CN109858165A - A kind of Two Grade Column Gear Reducer design method - Google Patents

A kind of Two Grade Column Gear Reducer design method Download PDF

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CN109858165A
CN109858165A CN201910110681.XA CN201910110681A CN109858165A CN 109858165 A CN109858165 A CN 109858165A CN 201910110681 A CN201910110681 A CN 201910110681A CN 109858165 A CN109858165 A CN 109858165A
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design
frog
speed
gear reducer
reducer
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赵转哲
张宇
赵帅帅
丁玉洁
刘永明
王海
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Anhui Polytechnic University
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Anhui Polytechnic University
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Abstract

The invention discloses a kind of Two Grade Column Gear Reducer design methods, the following steps are included: (1) determines operating condition: (2) determine objective function and design variable: the coding and project treatment of (3) design variable, specifically: the mapping processing of discrete variable and the processing of continuous variable coding；(4) determine constraint condition and fitness function: the mathematical model of above-mentioned foundation is substituted into mixed discrete and leapfroged algorithm by (5), output optimization calculated result.The design method can greatly reduce artificial calculating, only can need to calculate automatically and design the basic parameter of secondary gear reducer in the basic parameter inputs such as target type, operating condition and constraint condition program provided herein, as a result more accurate and reliable.

Description

A kind of Two Grade Column Gear Reducer design method
Technical field
The present invention relates to retarder technical fields, more particularly, to a kind of Two Grade Column Gear Reducer design method.
Background technique
Gear reduction unit is independent enclosed mechanical driving device between prime mover and working machine, can reduce revolving speed and increasing Large torque is a kind of mechanical part being widely used in the departments such as industrial and mining enterprises and transport, building.
Traditional design method is the data that designer provides according to various data, document, is passed through in conjunction with the design of oneself It tests and existing retarder carries out analogy, tentatively work up a design scheme, then this scheme is checked, such as check Pass through, then the program can determine, otherwise, redesign.Often size is bigger than normal for the retarder designed in this way, may be simultaneously It is not optimal design scheme, and inefficiency.Therefore, in order to reduce the cost of retarder, design efficiency is improved, proposes one The method of the new CAD gear reduction unit of kind is imperative.
The optimization design problem of speed changer has variable more, and the feature of type complexity first in essence, such as The number of teeth of gear is integer variable, and the modulus of gear is that non-equidistant dissipates variable, but helical angle is continuous variable；Secondly, Constraint condition is more, and objective function and constraint condition are that the Nonlinear Numerical function of design variable and multi- extreme value function belong to again Miscellaneous, belong to typical nonlinear programming problem.Therefore traditional optimization method is difficult fundamentally to solve speed changer optimization to set Globally optimal solution in meter.Currently used method has: 1) method based on continuous variable optimization method, as rounding method, Quasi- discrete method, discretization penalty function method；2) integer gradient method, discrete complex shape method；3) Nonlinear Implicit enumerative technique, branch and bound method Deng；These methods have the experience of successful application, but dependence of these algorithms to optimization design problem in Optimum design of engineering structure Property it is strong, i.e. certain algorithm may be effective to the model with certain characteristics, and may be not suitable with to another kind of optimization problem It is even invalid.Moreover, some algorithms can not usually get rid of locally optimal solution to get to globally optimal solution ability it is poor.
Shuffled frog leaping algorithm is a kind of novel meta-heuristic Swarm Intelligent Algorithm, and it is excellent that it inherits other optimization algorithms While point, also have many advantages, such as that optimizing ability is stronger, parameter is less.This algorithm is believed in the process by simulating frog and looking for food Breath is shared to be generated with the characteristics of exchange.The shuffled frog leaping algorithm of standard, generally be directed to continuous variable's and without constraint item The Optimization Solution of the objective function of part cannot be applicable in this mixed type variable optimization design of secondary gear reducer.
Summary of the invention
In view of the shortcomings of the prior art, technical problem to be solved by the invention is to provide a kind of Two Grade Column Gear Reducers Design method, to reach raising design efficiency, as a result more accurately and reliably purpose.
In order to solve the above-mentioned technical problem, the technical scheme adopted by the invention is as follows:
A kind of Two Grade Column Gear Reducer design method, comprising the following steps:
(1) operating condition is determined:
(2) objective function and design variable are determined:
(3) coding and project treatment of design variable, specifically: the mapping processing of discrete variable and continuous variable are compiled The processing of code；
(4) constraint condition and fitness function are determined:
(5) mathematical model of above-mentioned foundation is substituted into mixed discrete to leapfrog algorithm, output optimization calculated result.
