CN105573248A - Flexible member assembling dimensional deviation control method based on multi-station assembly jig compensation - Google Patents

Abstract

The invention provides a flexible member assembling dimensional deviation control method based on multi-station assembly jig compensation. The flexible member assembling dimensional deviation control method is characterized in that based on a state space method for controlling the theory, a jig compensation system is added in a positioning or re-positioning link for each station, wherein the system comprises three modules: a deviation data acquisition module, a compensation scheme decision module and a compensation implementation module; the deviation data acquisition module provides input for a system; except the first station, other stations needs acquisition of the dimensional deviation values of the assembly parts after assembling of the front stations; the compensation scheme decision module is the core content, and comprises three steps: assembly deviation modeling, compensation dosage optimization model modeling, and optimal compensation dosage solution, and is used for determining the jig positioning compensation dosage for the subsequent stations so as to enable the assembly deviation of the subsequent stations to be minimum; and the compensation implementation module adjusts a jig positioning point according to a compensation decision scheme. The flexible member assembling dimensional deviation control method based on multi-station assembly jig compensation can scientifically, accurately and instantly reduce the assembly deviation for each station, and can realize station-by-station control for multi-station assembly deviation of the flexible member, and can reduce the dimensional deviation after assembling of the multi-station for the flexible member.

Description

Flexible part assembling size deviation control method based on multi-station assembling clamp compensation

Technical Field

The invention relates to a computer-aided manufacturing technology, in particular to a flexible piece multi-station assembling deviation control method, and specifically relates to a flexible piece assembling size deviation control method based on multi-station assembling clamp compensation.

Background

The flexible parts have the characteristics of deformability and resilience, so that gaps and interference caused by errors can be overcome through deformation during assembly, but the assembly is deformed and assembly stress is generated. In actual engineering, complex products are often assembled on a plurality of stations. When the work station is changed, the assembly deviation can be transferred along with the advance of the work station and gradually accumulated, and the repositioning deviation can be generated due to the change of the positioning reference. In multi-station assembly, the problems of uneven fit clearance, poor assembly coordination and the like are often caused by overlarge size deviation, and the product quality is finally influenced. Therefore, an effective method is needed to reduce the multi-station assembly deviation of the flexible parts, improve the product quality and reduce the manufacturing cost.

By studying the transmission and accumulation of deviations during the assembly process, several methods for reducing the influence of deviations have been widely used to reduce the negative influence of dimensional deviations on the quality of the final assembled product and improve the quality of the product. Among them, the most common method is robust design, which works in the product design phase and minimizes the sensitivity of the product quality to deviations and disturbances in the production phase. Another approach is to use statistical process quality control (SPC) to detect mean shift and variation in the production process, requiring corrective or regulatory measures to restore the process to normal operating conditions. However, the robustness design can only reduce the influence of the deviation and cannot directly improve the quality; statistical process control has hysteresis and does not provide a systematic way to automatically control dimensional deviations. Statistical Process Control (SPC) requires a large number of samples to determine the source of error and so cannot compensate for errors in piece-by-piece assembly. Neither of these two methods described above can reduce errors instantaneously during assembly.

In 1996, Nguyen and Mills improved automatic, robust clampless assembly elements, using a variety of controllers that combined mechanical modeling of components with force sensor readings to precisely position sheet metal components to nominal positions. However, it is not possible to control the dimensional variations of the components by altering the component positions (off-nominal positions) to compensate for critical product feature variations in the final assembly. In 2006, Hu and Camelio used a method for controlling component errors to solve the problem of dimensional deviation in the assembly process of a flexible part, and proposed an adaptive control framework for controlling input component errors, which consists of pre-assembly measurement and optimization, and is used to determine an optimal control behavior, so that the deviation of Key Product Characteristics (KPC) after assembly is minimized. However, they only present a conceptual framework of such heuristic methods and do not refer to how to implement the bias compensation; and the method does not consider the application range, can only be used for determining the control behavior in the actual assembly process within a short time, and if the control process is used for real-time online control, an efficient offline algorithm is needed to obtain the relation between the error and the control behavior. In 2007 Lzquierdo and the like, a practical feedback control method for single-station assembly is provided, and deviation of a linear assembly system can be reduced in real time. In 2012, Xie proposed a piece-by-piece control error compensation method for flexible sheet assembly to improve the assembly deviation quality. The method comprises an off-line control module, and determines a control behavior by adopting a simulation model in consideration of contact and friction among parts, so that the KPC deviation of the assembly body is minimum. However, the method based on finite element simulation requires a simulation model to be established for each assembly, and has great limitations in real-time performance and feasibility for production control; and does not consider how to achieve continuous control of assembly deviation in a multi-station assembly mode.

Therefore, the adaptive control method suitable for the multi-station assembly process of the flexible parts is established, the assembly deviation is reduced by implementing the clamp compensation in the positioning or repositioning link, the assembly deviation in the multi-station assembly of the flexible parts can be scientifically and accurately reduced, and the engineering application value is achieved.

Disclosure of Invention

The invention aims to solve the problem of poor adaptability control of multi-station assembly deviation of a flexible part, and provides a flexible part assembly size deviation control method based on multi-station assembly fixture compensation.

The technical scheme of the invention is as follows:

a flexible part assembling size deviation control method based on multi-station assembling clamp compensation is characterized by comprising the following steps: firstly, predicting and compensating assembly deviation station by station in a flexible part multi-station assembly process, and enabling the position of a clamp positioning point participating in clamp compensation to be normally adjusted within a certain range; secondly, on the basis of a state space method in a control theory, a clamp compensation system is added in a positioning or repositioning link of multi-station assembly of the flexible part to acquire deviation data, optimize a compensation scheme and implement compensation so as to reduce assembly deviation on a station to be assembled. In other words, the positioning point normal adjustable clamp is taken as assembly equipment, and in the positioning or repositioning link of multi-station assembly of the flexible part, the normal deviation of the assembly part at the station is reduced by adopting a method of adjusting the normal compensation quantity of the positioning point of the clamp at the subsequent station, so that the deviation of the final assembly part is reduced. The clamp compensation system for multi-station assembly of the flexible parts comprises three modules of deviation data acquisition, compensation scheme decision and compensation implementation, and can be realized through the following technical routes:

1. deviation data acquisition

The deviation data acquisition module is an input part of the clamp compensation system. Because the input quantity of the whole assembly system, namely the manufacturing deviation of all parts participating in assembly is a known quantity, the input of the clamp compensation system of the first station is included, so that the first station does not need to carry out deviation data acquisition; for other stations except the first station, the deviation data acquisition refers to the acquisition of the size deviation value of the sub-assembly parts assembled by the front station and assembled in the subsequent stations. Taking Key Product Characteristics (KPC) of the sub-assembly parts, and the positions of the fixture positioning points and the assembly connecting points of the sub-assembly parts in subsequent stations as deviation data acquisition points, wherein the data acquisition mode comprises the following steps: derived from the assembly deviation transfer model of the preposed station and measured by a measuring tool.

2. Compensation scheme decision

The compensation scheme decision module is a core part of the clamp compensation system and comprises three steps of assembly deviation modeling, compensation quantity optimization model modeling and optimal compensation quantity solving.

2.1 Assembly offset modeling

And (3) taking the normal compensation quantity of the positioning point of the clamp as a group of adjustable variables to establish a flexible part assembly deviation transfer model on a subsequent station to be assembled. For the first station, the considered deviation sources are the manufacturing deviation and the positioning deviation of the clamp of the parts participating in assembly; for stations other than the first station, the sources of variation considered include subassembly variation, part manufacturing variation and jig positioning variation for subassemblies participating in assembly. The modeling process comprises four steps of positioning, clamping, connecting and releasing resilience, small deformation and linear elasticity assumption are adopted for deformation of the flexible part, Key Product Characteristics (KPC) are used as measuring points, and the relation between each measuring point of the flexible part and each deviation source in deformation and resilience in the assembling process is established by applying the theory of an influence coefficient method. And (3) simulating the assembly process by adopting finite element software, and extracting a super element rigidity matrix of each assembly force and deformation in the steps of positioning, clamping, connecting and releasing springback. And finally, establishing a normal compensation quantity of a positioning point of the fixture, a deviation transfer relation between the deviation source deviation and the deviation of a measuring point of the assembly part of the station, namely an assembly deviation transfer model of the station.

2.2 Compensation optimization model modeling

And establishing an assembly deviation optimization model of the station based on the clamp compensation according to the flexible part assembly deviation transfer model considering the normal compensation quantity of the clamp positioning point on the subsequent station. The optimization variable is the normal offset of the adjustable position of the clamp. There are multiple optimization objectives, including: the square sum of the deviation of each measuring point of the station assembly part is minimized, and the square sum of the compensation quantity of each adjustable positioning point of the fixture is minimized. The constraint conditions include: the compensation amount of each clamp positioning point is within a certain adjustable range, and the deviation of each measuring point of the assembly part is within an allowable range of the assembly process requirement.

