WO2024001377A1 - 一种机匣装配偏差建模方法 - Google Patents

一种机匣装配偏差建模方法 Download PDF

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WO2024001377A1
WO2024001377A1 PCT/CN2023/085948 CN2023085948W WO2024001377A1 WO 2024001377 A1 WO2024001377 A1 WO 2024001377A1 CN 2023085948 W CN2023085948 W CN 2023085948W WO 2024001377 A1 WO2024001377 A1 WO 2024001377A1
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deviation
casing
model
tolerance
flange surface
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PCT/CN2023/085948
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English (en)
French (fr)
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李志敏
刘涛
康贺贺
袁巍
吴玉萍
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上海交通大学
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Priority to US18/324,158 priority Critical patent/US20240005053A1/en
Publication of WO2024001377A1 publication Critical patent/WO2024001377A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
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    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0639—Performance analysis of employees; Performance analysis of enterprise or organisation operations
    • G06Q10/06395—Quality analysis or management
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
    • B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/08—Probabilistic or stochastic CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/16—Equivalence checking
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/18—Manufacturability analysis or optimisation for manufacturability

Definitions

  • the invention belongs to the field of aviation component assembly deviation analysis, and in particular relates to a casing assembly deviation modeling method.
  • the aircraft engine is a highly complex and precise thermal machinery, known as the "crown jewel" in the industrial field.
  • the operating efficiency of aeroengines depends on many factors such as structural design, material performance and manufacturing quality. Among them, manufacturing quality has a great correlation with geometric errors of components, which has a great impact on the overall dynamic balance performance and operational safety of the engine. With the development of gas turbine engines, the requirements for the efficiency, lifespan and safety of its components are becoming higher and higher. The assembly quality has a great impact on the performance and structural safety of the engine.
  • the casing As a key component in aeroengines, the casing has many manufacturing processes, including milling, pin pulling, polishing, heat treatment and other manufacturing processes. Different types of manufacturing deviations occur during the manufacturing and assembly process of structural parts. These deviations are mainly reflected in the fluctuations in the shape and position of the matching interface relative to the nominal values during the assembly process. The shape and position fluctuation values of each interface are transmitted and accumulated in the dimensional chain, causing deviations in the spatial position of the casing after assembly, which in turn affects the service performance of the casing, blades and even the entire engine.
  • the tolerance design of aero-engine casings is mostly based on experience and requires repeated trials to meet the requirements; while tolerance analysis is mainly based on the traditional one/two-dimensional dimension chain, which cannot fully reflect the discontinuous interface of each assembly in the three-dimensional space.
  • the geometric tolerance and the coupling relationship between assembly features lead to inaccurate analysis results and cannot provide an accurate basis for assembly quality calibration and tolerance optimization allocation.
  • the transmission of receiver deviations is complicated by locally parallel dimensional chains due to bolted connections between receivers.
  • a receiver assembly deviation prediction model including series and parallel dimensional chains is established. Provide guidance for manufacturing optimization, tolerance allocation and performance control of the casing.
  • the purpose of the present invention is to provide a casing assembly deviation modeling method that characterizes the uncertainty in the local multi-parallel dimensional chain in the casing bolted assembly structure, and predicts the casing space after assembly through tolerance analysis and stochastic simulated assembly. Attitude deviation and statistical distribution.
  • a casing assembly deviation modeling method includes the following steps:
  • Step (1) Prepare the tolerance requirements for each key geometric element required to establish the casing dimensional chain model; such as the casing circumferential dimensional tolerance, the contour tolerance value of each flange matching surface, and the bolt hole position tolerance value etc;
  • Step (2) Establish a screw model of the deviation of each key geometric element of the casing based on the small displacement screw theory
  • Step (3) Consider that the bolted connection structure of the casing belongs to a typical local multi-parallel dimension chain; couple the deviation transmission in the bolt connection and the flange surface deviation transmission to obtain an equivalent spinor model;
  • Step (4) Considering that the flange surface is subject to both contour and parallelism tolerance requirements, the limiting effect of the parallelism tolerance on the flange surface angular deviation is introduced into the three-dimensional dimensional chain model of the casing; the parallelism tolerance screw model is The angular component replaces the angular component in the casing flange surface profile screw model;
  • Step (5) Considering the boundary conditions of each tolerance zone of the casing, establish a constraint relationship between the angular deviation and the translational deviation in the screw model;
  • Step (6) Substitute the constraint relationship between the angular deviation and the translational deviation in the screw model into the three-dimensional dimensional chain model of the casing to obtain a modified three-dimensional deviation transmission model of the casing; this model takes into account the distortion caused by the bolt connection. Local parallel dimension chain, angular deviation constraints caused by flange surface flatness, and tolerance zone boundary constraints, etc.; the assembly quality of the receiver can be evaluated through this model.