Wherein:
The step 1) specifically:
The operating condition of Design of Speed Reducer requires offer parameter as follows: high speed shaft input power P, high speed shaft revolving speed nr、 Resultant gear ratio ib, coefficient of facewidth beAnd net cycle time, it is desirable that the smallest second level roller gear of one volume of design slows down Device.
The step 2) specifically:
2.1 objective functions:
Using the volume minimum of retarder as optimization aim, that is, make the head center of retarder away from minimum, center is away from can It is following to indicate using the objective function as the design:
In formula, mn1And mn2Refer to the pinion gear modulus of high speed grade and slow speed turbine stage, Z1And Z3Refer to high speed grade and slow speed turbine stage The pinion gear number of teeth, i1It is the transmission ratio of high speed grade gear, β indicates the helical angle of gear；
2.2 design variable
The independent variable that objective function is related to has mn1、Z1、mn2、Z3、i1, β, design variable is desirable are as follows: X=[x1,x2,x3, x4,x5,x6]=[mn1,Z1,mn2,Z3,i1, β], therefore above-mentioned objective function can be rewritten into following form:
The step 4) specifically:
The constraint condition of two stage reducer design has: the value range of each parameter itself, contact strength of tooth surface and tooth root are curved Bent intensity requirement, high speed grade gear wheel and slow-speed shaft do not interfere constraint condition；
It indicates to choose in bracket biggish one in two elements with max (), then penalty is writeable are as follows:
In formula, gjIt (X) is inequality constraints, γ is penalty factor, if selection is sufficiently large, unconstrained problem F (X, γ) Solution can approach original problem f (X) solution；
So far, the foundation to the mathematical model of Optimal Design for Two-Grade Helical Cylindrical Gear Reductor is completed.
The step 5) specifically:
Worst frog XwThe essence of location updating is: solution vector representated by frog tracks its local pole in continuous solution space The vector operation of value or global extremum；Wherein, rand represents frog XwFrom local extremum XbInformation inheriting degree, reflect to Xb The confidence index of information, i.e. expression XwTo XbLearn the process approached, wherein rand indicates the degree of study, and frog is updated Formula can be indicated with following formula:
Then as rand=1,Indicate that the frog is moved to the frog position of best performance；Work as rand=0 When,Indicate that the frog is not moved in current location；Defined function f (Xw,Xb) it is XwTo XbLearning process, The process can realize that cross method is as follows by crossover operation:
1. in XbOne intersection region of middle random selection, wherein rand decides the size of intersection region；
2. by XbIntersection region be added to XwAbove or below, and delete XwIn in XbThe zone of intersection in occurred Number；
As it can be seen that it is convenient to realize using this more new strategy, and it is easy to operate, and substring can inherit effective mould of father's string Formula, to realize from local extremum XbObtain the purpose of more new information.
The constraint condition of the design variable:
(1) high speed grade and slow speed turbine stage tooth face contact fatigue strength condition:
[σH] it is allowable contact stress；T1、T2For high speed shaft and jackshaft torque；K1、K2For loading coefficient；
(2) the large and small Gear Root bending fatigue strength condition of high speed grade:
[σF]1、[σF]2The respectively big pinion gear permissible bending stress of high speed grade；YFS1、YFS2Respectively high speed grade size tooth Form of gear tooth coefficient；
(3) the large and small Gear Root bending fatigue strength condition of slow speed turbine stage:
[σF]3、[σF]4The respectively big pinion gear permissible bending stress of slow speed turbine stage；YFS3、YFS4Respectively slow speed turbine stage size tooth Form of gear tooth coefficient；
(4) not interference condition:
g7(X)=2cos β (s+mn1)-mn2Z3(1+i2)+mn1Z1i1≤0
S is slow-speed shaft axis at a distance from jackshaft gear wheel gear tip clearance；
(5) boundary constraint to 6 design variables:
g8(X)=xk-xkmax≤ 0 (k=1~6)
g9(X)=xkmin-xk≤ 0 (k=1~6).