2.3 optimal Compensation solution

The assembly deviation transfer model can obtain: when a group of input deviation values are given by the deviation data acquisition module, the deviation of the assembly part measuring point and the normal compensation value of the clamp positioning point are in a linear relation, so that the solution of the optimization model is a quadratic programming problem. And constructing an objective function, and obtaining an optimal solution meeting the optimization objective within a range specified by the constraint condition. The case-by-case discussion here needs to be based on whether a feasible solution exists or not. If a feasible solution exists, adjusting the compensation quantity of the positioning point of the clamp in the next module according to the feasible solution; if there is no feasible solution, it needs to consider ensuring the assembly quality by other methods, such as: the concrete implementation of these methods is not in the research content of the present invention, considering that a new fixture positioning point is added at the station, etc.

3. Compensation implementation

The compensation implementation module is an implementation part of the clamp compensation system. And adjusting the normal compensation quantity of the positioning point of the adjustable clamp according to the solving result of the assembly deviation optimization model based on the clamp compensation in the decision module. If the positioning points of the adjusting clamp cannot meet the requirement on the quality of the assembling deviation of the station, methods such as increasing the number of the positioning points of the clamp are considered, and the content is out of the implementation range of the invention.

The invention has the beneficial effects that: the flexible part assembly size deviation control method based on multi-station assembly fixture compensation can utilize a positioning or repositioning link in multi-station assembly, and immediately and accurately adjust the normal compensation quantity of the fixture positioning point of a station according to the input deviation of a subsequent station to be assembled, so that the flexible part assembly deviation adaptability control from station to station is realized, and the qualification rate of the deviation quality of a final assembly product is ensured.

Drawings

FIG. 1 is a schematic diagram of a multi-station assembly process of a flexible part by using clamp compensation.

FIG. 2 is a flow chart of a jig compensation system for multi-station assembly dimension deviation control of flexible parts.

FIG. 3 is a schematic structural diagram of the positioning point normal adjustable clamp.

FIG. 4 is a schematic diagram of the multi-station assembly of the flexible parts at the 3-2-1 positioning stage in the station k.

FIG. 5 is a schematic diagram of a multi-station assembly of flexible parts at the N-2-1 positioning stage in station k.

Fig. 6 is a schematic diagram of a multi-station assembly of flexible parts in the clamping stage in station k.

Fig. 7 is a schematic diagram of a multi-station assembly of a flexible member at the connection (riveting) stage in station k.

Fig. 8 is a schematic diagram of the stage of releasing the riveter in station k during multi-station assembly of the flexible member.

Fig. 9 is a schematic diagram of a stage of multi-station assembly of the flexible piece in releasing an additional positioning point in a station k.

Fig. 10 is a schematic diagram of the stage of multi-station assembly of the flexible part in the station k for releasing the over-constrained anchor point.

Detailed Description

The invention is described in further detail below with reference to the figures and examples.

As shown in fig. 1-10.

A flexible part assembling size deviation control method based on multi-station assembling clamp compensation predicts and compensates assembling deviation station by station in the multi-station assembling process of a flexible part, and enables the position of a clamp positioning point participating in clamp compensation to be normally adjusted within a certain range. Meanwhile, on the basis of a state space method in a control theory, a clamp compensation system is added in a positioning or repositioning link of multi-station assembly of the flexible part to acquire deviation data, optimize a compensation scheme and implement compensation so as to reduce assembly deviation on a station to be assembled. The details are as follows:

FIG. 1 is a schematic diagram of a multi-station assembly process of flexible parts by using clamp compensation, and compared with the conventional multi-station assembly process described by using a state space method, a clamp compensation system is added in a positioning or repositioning link of each station. Wherein the first station is offset by a part offset X₀For system input, other stations except the first station output X by the assembly deviation of the preposed station_k-1Is the system input. The normal compensation quantity theta of the positioning point of the station fixture is output through calculation and derivation of the fixture compensation system_k. In the figure, k is 1,2, …, N indicates the total number of assembly stations, X₀For assembling manufacturing variations of parts, X_kFor assembly deviations of station k, U_kFor deviations of the clamps participating in the assembly at station k, w_kThe random error of the station k is ignored in the invention, and the normal compensation quantity theta of the positioning point of the clamp is_kThe deterministic setpoint is not compensated for at all, only the normal compensation of the additional setpoint is taken into account. Fig. 2 shows a flowchart of a fixture compensation system for multi-station assembly dimension deviation control of a flexible part, the fixture compensation system includes three modules of deviation data acquisition, compensation scheme decision and compensation implementation, a detailed description is given below for functions and contents of each module by taking a station k as an example, and it is not assumed that k is not equal to 1. Fig. 3 shows a schematic structural diagram of the positioning point normal adjustable clamp, and in specific implementation, the corresponding positioning point normal adjustable clamp can be designed according to needs or realized by referring to the positioning point normal adjustable clamp disclosed in related papers and patents.

1. Deviation data acquisition

The deviation data acquisition module obtains the output deviation of the station (k-1) by a measuring or calculating method, and the deviation is used as the station kThe clamp compensation system. Because of the inevitable error in both the measurement and calculation results, the deviation of the output of the station (k-1) acquired by the module from its true value X_k-1There is an error, and the deviation value obtained by this block is denoted as X'_k-1。X′_k-1The manufacturing deviation of the sub-assembly parts assembled by the front station, namely the manufacturing deviation of the parts to be assembled in the station k and the manufacturing deviation of the parts to be assembled which are not assembled in the station k are included. The input X being already contained in the entire assembly system due to manufacturing variations of the parts₀The data to be collected is the assembly deviation of the flexible sub-assembly assembled by the station (k-1), and the sub-assembly is marked as A^k. The sub-assembly A^kKey product features (KPC) and A in workstation k^kThe normal deviation of the positions of the positioning points and the positions of the connecting points (riveting points) of the clamp is taken as a deviation data acquisition object, the normal deviation value is a normal component of a deviation value of the flexible piece data acquisition points and the nominal position thereof, and the deviation value can be obtained in two ways: firstly, after the station (k-1) is assembled, a measuring tool (such as a laser tracker) is adopted to directly measure the quantum assembly A^kObtaining; and secondly, deducing the assembly deviation transfer model of the station (k-1), wherein the deducing process of the deviation transfer models of the flexible parts of different stations is similar, and the deducing process is divided into four steps of positioning, clamping, connecting and releasing springback, and the specific process can refer to the assembly deviation modeling in a scheme decision module. Obtained A^kThe normal deviation at the data acquisition point is denoted as V_A. In addition, the flexible part to be assembled in the station k is marked as P^kThe normal deviation of the KPC point is marked as V_P。

2. Compensation scheme decision

2.1 Assembly offset modeling

Normal compensation quantity theta of extra positioning point of clamp is considered on station k_kThe flexible member assembly deviation transfer model needs to consider the following deviation sources: assembling deviation of sub-assembly parts participating in assembly, manufacturing deviation of parts and positioning deviation of clamps. Will be provided withSub-assembly A^kAnd part P^kThe KPC points are used as measuring points, and the deviations are respectively marked as V_AmAnd V_Pm。A^kAnd P^kThe deviations of the position of the additional positioning points in the station k are respectively marked as V_AaAnd V_PaThe deviation of the position of the assembly connection point is respectively marked as V_AjAnd V_Pj. Is not provided with A^kAnd P^kThe positions of the measuring point, the additional positioning point and the assembling connection point are not coincident with each other.

The flexible part assembling deviation modeling can be respectively carried out four steps of positioning, clamping, connecting and releasing springback, and an assembling deviation transfer model of a station k is established by using an influence coefficient method and a super-element rigidity theory on the assumption of small deformation and linear elasticity.

(1) Positioning

In order to ensure the assembly rigidity and accuracy, the flexible part is generally positioned by adopting 'N-2-1' overconstrained positioning, and the positioning process can be divided into two stages: in the first stage, a deterministic positioning method based on a rigid body model is adopted to carry out deterministic positioning (namely 3-2-1 positioning), which is a process of complete constraint of freedom, and the flexible part does not deform; in the second stage, in order to reduce the error caused by the deformation of the flexible part, an additional positioning point needs to be added on the basis of the positioning of 3-2-1 to form an over-constrained positioning (namely the positioning of N-2-1), and the flexible part is deformed at the moment.

a) Deterministic positioning

In deterministic positioning analysis, all sub-assemblies and parts are assumed to be rigid bodies, and positioning deviation is caused by the change of the spatial pose of the rigid body parts after positioning. The deterministic positioning analysis establishes the relationship between the pose deviation of the parts involved in assembly and the assembly deviation of the sub-assembly parts, the part manufacturing deviation and the fixture positioning point deviation by using the rigid body kinematics theory.

