CN109858165A - A kind of Two Grade Column Gear Reducer design method - Google Patents
A kind of Two Grade Column Gear Reducer design method Download PDFInfo
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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
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. a kind of Two Grade Column Gear Reducer design method, the Two Grade Column Gear Reducer has transmission gear and axis,
It is characterized by: the Two Grade Column Gear Reducer design method the following steps are included:
(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 coding
Processing；
(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.
2. Two Grade Column Gear Reducer design method as described in claim 1, it is characterised in that: 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, total transmission
Compare ib, coefficient of facewidth beAnd net cycle time, it is desirable that one the smallest Two Grade Column Gear Reducer of volume of design.
3. Two Grade Column Gear Reducer design method as described in claim 1, it is characterised in that: 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 make
It is following to indicate for the objective function of the design:
In formula, mn1And mn2Refer to the pinion gear modulus of high speed grade and slow speed turbine stage, Z1And Z3Refer to the small tooth of high speed grade and slow speed turbine stage
Tooth number, 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:
4. Two Grade Column Gear Reducer design method as described in claim 1, it is characterised in that: the step 4) specifically:
The constraint condition of two stage reducer design has: value range, contact strength of tooth surface and the tooth root bending of each parameter itself are by force
Degree requires, 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, the solution meeting of unconstrained problem F (X, γ)
Close to the solution of original problem f (X)；
So far, the foundation to the mathematical model of Optimal Design for Two-Grade Helical Cylindrical Gear Reductor is completed.
5. Two Grade Column Gear Reducer design method as described in claim 1, it is characterised in that: the step 5) specifically:
Worst frog XwThe essence of location updating is: solution vector representated by frog continuous solution space track its local extremum or
The vector operation of global extremum；Wherein, rand represents frog XwFrom local extremum XbInformation inheriting degree, reflect to XbInformation
Confidence index, i.e., expression XwTo XbLearn the process approached, wherein rand indicates the degree of study, the formula that frog is updated
It can be indicated with following formula:
Then as rand=1,Indicate that the frog is moved to the frog position of best performance；As rand=0,Indicate that the frog is not moved in current location；Defined function f (Xw,Xb) it is XwTo XbLearning process, the mistake
Journey 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 the number that occurred；
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 the effective model of father's string, from
And it realizes from local extremum XbObtain the purpose of more new information.
6. Two Grade Column Gear Reducer design method as claimed in claim 3, it is characterised in that: the constraint of the design variable
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、YFS2The respectively high speed grade size 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、YFS4The respectively slow speed turbine stage size 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).
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