CN109815562B

CN109815562B - Assembly pose optimization method based on tolerance space

Info

Publication number: CN109815562B
Application number: CN201910012090.9A
Authority: CN
Inventors: 李泷杲; 黄翔; 江一帆
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2019-01-07
Filing date: 2019-01-07
Publication date: 2023-04-28
Anticipated expiration: 2039-01-07
Also published as: CN109815562A

Abstract

Firstly, establishing an assembly constraint feature model, wherein the assembly constraint feature model is a mathematical model of assembly features formed by geometric features of an assembly object, and can calculate the numerical value of corresponding features under the condition of given assembly pose parameters; secondly, determining the uncertainty of assembly positioning of an assembly system; thirdly, an assembly pose evaluation model based on a tolerance space is established, wherein the tolerance space is a feasible domain space formed by the tolerance of assembly constraint features and the assembly pose constraint. For a given assembly pose parameter, evaluating the given assembly pose according to the evaluation basis by taking the distance from the pose to the space boundary of the feasible region; fourth, the optimal assembly pose is solved according to the assembly pose evaluation model.

Description

Assembly pose optimization method based on tolerance space

Technical Field

The invention relates to an assembly technology, in particular to an assembly pose optimization technology, and specifically relates to an assembly pose optimization method based on a tolerance space.

Background

In the digital assembly of the aircraft parts, the state of an assembly object is acquired through sensors such as laser and vision and is transmitted in the form of digital quantity in the process that the parts are positioned to the target pose through an assembly fixture. For parts that are not so rigid or structurally deformed, the pose of the assembled object is usually expressed by geometric kinematic parameters (rigid body translation amount and rotation amount). The actual state of the component deviates from the theoretical digital-analog due to component machining errors and component-to-component assembly cumulative errors. In the assembly of the aircraft parts, the deviation cannot be completely eliminated, the pose can be optimized only through an assembly coordination technology, and the deviation distribution is adjusted to meet the assembly process requirement.

Typically, the assembly object is located by multiple constraint features, so pose optimization of the assembly object is essentially a multi-objective constraint solving problem. Because of the difficulty in solving the multi-objective problem in engineering, the traditional method is to convert the multi-objective problem into a single-objective problem by means of weighted summation. The weight value is usually determined by experience or repeated experiments, and for the assembly of some complex structures, the weight value is often difficult to accurately set, and the unmanageable weight value can influence the optimization result of the assembly pose.

Disclosure of Invention

The invention aims at solving the problem that the weight value is difficult to accurately set in the assembly pose optimization and the assembly pose optimization result is affected, and provides an assembly pose optimization method based on a tolerance space.

The technical scheme of the invention is as follows:

the assembly pose optimization method based on the tolerance space is characterized by comprising the following steps of:

firstly, establishing an assembly constraint feature model;

secondly, determining the uncertainty of assembly positioning of an assembly system;

thirdly, an assembly pose evaluation model based on a tolerance space is established;

fourth, the optimal assembly pose is solved according to the assembly pose evaluation model.

The assembly constraint feature model is a mathematical model of assembly features formed by geometric features of an assembly object, and can calculate the numerical value of the corresponding features under the condition of given assembly pose parameters. In the product design stage, for product quality control, tolerance is defined for each assembly constraint feature, and the assembly constraint feature value after the assembly pose optimization is within the tolerance range.

The assembly positioning uncertainty of the assembly system is expressed by pose parameters of an assembly object.

The tolerance space is a feasible domain space formed by the constraint of tolerance of assembly constraint features on the pose of the assembly. And for the given assembly pose parameters, evaluating the given assembly pose according to the evaluation basis by taking the distance from the pose to the space boundary of the feasible region.

The invention has the beneficial effects that:

(1) The invention realizes the optimization of the assembly pose. The multi-constraint assembly pose solving is converted from the multi-objective optimizing problem to the single-objective optimizing problem, so that the solving difficulty is effectively reduced.

(2) The assembly pose evaluation model based on the tolerance space is used for evaluating the assembly pose quality without depending on experience or repeated experiments, so that the influence of incorrect weight value on the pose optimization result is avoided.

(3) The invention not only can acquire the optimized assembly pose, but also can judge whether the assembly result under the optimized pose can meet the assembly constraint condition according to the assembly pose evaluation parameters.