6 degrees of freedom of any three-dimensional part can be completely restricted by 6 positioning blocks, and 3-2-1 deterministic positioning is realized. At this time, the deviation of any point on the part due to the deviation of the jig and the part occurring at the positioning block can be calculated by the equation (1):

q_o＝J^-1·N·R(1)

wherein q is_o＝[o_x,o_y,o_z,α,β,γ]^TAnd represents the translation deviation [ o ] at any measuring point o on the part_x,o_y,o_z]^TAnd rotational offset [ α, gamma ]]^T；J＝[J₁,J₂,…,J₆]^TThe Jacobian matrix of the jig positioning block is represented, and the Jacobian matrix of the ith jig positioning block is J_i＝[n_ix,n_iy,n_iz,n_izy_i-n_iyz_i,n_ixz_i-n_izx_i,n_iyx_i-n_ixy_i]Wherein the coordinate of the ith fixture positioning block is (x)_i,y_i,z_i)，n_i＝[n_ix,n_iy,n_iz]^T(i ═ 1,2, …,6) is the unit normal vector of the part surface at the fixture locating block; r ═ R₁,r₂,…,r₆]^TThe sum of the jig positioning deviation at 6 jig positioning blocks and the part manufacturing deviation (sub-assembly assembling deviation) is shown, where r_i＝[x_i,y_i,z_i]^T；

As shown in fig. 4, subassembly a^kAnd part P^kIn the stage of deterministic positioning, the normal deviations are all deviations in the z direction. At this time, A^kAnd P^kThe normal deviation at each point requires the superimposition of the effect of the fixture positioning deviation on that point. Known flexible member A^kAnd P^kThe deviation of the deterministic positioning points of the clamp is V respectively_AJdAnd V_PJdThe resulting normal deviation (i.e. z-direction) of any point on the flexureDirectional deviation) can be calculated by equation (1). In the deterministic positioning phase, the flexible part A^kAnd P^kThe measuring point deviations caused by the deterministic positioning point deviations are respectively marked as V_Am(d)And V_Pm(d)And the deviation of the position of the additional positioning point in the station k is respectively recorded as V_Aa(d)And V_Pa(d)And the deviation of the position of the assembly connection point (rivet point) is respectively marked as V_Aj(d)And V_Pj(d). Sub-assembly A after tolerance accumulation^kThe deviations of the above points are:

V_Am(1)＝V_Am+V_Am(d)(2)

V_Aa(1)＝V_Aa+V_Aa(d)(3)

V_Aj(1)＝V_Aj+V_Aj(d)(4)

part P^kThe deviations of the above points are:

V_Pm(1)＝V_Pm+V_Pm(d)(5)

V_Pa(1)＝V_Pa+V_Pa(d)(6)

V_Pj(1)＝V_Pj+V_Pj(d)(7)

b) adding additional anchor points

After additional anchor points are applied, subassembly A, as shown in FIG. 5^kAnd part P^kForm an "N-2-1" over-constrained positioning, flexible member A^kAnd P^kDeformation occurs and the deviation at the additional positioning point is 0. If it is at A^kAnd P^kRespectively introducing a normal compensation quantity theta of the clamp at the additional positioning points_AAnd theta_PThen in the stage of adding additional anchor points, A^kAnd P^kThe deviations at the additional positioning points are respectively theta_AAnd theta_P. For flexible part A^kAnd P^kAnd (3) making linear elasticity and small deformation assumptions, and establishing the relation between the deformation and the stress of the flexible part by using an influence coefficient method and a super-element rigidity theory. The following sub-assembly A^kThe analysis was performed as an example:

F_Aa＝K_Aa(V_AJa+θ_A-V_Aa(1))(8)

in the formula, F_AaIs a flexible sub-assembly A^kThe force experienced at its additional location point; k_AaThe method comprises the steps of establishing a super-element stiffness matrix by using '3-2-1' deterministic positioning constraint extracted by finite element software as a boundary condition and using additional positioning points as key points; v_AJaIs the fixture offset at the additional location point.

When in sub-assembly A^kAt the additional location point of (a) exerts a force F_AaAfter formation of the "N-2-1" orientation, A is caused^kDeformation occurs, and the deviation of the positions of the measuring points and the connecting points in the stage is as follows:

V_Am(a)＝C_Am(a)F_Aa(9)

V_Aj(a)＝C_Aj(a)F_Aa(10)

wherein, V_Am(a)And V_Aj(a)In the stage of adding additional anchor points, respectively, the sub-assembly A^kNormal deviations at the survey and connecting points. C_Am(a)And C_Aj(a)Are respectively A^kThe deviation V between the clamping force applied to the additional positioning point and the measuring point_Am(a)And deviation from the connection point V_Aj(a)A linear system matrix in between, which can be derived from the stiffness matrix.

Will V_Am(a)And V_Aj(a)Superposition to subassembly A^kObtaining the deviation A at the end of the stage in the measured point and the connecting point^kDeviation V at the measurement and connection points_Am(2)And V_Aj(2)Respectively as follows:

V_Am(2)＝V_Am(1)+V_Am(a)(11)

V_Aj(2)＝V_Aj(1)+V_Aj(a)(12)

according to the above method, the part P can be obtained in the same way^kIn the stage of adding the additional positioning point, the force F applied to the additional positioning point_PaAnd the normal deviation V generated at the measuring points and the connecting points_Pm(a)And V_Pj(a)。

F_Pa＝K_Pa(V_PJa+θ_P-V_Pa(1))(13)

V_Pm(a)＝C_Pm(a)F_Pa(14)

V_Pj(a)＝C_Pj(a)F_Pa(15)

Wherein, K_PaIs under the deterministic positioning constraint of '3-2-1', the part P^kThe meta-stiffness matrix at the additional location points; v_PJaIs the fixture offset at the additional location point. C_Pm(a)And C_Pj(a)Are respectively P^kForce F experienced at additional location point_PaDeviation V from its measuring point_Pm(a)And deviation from the connection point V_Pj(a)Linear system matrix in between.

After the stage of adding additional anchor points is finished, P^kDeviation V at the measurement and connection points_Pm(2)And V_Pj(2)Respectively as follows:

V_Pm(2)＝V_Pm(1)+V_Pm(a)(16)

V_Pj(2)＝V_Pj(1)+V_Pj(a)(17)

(2) clamping of

Sub-assembly A^kAnd part P^kAfter the positioning of N-2-1 is completed, the riveter applies pressing force to its assembling connection point to hold the connection point (riveting point) to its nominal position, i.e. the deviation of the connection point is respectively regulated by V_Aj(2)And V_Pj(2)Becomes 0 as shown in fig. 6. Under the action of the pressing force of the riveter, the flexible part A^kAnd P^kFurther deformation occurs, and at this time, the relationship between the stress and deformation at the connecting point can be expressed as:

F_j＝F_Aj+F_Pj(18)

in the formula, F_jIndicating the pressing force applied by the riveter at the point of connection, F_AjAnd F_PjAre respectively a flexible part A^kAnd P^kThe riveting force applied to the assembly connection point. Under the positioning constraint of 'N-2-1', the flexible part A^kAnd P^kThe meta-stiffness matrix at the connection point of (a) is K_AjAnd K_PjThen, there are:

F_Aj＝-K_AjV_Aj(2)(19)

F_Pj＝-K_PjV_Pj(2)(20)

in the clamping phase, the flexible part A^kAnd P^kThe deviation generated at the measuring point has a linear relation with the pressing force applied at the connecting point, and can be derived from the rigidity matrix at the stage. Will be caused by the caulking force of the riveter^kAnd P^kThe deviations at the measurement points are respectively denoted as V_Am(j)And V_Pm(j)，A^kForce F experienced at the connection point_AjDeviation V from its measuring point_Am(j)Linear system matrix in between is denoted as C_Am(j)，P^kForce F experienced at the connection point_PjDeviation V from its measuring point_Pm(j)Linear system matrix in between is denoted as C_Pm(j)Then, there are:

V_Am(j)＝C_Am(j)F_Aj(21)

V_Pm(j)＝C_Pm(j)F_Pj(22)

will V_Am(j)And V_Pm(j)Are respectively superposed to the sub-assemblies A^kAnd part P^kIn the deviation at the measuring point, the end A of the clamping phase is obtained^kAnd P^kDeviation V at its measurement point_Am(3)And V_Pm(3)Respectively as follows:

V_Am(3)＝V_Am(2)+V_Am(j)(23)

V_Pm(3)＝V_Pm(2)+V_Pm(j)(24)

(3) connection (riveting)

In the connection stage, the flexible components may be connected to form one assembly by a connection fastening means such as welding or caulking. For convenience of illustration, the flexible member A is not riveted^kAnd P^kThe connection is made.

As shown in fig. 7, at this stage, at a^kAnd P^kThe riveter clamping force applied at the attachment point location is not released and the riveter is used to rivet the two flexible members together. Due to wear and the like, the riveter may deviate during the riveting process, which may affect the deviation of the final assembly. The modeling process here does not take into account the riveter bias for the moment. At this time, the flexible member A^kAnd P^kThe clamping force is applied to the additional positioning points and the positions of the connecting points, and the deviation of the clamping force is not changed. When the riveter rivets two flexible parts together, the rigidity matrix is the assembly A^k+1Is different from subassembly A^kAnd part P^kThe stiffness matrix of (a).

