CN112214932A - Sliding bearing geometric tolerance optimization method based on SDT theory - Google Patents

Sliding bearing geometric tolerance optimization method based on SDT theory Download PDF

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CN112214932A
CN112214932A CN202011078092.7A CN202011078092A CN112214932A CN 112214932 A CN112214932 A CN 112214932A CN 202011078092 A CN202011078092 A CN 202011078092A CN 112214932 A CN112214932 A CN 112214932A
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sliding bearing
sdt
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cost
tolerance
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CN112214932B (en
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李冰
陈振宇
徐武彬
张子文
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Guangxi University of Science and Technology
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    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
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Abstract

The invention discloses a sliding bearing geometric tolerance optimization method based on an SDT theory, which comprises the following steps: s1: determining the form and position error type of the sliding bearing, and acquiring a cost-error function of the sliding bearing under the error; s2: aiming at the element freedom degree, obtaining a small displacement rotation parameter of the sliding bearing under the SDT theory; s3: processing the small displacement rotation parameter according to the requirement of a known tolerance domain; s4: establishing a sliding bearing cost-error model based on an SDT theory; s5: optimizing and solving the sliding bearing cost-error model by using a genetic algorithm; the invention can use a plurality of small displacement rotations to represent the form and position errors, and breaks the limitation that the traditional error model only considers single size errors.