  • step (3) is specifically divided into the following steps:
  • each bolt positioning hole has a positional tolerance requirement Tpo.
  • the shape of the tolerance zone is cylindrical and can be determined by the translational components u 2 and v 2 and the rotational components ⁇ 2 and ⁇ 2 along the x and y directions. representation.
  • the casing flange surface will have angular deviations ⁇ 1 and ⁇ 1 along the x and y directions within the tolerance zone of the profile Ts. Since the value of ⁇ 2 is usually greater than the value of ⁇ 1 , interference will occur in the receiver bolt hole assembly when both reach the maximum value allowed by their respective tolerance zones. Therefore, the deviation surface of the casing flange surface will limit the rotation of the bolt in the position Tpo, and the allowable rotation angle of the bolt is limited by the angular deviations ⁇ 1 and ⁇ 1 .
  • the position deviation of the two axially symmetric bolt positioning holes will cause the flange surface to produce a rotation deviation along the z-axis.
  • the position of the two bolt positioning holes When the deviation is in the opposite direction, it will produce an equivalent angular deviation ⁇ ' on the connected flange surface.
  • ⁇ 1 , ⁇ 1 and ⁇ ' are selected as the angular deviations in the equivalent screw model of the effective casing flange surface to calculate the size chain.
  • u 2 and v 2 in the bolt positioning hole screw model are translational deviations, which will directly affect the spatial position of the matching parts.
  • the matching flange surface After being connected by bolts, the matching flange surface will move to the same position following u 2 and v 2 .
  • the displacement deviation in the x and y directions is equal to 0. Therefore, when the flange surface is connected through bolts, the comprehensive translational deviation of the flange surface and the bolt positioning hole in the u and v directions can be expressed by u 2 and v 2 .
  • the various translational components in the bolt hole and flange surface screw models are combined, and u 2 and v 2 are selected as the effective translation deviations to calculate the dimensional chain.
  • T IFE1' [u 2 v 2 w 1 ⁇ 1 ⁇ 1 ⁇ '] T .
  • step (4) it is considered that the flange surface is subject to both contour and parallelism tolerance requirements, and the limiting effect of the parallelism tolerance on the angle deviation of the flange surface is introduced into the three-dimensional dimensional chain model of the casing.
  • the casing flange surface is also subject to other tolerance constraints.
  • the top end face of the receiver has both a contour tolerance Ts and a parallelism tolerance Tpa, so it is necessary to consider the impact of the parallelism tolerance.
  • the parallelism tolerance zone Tpa can move freely within a range of width Ts, but cannot exceed the boundary determined by the contour tolerance zone.
  • the actual surface red dotted line
  • the contour tolerance and the parallelism tolerance together form a composite tolerance.
  • step (5) the boundary conditions of each tolerance zone of the casing are considered, and a constraint relationship is established between the angular deviation and the translational deviation in the spinor model.
  • the casing assembly deviation modeling method of the present invention can represent the transmission and accumulation of complex three-dimensional tolerances in the multi-level casing assembly process. Based on this method, the influence rules and contribution of the tolerance or deviation of any size ring in the dimensional chain on the target deviation of the casing can be obtained.
  • the casing assembly deviation modeling method of the present invention takes into account the bolt connection assembly relationship, performs equivalent processing on the complex local parallel dimensional chain, and solves the problem of the difficulty of the local dimensional chain caused by the deviation transmission path between bolt matching surfaces. problem of expression.
  • the casing assembly deviation modeling method of the present invention can not only be used to predict the target position deviation in the initial state of the assembled casing, but can also be used to analyze the deviation at any position of the casing.
  • This method belongs to an explicit mathematical model and has the characteristics of simplicity and high solving efficiency.
  • the casing assembly deviation modeling method of the present invention can obtain the fluctuation range of the target table deviation through the extreme value method, and can also calculate the statistical distribution of the target geometric elements through Monte Carlo simulation. Different deviation distribution types that may exist in actual engineering, such as normal distribution, Pearson distribution, etc., can also be solved through this dimensional chain model.
  • the dimension chain modeling method of the present invention has good engineering application capabilities.
  • This method is universal and can be used for the dimensional chain analysis of any casing containing bolted connections.
  • the bolted casing mentioned in the present invention can be not only an aeroengine casing, but also a ship steam turbine casing, etc.