(4) Releasing rebound

Because the flexible piece receives the clamping force of extra setpoint and the clamping force effect of riveter in location, the clamping process, takes place to warp, has internal stress, and after release riveter and extra setpoint, the flexible assembly part can take place to kick-back deformation under the internal stress effect. At the moment, the flexible assembly part is still restrained by two groups of '3-2-1' deterministic positioning points, and in an over-restrained state, part of the positioning points are released to be changed into a deterministic positioning state, and the flexible assembly part is subjected to rebound deformation in the process.

a) Release riveter

As shown in fig. 8, this stage releases the riveter, i.e. releases the compressive force of the riveter at the point of connection. Based on the assumption of linear elasticity, small deformation, the resilience being approximately equal to the pressing forceCounter-forces, i.e. flexible fittings A^k+1Spring back force F at the joint due to release of the riveter_sjComprises the following steps:

F_sj＝-F_j(25)

under the action of the resilience force, the flexible assembly A^k+1Deformation occurs, and at this time, the relationship between the stress and the deformation at the connecting point can be expressed as:

F_sj＝K_sjV_j(sj)(26)

wherein, K_sjIs shown in subassembly A^kAnd part P^kUnder the constraint of two groups of 'N-2-1' positioning, assembly part A^k+1The meta-stiffness matrix at the connection point of (a). V_j(sj)For releasing the riveter stage, A^k+1The normal deviation generated at the connection point. Since the cumulative deviation at the connection point of the previous stage is 0, V_j(sj)I.e. afterloading part A at the end of this phase^k+1Deviation V at the connecting point_j(4)Namely:

V_j(4)＝V_j(sj)(27)

assembly A^k+1The measuring point is a sub-assembly A^kMeasuring point and part P^kA collection of measurement points. During this phase, A is caused by the release of the riveter^k+1The normal deviation produced at the measurement point is denoted as V_m(sj)And is provided with $V_{m\left(sj\right)}=\left[\begin{array}{c}{V}_{Am\left(sj\right)}\\ V_{Pm\left(sj\right)}\end{array}\right],$ Wherein, V_Am(sj)And V_Pm(sj)Are respectively A^kAnd P^kThe deviation generated at the measuring point.

V_m(sj)＝C_m(sj)F_sj(28)

In the formula, C_m(sj)Is A^k+1Spring back force F experienced at the connection point_sjDeviation V from its measuring point_m(sj)A linear system matrix in between, and $C_{m\left(sj\right)}=\left[\begin{array}{c}{C}_{Am\left(sj\right)}\\ C_{Pm\left(sj\right)}\end{array}\right],$ wherein, C_Am(sj)Is F_sjAnd sub-assembly A^kDeviation V of measuring point_Am(sj)Linear system matrix of C_Pm(sj)Is F_sjAnd part P^kDeviation V of measuring point_Pm(sj)The linear system matrix in between, then:

V_Am(sj)＝C_Am(sj)F_sj(29)

V_Pm(sj)＝C_Pm(sj)F_sj(30)

will V_Am(sj)And V_Pm(sj)Are respectively superposed to the sub-assemblies A^kAnd part P^kIn the deviation of the measured point, after the riveting gun releasing stage is finished, A^kAnd P^kDeviation V at the measurement point_Am(4)And V_Pm(4)Respectively as follows:

V_Am(4)＝V_Am(3)+V_Am(sj)(31)

V_Pm(4)＝V_Pm(3)+V_Pm(sj)(32)

b) releasing additional anchor points

This stage releases subassembly A as shown in FIG. 9^kAnd part P^kI.e. releasing the clamping force at the additional location point. Based on the assumption of linear elasticity and small deformation, the resilience is approximately equal to the counter force of the pressing force, i.e. the flexible assembly A^k+1Due to A^kAnd P^kIs released to generate a resilience force F_AsaAnd F_PsaRespectively as follows:

F_Asa＝-F_Aa(33)

F_Psa＝-F_Pa(34)

under the elastic force F_AsaAnd F_PsaUnder the action of (A), the flexible assembly part^k+1Further deformation occurs. At this time, A is not considered^kAnd P^kAdditional definitionResilience force F at site_AsaAnd F_PsaIn the order of release of (A)^kThe deformation at the extra positioning point can be considered equal to the deformation represented by A^kSpring back force F at additional location point_AsaThe point deformation caused is superposed by P^kSpring back force F at additional location point_PsaCausing the point to deform.

Then A is^kThe force versus deformation relationship at the additional location points may be expressed as:

V_Aa(sa)＝K_Asa ^-1F_Asa+C_{Aa_P(sa)}F_Psa(35)

wherein, K_AsaIs represented by A^k+1At subassembly A^kAnd part P^kUnder the restriction of the two groups of 3-2-1 positioning, A^kThe meta-stiffness matrix at the additional location points. C_{Aa_P(sa)}Is represented by A^k+1At P^kIs subjected to a spring back force F at the additional location point_PsaAnd is prepared from F_PsaCaused by A^kA linear system matrix between the additional anchor point biases. V_Aa(sa)In the stage of releasing the additional anchor point, A^k+1In A^kThe normal deviation generated at the additional location point.

Likewise, P^kThe deformation at the extra positioning point can be considered equal to P^kSpring back force F at additional location point_PsaThe point deformation caused is superposed by A^kSpring back force F at additional location point_AsaThe point caused is deformed, then P^kThe force versus deformation relationship at the additional location points may be expressed as:

V_Pa(sa)＝K_Psa ^-1F_Psa+C_{Pa_A(sa)}F_Asa(36)

wherein, K_PsaIs represented by A^k+1At subassembly A^kAnd part P^kUnder the constraint of the two groups of 3-2-1 positioning, P^kThe meta-stiffness matrix at the additional location points. C_{Pa_A(sa)}Is represented by A^k+1In A^kIs subjected to spring-back at the additional location pointForce F_AsaAnd is prepared from F_AsaInduced P^kA linear system matrix between the additional anchor point biases. V_Pa(sa)In the stage of releasing the additional anchor point, A^k+1At P^kThe normal deviation generated at the additional location point.

And at the end of the previous stage, the accumulated deviation of the additional positioning point of the clamp is the sum of the clamp deviation of the additional positioning point and the clamp compensation quantity. Accumulating the deviation generated in the stage to obtain A after the stage is finished^k+1In A^kAnd P^kDeviation V of position of additional location point_Aa(5)And V_Pa(5)。

V_Aa(5)＝V_AJa+θ_A+V_Aa(sa)(37)

V_Pa(5)＝V_PJa+θ_P+V_Pa(sa)(38)

In the stage of releasing the additional anchor point, due to the sub-assembly A^kAdditional anchor point release of (2) caused fitting part a^k+1The normal deviation produced at the measurement point is denoted as V_{m_A(sa)}And is provided with $V_{m\_A\left(sa\right)}=\left[\begin{array}{c}{V}_{Am\_A\left(sa\right)}\\ V_{Pm\_A\left(sa\right)}\end{array}\right],$ Wherein, V_{Am_A(sa)}And V_{Pm_A(sa)}Respectively caused by A^kDeviation sum P at measurement point^kDeviation at the measurement point; due to the part P^kAdditional anchor point release of (2) caused fitting part a^k+1The normal deviation produced at the measurement point is denoted as V_{m_P(sa)}And is provided with $V_{m\_P\left(sa\right)}=\left[\begin{array}{c}{V}_{Am\_P\left(sa\right)}\\ V_{Pm\_P\left(sa\right)}\end{array}\right],$ Wherein, V_{Am_P(sa)}And V_{Pm_P(sa)}Are respectively provided withA caused thereby^kDeviation sum P at measurement point^kDeviation at the measurement point.

In this stage, assembly A^k+1Deviation V occurring at the measuring point_m(sa)Is equal to A^kAnd P^kIs released from the additional anchor point_{m_A(sa)}、V_{m_P(sa)}And (c) the sum, i.e.:

V_m(sa)＝V_{m_A(sa)}+V_{m_P(sa)}(39)

V_{m_A(sa)}＝C_{m_A(sa)}F_Asa(40)

V_{m_P(sa)}＝C_{m_P(sa)}F_Psa(41)

in the formula, C_{m_A(sa)}Is A^k+1In A^kIs subjected to a spring back force F at the additional location point_AsaDeviation V from its measuring point_{m_A(sa)}A linear system matrix in between, and $C_{m\_A\left(sa\right)}=\left[\begin{array}{c}{C}_{Am\_A\left(sa\right)}\\ C_{Pm\_A\left(sa\right)}\end{array}\right],$ wherein, C_{Am_A(sa)}Is F_AsaAnd sub-assembly A^kDeviation V of measuring point_{Am_A(sa)}Linear system matrix of C_{Pm_A(sa)}Is F_AsaAnd part P^kDeviation V of measuring point_{Pm_A(sa)}A linear system matrix in between; c_{m_P(sa)}Is A^k+1At P^kIs subjected to a spring back force F at the additional location point_PsaDeviation V from its measuring point_{m_P(sa)}A linear system matrix in between, and $C_{m\_P\left(sa\right)}=\left[\begin{array}{c}{C}_{Am\_P\left(sa\right)}\\ C_{Pm\_P\left(sa\right)}\end{array}\right],$ wherein, C_{Am_P(sa)}Is F_PsaAnd sub-assemblyA^kDeviation V of measuring point_{Am_P(sa)}Linear system matrix of C_{Pm_P(sa)}Is F_PsaAnd part P^kDeviation V of measuring point_{Pm_P(sa)}The linear system matrix in between, then:

V_{Am_A(sa)}＝C_{Am_A(sa)}F_Asa(42)

V_{Pm_A(sa)}＝C_{Pm_A(sa)}F_Asa(43)

V_{Am_P(sa)}＝C_{Am_P(sa)}F_Psa(44)