Compared with prior art, the present invention having the advantage that
By the way of mapping, by cylinder gear speed reducer design in the design parameters that are related to encode, after convenient The computer of phase carries out auxiliary calculating；
Using the update mode of new initial method and frog, the renewal process of shuffled frog leaping algorithm is engineered Processing；
The concept of penalty will be introduced in objective function, thus objective function in gear reduction unit computation model and Constraint condition is combined into one, and is converted to the fitness function of this algorithm requirement；
Engineering design reality and Design-Oriented, the characteristic of the design variable of manufacture for secondary gear reducer, mention The Mixed Discrete Variable engineering processing method for having gone out a kind of simple, introduces a kind of new penalty construction method, To the characteristic of optimization design problem without particular/special requirement, and it is combined with the algorithm that leapfrogs of the mixed discrete based on crossover operation, Corresponding computer program design is completed, design efficiency greatly improved；
Design variable engineering processing method makes design variable preferably actually match with engineering design, manufacture, optimizes Parameter does not need rounding, can be directly used for engineering design, and practicability is stronger, which can get rid of locally optimal solution, obtains the overall situation The ability of optimal solution is stronger；It can solve the nonlinear optimal problem that polymorphic type design variable coexists in engineering；
Artificial calculating can be greatly reduced, it only need to be defeated by basic parameters such as target type, operating condition and constraint conditions Enter in program provided herein, can calculate automatically and design the basic parameter of secondary gear reducer, it is as a result more accurate Reliably.
Detailed description of the invention
Content expressed by each width attached drawing of this specification and the label in figure are briefly described below:
Fig. 1 is reducer structure schematic diagram.
Fig. 2 is the program flow diagram of standard shuffled frog leaping algorithm.
Fig. 3 is design method flow chart of the present invention.
Fig. 4 is the practical programs surface chart using design method of the present invention.
Fig. 5 is Two Grade Column Gear Reducer optimum results of the present invention.
Specific embodiment
Below against attached drawing, by the description of the embodiment, making to a specific embodiment of the invention further details of Explanation.
As shown in Figures 1 to 5, the Two Grade Column Gear Reducer design method, comprising the following steps:
(1) operating condition is determined:
The operating condition of Design of Speed Reducer requires offer parameter as follows: high speed shaft input power P, high speed shaft revolving speed nr、 Resultant gear ratio ib, coefficient of facewidth beAnd net cycle time, it is desirable that the smallest second level roller gear of one volume of design slows down Device；
(2) objective function and design variable are determined:
2.1 objective functions:
Using the volume minimum of retarder as optimization aim, that is, make the head center of retarder away from minimum, center is away from can It is following to indicate using the objective function as the design:
In formula, mn1And mn2Refer to the pinion gear modulus of high speed grade and slow speed turbine stage, Z1And Z3Refer to high speed grade and slow speed turbine stage The pinion gear number of teeth, i1It is the transmission ratio of high speed grade gear, β indicates the helical angle of gear；
2.2 design variable
The independent variable that objective function is related to has mn1、Z1、mn2、Z3、i1, β, design variable is desirable are as follows: X=[x1,x2,x3, x4,x5,x6]=[mn1,Z1,mn2,Z3,i1, β], therefore above-mentioned objective function can be rewritten into following form:
(3) coding and project treatment of design variable, specifically: the mapping processing of discrete variable and continuous variable are compiled The processing of code；
(4) constraint condition and fitness function are determined:
The constraint condition of two stage reducer design has: the value range of each parameter itself, contact strength of tooth surface and tooth root are curved Bent intensity requirement, high speed grade gear wheel and slow-speed shaft do not interfere constraint condition；
It indicates to choose in bracket biggish one in two elements with max (), then penalty is writeable are as follows:
In formula, gjIt (X) is inequality constraints, γ is penalty factor, if selection is sufficiently large, unconstrained problem F (X, γ) Solution can approach original problem f (X) solution；
So far, the foundation to the mathematical model of Optimal Design for Two-Grade Helical Cylindrical Gear Reductor is completed；
(5) mathematical model of above-mentioned foundation mixed discrete is substituted into leapfrog algorithm:
Worst frog XwThe essence of location updating is: solution vector representated by frog tracks its local pole in continuous solution space The vector operation of value or global extremum；Wherein, rand represents frog XwFrom local extremum XbInformation inheriting degree, reflect to Xb The confidence index of information, i.e. expression XwTo XbLearn the process approached, wherein rand indicates the degree of study, and frog is updated Formula can be indicated with following formula:
Then as rand=1,Indicate that the frog is moved to the frog position of best performance；Work as rand=0 When,Indicate that the frog is not moved in current location；Defined function f (Xw,Xb) it is XwTo XbLearning process, The process can realize that cross method is as follows by crossover operation:
1. in XbOne intersection region of middle random selection, wherein rand decides the size of intersection region；
2. by XbIntersection region be added to XwAbove or below, and delete XwIn in XbThe zone of intersection in occurred Number；
As it can be seen that it is convenient to realize using this more new strategy, and it is easy to operate, and substring can inherit effective mould of father's string Formula, to realize from local extremum XbObtain the purpose of more new information
Wherein, the constraint condition of design variable:
(1) high speed grade and slow speed turbine stage tooth face contact fatigue strength condition:
[σH] it is allowable contact stress；T1、T2For high speed shaft and jackshaft torque；K1、K2For loading coefficient；
(2) the large and small Gear Root bending fatigue strength condition of high speed grade:
[σF]1、[σF]2The respectively big pinion gear permissible bending stress of high speed grade；YFS1、YFS2Respectively high speed grade size tooth Form of gear tooth coefficient；
(3) the large and small Gear Root bending fatigue strength condition of slow speed turbine stage:
[σF]3、[σF]4The respectively big pinion gear permissible bending stress of slow speed turbine stage；YFS3、YFS4Respectively slow speed turbine stage size tooth Form of gear tooth coefficient；
(4) not interference condition:
g7(X)=2cos β (s+mn1)-mn2Z3(1+i2)+mn1Z1i1≤0
S is slow-speed shaft axis at a distance from jackshaft gear wheel gear tip clearance；
(5) boundary constraint to 6 design variables:
g8(X)=xk-xkmax≤ 0 (k=1~6)
g9(X)=xkmin-xk≤ 0 (k=1~6).