  • Figure 1 is a schematic structural diagram of a typical aeroengine casing
  • Figure 2 shows the typical tolerance requirements of the intermediate casing
  • Figure 3 shows the typical tolerance requirements of the high-voltage casing
  • Figure 4 is a chain diagram of the receiver assembly relationship
  • Figure 5(a) shows the spinor representation of plane profile tolerance
  • Figure 5(b) shows the spinor representation of coaxiality tolerance
  • Figure 6(a), Figure 6(b), and Figure 6(c) are schematic diagrams of the effective deviation of bolt positioning hole connections.
  • Figure 7 is a schematic diagram of the parallelism of the flange surface
  • Figure 8(a) and Figure 8(b) are schematic diagrams of the contour boundary
  • Figure 9(a) and Figure 9(b) are schematic diagrams of bolt hole position boundaries
  • Figure 10(a) is the statistical distribution diagram of u in FR;
  • Figure 10(b) is the statistical distribution diagram of v in FR;
  • Figure 10(c) is the statistical distribution diagram of w in FR.
  • the object described in the embodiment of the present invention is a typical aeroengine casing assembly.
  • the main body of the casing is a cylindrical structure, and the casings are connected by bolts.
  • Step (1) Based on the matching relationship between the casings during assembly and the tolerance requirements in the actual manufacturing process, define the tolerance types and tolerance values of each key geometric element.
  • the bottom surface and inner surface of the casing are defined as datums A and B respectively.
  • the top bolt positioning hole has a position degree ⁇ Tpo requirement relative to datum B, while the datum and bottom positioning holes are considered to be in a nominal state.
  • the top flange surface of the receiver has a profile Ts requirement relative to datum A, accompanied by a parallelism tolerance Tpa.
  • Da and Db are the outer diameters of the two receiver flange surfaces respectively.
  • D′ a and D′ b respectively represent the distance between two axisymmetric holes on the top flange surfaces of the two casings.
  • La and Lb are the axial lengths of the two receivers respectively.
  • the superscript Tu and the subscript Td are the upper limit and lower limit deviation of the axial size.
  • Step (2) According to the matching relationship between the casings and the characteristics of the relevant geometric elements, the deviation transmission path of the casing can be divided into a series dimensional chain and a local parallel dimensional chain.
  • LCS ‘0’ is the center point of the bottom surface of the intermediate receiver and serves as a reference point for evaluating the assembly quality of the receiver.
  • LCS ‘1’, ‘4’ and ‘7’ are the flange surface centers of the corresponding receivers respectively.
  • LCS ‘2’, ‘3’, ‘5’ and ‘6’ respectively represent the geometric centers of bolt positioning holes.
  • the flange surface connection is used to limit the translation of the casing along the z-axis and the rotation along the x/y axis.
  • the geometric elements here are centered on the axis of the casing, and the corresponding deviation transmission belongs to the series dimensional chain. .
  • the bolt holes on the flange surface mainly restrict the translation of the casing in the x/y direction and the rotation in the z direction. Relative to the central axis of the casing, the deviation caused by the bolt hole is transmitted from both sides in the radial direction of the casing, belonging to a local parallel dimensional chain.
  • two of the bolt holes evenly distributed on the flange surface and distributed axially symmetrically are defined as positioning holes, while the other bolt holes are only used as connection holes.
  • the assembly connection relationship of the receiver is shown in Figure 4.
  • the dimension ring is: IFE1-CFE1-IFE2-FR.
  • IFE1 is the contour deviation of the functional element corresponding to coordinate system '1' relative to coordinate system '0'.
  • CFE1 is defined as the dimensional deviation between coordinate system '1' and coordinate system '4'.
  • IFE2 is the contour deviation of coordinate system '7' relative to coordinate system '4'.
  • the functional size requirement FR is the target deviation for evaluating the assembly quality of the receiver.
  • FR is defined here as the relative spatial position relationship between the center points on both sides of the casing, that is, the relative position deviation between coordinate system '0' and coordinate system '7'.
  • T CFE1 [0 0 w 0 0 0] T ,-Td ⁇ w ⁇ Tu (2)
  • the spinor w in TIFE2 is changed to the following expression:
  • Step (3) The dotted connection shown in Figure 4 is the local parallel dimension chain PFE1 and PFE2 caused by the bolt.
  • PFE1 and PFE2 are the position deviations of the positioning holes corresponding to coordinate systems ‘2’ and ‘3’ relative to coordinate systems ‘5’ and ‘6’ respectively.
  • the equivalent screw model is obtained by coupling the deviation transmission in bolted connections with the flange surface deviation transmission. Specifically, it is divided into the following small steps:
  • each bolt positioning hole has a positional tolerance requirement Tpo.
