to parallel teeth wheel set, be only suitable for planet wheel pair):

In planetary gears, planetary gear, sun gear and ring gear are all arranged on the same plane perpendicular to gear shaft, multiple planetary gears are distributed between sun gear and ring gear, and for two adjacent planetary gears are not collided with each other, requiring has certain gap between its point circle.

If the distance between adjacent two planetary gear centers is L, maximum row star-wheel tip diameter is d _ap, in abutting connection with condition be:

L > d _apthat is: $2a_{\mathrm{sp}}\sin \frac{\mathrm{\&pi;}}{n_p}>d_{\mathrm{ap}};$

In formula: n _p---number of planet gears;

A _sp---sun gear and planetary gear centre distance.

Condition (inapplicable to parallel teeth wheel set, to be only suitable for planet wheel pair) with one heart:

The feature of planetary transmission is that input is coaxial cable with output, and the axis of sun gear and the axis of planet carrier are on same straight line, overlap.For ensureing the correct engagement under sun gear and planet carrier axis coincidence condition, the operating center distance of the each Meshing Pair being made up of sun gear and planetary gear must equate, that is:

$\frac{z_s+z_p}{\cos {\mathrm{\&alpha;}}_{\mathrm{sp}}}=\frac{z_r-z_p}{\cos {\mathrm{\&alpha;}}_{\mathrm{pr}}};$

In formula: α _prthe actual engaging angle of-planetary gear and ring gear Meshing Pair; z _s, z _p, z _r-be respectively sun gear, planetary gear, the ring gear number of teeth.

Assembled condition (inapplicable to parallel teeth wheel set, to be only suitable for planet wheel pair):

For the Planetary Gear Transmission of NGW pattern, in the time that planetary gear number is greater than 1, after first planetary gear packs into and engages with two sun gears, the relative position of sun gear and ring gear has just been determined.If will pack uniformly other planetary gears into, just must meet some requirements.Assembled condition is:

In formula: z _s, z _rbe respectively sun gear, the ring gear number of teeth, n _pfor number of planet gears.

Ratio error constraint condition (planet wheel pair, parallel teeth wheel set are all suitable for):

The number percent of ratio error need be in certain scope:

${\mathrm{Err}}_{\min }<(\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{i}_j-i_0)/i_0<{\mathrm{Err}}_{\max };$

In formula: n is the progression of gear train assembly gear pair, i _jbe the ratio of gear of j level gear pair, i ₀for the ratio of gear requiring.

Strength constraint (planet wheel pair, parallel teeth wheel set are all suitable for):

Cogged flank of tooth contact fatigue strength safety coefficient is all greater than minimal-contact fatigue strength safety coefficient, and cogged tooth root bending fatigue strength safety coefficient is all greater than minimum bend fatigue strength safety coefficient, that is: $\&ForAll;S_{\mathrm{Hj}}>S_{H\min },$

$\&ForAll;S_{\mathrm{Fj}}>S_{F\min };$

Number of teeth constraint (planet wheel pair, parallel teeth wheel set are all suitable for):

Described number of teeth constraint condition comprises: to all gear pairs that are meshed, the number of teeth correspondence of two gears that are meshed meets highest common divisor said conditions gcd (z ₁, z ₂)≤k, k is less than or equal to 3 positive integer.Further, the cogged number of teeth should all be greater than 17; Further, the gear that is greater than 100 for the number of teeth, for easy to process, its number of teeth should not be prime number.

For all gear pairs that are meshed, no matter be Planetary Gear Transmission or parallel gears transmission, all should meet the number of teeth requirement of above-mentioned two gears that are meshed; For the Multi-stage transmission system being formed by multiple gear pairs, no matter be Gear Planet Transmission or parallel gears transmission, all should meet ratio error constraint condition.

Feature 2: according to Optimization Experience, the standard deviation of all outer rotor contact fatigue strength safety coefficient is subject to the impact of modulus, centre distance larger (after modulus is definite, centre distance can be determined by the number of teeth), and be subject to the impact of the facewidth less, and helix angle generally get can value the upper limit.The bending fatigue strength safety coefficient standard deviation of all outer rotors, except being subject to the impact of modulus, centre distance, is subject to the impact of the facewidth also larger.

Feature 1 is comparatively harsh constrained, has determined that population most of particle in evolution cannot form efficient solution;

Feature 2 is the difference of optimization aim and the impact of optimized variable on optimization aim, has determined to adopt the different stages to be optimized, the emphasis difference of the optimization aim that each stage adopts.