It is leapfroged the computer-implemented method of the secondary gear reducer of algorithm, can be greatly reduced based on mixed discrete It is artificial to calculate, it only need to be by the basic parameter inputs such as target type, operating condition and constraint condition program provided herein, i.e., The basic parameter of secondary gear reducer can be calculated automatically and design, it is as a result more accurate and reliable.
Engineering Oriented design of the present invention is practical with manufacture, devises novel Discrete shuffled frog leaping algorithm, treats optimized variable Less-restrictive, can be micro- to objective function and its constraint condition neither requirement, do not require continuous, the problem of only requiring is can to calculate yet 's.Its search simultaneously can spread entire solution space, can find intimate globally optimal solution, thus be suitable for processing tradition and search The insoluble speed changer optimization problem of Suo Fangfa, can also be used as it is a kind of it is versatile, solve a problem it is reliable and high-efficient non-linear Optimization with Mixed Discrete Variables method has very important practical significance for solving Optimum design of engineering structure problem.
Preferred embodiment are as follows:
1. the engineering treatment method of novel Discrete shuffled frog leaping algorithm coding
Traditional shuffled frog leaping algorithm, generally be directed to continuous variable's and the optimization of unconfined condition objective function Solve, for the Solve problems of this mixed type variable of secondary gear reducer, it is necessary to conventional hybrid leapfrog algorithm carry out It improves, could be applicable in and Practical Project problem.
The mapping of 1.1 discrete variables is handled
All discrete types are mapped in table form, indicate the big of the variable with position in the table It is small, while according to its variable change range, its table size is set automatically, specific as follows:
1) number of teeth: integer type variable this kind of for the number of teeth, because its spacing is fixed as 1, when being mapped, the of table One number is the minimum value of variable, then, gradually plus 1, until the maximum value of variable.If i-th of discrete variable XiValue range is Xi=[Xmin,Xmax], engineering treatment method is expressed as with MATLAB language:
Xi=Xmin:1:Xmax
Mapping relations i.e. at this time are as follows:
Xi[n]=Xmin+(n-1)
Such as Xi[3] the third number in table, size X are indicatedmin+2。
2) modulus: non-discrete non-integer variable at equal intervals this kind of for modulus is converted into equidistant when being mapped Integer indicate, i.e., all moduluses (28) are not arranged into a table according to from small big sequence, one with not leaking, modulus Size is mapped to the position size of table.If modulus is Y, then this mapping mode is expressed as with MATLAB language:
Y=[0.10 0.12 0.15 0.2 0.25 ... 25 32 40 50]
This table does not list 28 moduluses all because length is limited；
Mapping relations at this time are as follows:
Nth in Y [n]=Y
Such as Y [3] indicates the 3rd number in table, i.e. the size of modulus is 0.15；Y [10] indicates the 10th number in table, I.e. the size of modulus is 0.8；
The processing of 1.2 continuous variables coding
Helical angle as gear variable is continuous variable in form, but its value is by design specification and the accuracy of manufacture Constraint.If being calculated in optimization design by floating point real number or double precision real numbers, further according to the precision of actual requirement after optimization Data processing is carried out, often leading to result is not optimal solution, or even is not feasible solution.If its valued space of helical angle is a≤β ≤ b retains k decimals by engineering actual demand precision, and engineering treatment method is indicated with MATLAB language:
β=round (a+rand* (b-a))/10^k.