  • the shape of the tolerance domain is cylindrical and can be characterized by the translational components u, v and rotational components ⁇ , ⁇ along the x and y directions.
  • the position of the bolt positioning hole will affect the coaxiality of both sides of the casing, which will lead to changes in the target deviation FR.
  • the rotation component ⁇ along the y-axis will cause the top surface of the casing to produce a positional deviation w along the z-direction.
  • the casing flange surface will have an angular deviation ⁇ 1 along the y direction within the tolerance zone of the profile Ts.
  • ⁇ 2 is the angular deviation of the bolt positioning hole along the y direction in the position Tpo tolerance domain. Since the value of ⁇ 2 is usually greater than the value of ⁇ 1, when both reach the maximum value allowed by their respective tolerance zones, interference will occur in the assembly of the receiver bolt holes, but in reality this interference assembly state is not allowed to exist.
  • the deviation surface of the casing flange surface will limit the rotation of the bolt in the position Tpo, and the allowable rotation angle of the bolt is limited by the angle deviation ⁇ 1.
  • the angular deviations ⁇ 2 and ⁇ 2 of the bolt holes in the parallel dimension chain need to be less than or equal to the angular deviations ⁇ 1 and ⁇ 1 of the flange surface profile.
  • u2 and v2 in the bolt positioning hole screw model TPFE belong to translational deviations, which will directly affect the spatial position of the matching parts.
  • the matching flange surface After being connected by bolts, the matching flange surface will move to the same position following u2 and v2.
  • the displacement deviation in the x and y directions is equal to 0. Therefore, when the flange surface is connected through bolts, the comprehensive translational deviation of the flange surface and the bolt positioning hole in the u and v directions can be expressed by u2 and v2.
  • the various translational components in TPFE and TIFE1 are combined, and u2 and v2 are selected as the effective translational deviations to calculate the size chain.
  • T IFE1' [u 2 v 2 w 1 ⁇ 1 ⁇ 1 ⁇ '] T (6)
  • elements C1l, C2l and C3l are unit vectors, which represent the projection vector of the i-th element sitting in the three-coordinate direction of the local coordinate system relative to the "0" three-coordinate direction of the global coordinate system. They correspond to the x, y and z axes respectively. direction.
  • dxi, dyi, and dzi are the distances in the x, y, and z directions of the coordinate system where the i-th element is located relative to the global coordinate system.
  • R Pti is the projection matrix, which represents the projection matrix between the deviation analysis direction and the tolerance zone.
  • Step (4) Considering that the flange surface is subject to both contour and parallelism tolerance requirements, the limiting effect of the parallelism tolerance on the angle deviation of the flange surface is introduced into the three-dimensional dimensional chain model of the casing.
  • the tolerance domains corresponding to IFE1 and IFE2 of the connecting chain are only characterized by their contours.
  • the receiver flange surface is also subject to other tolerance constraints.
  • the top end surface of the casing has both a profile tolerance Ts and a parallelism tolerance Tpa, so it is necessary to consider the impact of the parallelism tolerance.
  • Figure 7 shows the contour tolerance zone and parallelism tolerance zone. It can be seen that the parallelism tolerance zone Tpa (red line) can move freely within the range of width Ts, but cannot exceed the boundary determined by the contour tolerance zone. The actual surface (red dotted line) can translate up and down and rotate within the flatness tolerance zone Tpa.
  • the contour tolerance and the parallelism tolerance together form a composite tolerance.
  • the screw model of the flange surface needs to be modified to meet the actual deviation constraints.
  • the expression of the corresponding spinor is as follows:
  • Step (5) Considering the boundary conditions of each tolerance zone of the casing, establish a constraint relationship between the angular deviation and the translation deviation in the screw model.
  • the tolerance zone of the flange surface profile Ts is shown in Figures 8(a) and 8(b).
  • w 1 and ⁇ ' both take the maximum value, part of the actual flange surface represented by the red dotted line will exceed the upper boundary of Ts.
  • the value of ⁇ ' needs to be changed to 0 when w 1 is the largest. This shows that there is a constraint relationship between the translational component and the rotational component to satisfy the boundary of the tolerance domain Ts.
  • Step (6) Substitute the constraint relationship between the angular deviation and the translational deviation in step (5) into the three-dimensional dimensional chain model of the casing to obtain the modified three-dimensional deviation transfer model of the casing.
  • the specific expression is as follows: Equation (17) ). This model considers the local parallel dimension chain caused by bolted connections, the angular deviation constraints caused by the flatness of the flange surface, and the tolerance zone boundary constraint relationships.