Description

Sliding bearing geometric tolerance optimization method based on SDT theory
Technical Field
The invention relates to the technical field of tolerance optimization of sliding bearings, in particular to a sliding bearing geometric tolerance optimization method based on an SDT (software development kit) theory.
Background
At present, the tolerance almost runs through each link of the design and manufacture of the sliding bearing, which not only relates to the manufacturing and assembly process of the sliding bearing, but also greatly influences the quality, the function, the production efficiency and the manufacturing cost of the product.
However, currently, a research model in the field of tolerance optimization of sliding bearings is mainly a traditional "cost-error" optimization model, and single-target tolerance optimization is usually performed based on a "cost-error" model of an elementary function, however, in the traditional cost-error optimization model based on the elementary function, independent variables are all size errors, dependent variables are costs, form and position errors are not considered, the form and position errors cannot be represented by only a single variable, and the traditional model has a certain limitation, so that the cost-error optimization model based on the SDT theory is provided.
Therefore, how to provide a sliding bearing tolerance optimization method based on the SDT theory is a problem that needs to be solved urgently by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a sliding bearing geometric tolerance optimization method based on an SDT theory, which applies the SDT theory to a sliding bearing rotor system model considering geometric errors to build a relationship between an operating characteristic and tolerance optimization, and realizes tolerance optimization of a sliding bearing rotor system by combining an influence rule.
In order to achieve the purpose, the invention adopts the following technical scheme:
a sliding bearing geometric tolerance optimization method based on an SDT theory comprises the following steps:
s1: determining the form and position error type of the sliding bearing, and acquiring a cost-error function of the sliding bearing under the error;
s2: aiming at the element freedom degree, obtaining a small displacement rotation parameter of the sliding bearing under the SDT theory;
s3: processing the small displacement rotation parameter according to the requirement of a known tolerance domain;
s4: establishing a sliding bearing cost-error model based on an SDT theory;
s5: and (4) carrying out optimization solution on the sliding bearing cost-error model by utilizing a genetic algorithm.
Preferably, the step S2 specifically includes: and (4) taking the form and position error and the dimensional tolerance of the sliding bearing into consideration to obtain the small displacement rotation parameter of the sliding bearing under the SDT theory.
Preferably, the step S3 further includes:
s31: mapping the small displacement rotation parameter from the known tolerance domain according to the known tolerance domain, and solving the variation range of the small displacement rotation parameter;
s32: and establishing a constraint inequality and a variation inequality of the small displacement rotation parameter to obtain a form and position error model.
Preferably, the step S4 specifically includes: and establishing a sliding bearing cost-error model by taking the known tolerance domain as a constraint condition with the lowest machining cost as a target.
Preferably, the step S5 further includes: before solving by using a genetic algorithm, a fitness function needs to be set.
Compared with the prior art, the invention discloses and provides a sliding bearing geometric tolerance optimization method based on the SDT theory, and the method has the following beneficial effects:
1. on the basis of a traditional cost-error model, an SDT theory is applied, a cost error model based on the SDT theory is provided, and the relation between form and position errors and cost is explored;
2. providing a cost-error model based on SDT, expressing the processing cost in a product form of a function with deviation parameters as independent variables, combining a cost tolerance model, and converting the cost tolerance function into a cost error function;
3. and applying the genetic algorithm to a tolerance optimization solving process.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flow chart illustrating an implementation of a sliding bearing geometric tolerance optimization method based on SDT theory according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
Referring to the attached fig. 1, an embodiment 1 of the present invention discloses a sliding bearing geometric tolerance optimization method based on an SDT theory, including:
s1: determining the form and position error type of the sliding bearing, and acquiring a cost-error function of the sliding bearing under the error;
s2: aiming at the element freedom degree, converting the cost-error function to obtain a small displacement rotation parameter of the sliding bearing under the SDT theory;
s3: processing the small displacement rotation parameter according to the requirement of a known tolerance domain;
s4: establishing a sliding bearing cost-error model based on an SDT theory;
s5: and (4) carrying out optimization solution on the sliding bearing cost-error model by utilizing a genetic algorithm.
Specifically, in step S1, the cost-error function is the basis of the tolerance optimization design, and according to this model, a target function of tolerance optimization can be established, and according to the current research summary, the relationship between the machining size and the cost is clear, that is, the larger the machining size is, the higher the corresponding cost is, and for the same machining feature, different enterprises use different machining processes, the obtained model parameters are different, and the finally formed cost-tolerance curves are also different, and table 1 is a common cost-error function expression.
TABLE 1 commonly used cost-error function expressions
Figure BDA0002717977540000041
In one specific embodiment, when multiple tolerances are applied to the same geometric element at the same time, the corresponding cost-error function is shown in equation (1):
Figure BDA0002717977540000042
wherein T ═ T1,T2,T3,...,TnDenotes all tolerance terms of the geometric elements, n is the number of tolerance terms, and C is the cost.
In a specific embodiment, step S2 specifically includes: and (4) taking the form and position error and the dimensional tolerance of the sliding bearing into consideration to obtain the small displacement rotation parameter of the sliding bearing under the SDT theory.
Specifically, step S2 further includes: the small displacement momentum parameter is a vector formed by micro displacement generated by a rigid body with 6 motion components, the geometric variation of the sliding bearing part relative to the nominal state is expressed by 6 small variable parameters of the SDT, each feature has a corresponding SDT, the micro variation vectors of the translational and rotational degrees of freedom are respectively expressed by D ═ u, v, ω and θ ═ α, γ, δ, and a resultant vector D ═ D,0 ═ u, v, ω, α, γ, δ formed by the two groups of vectors is called a small displacement momentum (SDT), so the small displacement momentum parameter can be a small displacement momentum parameter
Figure BDA0002717977540000043
In a specific embodiment, the step S3 further includes:
s31: mapping the small displacement rotation parameter from the known tolerance domain according to the known tolerance domain, and solving the variation range of the small displacement rotation parameter;
s32: and establishing a constraint inequality and a variation inequality of the small displacement rotation parameter to obtain a form and position error model.
In a specific embodiment, the step S4 specifically includes: and establishing a sliding bearing cost-error model by taking the known tolerance domain as a constraint condition with the lowest machining cost as a target.
In a specific embodiment, the step S5 further includes: before solving by using a genetic algorithm, a fitness function needs to be set.
Example 2
In the embodiment 2, taking the cost-error function of the tolerance of the characteristic dimension of the inner hole and the form and position tolerance of the sliding bearing as an example, the expression of the cost-error function of the tolerance of the position of the hole and the shaft of the sliding bearing is shown in the formula (2):
Figure BDA0002717977540000051
wherein T ═ T1,T2,T3,...,TnDenotes all tolerance terms of the geometric elements, n is the number of tolerance terms, and C is the cost.
The tolerance field of the sliding bearing is known and can be set to be 0.04, and mapping is carried out on the SDT according to the known tolerance field, wherein the mapping expression can be shown as formula (3):
Figure BDA0002717977540000052
wherein t is a tolerance, tsTo a dimensional tolerance, tFTo a shape tolerance, tOTo orientation tolerance, tPFor positional tolerance, TF, TO, TP are their corresponding spatial variation ranges, and Δ τ is any component of τ.
In the spatial xyz coordinate system, the small displacement momentum parameter may be
Figure BDA0002717977540000053
Therefore, the cost-error function of the hole-to-shaft position tolerance of the sliding bearing can be converted into a cost-error model of the hole-to-shaft position tolerance, and the specific expression is shown in formula (4):
Figure BDA0002717977540000054
the cost is related to the 6 degree-of-freedom parameters of the tolerance, which are derived from the 6 independent and linearly independent components in the same coordinate system, as shown in equation (4), so that the above equation is converted into the product of independent variables, which is conveniently calculated as shown in equation (5):
Figure BDA0002717977540000055
the six components on the right side of the equation are the costs generated by satisfying the corresponding rotation amount and translation amount, but not the direct costs, but the variation of the three rotation amounts and the three translation amounts must be limited within the tolerance range, and the cost is also influenced in a crucial way.
For a variable of 0 for a rotation or translation in one direction, i.e. Δ τ is 0, then
Figure BDA0002717977540000061
The overall cost is not influenced; the error of the cylindricity of the sliding bearing is taken as form and position tolerance, and when the center of the cylinder is coincident with the origin of the nominal coordinate system, the rotation amount and the translation amount of the cylinder along the axial direction (Z axis) are 0, namely
Figure BDA0002717977540000062
Then
Figure BDA0002717977540000063
And then solving the formula (5) by using a genetic algorithm, wherein a mathematical model of the standard genetic algorithm is shown as the formula (6):
Figure BDA0002717977540000064
wherein C is the encoding method of the individual; e is the fitness evaluation function of the individual; p0Is an initial population; n is the size of the population;
Figure BDA0002717977540000065
to select an operator; gamma is a crossover operator; Ψ is a mutation operator; t is genetic operation termination condition.
The specific operation process is as follows:
(1) generating an initial population, wherein two methods are adopted for generating the initial population, and a random method is adopted under the condition of no precondition; if some preconditions exist, generating a population according to the preconditions, and then randomly selecting an initial population.
In general, there are two aspects to the selection of the initial population, if a larger initial population is selected, more individuals are meant, when genetic manipulation is performed, more objects are manipulated, and it is easier to obtain a global optimal solution, and if a smaller initial population is selected, each selection, crossover, and mutation manipulation iteration is faster, and the time consumption is shorter, so the number of initial populations is generally selected to be 20-100 or 20-49.
(2) A fitness function is determined, the value of the fitness function determines the probability that the individual in the initial population is inherited to the next generation population, and the probability is always non-negative, so that the method in embodiment 2 can be implemented by using the non-negative fitness function, such as a fitness function based on the Fisher criterion, a fitness function based on the mean variance ratio, and the like.
(3) When using the genetic algorithm program for optimization, the operation parameters N, T and P are set0They affect the solution result and solution efficiency of the genetic algorithm.
The crossover operator influences the frequency of crossover operation, the higher the frequency selection is, the faster the iteration is, the easier the optimal solution is to be reached, and the too high frequency can cause the premature convergence, so that 0.4-0.99 or 0.4-0.49 is generally selected; the mutation operator can cause unstable conditions due to the reasons of population size, chromosome length and the like when being selected too high, and can cause the lack of diversity of samples when being selected too low, so that the mutation operator is generally selected from 0.0001-0.1, and can also be selected from 0.0001-0.01; the length of the chromosome is mainly determined by the precision of problem solving, the higher the precision is, the longer the length of the chromosome is, the larger the search space is, and the larger the corresponding required population is; the maximum evolution algebra is used as a termination condition, and generally, depending on the specific problem, it can be 100-500,
in this embodiment 2, by the above method, calculation and optimization can be finally realized by an MATLAB computer program.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (5)