Below elaborating for the Optimization Design of the present embodiment:

The objective function that a, setting are optimized:

In Planetary Gear Transmission, because the ring gear number of teeth is maximum, ring gear be herein the gear teeth at inner gear ring, be phase external gear wheel and fixed.The gear teeth of this ring gear engage least number of times in whole life cycle, also can as planetary gear, not bear two-sided load, so its contact and bending fatigue strength generally all can be more high than sun gear and planetary gear.So the method for in some document, all gears all being carried out to equal strength optimization is irrational in the past, be also difficult to realize.

The optimization of the present embodiment with all outer rotors in planetary transmission system (for the gear pair of NGW form, outer rotor is sun gear and planetary gear) the standard deviation, the standard deviation of bending fatigue strength safety coefficient of contact fatigue strength safety coefficient be objective function, embodied better the inherent characteristics of planet wheel pair.Certainly, be also applicable to parallel teeth wheel set simultaneously.

Contact fatigue strength safety coefficient standard deviation:

$f_H=\sqrt{\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(S_{\mathrm{Hj}}-{\stackrel{\&OverBar;}{S}}_H)}^2};$

${\stackrel{\&OverBar;}{S}}_H=\frac{1}{H}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{S}_{\mathrm{Hj}};$

The total quantity that wherein N is all outer rotors, S _hjfor the contact fatigue strength safety coefficient of each outer rotor, for the mean value of the contact fatigue strength safety coefficient of each outer rotor;

Bending fatigue strength safety coefficient standard deviation:

$f_F=\sqrt{\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(S_{\mathrm{Fj}}-{\stackrel{\&OverBar;}{S}}_F)}^2};$

${\stackrel{\&OverBar;}{S}}_F=\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{S}_{\mathrm{Fj}};$

Wherein S _fjfor the bending fatigue strength safety coefficient of each outer rotor, for the mean value of the bending fatigue strength safety coefficient of each outer rotor.

Optimized model is with f _hand f _fthe weighted mean value of the two is optimization aim function:

f=a ₁f _H+a ₂f _F

In formula, a ₁, a ₂weight factor, a ₁+ a ₂=1.

The optimized variable that b, setting are optimized:

The optimized variable of gear train assembly generally comprises ratio of gear i, number of teeth z, modulus m, helixangleβ, facewidth b.Suppose that whole kinematic train has the transmission of n level, the optimized variable of ratio of gear has i ₁, i ₂... i _n-1, the ratio of gear of afterbody can be by formula

try to achieve, remember that all ratio of gear optimized variables are

each gear number of teeth is subject to the restriction of predefined ratio of gear and the restriction that condition, assembled condition etc. retrain with one heart, in the number of teeth of Meshing Pair at different levels, only need choose each driving gear number of teeth z ₁, z ₂... z _nfor optimized variable, remember that all number of teeth optimized variables are

also need in addition to choose the modulus m of gear pairs at different levels ₁, m ₂... m _n, remember that all modulus optimized variables are helixangleβ ₁, β ₂... β _n, remember that all helix angle optimized variables are

the work facewidth of every one-level transmission is with the ratio of the reference diameter of the work facewidth and driving gear, i.e. coefficient of facewidth replace, remember that all coefficient of facewidth optimized variables are

the facewidth

d wherein _jfor the reference diameter of driving gear; Use coefficient of facewidth but not the facewidth itself as optimized variable, can control better the variation range of the facewidth, also more reasonably separated.

All optimized variable vectors are:

The constraint condition that c, setting are optimized

Constraint condition except need meet the each constraint condition in These characteristics 1,

Also need to set the bound of optimized variable, that is:

D, Optimization Steps:

One, global optimization flow process:

This optimization divides two levels to carry out, and first sets population scale n, and ground floor is k from scale ₁* the population of n starts to optimize; Set ground floor particle group optimizing iterations g ₁, second layer particle group optimizing iterations g ₂; Set the inertia weight ω of ground floor particle group optimizing ₁, study factor c ₁₁and c ₁₂; Set the inertia weight ω of second layer particle group optimizing ₂, study factor c ₂₁and c ₂₂; Set the weight factor a of objective function in ground floor particle group optimizing ₁₁, a ₁₂, wherein a ₁₁+ a ₁₂=1; The weight factor a of objective function in second layer particle group optimizing ₂₁, a ₂₂, wherein a ₂₁+ a ₂₂=1.Wherein, a ₁₁> a ₁₂, a ₂₁< a ₂₂, ω ₁> ω ₂, c ₁₁< c ₂₁, c ₁₂< c ₂₂.