Drawings

FIG. 1 is a two-dimensional tolerance space diagram of the present invention.

FIG. 2 is a three-dimensional multi-constraint part tolerance space schematic of the present invention.

Detailed Description

The invention is further described below with reference to the drawings and examples.

As shown in fig. 1-2.

An assembly pose optimization method based on tolerance space comprises the following steps:

firstly, establishing an assembly constraint feature model;

Wherein: the assembly constraint feature model is a mathematical model of assembly features formed by geometric features of an assembly object, and can calculate the numerical value of the corresponding features under the condition of given assembly pose parameters. The specific modeling method of the assembly constraint characteristic model needs to be determined according to the specific geometric characteristics of the assembly object, and the established characteristic model is expressed as C _ij (t _i )∈[C _ijmin ,C _ijmax ]Wherein C _ij Is the characteristic value, t _i ＝[x y z α β γ] ^T Representing the assembly pose parameters, C _ijmin ,C _ijmax Upper and lower tolerance limits for assembly constraint features.

The positioning uncertainty space is represented by six-dimensional pose parameters as shown in a formula (6) when the positioning uncertainty δt of the assembly system is described by the position uncertainty δd and the pose uncertainty δθ, the uncertainty parameters can be determined according to the performance evaluation of the actual positioning system, and the change of the parameters can influence the assembly feasibility judgment but cannot influence the numerical value of the optimal pose.

Wherein δx δyδzδαδβδγ represents six-dimensional pose parameters of uncertainty space, and R represents real number domain.

The assembly pose evaluation model is established through the following processes:

first, a definition of the tolerance space is given, and as shown in fig. 1 (a) and 1 (b), a point P (x, y) ∈r is given on a two-dimensional plane ² Is of the feasible region of (1)

For any one feasible solution P in the feasible domain _i E.OMEGA, set P _i To locate the theoretical target position, the actual locating position P is due to uncertainty in locating _i ' deviations may exist. Definition: all P's meeting constraints under a certain positioning uncertainty _i The' set of formations S is the tolerance space. Point-to-point P _i In other words, if the uncertainty of positioning is consistent in all directions, the inscribed circle of the feasible region Ω is the point P _i Is not limited by the tolerance space of (a). To ensure the integrity of the solution, for points P outside the feasible region _i A similar definition is also given, as in fig. 1 (c), represented as an circumscribed circle of the feasible region Ω.

To quantify the tolerance space, the tolerance space is assessed in units of the set positioning uncertainty δt, defining this parameter as ease:

E＝F(S,δt) (7)

the greater the ease E indicates the easier the positioning of the pose with the current solution as the target, the lower the positioning accuracy requirement. At point P _i Taking the example as the case, the circle radius of the area corresponding to the positioning uncertainty δt is r _i The circle radius of the corresponding area of the tolerance space S is R _i (negative value of corresponding radius if S is corresponding to the circumscribed circle), the easiness of tolerance space correspondence is expressed as:

the visibility is a dimensionless constant for quantifying the tolerance space, from which definition the following law can be derived:

1) If E is more than or equal to 1, the current solution is in a feasible domain, and the positioning uncertainty requirement is met;

2) If E <1 is more than or equal to 0, the current solution is in a feasible region, and the actual position possibly exceeds the feasible region in consideration of positioning uncertainty;

3) If E <0, it indicates that the current solution is outside the feasible region, or that the feasible region does not exist.

Expanding the tolerance space assessment model into the part assembly pose assessment of the three-dimensional space, as shown in fig. 2, the feasible region omega is formed by various constraint features and the tolerance C thereof _ij (t _i )∈[C _ijmin ,C _ijmax ]Determining, wherein t _i ＝[x y z α β γ] ^T Representing the fitting pose of the parts. To quantitatively describe the part positioning tolerance space, a scale variable ζ is introduced:

Δt _i ＝(δt _i ,ζ)＝[ζ·δx ζ·δy ζ·δz δα δβ δγ] ^T (9)

then the part is in position t according to the definition of the tolerance space _i Ease of (E) _i Can be described as to any δt _i E V, satisfy t _i ′＝t _i +Δt _i The maximum ζ still belonging to the tolerance space Ω:

if ζ _i Ease of absence E _i Described as the presence of δt _i E V satisfies t _i ′＝t _i +Δt _i A negative value of the minimum ζ belonging to the tolerance space Ω.