  • this embodiment randomly generates 5,000 sample points based on the normal distribution function, selects deviations that meet the tolerance boundary constraints, and calculates the casing assembly through the established deviation model.
  • the local parallel dimensional chain connected by bolts and the casing series dimensional chain are coupled.
  • the method caused by parallelism is considered.
  • the influence of the blue surface composite tolerance and the boundary constraints of the tolerance zone, etc. Through this model, the statistical distribution of the position deviation of the cassette assembly and the target deviation can be calculated.

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Abstract

本发明适用于航空部件装配偏差分析领域，提供了一种机匣装配偏差建模方法，包括以下步骤：步骤(1)：准备好建立机匣尺寸链模型所需的各个关键几何要素的公差要求；步骤(2)：基于小位移旋量理论建立机匣各个关键几何要素偏差的旋量模型；步骤(3)：将螺栓连接中偏差的传递和法兰面偏差传递相耦合，得到等效旋量模型；步骤(4)：将平行度公差对法兰面角度偏差的限制作用引入到机匣三维尺寸链模型中；将平行度公差旋量模型中的角度分量替换机匣法兰面轮廓度旋量模型中的角度分量。本发明所述的机匣装配偏差建模方法，可以表征复杂三维公差在多级机匣装配过程中的传递和累积。

Description

一种机匣装配偏差建模方法 技术领域
本发明属于航空部件装配偏差分析领域，尤其涉及一种机匣装配偏差建模方法。
背景技术
航空发动机是一种高度复杂和精密的热力机械，被誉为工业领域“皇冠上的明珠”。航空发动机的运行效率依赖于结构设计、材料性能及制造质量等多方面因素。其中，制造质量与零部件几何误差呈现极大相关性，对发动机的整体动平衡性能、运行安全均有较大影响。随着燃气涡轮发动机的发展，对其部件效率、寿命和安全性要求也越来越高，装配质量对发动机的性能和结构安全性的影响很大。
作为航空发动机中的关键部件，机匣加工制造过程繁多，涉及到铣削、拉销、抛光、热处理等制造工艺。结构零部件在制造与装配过程中，产生不同种类的制造偏差。这些偏差主要体现在装配过程中匹配界面的形状和位置相对于名义值的波动。各个界面的形位波动值在尺寸链中传递和累积，造成装配后机匣空间位置产生偏差，进而影响到机匣、叶片乃至整个发动机的服役性能。
目前针对航空发动机机匣的公差设计多以经验为主，需要反复试凑以达到要求；而公差分析以传统的一/二维尺寸链为主，无法完全反映出三维空间各个装配体非连续界面的形位公差以及装配特征之间的耦合关系，从而导致分析结果不准确，无法为装配质量标定和公差优化分配提供准确的依据。此外，由于机匣之间的螺栓连接，导致出现局部并联尺寸链，导致机匣偏差传递变得复杂。
因此，有必要研究含螺栓连接多级机匣装配的复杂尺寸链传递。根据机匣的制造装配精度和连接匹配关系，建立包含串并联尺寸链的机匣装配偏差预测模型。为机匣的制造优化、公差分配以及性能调控提供指导依据。
发明内容
本发明的目的在于提供一种机匣装配偏差建模方法，表征机匣螺栓连接装配结构中局部多并联尺寸链中的不确定性，通过公差分析和随机性模拟装配，预测装配后机匣空间姿态偏差以及统计学分布。