2. Gear Reducer Optimal Design mathematical model
Retarder is general mechanical part, and most products of cylinder gear speed reducer have been standardized, but of its parameter It is optimal with being not necessarily.It is optimized herein for Two Grade Column Gear Reducer.The operating condition or requirement of design The parameter of offer is as follows:
High speed shaft input power P, high speed shaft revolving speed nr, resultant gear ratio ib, coefficient of facewidth B；Gear material and heat treatment, Net cycle time.
2.1 objective function
It is as shown in Figure 1 reducer structure schematic diagram.
Using the volume minimum of retarder as optimization aim, it is desirable that structure is most compact, weight is most light, that is, makes retarder Head center away from minimum.Therefore center is indicated away from can be used as objective function with f (x):
M in formulan1,mn3The pinion gear modulus of high speed grade and slow speed turbine stage；Z1,Z3The pinion gear teeth of high speed grade and slow speed turbine stage Number；i1It is high speed stage gear ratio.
2.2 design variable
It is required according to retarder input, output, resultant gear ratio is determining.Therefore the independent variable that above formula is related to has mn1, mn3, Z1, Z3, i1, β, therefore design variable is desirable are as follows:
X=[x1,x2,x3,x4,x5,x6]=[mn1,mn3,Z1,Z3,i1,β]
2.3 constraint condition
The constraint condition of two stage reducer design has: the value range of each parameter itself, contact strength of tooth surface and tooth root are curved Bent intensity requirement, high speed grade gear wheel and slow-speed shaft interference and collision etc..Because content is more, it is uniformly denoted as g hereinj(X), j is about The number of beam condition.
(1) high speed grade and slow speed turbine stage tooth face contact fatigue strength condition:
[σH] it is allowable contact stress；T1、T2For high speed shaft and jackshaft torque；K1、K2For loading coefficient.
(2) the large and small Gear Root bending fatigue strength condition of high speed grade:
[σF]1、[σF]2The respectively big pinion gear permissible bending stress of high speed grade；YFS1、YFS2Respectively high speed grade size tooth Form of gear tooth coefficient；
(3) the large and small Gear Root bending fatigue strength condition of slow speed turbine stage:
[σF]3、[σF]4The respectively big pinion gear permissible bending stress of slow speed turbine stage；YFS3、YFS4Respectively slow speed turbine stage size tooth Form of gear tooth coefficient；
(4) not interference condition
g7(X)=2cos β (s+mn1)-mn2Z3(1+i2)+mn1Z1i1≤0
S is slow-speed shaft axis at a distance from jackshaft gear wheel gear tip clearance.
(5) to the boundary constraint of 6 design variables
g8(X)=xk-xkmax≤ 0 (k=1~6)
g9(X)=xkmin-xk≤ 0 (k=1~6)
2.4 mathematical model of optimizing design
From the above analysis, the mathematical model that Optimal Design for Two-Grade Helical Cylindrical Gear Reductor can be obtained is as follows:
min f(X)
s.t.gj(X)。
3. the novel Discrete shuffled frog leaping algorithm of two stage reducer optimization design
It is non-linear under nonlinear complementary problem for can be seen that secondary gear reducer optimization design from above-mentioned model Function optimization.The new penalty building method of one kind is introduced to solve restricted problem.
If indicating to choose in bracket biggish one in two elements with max (), then penalty is writeable are as follows:
G (X) and h (X) is respectively inequality and equality constraints in formula.γ is penalty factor, if selection is sufficiently large, no constraint The solution of problem F (x, γ) can be close to the solution of former problem f (X).
Therefore the penalty of this paper is writeable are as follows:
Being converted into this example to the optimization of complicated constrained optimization problem f (X) is asked to simply without about by above formula The optimization of Shu Wenti F (x, γ).
3.2 mixed discretes leapfrog algorithm and its improvement
Shuffled frog leaping algorithm basic step is done described below first:
(1) global search initializes: frog number P in selected population, group number m, frog number n in group.It is specified Global maximum evolutionary generation Gmax, the maximum evolutionary generation L in group insidemax。
1. in all P frogs of search space random initializtion of d dimension；
2. calculating the fitness function of each frog；
3. being ranked up according to fitness to all frogs, global optimum frog X is obtainedg；
4. all frogs are divided into m group, each group includes that the 1st frog of n frog is divided into the 1st group, the 2 are divided into the 2nd group ... ..., are divided into m-th of group m-th, and the m+1 frog is divided into the 1st group again, and so on；
5. executing the local search in subgroup in each group；
6. re-mixing all frogs；
7. going to and 1., 2. walking if not reaching stop condition.