The optimal assembly pose can be solved by adopting a particle swarm algorithm as a standard constraint optimization problem.

The invention is not related in part to the same as or can be practiced with the prior art.

Claims

1. The assembly pose optimization method based on the tolerance space is characterized by comprising the following steps of:

firstly, establishing an assembly constraint feature model; the assembly constraint feature model is a mathematical model of assembly features formed by geometric features of an assembly object, and can calculate the numerical value of the corresponding features under the condition of given assembly pose parameters; in the product design stage, tolerance is defined for each assembly constraint feature for product quality control, and the assembly constraint feature value after the optimization of the assembly pose is within the tolerance range;

fourthly, solving the optimal assembly pose according to the assembly pose evaluation model;

the assembly positioning uncertainty δt of the assembly system is described by the position uncertainty δd and the attitude uncertainty δθ, a positioning uncertainty space is represented by six-dimensional pose parameters as shown in a formula (6), the uncertainty can be determined according to the performance evaluation of an actual positioning system, and the change of the uncertainty can influence the assembly feasibility judgment but cannot influence the numerical value of the optimal pose;

wherein δx δy δz δα δβδγ respectively represent six-dimensional pose parameters of an uncertainty space, and R represents a real number domain;

the tolerance space is a feasible region space formed by the constraint of tolerance of assembly constraint features on the pose of the assembly; for a given assembly pose parameter, evaluating the given assembly pose according to the evaluation basis by taking the distance from the pose to the space boundary of the feasible region;

the method for establishing the assembly pose evaluation model comprises the following steps:

first, a definition of the tolerance space is given, and the point P (x, y) εR is given on the two-dimensional plane ² Is of the feasible region of (1)

For any one feasible solution P in the feasible domain _i E.OMEGA, set P _i To locate the theoretical target position, the actual locating position P is due to uncertainty in locating _i ' there may be a bias; definition: all P's meeting constraints under a certain positioning uncertainty _i ' the set S of formations is a tolerance space; point-to-point P _i In other words, if the uncertainty of positioning is consistent in all directions, the inscribed circle of the feasible region Ω is the point P _i Is a tolerance space of (2); to ensure the integrity of the solution, for points P outside the feasible region _i Similar definitions are also made;

E＝F(S,δt) (2)

the greater the easiness E is, the easier the positioning of the pose with the current solution as the target pose is, and the lower the positioning precision requirement is; at point P _i Taking the example as the case, the circle radius of the area corresponding to the positioning uncertainty δt is r _i The circle radius of the corresponding area of the tolerance space S is R _i If S is a negative value of the corresponding radius for the corresponding circumscribed circle, the easiness of the tolerance space correspondence is expressed as:

ease is a dimensionless constant used to quantify the tolerance space, from its definition, the following law can be derived:

3) If E <0, the current solution is outside the feasible domain, or the feasible domain does not exist;

expanding the tolerance space evaluation model to part assembly pose evaluation in three-dimensional space, wherein the feasible domain omega is formed by various constraint features and tolerance C thereof _ij (t _i )∈[C _ijmin ,C _ijmax ]Determining, wherein t _i ＝[x y z α β γ] ^T Representing the fitting pose of the parts; to quantitatively describe the part positioning tolerance space, a scale variable ζ is introduced:

Δt _i ＝(δt _i ,ζ)＝[ζ·δx ζ·δy ζ·δz δα δβ δγ] ^T (4)

E _i ＝F(S _i ,δt _i )＝maxζ _i

2. The method for optimizing assembly pose as claimed in claim 1, wherein said mathematical model of assembly features is C _ij (t _i )∈[C _ijmin ,C _ijmax ]Wherein C _ij Is the characteristic value, t _i ＝[x y z α β γ] ^T Representing the assembly pose parameters, C _ijmin ,C _ijmax Upper and lower tolerance limits for assembly constraint features.

3. The assembly pose optimization method according to claim 1, wherein the assembly positioning uncertainty of the assembly system is represented by pose parameters of the assembly object.