1. A sliding bearing geometric tolerance optimization method based on an SDT theory is characterized by comprising the following steps:
s1: determining the form and position error type of the sliding bearing, and acquiring a cost-error function of the sliding bearing under the error;
s2: aiming at the element freedom degree, obtaining a small displacement rotation parameter of the sliding bearing under the SDT theory;
s3: processing the small displacement rotation parameter according to the requirement of a known tolerance domain;
s4: establishing a sliding bearing cost-error model based on an SDT theory;
s5: and (4) carrying out optimization solution on the sliding bearing cost-error model by utilizing a genetic algorithm.
2. The sliding bearing geometric tolerance optimization method based on the SDT theory as claimed in claim 1, wherein the step S2 specifically includes: and (4) taking the form and position error and the dimensional tolerance of the sliding bearing into consideration to obtain the small displacement rotation parameter of the sliding bearing under the SDT theory.
3. The sliding bearing geometric tolerance optimization method based on the SDT theory as claimed in claim 2, wherein the step S3 further includes:
s31: mapping the small displacement rotation parameter from the known tolerance domain according to the known tolerance domain, and solving the variation range of the small displacement rotation parameter;
s32: and establishing a constraint inequality and a variation inequality of the small displacement rotation parameter to obtain a form and position error model.
4. The sliding bearing geometric tolerance optimization method based on the SDT theory as claimed in claim 3, wherein the step S4 specifically includes: and establishing a sliding bearing cost-error model by taking the known tolerance domain as a constraint condition with the lowest machining cost as a target.
5. A sliding bearing geometric tolerance optimization method based on SDT theory according to claim 3, wherein the step S5 further comprises: before solving by using a genetic algorithm, a fitness function needs to be set.
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