In ground floor Optimization Steps, lay particular emphasis on the less requirement of standard deviation that meets all outer rotor contact fatigue strength safety coefficient, f in objective function _hcorresponding weight factor should compare f _fhigher.Optimized variable is

all optimized variables are all processed as continuous variable.The Optimizing Flow of ground floor is a particle group optimizing flow process of having improved.After ground floor optimization completes, the population that is n by the scale that obtains meeting each constraint condition.The inertia weight ω of ground floor ₁should be than the inertia weight ω of the second layer ₂greatly, study factor c ₁₁, c ₁₂than second layer c ₂₁, c ₂₂little.So when ground floor is optimized, particle is subject to the impact of speed own, position larger, and be subject to the impact of memory own and population less, so its flight is comparatively dispersed, be not easy to be absorbed in locally optimal solution;

First second layer optimization solidify the number of teeth in optimized variable and ratio of gear, and optimized variable only comprises modulus, helix angle and coefficient of facewidth, becomes

in second layer Optimization Steps, lay particular emphasis on the less requirement of bending fatigue strength safety coefficient standard deviation that meets all outer rotors, f in objective function _fcorresponding weight factor should compare f _hhigher.The Optimizing Flow of the second layer is a typical particle cluster algorithm flow process.Due to the inertia weight ω of ground floor ₁than the inertia weight ω of the second layer ₂greatly, study factor c ₁₁, c ₁₂than second layer c ₂₁, c ₂₂little, so when the second layer is optimized, particle is subject to the impact of speed own, position less, and be subject to the impact of memory own and population larger, so its air objective is stronger, more easily convergence.

Two, ground floor Optimizing Flow:

In this step, objective function weight factor a ₁₁> a ₁₂, target setting function is f=a ₁₁f _h+ a ₁₂f _f, optimized variable is

due to uncured ratio of gear and the number of teeth, population is subject to the restriction of concentric condition and assembled condition and to produce the possibility of solution trivial higher.So during this layer is optimized, need increase a circulation of controlling number of effective particles amount on the basis of conventional particle cluster algorithm, to ensure that population reaches certain scale.

Therefore its Optimizing Flow is:

1) initialization a group particle, population scale is 3 times of default population scale n, then each number of teeth in rounding particle

and whether checking meets each constraint condition;

2) in the population scale of selection 3*n, choose n the particle that meets each constraint condition, calculate its target function value; And by the position mark of this n particle be

choose the particle that described target function value is minimum, be labeled as g ^best;

3) in initialization gained population, the speed of each particle is

0.25 < rand _i< 0.75;

4) enter iteration phase, setting flying speed is:

$V_i^{k+1}={\mathrm{\&omega;}}_1{V}_i^k+{\mathrm{<figure-callout\; id="11"\; label="c"\; filenames="HDA0000485447940000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_{11}*{\mathrm{rand}}_1*(p_i^{\mathrm{best}}-x_i)+{\mathrm{<figure-callout\; id="12"\; label="c"\; filenames="HDA0000485447940000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_{12}*{\mathrm{rand}}_2*(g^{\mathrm{best}}-x_i);$

In formula, ω ₁for inertia weight, reduce c with iterative process linearity between [0.9,0.4] ₁₁, c ₁₂for the study factor, be two nonnegative constants, rand ₁, rand ₂it is the random number between [0,1]; This random number can be selected arbitrarily;

Population reposition is: $x_i^k=x_i+V_i^{k+1};$

5) the rounding number of teeth, the ratio of gear of reruning, verifies whether each particle meets constraint condition, for ungratified particle, repeating step 4 regenerates reposition;

6) repeating step 4), 5) three times, if particle is still solution trivial, with

substitute solution trivial;

7) calculate the target function value of each particle, more each particle current goal functional value is corresponding with it

target function value, and will

be set as the position that target function value is relatively minimum; The optimal objective function value of all particles and g in more current population ^besttarget function value, and by g ^bestbe set as the position that target function value is relatively minimum;

8) repeating step 4) to 7), until reach end condition; Acquisition meets the population that the scale of each constraint condition is n, and now, this population has obtained feasible number of teeth allocation plan, and g ^bestobtain the standard deviation of contact fatigue strength safety coefficient and the standard deviation of bending fatigue strength safety coefficient after ground floor particle group optimizing.End condition is now: the iterations g that reaches ground floor ₁.