V_{Pm_P(sa)}＝C_{Pm_P(sa)}F_Psa(45)

the combination (39) gives A which is produced in this stage^kAnd P^kThe deviation at the measurement points is:

V_Am(sa)＝V_{Am_A(sa)}+V_{Am_P(sa)}(46)

V_Pm(sa)＝V_{Pm_A(sa)}+V_{Pm_P(sa)}(47)

will V_Am(sa)And V_Pm(sa)Are respectively superposed to the sub-assemblies A^kAnd part P^kIn the deviation of the measured point, after the stage of obtaining the additional positioning point is finished, A^kAnd P^kDeviation V at the measurement point_Am(5)And V_Pm(5)Respectively as follows:

V_Am(5)＝V_Am(4)+V_Am(sa)(48)

V_Pm(5)＝V_Pm(4)+V_Pm(sa)(49)

similarly, at this stage, assembly A^k+1Deviation V occurring at the connecting point_j(sa)Is equal to A^kAnd P^kIs released from the additional anchor point of_{j_A(sa)}、V_{j_P(sa)}And (c) the sum, i.e.:

V_j(sa)＝V_{j_A(sa)}+V_{j_P(sa)}(50)

V_{j_A(sa)}＝C_{j_A(sa)}F_Asa(51)

V_{j_P(sa)}＝C_{j_P(sa)}F_Psa(52)

in the formula, C_{j_A(sa)}Is A^k+1In A^kIs subjected to a spring back force F at the additional location point_AsaDeviation V from its connection point_{j_A(sa)}Linear system matrix of C_{j_P(sa)}Is A^k+1At P^kIs subjected to a spring back force F at the additional location point_AsaDeviation V from its connection point_{j_P(sa)}Linear system matrix in between.

Will V_j(sa)Superimposed on assembly A^k+1Obtaining the deviation V of the connecting point after the stage of releasing the additional positioning point is finished in the deviation of the connecting point_j(5)Comprises the following steps:

V_j(5)＝V_j(4)+V_j(sa)(53)

c) release fitting over-constraint anchor

Due to the sub-assembly A^kAnd part P^kEach having a set of 3-2-1 deterministic positions, so that when the stages of releasing the riveter and releasing the additional positioning points are over, the flexible assembly A^k+1And the stress is still restrained by two groups of '3-2-1' deterministic positioning points and is in an over-restrained state, and the internal stress still exists. When partial anchor points are released, the assembly A is made^k+1Upon formation of a positively positioned state, the flexible assembly will resiliently deform as a result of the release of internal stresses.

Without releasing the part P here^kThe "3-2-1" deterministic anchor point of (1) as shown in fig. 10. At the point of releasing over-constraint, i.e. part P^kBefore the "3-2-1" deterministic anchor point, P^kThe constraint state of the positioning block is the same as that of the deterministic positioning stage, and is constrained by 6 positioning blocks. Due to the existence of the assembly deviation of the preposed station, the manufacturing deviation of the part and the positioning deviation of the clamp, the part P^kAt the sub-assembly A^kAfter joining (riveting), there is an assembly deformation, such that P^kAgainst which the force is acting. If the 6 positioning blocks are released, the method is equivalent to the method for assembling the component A^k+1The positions corresponding to the positioning blocks exert reverse acting force, and the assembly part A^k+1Deformation will occur and assembly deviation will further accumulate.

Normal deviation direction of measurement point and assembly part A^k+1The normal direction of the main plane of (b) is consistent. During the stage of releasing the over-constrained positioning points of the assembly, the normal deviation generated at the measuring points is mainly related to the normal deviation positioned on the main plane of the assembly (namely, the part P)^kMajor plane) is associated, ignoring the effects of the other 3 locating blocks being released.

Holding force of positioning block and part P^kAnd sub-assembly A^kThe interaction force between the two is related. Firstly, before the release of the over-constrained positioning points is calculated, the sub-assembly A at the assembly connecting point is assembled^kTo part P^kNormal acting force F_{P_A(5)}. Let K_{P_A(1)}Is a part P^kAnd a hyper-element stiffness matrix established by taking the deterministic positioning constraint of '3-2-1' as a boundary condition and taking the connection points as key points. Normal force F_{P_A(5)}Is equal to part P^kThe variation of the deviation of the connection point position before and after riveting and P^kStiffness matrix K_{P_A(1)}The product of the two, namely:

F_{P_A(5)}＝K_{P_A(1)}(V_j(5)-V_Pj(1))(54)

then through the part P^kNormal force F experienced at the connection point_{P_A(5)}Calculating P before releasing over-constrained anchor point^kMain plane 3 positioning block pair assembly A^k+1Applied force F_PJd(5)。

F_PJd(5)＝C_PJd(1)F_{P_A(5)}(55)

Wherein, C_PJd(1)To reaction A^kTo P^kActing force F_{P_A(5)}And P^kPrincipal plane locating block acting force F_PJd(5)Linear system matrix of relationship between them, can pass through the part P^kAnd under the constraint of deterministic positioning, deriving the super-element stiffness matrix at the connecting point and the main plane positioning block.

When release fitting A^k+1Over-constrained location point of (i.e. part P)^kWhen the positioning point is determined, the main plane positioning block generates a resilience force F_sdApproximately equal to the pair of main plane positioning blocks A before release^k+1Acting force F_PJd(5)The counter force of (c), namely:

F_sd＝-F_PJd(5)(56)

under the elastic force F_sdUnder the action of (A), the flexible assembly part^k+1Further deformation occurs. At this time, then A^k+1At P^kMain plane positioning block position due to resilience force F_sdDeviation V caused by action_Pd(sd)Comprises the following steps:

V_Pd(sd)＝K_sd ^-1F_sd(57)

wherein, K_sdIs represented by A^k+1At subassembly A^kUnder the constraint of the "3-2-1" positioning of (A), P^kThe principal plane of (1) positioning a block of the meta-stiffness matrix.

Since P is at the end of the previous stage^kThe accumulated deviation of the main plane positioning block is the corresponding clamp deviation and is marked as V_{PJd_z}Is a part P^kDeterministic setpoint deviation V_PJdA subset of (a). Accumulating the deviation generated in the stage to obtain A after the stage is finished^k+1At P^kDeviation V of main plane positioning block position_Pd(6)。

V_Pd(6)＝V_{PJd_z}+V_Pd(sd)(58)

During the stage of releasing over-constraint anchor point of assembly part, the part P^kSpring back force F at main plane positioning block_sdInduced assembly A^k+1Normal deflection at the measuring pointThe difference is denoted as V_m(sd)And is provided with $V_{m\left(sd\right)}=\left[\begin{array}{c}{V}_{Am\left(sd\right)}\\ V_{Pm\left(sd\right)}\end{array}\right],$ Wherein, V_Am(sd)And V_Pm(sd)Respectively A caused thereby^kAnd P^kThe deviation generated at the measuring point.

V_m(sd)＝C_m(sd)F_sd(59)

In the formula, C_m(sd)Is A^k+1At P^kThe main plane positioning block is subjected to resilience force F_sdDeviation V from its measuring point_m(sd)A linear system matrix in between, and $C_{m\left(sd\right)}=\left[\begin{array}{c}{C}_{Am\left(sd\right)}\\ C_{Pm\left(sd\right)}\end{array}\right],$ wherein, C_Am(sd)Is F_sdAnd sub-assembly A^kMeasuring point normal deviation V_Am(sd)Linear system matrix of C_Pm(sd)Is F_sdAnd part P^kMeasuring point normal deviation V_Pm(sd)The linear system matrix in between, then:

V_Am(sd)＝C_Am(sd)F_sd(60)

V_Pm(sd)＝C_Pm(sd)F_sd(61)

will V_Am(sd)And V_Pm(sd)Are respectively superposed to the sub-assemblies A^kAnd part P^kIn the deviation of the measuring point, after the stage of obtaining the over-constrained positioning point of the release assembly is finished^kAnd P^kDeviation V at the measurement point_Am(6)And V_Pm(6)Respectively as follows:

V_Am(6)＝V_Am(5)+V_Am(sd)(62)

V_Pm(6)＝V_Pm(5)+V_Pm(sd)(63)

in accordance with the above method, it is likewise possible to obtain A caused by the release of the over-constrained anchor point of the assembly during this phase^k+1Deviation V at the junction_j(sd)And A is^kAnd P^kDeviation V at additional location points_Aa(sd)And V_Pa(sd)。

V_j(sd)＝C_j(sd)F_sd(64)

V_Aa(sd)＝C_Aa(sd)F_sd(65)

V_Pa(sd)＝C_Pa(sd)F_sd(66)

In the formula, C_j(sd)Is A^k+1At P^kThe main plane positioning block is subjected to resilience force F_sdNormal deviation V from its connection point_j(sd)Linear system matrix of C_Aa(sd)Is F_sdAnd sub-assembly A^kAdditional positioning point normal deviation V_Aa(sd)Linear system matrix of C_Pa(sd)Is F_sdAnd part P^kAdditional positioning point normal deviation V_Pa(sd)Linear system matrix in between.