(2) local search in group
1. the optimal frog X of determination in each groupb, worst frog Xw；2. to worst frog XwBe updated (into Change).The more new formula of the frog is as follows:
Wherein, min () and max () is to be minimized and max function respectively, and int () is bracket function, and r is 0 to 1 Random number, Smax be allow frog jump maximum step-length；
3. replacing worst frog with it if previous step generates a better frog.Otherwise, it carries out in next step；
4. with global optimum XgAlternate form XbIf finding a better frog, worst frog is replaced with it；If Or the better frog of performance cannot be found, then a frog is randomly generated instead of worst frog；
5. repeating the process according to scheduled number.
The more new strategy of shuffled frog leaping algorithm need to be improved.The specific method is as follows:
Firstly, the change of frog initialization, that is, the generation solved, the solution of traditional shuffled frog leaping algorithm are in variable model Enclose it is interior generate at random, be continuous；Due to the limitation of practical problem, solution is discrete sequence, and therefore, it is right to have resettled herein After the table mapping answered, according to range of variables, the sequence of one solution of element composition in all corresponding tables in location is chosen, It randomly chooses in the sequence again.
Then, the change of more new strategy, in traditional shuffled frog leaping algorithm, being updated simply for frog position is abstract general It reads, which is substantially suitable only for the solution of continuous problem, for discrete combinatorial optimization problem, needs to design specific update Operator.As the principle of shuffled frog leaping algorithm it is found that the essence of worst frog Xw location updating is: solution vector representated by frog exists Continuous solution space tracks the vector operation of its local extremum or global extremum.Wherein, rand represents frog Xw from local extremum Xb Information inheriting degree, reflect the confidence index to Xb information.In other words, indicate that Xw learns the process approached to Xb, wherein Rand indicates the degree of study, and the formula that frog updates can be indicated with following formula:
Then as rand=1,Indicate that the frog is moved to the frog position of best performance；Work as rand=0 When,Indicate that the frog is not moved in current location.Defined function f (Xw,Xb) it is learning process of the Xw to Xb, The process can be realized by crossover operation.Cross method is as follows:
1. randomly choosing an intersection region in Xb, wherein rand decides the size of intersection region.
2. by XbIntersection region be added to XwAbove or below, and delete XwIn in XbThe zone of intersection in occurred Number.Such as:
Current location Xw=371892465 10 rand=0.3
Local extremum Xb=95 10 432678
Assuming that randomly selected intersection region are as follows: 432
After intersection are as follows:
432718965 10 or 718965 10 432
As it can be seen that it is convenient to realize using this more new strategy, and it is easy to operate, and substring can inherit effective mould of father's string Formula, to realize from local extremum XbObtain the purpose of more new information.
3.3 program charts based on novel Discrete shuffled frog leaping algorithm
The discrete change of mixing combined with MATLAB language design novel Discrete shuffled frog leaping algorithm with Means of Penalty Function Methods The algorithm routine of amount, shown in program circuit Fig. 2 and 3.
Its actual calculating structure is as shown in Figure 4.Engineering design for secondary gear reducer is practical, and towards setting The characteristic of meter, the design variable manufactured proposes a kind of Mixed Discrete Variable engineering processing method of simple, introduces A kind of new penalty construction method, to the characteristic of optimization design problem without particular/special requirement, and by its be based on crossover operation The mixed discrete algorithm that leapfrogs combine, complete corresponding computer program design.Design variable engineering processing method makes Design variable preferably actually matches with engineering design, manufacture, and Optimal Parameters do not need rounding, can be directly used for engineering and set Meter, practicability is stronger, which can get rid of locally optimal solution, and the ability for obtaining globally optimal solution is stronger.It can solve in engineering The nonlinear optimal problem that polymorphic type design variable coexists.
The present invention is exemplarily described above in conjunction with attached drawing, it is clear that the present invention implements not by aforesaid way Limitation, if use the improvement for the various unsubstantialities that conception and technical scheme of the invention carry out, or it is not improved will Conception and technical scheme of the invention directly apply to other occasions, within the scope of the present invention.