Three, second layer optimized algorithm flow process:

In this step, reset new objective function f=a ₂₁f _h+ a ₂₂f _f, objective function weight factor a ₂₁< a ₂₂, optimized variable is

the method of solidifying ratio of gear and the number of teeth be by

middle correspondence

the Speed Setting of dimension is 0.Now population is no longer subject to the restriction of concentric condition and assembled condition, so this layer of optimization can adopt conventional particle group optimizing mode.

1) reset objective function f=a ₂₁f _h+ a ₂₂f _f, for evaluate the population obtaining after ground floor particle group optimizing each particle and

g ^besttarget function value;

2) set in

the speed of dimension is 0;

3) enter second layer iteration phase, setting flying speed is:

$V_i^{k+1}={\mathrm{\&omega;}}_2{V}_i^k+c_{21}*{\mathrm{rand}}_1*(p_i^{\mathrm{best}}-x_i)+c_{22}*{\mathrm{rand}}_2*(g^{\mathrm{best}}-x_i);$

In formula, ω ₂for inertia weight, reduce c with iterative process linearity between [0.9,0.4] ₂₁, c ₂₂for the study factor, be two nonnegative constants, rand ₁, rand ₂it is the random number between [0,1];

Population reposition is: $x_i^k=x_i+V_i^{k+1};$

4) calculate the target function value of each particle, more each particle current goal functional value is corresponding with it

target function value, and will

be set as the position that target function value is relatively minimum; The optimal objective function value of all particles and g in more current population ^besttarget function value, and by g ^bestbe set as the position that target function value is relatively minimum;

5) repeating step 3), 4), until reach end condition; The population that now scale is n meets each constraint condition, and g ^bestobtain contact fatigue strength safety coefficient standard deviation and bending fatigue strength safety coefficient standard deviation after second layer particle group optimizing;

Above-mentioned steps 5) in end condition be set as: reach maximum iteration time g ₁+ g ₂or meet precision conditions:

G ^bestthe variable quantity of j iteration of target function value f accumulative total be less than a predefined threshold value e, | f _n-f _n-j| < e;

Wherein f _nfor current g ^besttarget function value, f _n-jfor the g before j iteration ^besttarget function value.

6) rounding g ^bestin modulus, calculate and the rounding facewidth, thereby obtain the final numerical value of whole described optimized variable X.

In the embodiment of the present invention: the iterations g of ground floor particle group optimizing ₁be no less than the iterations g of second layer particle group optimizing 30 times ₂be no less than 20 times.

Because modern Gear Manufacture Industry is no longer harsh to the requirement of modulus, and the most of customization cutter that adopts of current gear manufacturer, can not be subject to the restriction of master gear modulus, module can be got 0.5 integral multiple value and be carried out rounding.

Below in conjunction with accompanying drawing, introduce the process of optimization of the concrete gear train assembly of the above-mentioned optimization method of a use.

The gear case that partly directly drives in this example is set as power input 3300KW, input speed 12.6rpm, and output speed 315rpm, ratio of gear requires i ₀=25, optimize 175200 hours life-spans.Two-stage NGW Gear Planet Transmission, input end is the planet carrier of first order transmission, and output terminal is the sun gear of second level transmission, and first order planetary gear number is 5, and second level planetary gear number is 3, driving-chain basic structure is as shown in Figure 1.

While requiring optimal design, set gear material and heat treatment mode, for example: gear material is 17CrNiMo6, thermal treatment is carburizing and quenching, this is for presetting, after material decision, look into again relevant handbook, as GL specification 2010 editions, i.e. Guideline for the Certification of Wind Turbines Edition2010 ", to determine the fatigue strength binding occurrence that will optimize.The pressure angle of gear pairs at different levels is set as 20 °, equates with the facewidth of each gear in gear pair, and the precision of outer rotor is 5 grades, 6 grades of ring gear precision.

Because gear case of blower is gearbox, can regard its input end as output terminal, output terminal is regarded input end as, becomes reducing gear, and two sun gears are input gear at different levels.

Optimized variable:

The gear being optimized in this example is first order sun gear, planetary gear and second level sun gear and planetary gear, therefore optimized variable is:

Constraint condition: comprise number of teeth constraint condition, in abutting connection with condition, with one heart condition and assembled condition etc., all with noted earlier, no longer repeat at this.

Ratio error constraint is set as Err _min=-1%, Err _max=1% is that ratio error scope is: $-1<(\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{i}_j-i_0)/i_0<1\%;$

Minimal-contact fatigue strength safety coefficient, minimum bend fatigue strength safety coefficient require to be respectively S _hmin=1.2, S _fmin=1.5,

The scope of optimized variable is set as: X _min=[3,17,17,15,12,0,0,0.4,0.4] ^t, X _max=[5,60,60,30,25,7,7,1.8,1.8] ^t

Particle group optimizing parameter:

Set population scale n=30, ground floor iterations g ₁=30, second layer iterations g ₂=20.