本发明是这样实现的，一种机匣装配偏差建模方法，包括以下步骤：
步骤(1)：准备好建立机匣尺寸链模型所需的各个关键几何要素的公差要求；如机匣周向尺寸公差、各个法兰匹配面的轮廓度公差值以及螺栓孔位置度公差值等；
步骤(2)：基于小位移旋量理论建立机匣各个关键几何要素偏差的旋量模型；
步骤(3)：考虑机匣的螺栓连接结构属于典型的局部多并联尺寸链；将螺栓连接中偏差的传递和法兰面偏差传递相耦合，得到等效旋量模型；
步骤(4)：考虑法兰面同时受到轮廓度和平行度公差要求，将平行度公差对法兰面角度偏差的限制作用引入到机匣三维尺寸链模型中；将平行度公差旋量模型中的角度分量替换机匣法兰面轮廓度旋量模型中的角度分量；
步骤(5)：考虑机匣各个公差带边界条件限制，在旋量模型中的角度偏差和平动偏差之间建立约束关系；
步骤(6)：将旋量模型中角度偏差和平动偏差之间的约束关系代入到机匣三维尺寸链模型中，得到经过修改后的机匣三维偏差传递模型；该模型考虑了螺栓连接导致的局部并联尺寸链、法兰面平面度引起的角度偏差约束以及公差带边界约束关系等；通过该模型可以进行机匣装配质量的评估。
进一步的技术方案，所述步骤(3)具体又分为以下步骤：
3.1根据实际装配状态，通过交并运算，筛选螺栓孔位置度旋量以及法兰面轮廓度旋量中的有效转动分量。具体地，每一个螺栓定位孔都有一个位置度公差要求Tpo，该公差域形状为圆柱形，可以用沿x和y方向的平动分量u2、v2和转动分量α2、β2来表征。机匣法兰面在轮廓度Ts的公差域内会有沿x和y方向的角度偏差α1、β1。由于β2的值通常大于β1的值，在二者都达到各自公差域所允许的最大值时，机匣螺栓孔装配会出现干涉。因此，机匣法兰面的偏差面会限制螺栓在位置度Tpo中的转动，螺栓所允许的转动角度受到角度偏差α1和β1的限制。
此外，由于法兰面轮廓度并不限制沿z轴方向的转动，而轴对称的两个螺栓定位孔位置偏差会使法兰面产生沿z轴的转动偏差，当两个螺栓定位孔的位置偏差呈现相反方向时，将使连接的法兰面产生等效角度偏差γ'。
对上述各个转动分量进行合并操作，选取α1、β1和γ'作为有效机匣法兰面等效旋量模型中的角度偏差进行尺寸链的计算。
3.2根据实际装配状态，通过交并运算，筛选螺栓孔位置度旋量以及法兰面轮廓度旋量中的有效平动分量。
具体地，螺栓定位孔旋量模型中的u2和v2属于平动偏差，会直接影响匹配件的空间位置。通过螺栓连接后匹配法兰面会跟随着u2和v2移动相同的位置。而法兰面的旋量模型中关于x和y方向的位移偏差等于0。因此经螺栓对法兰面进行连接时，法兰面和螺栓定位孔在u和v方向综合平动偏差可以用u2和v2来表示。对螺栓孔和法兰面旋量模型中的各个平动分量进行合并操作，选取u2和v2作为有效平动偏差进行尺寸链的计算。
3.3将法兰面与螺栓孔中有效的平动分量和转动分量耦合在一起，形成机匣法兰面连接处的等效旋量模型，表达式如下：
TIFE1'＝[u2 v2 w1 α1 β1 γ']T。
进一步的技术方案，步骤(4)中考虑法兰面同时受到轮廓度和平行度公差要求，将平行度公差对法兰面角度偏差的限制作用引入到机匣三维尺寸链模型中。
具体地，机匣法兰面除了受到轮廓度要求外，还受到其他公差的约束。例如机匣顶部端面同时有轮廓度公差Ts和平行度公差Tpa，因此有必要考虑平行度公差所带来的影响。
具体地，平行度公差带Tpa在宽度为Ts的范围内可以自由活动，但不能超出轮廓度公差带所确定的边界。实际表面(红色虚线)则在平面度公差带Tpa里可以上下平移和转动。也就是说，轮廓度公差和平行度公差共同组成了复合公差。考虑到平行度公差Tpa对法兰面转动角度的限制，旋量模型中的角度偏差用平行度公差中的角度偏差来代替，表达式如下：
进一步的技术方案，步骤(5)中考虑机匣各个公差带边界条件限制，在旋量模型中的角度偏差和平动偏差之间建立约束关系。
具体地，法兰面轮廓度Ts公差带中当w1和β'都取最大值时，实际法兰面将有一部分超出Ts的上边界。为了使法兰面处于公差域内，则在w1最大时需要将β'的值变为0才行。在考虑公差域的边界约束后，旋量TIFE1'中w1和α'、β'之间的关系如下：

与轮廓度公差中的约束类似，TIFE1'中u2、v2和γ'之间也存在约束关系。约束关系如下：