Claims (6)

1.一种二级圆柱齿轮减速器设计方法，所述二级圆柱齿轮减速器具有传动齿轮和轴，其特征在于：所述二级圆柱齿轮减速器设计方法包括以下步骤：1. a design method for a secondary cylindrical gear reducer, the secondary cylindrical gear reducer has a transmission gear and a shaft, it is characterized in that: the design method for the secondary cylindrical gear reducer comprises the following steps: (1)确定工作条件：(1) Determine the working conditions: (2)确定目标函数和设计变量：(2) Determine the objective function and design variables: (3)设计变量的编码及工程处理，具体为：离散型变量的映射处理和连续型变量编码的处理；(3) Coding and engineering processing of design variables, specifically: mapping processing of discrete variables and processing of coding of continuous variables; (4)确定约束条件及适应度函数：(4) Determine the constraints and fitness function: (5)将上述建立的数学模型代入离散混合蛙跳算法，输出优化计算结果。(5) Substitute the mathematical model established above into the discrete hybrid leapfrog algorithm, and output the optimal calculation result. 2.如权利要求1所述二级圆柱齿轮减速器设计方法，其特征在于：所述步骤1)具体为：2. the design method of secondary cylindrical gear reducer as claimed in claim 1, is characterized in that: described step 1) is specially: 减速器设计的工作条件或要求提供参数如下：高速轴输入功率P、高速轴转速nr、总传动比ib、齿宽系数为以及总工作时间，要求设计一个体积最小的二级圆柱齿轮减速器。The working conditions or parameters required for the design of the reducer are as follows: the input power P of the high-speed shaft, the rotational speed of the high-speed shaft n r , the total transmission ratio ib , and the tooth width coefficient is As well as the total working time, it is required to design a secondary cylindrical gear reducer with the smallest volume. 3.如权利要求1所述二级圆柱齿轮减速器设计方法，其特征在于：所述步骤2)具体为：3. the design method of secondary cylindrical gear reducer as claimed in claim 1, is characterized in that: described step 2) is specially: 2.1目标函数：2.1 Objective function: 将减速器的体积最小作为优化目标，也就是使减速器的总中心距最小，中心距可以作为本设计的目标函数，如下表示：Taking the minimum volume of the reducer as the optimization goal, that is, to minimize the total center distance of the reducer, the center distance can be used as the objective function of this design, as follows: 式中，mn1和mn2是指高速级与低速级的小齿轮模数，Z1和Z3是指高速级与低速级的小齿轮齿数，i1是高速级齿轮的传动比，β表示齿轮的螺旋角；In the formula, m n1 and m n2 refer to the pinion modules of the high-speed stage and low-speed stage, Z 1 and Z 3 refer to the number of pinion gear teeth of the high-speed stage and low-speed stage, i 1 is the transmission ratio of the high-speed stage gear, and β represents the helix angle of the gear; 2.2设计变量2.2 Design variables 目标函数涉及的独立变量有mn1、Z1、mn2、Z3、i1、β，设计变量可取为：X＝[x1,x2,x3,x4,x5,x6]＝[mn1,Z1,mn2,Z3,i1,β]，因此上述的目标函数可以改写成如下形式：The independent variables involved in the objective function are m n1 , Z 1 , m n2 , Z 3 , i 1 , β, and the design variables can be taken as: X=[x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ] =[m n1 , Z 1 , m n2 , Z 3 , i 1 , β], so the above objective function can be rewritten into the following form: 4.如权利要求1所述二级圆柱齿轮减速器设计方法，其特征在于：所述步骤4)具体为：4. the design method of secondary cylindrical gear reducer as claimed in claim 1, is characterized in that: described step 4) is specially: 二级减速器设计的约束条件有：各参数自身的取值范围、齿面接触强度与齿根弯曲强度要求、高速级大齿轮与低速轴不发生干涉约束条件；The constraints for the design of the secondary reducer are: the value range of each parameter itself, the contact strength of the tooth surface and the bending strength of the tooth root, and the constraints that the high-speed large gear and the low-speed shaft do not interfere; 用max(·,·)表示选取括号内两个元素中较大的一个，则惩罚函数可写为：Using max(·,·) to indicate that the larger of the two elements in the brackets is selected, the penalty function can be written as: 式中，gj(X)即为不等式约束，γ为惩罚因子，若选取足够大，无约束问题F(X,γ)的解会接近原问题f(X)的解；In the formula, g j (X) is the inequality constraint, and γ is the penalty factor. If the selection is large enough, the solution of the unconstrained problem F(X,γ) will be close to the solution of the original problem f(X); 至此，完成对二级圆柱齿轮减速器优化设计的数学模型的建立。