Set ground floor particle group optimizing parameter ω ₁=0.8, c ₁₁=1.5, c ₁₂=1.5, set second layer particle group optimizing parameter ω ₂=0.6, c ₂₁=2, c ₂₂=2.Such setting, the inertia weight of ground floor is larger than the second layer, and the study factor is less than the second layer, when ground floor is optimized, particle is subject to the impact of speed own, position larger, and is subject to the impact of memory own and population less, so its flight is comparatively dispersed, and is not easy to be absorbed in locally optimal solution; When the second layer is optimized, particle is subject to the impact of speed own, position less, and is subject to the impact of memory own and population larger, so its air objective is stronger, and more easily convergence.

Set objective function weight factor a in ground floor ₁₁=0.8, a ₁₂=0.2, objective function is f=0.8f _h+ 0.2f _f; After ground floor is optimized, obtain and meet the population that the scale of each constraint condition is n, now, this population has obtained feasible number of teeth scheme, and g ^bestobtain the standard deviation of contact fatigue strength safety coefficient and the standard deviation of bending fatigue strength safety coefficient after ground floor is optimized; Current g ^bestfor

By current g ^bestcan obtain current Design of Gear Drive System scheme, as shown in Table 1:

Table one: the Design of Gear Drive System scheme obtaining after ground floor optimization

The standard deviation of the contact fatigue strength safety coefficient of all outer rotors is: f _h=0.0352;

The standard deviation of the bending fatigue strength safety coefficient of all outer rotors is: f _f=0.7685;

Can see, now the standard deviation of contact fatigue strength safety coefficient is less, and the standard deviation of bending fatigue strength safety coefficient is also in larger value.This is because of in this layer of optimization, is to be close to main target with the contact fatigue strength safety coefficient of each outer rotor.From this table one, can see, although ground floor optimization has had a preliminary optimal value to parameters, it is feasible wherein only having " number of teeth " this parameter; Other parameter, as centre distance, modulus etc. are non-integer, i.e. infeasible (from manufacturing angle easy to process, normally integer), so ground floor optimization is to obtain feasible number of teeth scheme.

Set objective function weight factor a in the second layer ₂₁=0.2, a ₂₂=0.8, objective function is f=0.2f _h+ 0.8f _f.

Optimum results: by (containing ground floor iterations) after 50 iteration optimization, the population that now scale is n meets each constraint condition, and g ^bestobtain the standard of lower contact fatigue strength safety coefficient and the standard of lower bending fatigue strength safety coefficient;

Obtain the best particle of population as follows:

The rounding facewidth is also joined and is gathered after centre distance, obtains the design proposal of following gear train assembly:

Table two: the Design of Gear Drive System scheme obtaining after second layer optimization

After the second layer is optimized, the standard deviation of the contact fatigue strength safety coefficient of all outer rotors is: f _h=0.0219;

The standard deviation of the bending fatigue strength safety coefficient of all outer rotors is: f _f=0.5128;

Can see, in final plan, the contact fatigue strength safety coefficient of each outer rotor and bending fatigue strength safety coefficient can both meet the requirement of minimal-contact fatigue strength/bending fatigue strength safety coefficient, and the standard deviation of safety coefficient is less value, the reliability index that these gears are described is comparatively approaching, does not have short-board effect.The standard deviation of bending fatigue strength safety coefficient is slightly larger, the bending fatigue strength safety coefficient that in two-stage NGW is all planetary gear is less than normal, this is because tooth of planet need to be born two-sided load, and ring gear and sun gear only bear one side load, planetary gear should engage with ring gear, engage with sun gear again, bear two-sided load.And ring gear only engages with planetary gear, and its number of teeth is more, and the load of relatively bearing is less.

The present invention does not treat with a certain discrimination planetary gear and ring gear, the sun gear facewidth, but conventionally the Design of Tooth Width of Right Shaft of planetary gear can be become to slightly larger than ring gear and sun gear in concrete structure design, thereby increases its bending fatigue safety coefficient.So in concrete structure design, the standard deviation of bending fatigue strength safety coefficient can be less than the value of current optimization.