After the stage of releasing the assembly over-constraint anchor point is finished, A^k+1Deviation V at the junction_j(6)And A is^kAnd P^kDeviation V at additional location points_Aa(6)And V_Pa(6)Respectively as follows:

V_j(6)＝V_j(5)+V_j(sd)(67)

V_Aa(6)＝V_Aa(5)+V_Aa(sd)(68)

V_Pa(6)＝V_Pa(5)+V_Pa(sd)(69)

in conclusion, when the assembly of the station k is completed, the assembly part A^k+1The final normal deviation at the measurement point is V_Am(6)And V_Pm(6)The final normal deviation at the junction is V_j(6)，A^kAnd P^kThe final normal deviation at the extra positioning points is V_Aa(6)And V_Pa(6)，P^kFinal method at main plane positioning blockDeviation in direction of V_Pd(6). After finishing, the method can be obtained:

V_Am(6)＝V_Am+V_Am(d)+(C_Am(a)-C_{Am_A(sa)}+C_Am(sd)C_PJd(1)K_{P_A(1)}C_{j_A(sa)})K_Aa(V_AJa+θ_A-V_Aa-V_Aa(d))

+(C_Am(sj)-C_Am(j)-C_Am(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_Aj[V_Aj+V_Aj(d)+C_Aj(a)K_Aa(V_AJa+θ_A-V_Aa-V_Aa(d))]

+(C_Am(sj)-C_Am(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_Pj[V_Pj+V_Pj(d)+C_Pj(a)K_Pa(V_PJa+θ_P-V_Pa-V_Pa(d))]

+(-C_{Am_P(sa)}+C_Am(sd)C_PJd(1)K_{P_A(1)}C_{j_P(sa)})K_Pa(V_PJa+θ_P-V_Pa-V_Pa(d))

+C_Am(sd)C_PJd(1)K_{P_A(1)}(V_Pj+V_Pj(d))

(70)

V_Pm(6)＝V_Pm+V_Pm(d)+(C_Pm(a)-C_{Pm_P(sa)}+C_Pm(sd)C_PJd(1)K_{P_A(1)}C_{j_P(sa)})K_Pa(V_PJa+θ_P-V_Pa-V_Pa(d))

+(C_Pm(sj)-C_Pm(j)-C_Pm(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_Pj[V_Pj+V_Pj(d)+C_Pj(a)K_Pa(V_PJa+θ_P-V_Pa-V_Pa(d))]

+(C_Pm(sj)-C_Pm(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_Aj[V_Aj+V_Aj(d)+C_Aj(a)K_Aa(V_AJa+θ_A-V_Aa-V_Aa(d))]

+(-C_{Pm_A(sa)}+C_Pm(sd)C_PJd(1)K_{P_A(1)}C_{j_A(sa)})K_Aa(V_AJa+θ_A-V_Aa-V_Aa(d))

+C_Pm(sd)C_PJd(1)K_{P_A(1)}(V_Pj+V_Pj(d))

(71)

$\begin{array}{c}{V}_{j\left(6\right)}=(I-C_{j\left(sd\right)}{C}_{PJD\left(1\right)}{K}_{P\_A\left(1\right)})\{{K_{sj}}^{-1}{K}_{Aj}\[V_{Aj}+V_{Aj\left(d\right)}+C_{Aj\left(a\right)}{K}_{Aa}(V_{AJa}+{\mathrm{\θ}}_A-V_{Aa}-V_{Aa\left(d\right)})\]\\ +{K_{sj}}^{-1}{K}_{Pj}\[V_{Pj}+V_{Pj\left(d\right)}+C_{Pj\left(a\right)}{K}_{Pa}(V_{PJa}+{\mathrm{\θ}}_P-V_{Pa}-V_{Pa\left(d\right)})\]\\ -C_{j\_A\left(sa\right)}{K}_{Aa}(V_{AJa}+{\mathrm{\θ}}_A-V_{Aa}-V_{Aa\left(d\right)})\\ -C_{j\_P\left(sa\right)}{K}_{Pa}(V_{PJa}+{\mathrm{\θ}}_P-V_{Pa}-V_{Pa\left(d\right)})\}\\ +C_{j\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}(V_{Pj}+V_{Pj\left(d\right)})\end{array}---\left(72\right)$

$\begin{array}{c}{V}_{Aa\left(6\right)}=V_{AJa}+{\mathrm{\θ}}_A+(-{K_{Asa}}^{-1}+C_{Aa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_A\left(sa\right)})K_{Aa}(V_{AJa}+{\mathrm{\θ}}_A-V_{Aa}-V_{Aa\left(d\right)})\\ +(-C_{Aa\_P\left(sa\right)}+C_{Aa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_P\left(sa\right)})K_{Pa}(V_{PJa}+{\mathrm{\θ}}_P-V_{Pa}-V_{Pa\left(d\right)})\\ -C_{Aa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1}{K}_{Aj}\[V_{Aj}+V_{Aj\left(d\right)}+C_{Aj\left(a\right)}{K}_{Aa}(V_{AJa}+{\mathrm{\θ}}_A-V_{Aa}-V_{Aa\left(d\right)})\]\\ -C_{Aa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1}{K}_{Pj}\[V_{Pj}+V_{Pj\left(d\right)}+C_{Pj\left(a\right)}{K}_{Pa}(V_{PJa}+{\mathrm{\θ}}_P-V_{Pa}-V_{Pa\left(d\right)})\]\\ +C_{Aa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}(V_{Pj}+V_{Pj\left(d\right)})\end{array}---\left(73\right)$

$\begin{array}{c}{V}_{Pa\left(6\right)}=V_{PJa}+{\mathrm{\θ}}_P+(-{K_{Psa}}^{-1}+C_{Pa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_P\left(sa\right)})K_{Pa}(V_{PJa}+{\mathrm{\θ}}_P-V_{Pa}-V_{Pa\left(d\right)})\\ +(-C_{Pa\_A\left(sa\right)}+C_{Pa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_A\left(sa\right)})K_{Aa}(V_{AJa}+{\mathrm{\θ}}_A-V_{Aa}-V_{Aa\left(d\right)})\\ -C_{Pa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1}{K}_{Aj}\[V_{Aj}+V_{Aj\left(d\right)}+C_{Aj\left(a\right)}{K}_{Aa}(V_{AJa}+{\mathrm{\θ}}_A-V_{Aa}-V_{Aa\left(d\right)})\]\\ -C_{Pa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1}{K}_{Pj}\[V_{Pj}+V_{Pj\left(d\right)}+C_{Pj\left(a\right)}{K}_{Pa}(V_{PJa}+{\mathrm{\θ}}_P-V_{Pa}-V_{Pa\left(d\right)})\]\\ +C_{Pa\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}(V_{Pj}+V_{Pj\left(d\right)})\end{array}---\left(74\right)$

V_Pd(6)＝V_{PJd_z}-K_sd ^-1C_PJd(1)K_{P_A(1)}K_sj ^-1K_Aj[V_Aj+V_Aj(d)+C_Aj(a)K_Aa(V_AJa+θ_A-V_Aa-V_Aa(d))]

-K_sd ^-1C_PJd(1)K_{P_A(1)}K_sj ^-1K_Pj[V_Pj+V_Pj(d)+C_Pj(a)K_Pa(V_PJa+θ_P-V_Pa-V_Pa(d))]

+K_sd ^-1C_PJd(1)K_{P_A(1)}C_{j_A(sa)}K_Aa(V_AJa+θ_A-V_Aa-V_Aa(d))

+K_sd ^-1C_PJd(1)K_{P_A(1)}C_{j_P(sa)}K_Pa(V_PJa+θ_P-V_Pa-V_Pa(d))

+K_sd ^-1C_PJd(1)K_{P_A(1)}(V_Pj+V_Pj(d))

(75)

2) modeling of compensation optimization model

And establishing a flexible part assembling deviation optimization model based on clamp compensation on the station k. Optimizing the normal compensation quantity theta of the extra positioning point of the fixture on the variable selection station k_AAnd theta_P. The optimization target is as follows: when the station is assembled, the assembly part A^k+1The sum of squares of the final normal deviations of the measuring points is minimum; and minimizes the sum of the squares of the additional location point normal compensation amounts for each fixture. A flexible part assembly deviation transfer model combined with a station k in the assembly deviation modeling module and an assembly part A^k+1In A^kHas m measuring points, P^kN measuring points of, A^k+1Final normal deviation V of each measuring point_m(6)Can be expressed as:

V_m(6)＝[V_Am(6),V_Pm(6)]^T＝[V_Am(6)1,V_Am(6)2,…,V_Am(6)m,V_Pm(6)1,V_Pm(6)2,…,V_Pm(6)n]^T(76)

wherein, V_Am(6)i(i-1, 2, …, m) represents A^kFinal method of m measuring pointsDeviation in direction, V_Pm(6)j(j ═ 1,2, …, n) denotes P^kThe final normal deviation of n measurement points.

Mounting accessory A^k+1In A^kHas u additional anchor points, P^kHas v additional anchor points, then A^k+1Normal compensation quantity theta of each additional positioning point_kCan be expressed as:

θ_k＝[θ_A,θ_P]^T＝[θ_A1,θ_A2,…,θ_Au,θ_P1,θ_P2,…,θ_Pv]^T(77)

wherein, theta_As(s-1, 2, …, u) represents A^kOf u additional positioning points, theta_Pt(t-1, 2, …, v) represents P^kThe normal compensation amount of the v additional setpoint.