So far, the establishment of the mathematical model for the optimal design of the secondary cylindrical gear reducer is completed. 5.如权利要求1所述二级圆柱齿轮减速器设计方法，其特征在于：所述步骤5)具体为：5. the design method of secondary cylindrical gear reducer as claimed in claim 1, is characterized in that: described step 5) is specially: 最差青蛙Xw位置更新的本质是：青蛙所代表的解向量在连续解空间跟踪其局部极值或全局极值的向量运算；其中，rand代表青蛙Xw从局部极值Xb的信息继承度，反映了对Xb信息的置信指标，即表示Xw向Xb学习逼近的过程，其中rand表示学习的程度，将青蛙更新的公式可以用下式表示：The essence of the position update of the worst frog Xw is: the solution vector represented by the frog tracks its local extremum or global extremum vector operation in the continuous solution space; where rand represents the information inheritance of the frog Xw from the local extremum Xb degree, which reflects the confidence index of X b information, that is, the process of X w learning approximation to X b , where rand represents the degree of learning, and the formula for updating the frog can be expressed by the following formula: 则当rand＝1时，表示该青蛙移动至性能最优的青蛙位置；当rand＝0时，表示该青蛙在当前位置并未移动；定义函数f(Xw,Xb)为Xw向Xb的学习过程，该过程可以通过交叉操作实现，交叉方法如下：Then when rand=1, Indicates that the frog moves to the frog position with the best performance; when rand=0, Indicates that the frog has not moved at the current position; the function f(X w , X b ) is defined as the learning process from X w to X b , which can be realized by crossover operation. The crossover method is as follows: ①在Xb中随机选择一个交叉区域，其中rand决定着交叉区域的大小；①Randomly select an intersection area in X b , where rand determines the size of the intersection area; ②将Xb的交叉区域加到Xw的前面或后面，并删除Xw中已在Xb的交叉区中出现过的数字；②Add the intersection area of X b to the front or back of X w , and delete the numbers in X w that have appeared in the intersection area of X b ; 可见，采用这种更新策略，实现方便，操作简单，并且子串能够继承父串的有效模式，从而实现了从局部极值Xb获得更新信息的目的。It can be seen that this update strategy is convenient to implement and simple to operate, and the substring can inherit the effective mode of the parent string, thereby achieving the purpose of obtaining update information from the local extreme value X b . 6.如权利要求3所述二级圆柱齿轮减速器设计方法，其特征在于：所述设计变量的约束条件：6. The design method of the secondary cylindrical gear reducer according to claim 3, wherein: the constraints of the design variables: (1)高速级与低速级齿面接触疲劳强度条件：(1) Contact fatigue strength conditions of high-speed and low-speed tooth surfaces: [σH]为许用接触应力；T1、T2为高速轴与中间轴扭矩；K1、K2为载荷系数；[σ H ] is the allowable contact stress; T 1 , T 2 are the torques of the high-speed shaft and the intermediate shaft; K 1 , K 2 are the load coefficients; (2)高速级大、小齿轮齿根弯曲疲劳强度条件：(2) Bending fatigue strength conditions of tooth roots of high-speed large and small gears: [σF]1、[σF]2分别为高速级大小齿轮许用弯曲应力；YFS1、YFS2分别为高速级大小齿轮齿形系数；[σ F ] 1 , [σ F ] 2 are the allowable bending stress of the large and small gears of the high-speed stage respectively; Y FS1 and Y FS2 are the tooth profile coefficients of the large and small gears of the high-speed stage respectively; (3)低速级大、小齿轮齿根弯曲疲劳强度条件：(3) The bending fatigue strength conditions of the tooth root of the large and small gears of the low speed stage: [σF]3、[σF]4分别为低速级大小齿轮许用弯曲应力；YFS3、YFS4分别为低速级大小齿轮齿形系数；[σ F ] 3 , [σ F ] 4 are the allowable bending stress of the low-speed gears, respectively; Y FS3 , Y FS4 are the tooth profile coefficients of the low-speed gears; (4)不干涉条件：(4) Non-interference conditions: g7(X)＝2cosβ(s+mn1)-mn2Z3(1+i2)+mn1Z1i1≤0g 7 (X)=2cosβ(s+m n1 )-m n2 Z 3 (1+i 2 )+m n1 Z 1 i 1 ≤0 s为低速轴轴线与中间轴大齿轮齿顶间的距离；s is the distance between the axis of the low-speed shaft and the tooth top of the large gear of the intermediate shaft; (5)对6个设计变量的边界约束：(5) Boundary constraints on 6 design variables: g8(X)＝xk-xkmax≤0(k＝1～6)g 8 (X)=x k -x kmax ≤0 (k=1～6) g9(X)＝xkmin-xk≤0(k＝1～6)。g 9 (X)=x kmin −x k ≦0 (k=1˜6).
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