相较于现有技术，本发明的有益效果如下：
(1)本发明所述的机匣装配偏差建模方法，可以表征复杂三维公差在多级机匣装配过程中的传递和累积。基于本方法，可以得到尺寸链中任一尺寸环的公差或偏差大小对机匣目标偏差的影响规律及贡献度。
(2)本发明所述的机匣装配偏差建模方法，考虑了螺栓连接装配关系，将复杂的局部并联尺寸链进行了等效处理，解决了螺栓匹配面间偏差传递路径导致局部尺寸链难以表述的问题。
(3)本发明所述的机匣装配偏差建模方法，不仅可以用于装配后机匣初始状态下的目标位置偏差预测，也可以用于机匣任何位置的偏差分析。该方法属于显式数学模型，具有简洁、求解效率高的特点。
(4)本发明所述的机匣装配偏差建模方法，可以通过极值法得到目标表偏差的波动范围，也可以通过蒙特卡洛仿真计算目标几何要素的统计学分布。针对实际工程中可能存在的不同偏差分布类型，如正态分布、皮尔逊分布等，也可以通过该尺寸链模型进行求解。本发明所述的尺寸链建模方法具有较好的工程应用能力。
(5)本方法具有普适性，可用于任何含螺栓连接的机匣的尺寸链分析。此外，本发明所提到的含螺栓连接的机匣不仅可以是航空发动机机匣，也可以是轮船汽轮机机匣等。
附图说明
图1为典型航空发动机机匣结构示意图；
图2为中介机匣典型公差要求图；
图3为高压机匣典型公差要求图；
图4为机匣装配关系链图；
图5(a)为为平面轮廓度公差的旋量表征；图5(b)为同轴度公差的旋量表征；
图6(a)、图6(b)、图6(c)为螺栓定位孔连接有效偏差示意图
图7为法兰面平行度示意图
图8(a)、图8(b)为轮廓度边界示意图；
图9(a)、图9(b)为螺栓孔位置度边界示意图；
图10(a)为FR中u的统计学分布图；图10(b)为FR中v的统计学分布图；图10(c)为FR中w的统计学分布图。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
以下结合具体实施例对本发明的具体实现进行详细描述。
如图1所示，本发明实施例中所描述的对象是典型航空发动机机匣装配体。其中，机匣主体为圆柱形结构，机匣之间通过螺栓连接。
基于以上所述的机匣，建立考虑螺栓连接的机匣尺寸链模型。具体步骤如下：
步骤(1)：根据机匣之间装配时的匹配关系以及实际制造过程中的公差要求，定义各个关键几何要素的公差类型以及公差值。如机匣轴向尺寸公差、法兰面轮廓度公差、法兰面平行度公差、螺栓定位孔位置度公差，如图2、图3所示。机匣底面和内侧面分别定义为基准A和B。顶部螺栓定位孔相对于基准B有位置度φTpo要求，而基准与底部定位孔则认为处于名义状态。此外，机匣顶部法兰面相对于基准A有轮廓度Ts要求，同时伴随着平行度公差Tpa。Da和Db分别是两个机匣法兰面的外径。D′a和D′b分别表示两个机匣顶部法兰面上两个轴对称孔之间的距离。La和Lb分别是两个机匣的轴向长度。上标Tu和下标Td是轴向尺寸的上限偏差和下限偏差。以上的几何参数具体值如下：La＝962mm，Lb＝820mm,Da＝823mm，D′a＝780mm，Db＝900mm，D′b＝840mm，Tu＝0.03mm，Td＝0.03mm，Wa＝8.6mm，Tpo＝0.05mm，Tpa＝0.03mm，Ts＝0.05mm，Wb＝12mm。
步骤(2)：根据机匣之间匹配关系和相关几何要素的特点，机匣的偏差传递路径可以划分为串联尺寸链和局部并联尺寸链。
具体地，LCS‘0’是中介机匣底面的中心点并作为评价机匣装配质量的一个基准点。LCS‘1’、‘4’和‘7’分别是相应机匣的法兰面中心。LCS‘2’、‘3’、‘5’和‘6’分别表示螺栓定位孔几何中心。在机匣装配中通过法兰面的连接来限制机匣沿z轴的平动和沿x/y轴方向的转动，这里的几何要素以机匣轴线为中心，相应的偏差传递属于串联尺寸链。而法兰面上的螺栓孔主要约束机匣沿x/y方向上的平动和沿z方向上的转动。相对于机匣中心轴线，由螺栓孔引起的偏差传递从机匣径向方向上的两侧开始传递，属于局部并联尺寸链。为了方便分析，这里定义法兰面上均布的螺栓孔中以轴对称分布的其中两个孔为定位孔，而其他螺栓孔仅作为连接孔。