After the second layer is optimized, all outer rotors are when the standard deviation that ensures contact fatigue strength safety coefficient reduces, and the standard deviation of its bending fatigue strength safety coefficient has also obtained obvious reduction.This is to be close to main target because start in second layer optimization with the bending fatigue strength safety coefficient of each outer rotor.But because now number of teeth scheme is fixing, the design variable that can all exert an influence to two performances is less, so the change that amplitude is larger can't appear in objective function.This also proves, the feature of bilevel optimization is: feasible program is searched in ground floor optimization, makes the quick optimizing of population; Second layer optimization is to carry out slowly and the optimizing of refinement to more excellent direction under existing conceptual design.Bilevel optimization mode combines, and makes whole optimizing process neither can be absorbed in faster locally optimal solution, can find again practically, and tooth scheme is joined in the refinement of superior performance.

The gear case sectional structure schematic diagram (non-strict ratio) that accompanying drawing 2 is this prioritization scheme.With reference to the accompanying drawings 2, the moment of torsion of hub of wind power generator by main shaft be passed to gear case-input planet carrier 1 after, after first order NGW Gear Planet Transmission speedup, export to second level planet carrier 10 by first order sun gear 8, the two passes through spline joint, wherein sun gear is male splines, and planet carrier is female spline; After the Gear Planet Transmission speedup of the second level, export to output shaft 14 by second level sun gear 13, the two is by spline joint, and wherein sun gear is female spline, and output shaft is male splines.

Comprise gear train at gear train assembly, gear train comprises multiple gear pairs, these gear pairs are likely Planetary Gear Transmission or parallel gears transmission, the difference about planet pinion between secondary and parallel teeth wheel set: planet pinion pair comprises: gear ring, at least 3 planetary gears, sun gear; And parallel gears pair is equivalent to two transmissions between gear, so fairly simple, do not need to consider in abutting connection with, with one heart, the constraint condition such as assembling, only need to consider the bound of number of teeth constraint condition, ratio error constraint condition, flank of tooth contact fatigue strength constraint condition, tooth root bending fatigue strength constraint condition, optimized variable just.Therefore, though only chosen NGW Gear Planet Transmission mode in the present embodiment for optimizing case.But should understand the optimization method proposing in the present invention is suitable for too for parallel gears transmission.

The present invention is not limited to aforementioned embodiments, and those skilled in the art, under the enlightenment of the technology of the present invention marrow, also may make other and change, but as long as function and the present invention of its realization are same or similar, all should belong to protection scope of the present invention.

Claims (16)

1. the Design of Gear Drive System method based on population bilevel optimization, described gear train assembly comprises 2 and above planet wheel pair or parallel teeth wheel set, or the combination of at least 1 planet wheel pair and at least 1 parallel teeth wheel set; Obtain the optimum solution g of the optimized variable X of described gear train assembly by population dual-layer optimization ^best; Described optimized variable X comprises: ratio of gear i, number of teeth z, modulus m, helixangleβ, and coefficient of facewidth

described coefficient of facewidth for the ratio of the reference diameter of the work facewidth and driving gear, it is characterized in that, described Design of Gear Drive System method comprises the following steps:

A, setting the objective function of optimizing is f=a ₁f _h+ a ₂f _f, in formula, f _hfor the standard deviation of contact fatigue strength safety coefficient, f _ffor the standard deviation of bending fatigue strength safety coefficient, a ₁, a ₂weight factor, a ₁+ a ₂=1;

B, sets optimized variable to be optimized and is in formula,

for all ratio of gear optimized variables,

for all number of teeth optimized variables,

for all modulus optimized variables,

for all helix angle optimized variables,

for all coefficient of facewidth optimized variables;

C, sets the constraint condition of optimizing;

D, based on aforesaid objective function and constraint condition, obtains the optimum solution g of optimized variable by population bilevel optimization ^best:

First set population scale n; Ground floor is k from scale ₁* the population of n starts to optimize;

Set the iterations g of ground floor particle group optimizing ₁;

Set the inertia weight ω of ground floor particle group optimizing ₁, study factor c ₁₁and c ₁₂; Set the objective function weight factor a of ground floor particle group optimizing ₁₁, a ₁₂, wherein a ₁₁+ a ₁₂=1;

Set the iterations g of second layer particle group optimizing ₂;

Set the inertia weight ω of second layer particle group optimizing ₂, study factor c ₂₁and c ₂₂; Set the objective function weight factor a of second layer particle group optimizing ₂₁, a ₂₂, wherein a ₂₁+ a ₂₂=1;

Wherein, a ₁₁> a ₁₂, a ₂₁< a ₂₂, ω ₁> ω ₂, c ₁₁< c ₂₁, c ₁₂< c ₂₂;

The objective function of setting ground floor particle group optimizing is f=a ₁₁f _h+ a ₁₂f _f, and the optimized variable of ground floor particle group optimizing is

after ground floor particle group optimizing, select and meet the population that the scale of each constraint condition is n, and obtain feasible number of teeth allocation plan;

Reset the new objective function f=a of second layer particle group optimizing ₂₁f _h+ a ₂₂f _f, when second layer particle group optimizing by number of teeth optimized variable

with ratio of gear optimized variable

solidify, the optimized variable of second layer particle group optimizing is

E, rounding g ^bestin modulus, calculate and the rounding facewidth, thereby obtain the final numerical value of whole described optimized variable X.

2. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 1, is characterized in that, ground floor particle group optimizing comprises the following steps:

11) initialization a group particle, population scale is the k of default population scale n ₁doubly, then each number of teeth in rounding particle

, and whether checking meets each constraint condition;

12) select k ₁* in the population scale of n, choose n the particle that meets each constraint condition, calculate its target function value; And by the position mark of this n particle be

choose the particle that described target function value is minimum, be labeled as g ^best;

13) in initialization gained population, the speed of each particle is

0.25 < rand _i< 0.75;

14) enter iteration phase, setting flying speed is:

$V_i^{k+1}={\mathrm{\&omega;}}_1{V}_i^k+c_{11}*{\mathrm{rand}}_1*(p_i^{\mathrm{best}}-x_i)+c_{12}*{\mathrm{rand}}_2*(g^{\mathrm{best}}-x_i);$

In formula, ω ₁for inertia weight, reduce c with iterative process linearity between [0.9,0.4] ₁₁, c ₁₂for learning the factor, be two nonnegative constants, rand ₁, rand ₂it is the random number between [0,1];

Population reposition is: $x_i^k=x_i+V_i^{k+1};$

15) the rounding number of teeth, the ratio of gear of reruning, verifies whether each particle meets constraint condition, for ungratified particle, repeating step 14 regenerates reposition;

16) repeating step 14), 15) several times, if particle is still solution trivial, with

substitute solution trivial;

17) calculate the target function value of each particle, more each particle current goal functional value is corresponding with it

target function value, and will be set as the position that target function value is relatively minimum; The optimal objective function value of all particles and g in more current population ^besttarget function value, and by g ^bestbe set as the position that target function value is relatively minimum;

18) repeating step 14)-17), until reach the iterations g of ground floor ₁; Acquisition meets the population that the scale of each constraint condition is n, and now, this population has obtained feasible number of teeth allocation plan, and g ^bestobtain the standard deviation of contact fatigue strength safety coefficient and the standard deviation of bending fatigue strength safety coefficient after ground floor particle group optimizing.

3. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 2, is characterized in that, second layer particle group optimizing comprises the following steps:

21) reset objective function f=a ₂₁f _h+ a ₂₂f _f, for evaluate the population obtaining after ground floor particle group optimizing each particle and

g ^besttarget function value;

22) set

in

the speed of dimension is 0;

23) enter second layer iteration phase, setting flying speed is:

$V_i^{k+1}={\mathrm{\&omega;}}_2{V}_i^k+c_{21}*{\mathrm{rand}}_1*(p_i^{\mathrm{best}}-x_i)+c_{22}*{\mathrm{rand}}_2*(g^{\mathrm{best}}-x_i);$

In formula, ω ₂for inertia weight, reduce c with iterative process linearity between [0.9,0.4] ₂₁, c ₂₂for the study factor, be two nonnegative constants, rand ₁, rand ₂it is the random number between [0,1];

Population reposition is: $x_i^k=x_i+V_i^{k+1};$

24) calculate the target function value of each particle, more each particle current goal functional value is corresponding with it

target function value, and will

be set as the position that target function value is relatively minimum; The optimal objective function value of all particles and g in more current population ^besttarget function value, and by g ^bestbe set as the position that target function value is relatively minimum;

25) repeating step 23)-24), until reach end condition; The population that now scale is n meets each constraint condition, and g ^bestobtain contact fatigue strength safety coefficient standard deviation and bending fatigue strength safety coefficient standard deviation after second layer particle group optimizing.

4. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 3, is characterized in that described step 25) in end condition be set as: reach maximum iteration time g ₁+ g ₂or meet precision conditions:

G ^bestthe variable quantity of j iteration of target function value f accumulative total be less than a predefined threshold value e, | f _n-f _n-j| < e;

Wherein f _nfor current g ^besttarget function value, f _n-jfor the g before j iteration ^besttarget function value.

5. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 1, is characterized in that,

The standard deviation f of described contact fatigue strength safety coefficient _hfor:

$f_H=\sqrt{\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(S_{\mathrm{Hj}}-{\stackrel{\&OverBar;}{S}}_H)}^2},$

${\stackrel{\&OverBar;}{S}}_H=\frac{1}{H}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{S}_{\mathrm{Hj}},$

The total quantity that wherein N is all outer rotors, S _hjfor the contact fatigue strength safety coefficient of each outer rotor,

for the mean value of the contact fatigue strength safety coefficient of each outer rotor;

The standard deviation f of described bending fatigue strength safety coefficient _ffor:

$f_F=\sqrt{\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{(S_{\mathrm{Fj}}-{\stackrel{\&OverBar;}{S}}_F)}^2},$

${\stackrel{\&OverBar;}{S}}_F=\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{S}_{\mathrm{Fj}},$

The total quantity that wherein N is all outer rotors, S _fjfor the bending fatigue strength safety coefficient of each outer rotor,

for the mean value of the bending fatigue strength safety coefficient of each outer rotor.

6. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 1, it is characterized in that, the constraint condition of described planet wheel pair or parallel teeth wheel set comprises the bound of number of teeth constraint condition, ratio error constraint condition, flank of tooth contact fatigue strength constraint condition, tooth root bending fatigue strength constraint condition, optimized variable.

7. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 6, is characterized in that, the constraint condition of described planet wheel pair also comprises in abutting connection with condition, concentric condition and assembled condition.

8. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 6, is characterized in that, described number of teeth constraint condition comprises: the number of teeth correspondence of two gears that are meshed meets highest common divisor said conditions gcd (z ₁, z ₂)≤k, k is less than or equal to 3 positive integer.

9. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 6, is characterized in that, described ratio error is constrained to:

${\mathrm{Err}}_{\min }<(\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{i}_j-i_0)/i_0<{\mathrm{Err}}_{\max },$

In formula: n is the progression of gear train assembly gear pair, i _jbe the ratio of gear of j level gear pair, i ₀for the ratio of gear requiring.

10. a kind of Design of Gear Drive System method based on population bilevel optimization according to claim 6, is characterized in that, described flank of tooth contact fatigue strength constraint condition, tooth root bending fatigue strength constraint condition are:

Cogged flank of tooth contact fatigue strength safety coefficient is all greater than minimal-contact fatigue strength safety coefficient, and cogged tooth root bending fatigue strength safety coefficient is all greater than minimum bend fatigue strength safety coefficient, that is:

$\&ForAll;S_{\mathrm{Hj}}>S_{H\min },$

$\&ForAll;S_{\mathrm{Fj}}>S_{F\min },$

In formula: S _hjfor the flank of tooth contact fatigue strength safety coefficient of each gear; S _fjfor the tooth root bending fatigue strength safety coefficient of each gear.

11. a kind of Design of Gear Drive System methods based on population bilevel optimization according to claim 6, is characterized in that, being limited to up and down of described optimized variable:

12. a kind of Design of Gear Drive System methods based on population bilevel optimization according to claim 7, is characterized in that,

Describedly in abutting connection with condition be:

L > d _ap, that is: $2a_{\mathrm{sp}}\sin \frac{\mathrm{\&pi;}}{n_p}>d_{\mathrm{ap}},$

In formula: L is the distance between adjacent two planetary gear centers, d _apfor maximum row star-wheel tip diameter, n _pfor number of planet gears, a _spfor sun gear and planetary gear centre distance.

13. a kind of Design of Gear Drive System methods based on population bilevel optimization according to claim 7, is characterized in that,

Described concentric condition is:

$\frac{z_s+z_p}{\cos {\mathrm{\&alpha;}}_{\mathrm{sp}}}=\frac{z_r-z_p}{\cos {\mathrm{\&alpha;}}_{\mathrm{pr}}},$

In formula: α _prfor the actual engaging angle of planetary gear and ring gear Meshing Pair; z _s, z _p, z _rbe respectively sun gear, planetary gear, the ring gear number of teeth.

14. a kind of Design of Gear Drive System methods based on population bilevel optimization according to claim 7, is characterized in that,

Described assembled condition is:

In formula: z _s, z _rbe respectively sun gear, the ring gear number of teeth, n _pfor number of planet gears.

15. a kind of Design of Gear Drive System methods based on population bilevel optimization according to claim 1, is characterized in that, in rounding, module is got 0.5 integral multiple.

16. a kind of Design of Gear Drive System methods based on population bilevel optimization according to claim 1, is characterized in that, described gear train assembly is the gear train assembly in gear case of blower.

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