Setting the objective function of the optimization model as:

$f_1\left({\mathrm{\θ}}_k\right)=\underset{i=1}{\overset{m}{\Σ}}{\left(V_{Am\left(6\right)i}\right)}^2+\underset{j=1}{\overset{n}{\Σ}}{\left(V_{Pm\left(6\right)j}\right)}^2---\left(78\right)$

$f_2\left({\mathrm{\θ}}_k\right)=\underset{s=1}{\overset{u}{\Σ}}{\left({\mathrm{\θ}}_{As}\right)}^2+\underset{t=1}{\overset{v}{\Σ}}{\left({\mathrm{\θ}}_{Pt}\right)}^2---\left(79\right)$

the constraint conditions considered by the optimization model are as follows: after the station k is assembled, the assembly part A^k+1Final normal deviation V of each measuring point_m(6)Within the tolerance allowed by the process requirements; and, according to the structural parameter characteristics of the adjustable clamp, A^k+1Compensation quantity theta of additional positioning point of each clamp_kShould be within the adjustable range of the clamp positioning point.

Let A^k+1Maximum deviation V of each measuring point in the process requirement range_{m(6)_max}Comprises the following steps:

$\begin{array}{c}{V}_{m\left(6\right)\_\max }={\[V_{Am\left(6\right)\_\max },V_{Pm\left(6\right)\_\max }\]}^T\\ ={\[V_{Am\left(6\right)1\_\max },V_{Am\left(6\right)2\_\max },\mathrm{...},V_{Am\left(6\right)m\_\max },V_{Pm\left(6\right)1\_\max },V_{Pm\left(6\right)2\_\max },\mathrm{...},V_{Pm\left(6\right)n\_\max }\]}^T\end{array}---\left(80\right)$

let A^k+1Compensation quantity theta of additional positioning point of each clamp_kIncludes an adjustable upper limit theta_{k_up}And an adjustable lower limit theta_{k_low}They are respectively:

$\begin{array}{c}{\mathrm{\θ}}_{k\_up}={\[{\mathrm{\θ}}_{A\_up},{\mathrm{\θ}}_{P\_up}\]}^T\\ ={\[{\mathrm{\θ}}_{A1\_up},{\mathrm{\θ}}_{A2\_up},\mathrm{...},{\mathrm{\θ}}_{Au\_up},{\mathrm{\θ}}_{P1\_up},{\mathrm{\θ}}_{P2\_up},\mathrm{...},{\mathrm{\θ}}_{Pv\_up}\]}^T\end{array}---\left(81\right)$

$\begin{array}{c}{\mathrm{\θ}}_{k\_low}={\[{\mathrm{\θ}}_{A\_low},{\mathrm{\θ}}_{P\_low}\]}^T\\ ={\[{\mathrm{\θ}}_{A1\_low},{\mathrm{\θ}}_{A2\_low},\mathrm{...},{\mathrm{\θ}}_{Au\_low},{\mathrm{\θ}}_{P1\_low},{\mathrm{\θ}}_{P2\_low},\mathrm{...},{\mathrm{\θ}}_{Pv\_low}\]}^T\end{array}---\left(82\right)$

the optimization model is multi-objective optimization, and the mathematical model can be expressed as:

minf₁(θ_k)

minf₂(θ_k)

$\begin{array}{c}\begin{array}{cc}s.t.& {\mathrm{\θ}}_k\∈G=\left\{{\mathrm{\θ}}_k\right|\left|V_{Am\left(6\right)i}\right|\≤V_{Am\left(6\right)i\_\max },\left|V_{Pm\left(6\right)j}\right|\≤V_{Pm\left(6\right)j\_max},\end{array}\\ i=1,2,\mathrm{...},m,j=1,2,\mathrm{...},n\}\end{array}---\left(83\right)$

θ_k∈H＝{θ_k|θ_{As_low}≤θ_As≤θ_{As_up},θ_{Pt_low}≤θ_Pt≤θ_{Pt_up},

s＝1,2,…,u,t＝1,2,…,v}

according to the assembly deviation modeling module, the normal compensation quantity theta of the additional positioning point of the clamp is considered on the established station k_kThe flexible member assembly deviation transfer model can obtain A^k+1Is additionally located point normal compensation quantity theta_kFinal normal deviation V from its measuring point_m(6)See equations (70) and (71).

In flexible assembly A^k+1Middle, sub-assembly A^kThe assembly deviation on the station (k-1) can be obtained by a data acquisition module, including A^kDeviation of assembling connection point positions at a measuring point, a clamp positioning point and a station k; part P^kIncluding P^kThe deviation of the positions of the measuring point, the positioning point of the clamp, the assembly connecting point and the positioning deviation of the clamp of the station k are all contained in the input X of the station k_k-1In (1), is a known amount. And in the assembling process of the station k, when the assembling process is not changed, all the rigidity matrixes and all the linear system matrixes are kept unchanged. Therefore, formula (7)0) And formula (71) may be represented as:

V_Am(6)＝T_A+S_{A_A}θ_A+S_{A_P}θ_P(84)

V_Pm(6)＝T_P+S_{P_A}θ_A+S_{P_P}θ_P(85)

wherein,

$\begin{array}{c}{T}_A=V_{Am}+V_{Am\left(d\right)}+(C_{Am\left(a\right)}-C_{Am\_A\left(sa\right)}+C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_A\left(sa\right)})K_{Aa}(V_{AJa}-V_{Aa}-V_{Aa\left(d\right)})\\ +(C_{Am\left(sj\right)}-C_{Am\left(j\right)}-C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Aj}{C}_{Aj\left(a\right)}{K}_{Aa}(V_{AJa}-V_{Aa}-V_{Aa\left(d\right)})\\ +(C_{Am\left(sj\right)}-C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Pj}{C}_{Pj\left(a\right)}{K}_{Pa}(V_{PJa}-V_{Pa}-V_{Pa\left(d\right)})\\ +(-C_{Am\_P\left(sa\right)}+C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_P\left(sa\right)})K_{Pa}(V_{PJa}-V_{Pa}-V_{Pa\left(d\right)})\\ +(C_{Am\left(sj\right)}-C_{Am\left(j\right)}-C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Aj}(V_{Aj}+V_{Aj\left(d\right)})\\ +\[(C_{Am\left(sj\right)}-C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Pj}+C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}\](V_{Pj}+V_{Pj\left(d\right)})\end{array}---\left(86\right)$

T_P＝V_Pm+V_Pm(d)+(C_Pm(a)-C_{Pm_P(sa)}+C_Pm(sd)C_PJd(1)K_{P_A(1)}C_{j_P(sa)})K_Pa(V_PJa-V_Pa-V_Pa(d))

+(C_Pm(sj)-C_Pm(j)-C_Pm(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_PjC_Pj(a)K_Pa(V_PJa-V_Pa-V_Pa(d))

+(C_Pm(sj)-C_Pm(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_AjC_Aj(a)K_Aa(V_AJa-V_Aa-V_Aa(d))

+(-C_{Pm_A(sa)}+C_Pm(sd)C_PJd(1)K_{P_A(1)}C_{j_A(sa)})K_Aa(V_AJa-V_Aa-V_Aa(d))

+[(C_Pm(sj)-C_Pm(j)-C_Pm(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_Pj+C_Pm(sd)C_PJd(1)K_{P_A(1)}](V_Pj+V_Pj(d))

+(C_Pm(sj)-C_Pm(sd)C_PJd(1)K_{P_A(1)}K_sj ^-1)K_Aj(V_Aj+V_Aj(d))

(87)

$\begin{array}{c}{S}_{A\_A}=\[C_{Am\left(a\right)}-C_{Am\_A\left(sa\right)}+C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_A\left(sa\right)}\\ +(C_{Am\left(sj\right)}-C_{Am\left(j\right)}-C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Aj}{C}_{Aj\left(a\right)}\]K_{Aa}\end{array}---\left(88\right)$

$\begin{array}{c}{S}_{A\_P}=\[C_{Am\left(sj\right)}-C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Pj}{C}_{Pj\left(a\right)}\\ -C_{Am\_P\left(sa\right)}+C_{Am\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_P\left(sa\right)}\]K_{Pa}\end{array}---\left(89\right)$

$\begin{array}{c}{S}_{P\_A}=\[(C_{Pm\left(sj\right)}-C_{Pm\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Aj}{C}_{Aj\left(a\right)}\\ -C_{Pm\_A\left(sa\right)}+C_{Pm\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_A\left(sa\right)}\]K_{Aa}\end{array}---\left(90\right)$

$\begin{array}{c}{S}_{P\_P}=\[C_{Pm\left(a\right)}-C_{Pm\_P\left(sa\right)}+C_{Pm\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{C}_{j\_P\left(sa\right)}\\ +(C_{Pm\left(sj\right)}-C_{Pm\left(j\right)}-C_{Pm\left(sd\right)}{C}_{PJd\left(1\right)}{K}_{P\_A\left(1\right)}{K_{sj}}^{-1})K_{Pj}{C}_{Pj\left(a\right)}\]K_{Pa}\end{array}---\left(91\right)$

let S_A＝[S_{A_A},S_{A_P}]，S_P＝[S_{P_A},S_{P_P}]，θ_k＝[θ_A,θ_P]^TThen equations (84) and (85) can be expressed as:

V_Am(6)＝T_A+S_Aθ_k(92)

V_Pm(6)＝T_P+S_Pθ_k(93)

order to $V_{m\left(6\right)}=\left[\begin{array}{c}{V}_{Am\left(6\right)}\\ V_{Pm\left(6\right)}\end{array}\right],T=\left[\begin{array}{c}{T}_A\\ T_P\end{array}\right],S=\left[\begin{array}{c}{S}_A\\ S_P\end{array}\right],$ Then there are:

V_m(6)＝T+Sθ_k(94)

thus, in station k, assembly A^k+1Normal deviation V of measuring point_m(6)Normal compensation quantity theta with additional positioning point of clamp_kIs a wireAnd (4) sexual relations. According to the objective function of the optimization model, the combination formula (94), the objective function f₁(θ_k) And can be represented as:

f₁(θ_k)＝V_m(6) ^TV_m(6)＝(T+Sθ_k)^T(T+Sθ_k)＝T^TT+T^TSθ_k+θ_k ^TS^TT+θ_k ^T(S^TS)θ_k(95)

let T^TS＝A，S^TWhen S is equal to B, then TS^T＝A^TEquation (95) can be:

f₁(θ_k)＝T^TT+Aθ_k+θ_k ^TA^T+θ_k ^TBθ_k(96)

obviously, S rows are full, with rand (S) ═ m + n, and S^TS is B, so B is a semi-positive definite symmetric matrix. Thus, the mathematical model equation (83) of the optimization model can be expressed in the form:

$\begin{array}{c}{\mathrm{minf}}_1\left({\mathrm{\θ}}_k\right)={{\mathrm{\θ}}_k}^T{\mathrm{B\θ}}_k+{\mathrm{A\θ}}_k+{{\mathrm{\θ}}_k}^T{A}^T+T^{T}T\\ {\mathrm{minf}}_2\left({\mathrm{\θ}}_k\right)={{\mathrm{\θ}}_k}^T{\mathrm{\θ}}_k\\ \begin{array}{ccc}s.t.& -V_{m\left(6\right)i\_\max }\≤S_i{\mathrm{\θ}}_k+T_i\≤V_{m\left(6\right)i\_\max }& i=1,2,\mathrm{...},m+n\end{array}\\ \begin{array}{cc}{\mathrm{\θ}}_{kj\_low}\≤I_j{\mathrm{\θ}}_k\≤{\mathrm{\θ}}_{kj\_up}& j=1,2,\mathrm{...},u+v\end{array}\end{array}---\left(97\right)$

wherein, i is a unit matrix, and S, T, A, B are real number matrices. As can be seen, the optimization model is a convex quadratic programming model.

3) Optimal compensation solution

As can be seen from equation (97), the solution of the optimization model is an inequality-constrained multi-objective convex quadratic programming solution. For the multi-objective optimization problem, the priority orders of the optimization objectives are different, namely: first optimization goal minf₁(θ_k) Is prioritized over the second optimization target minf₂(θ_k) Therefore, a hierarchical sequence method can be adopted for solving. The most important objective function is firstly optimized, then the secondary objective function is optimized in a layering mode, and the former must be kept to be changed within an allowable range when the latter is optimized.

The feasible domain D of the optimization model is as follows:

D＝{θ_k|-V_{m(6)i_max}≤S_iθ_k+T_i≤V_{m(6)i_max},θ_{kj_low}≤Ι_jθ_k≤θ_{kj_up}}

wherein, i is 1,2, …, m + n, j is 1,2, …, u + v.

Since B is a semi-positive definite symmetric matrix, for the first optimization objective minf₁(θ_k) If the feasible domain is not empty and the objective function has a lower bound in the feasible domain, then the optimization problem has a global minimum point, but may not be unique. And for a second optimization target minf₂(θ_k) If the feasible region is not empty and the objective function has a lower bound in the feasible region, then the optimization problem has a global minimum point and is unique.

Because the constraint condition of the optimization model is inequality constraint, methods such as an active set method and the like can be adopted when each optimization target is solved. First, a first optimization objective minf is solved₁(θ_k) In the optimal solution in the feasible region D, due to the limitation of constraint conditions, the situation of no feasible solution may occur, and at the moment, the process requirements cannot be met only by a method of adjusting the normal compensation quantity of the positioning point of the clamp, and other methods are needed; when the first optimization target minf₁(θ_k) When the feasible domain D has a feasible solution, if the feasible solution is the only solution, the feasible solution is the optimal solution of the optimization model represented by the formula (97), and if the feasible solution is not the only solution, the second optimization target minf is solved in the optimal solution set domain of the feasible solution₂(θ_k) I.e. the first objective function is converted into an auxiliary constraint to obtain an optimal solution.

3. Compensation implementation

And executing relevant operation according to a solving result of the assembly deviation optimization model based on the clamp compensation in the compensation scheme decision module. And if the feasible solution exists, adjusting the normal compensation quantity of the positioning point of the additional clamp in the station k according to the group of data. If no feasible solution exists, it is shown that the extra positioning point of the fixture for adjusting the station cannot meet the requirement of matching deviation quality, and then other modes need to be considered to ensure the assembly quality, such as: the specific scheme of adopting the clamp positioner with a larger adjustable range, adding a new clamp positioning point at the station and the like is out of the scope of the invention.

Claims (5)

1. A flexible part assembling size deviation control method based on multi-station assembling clamp compensation is characterized by comprising the following steps: firstly, predicting and compensating assembly deviation station by station in a flexible part multi-station assembly process, and enabling the position of a clamp positioning point participating in clamp compensation to be normally adjusted within a certain range; secondly, on the basis of a state space method in a control theory, a clamp compensation system is added in a positioning or repositioning link of multi-station assembly of the flexible part to acquire deviation data, make a compensation scheme decision and perform compensation so as to reduce assembly deviation on a subsequent station to be assembled.

2. The method of claim 1, wherein the fixture compensation system comprises a deviation data collection module, a compensation recipe decision module, and a compensation implementation module.

3. The method of claim 2, wherein the deviation data collection module is an input to a fixture compensation system; the first station does not execute the module because the input of the whole assembly system, i.e. the manufacturing deviation of all the parts involved in the assembly, is a known quantity, including the input of the jig compensation system of the first station; for other stations except the first station, the step of acquiring deviation data refers to acquiring the size deviation value of a sub-assembly part assembled by a front station and to be assembled in a subsequent station; taking Key Product Characteristics (KPC) of the sub-assembly parts, and the positions of the fixture positioning points and the assembly connecting points of the sub-assembly parts in subsequent stations as deviation data acquisition points, wherein the data acquisition mode comprises the following steps: derived from the assembly deviation transfer model of the preposed station and measured by a measuring tool.

4. The method as claimed in claim 2, wherein the compensation scheme decision module is a core part of the fixture compensation system, and comprises three steps of assembling deviation modeling, compensation quantity optimization model modeling and optimal compensation quantity solving, wherein:

(1) the assembly deviation modeling means that: the normal compensation quantity of the positioning point of the clamp is used as a group of adjustable variables, and a flexible part assembly deviation transfer model of a subsequent station is established;

for the first station, the considered deviation sources are the manufacturing deviation and the positioning deviation of the clamp of the parts participating in assembly; for other stations except the first station, the considered deviation sources comprise sub-assembly deviation, part manufacturing deviation and fixture positioning deviation which participate in assembly;

the modeling process comprises four steps of positioning, clamping, connecting and releasing resilience, small deformation and linear elasticity assumption are carried out on the flexible part, and a deviation transfer relation between the normal compensation quantity of the positioning point of the clamp, the deviation source deviation and the deviation of the measuring point of the station assembly part is established by using an influence coefficient method, a finite element analysis method and a super element rigidity matrix theory;

(2) the modeling of the compensation optimization model refers to: establishing an assembly deviation optimization model of the station based on clamp compensation; the optimization variable is the normal compensation quantity of the adjustable positioning points of the clamp; the optimization objectives include: the square sum of the deviation of each measuring point of the station assembly part is minimized, and the square sum of the compensation quantity of each adjustable positioning point of the fixture is minimized; the constraint conditions include: the normal compensation quantity of each clamp positioning point is within a certain adjustable range, and the deviation of each measuring point of the assembly part is within the allowable range of the assembly process requirement;

(3) solving the optimal compensation quantity comprises the following steps: converting the solution of the established compensation optimization model into a quadratic programming problem; the quadratic programming has a plurality of optimization targets, and the constraint conditions are inequalities; solving by adopting a hierarchical sequence method, and obtaining an optimal solution meeting an optimization target within a range specified by a constraint condition; and discussing whether a feasible solution exists or not, if the feasible solution does not exist, the assembly quality requirement of the station cannot be met only by adopting a mode of adjusting the positioning point of the clamp, and other methods need to be considered.

5. The method of claim 2, wherein said compensation enforcement module is an executive part of a fixture compensation system; and the system is used for adjusting the positioning point of the clamp according to the solution result of the optimal compensation amount in the compensation scheme decision module.