机匣的装配连接关系如图4所示。共有5个功能单元FE，分别是两个内部功能单元IFE、两个并联功能单元PFE和一个接触功能单元CFE，用于表征一个串联尺寸链和两个局部并联尺寸链。对于串联尺寸链而言，尺寸环是：IFE1-CFE1-IFE2-FR。其中IFE1是坐标系‘1’所对应功能要素相对于坐标系‘0’的轮廓度偏差。CFE1定义为坐标系‘1’与坐标系‘4’之间的尺寸偏差。IFE2是坐标系‘7’相对于坐标系‘4’的轮廓度偏差。功能尺寸要求FR，是评价机匣装配质量的目标偏差。这里定义FR为机匣两侧中心点之间的相对空间位置关系，也即是坐标系‘0’与坐标系‘7’之间的相对位置偏差。
基于小位移旋量理论表征各个关键几何要素的公差。常见典型公差类型下的旋量表征如图5(a)、图5(b)所示，其中Sv是实际偏差面，Sn是名义平面，α、β、γ分别是关于x、y、z轴的转动角度偏差，u、v、w分别是关于x、y、z轴的平动偏差。根据步骤(1)中的公差要求，建立相应旋量模型。
具体地，在机匣各个功能单元公差的旋量表征如下：

TCFE1＝[0 0 w 0 0 0]T,-Td≤w≤Tu  (2)
考虑到高压机匣轴向尺寸公差会对FR在z方向分量产生显著影响，这里将TIFE2中的旋量w改为如下表达：
步骤(3)：图4中所示的虚线连接是螺栓导致的局部并联尺寸链PFE1和PFE2。PFE1和PFE2分别是坐标系‘2’和‘3’所对应定位孔相对于坐标系‘5’和‘6’的位置度偏差。将螺栓连接中偏差的传递和法兰面偏差传递相耦合，得到等效旋量模型。具体又分为以下几小步：
(1)根据实际装配状态，通过交并运算，筛选螺栓孔位置度旋量以及法兰面轮廓度旋量中的有效转动分量。
具体地，每一个螺栓定位孔都有一个位置度公差要求Tpo，该公差域形状为圆柱形，可以用沿x和y方向的平动分量u、v和转动分量α、β来表征，旋量表达式如下：
TPFE＝[u2 v2 0 α2 β2 0]T  (5)
显然，由于角度偏差的杠杆效应，螺栓定位孔的位置度会影响到机匣两侧的同轴度，进而导致目标偏差FR的变化。例如，在位置度公差域中沿y轴的转动分量β会导致机匣顶端面产生沿z方向的位置偏差w。
需要注意的是，螺栓定位孔位置度偏差与机匣定端面轮廓度偏差之间会产生干涉现象。如图6(a)、图6(b)、图6(c)所示，机匣法兰面在轮廓度Ts的公差域内会有沿y向的角度偏差β1。β2是螺栓定位孔在位置度Tpo公差域中沿y方向的角度偏差。由于β2的值通常大于β1的值，在二者都达到各自公差域所允许的最大值时，机匣螺栓孔装配会出现干涉，但现实中不允许这种干涉装配状态存在。机匣法兰面的偏差面会限制螺栓在位置度Tpo中的转动，螺栓所允许的转动角度受到角度偏差β1的限制。
为了避免连接中的这种干涉，并联尺寸链中螺栓孔的角度偏差α2和β2需要小于或等于法兰面轮廓角度偏差α1和β1。
此外，由于法兰面轮廓度并不限制沿z轴方向的转动，而轴对称的两个螺栓定位孔位置偏差会使法兰面产生沿z轴的转动偏差，如图6(a)、图6(b)、图6(c)所示。当两个螺栓定位孔的位置偏差呈现相反方向时，将使连接的法兰面产生等效角度偏差γ'。
因此，对TPFE和TIFE1中的各个转动分量进行合并操作，选取α1、β1和γ'作为有效角度偏差进行尺寸链的计算。
(2)根据实际装配状态，通过交并运算，筛选螺栓孔位置度旋量以及法兰面轮廓度旋量中的有效平动分量。
具体地，螺栓定位孔旋量模型TPFE中的u2和v2属于平动偏差，会直接影响匹配件的空间位置。通过螺栓连接后匹配法兰面会跟随着u2和v2移动相同的位置。而法兰面的旋量模型中关于x和y方向的位移偏差等于0。因此经螺栓对法兰面进行连接时，法兰面和螺栓定位孔在u和v方向综合平动偏差可以用u2和v2来表示。对TPFE和TIFE1中的各个平动分量进行合并操作，选取u2和v2作为有效平动偏差进行尺寸链的计算。
(3)将法兰面与螺栓孔中有效的平动分量和转动分量耦合在一起，形成机匣法兰面连接处的等效旋量模型，表达式如下：
TIFE1'＝[u2 v2 w1 α1 β1 γ']T  (6)
(4)将(3)中的等效旋量模型耦合到机匣串联尺寸链中，基于雅克比-旋量理论得到机匣的三维尺寸链模型。雅克比-旋量模型一般表达式如下：
具体地，是一个3×3方向矩阵，是第i个FE相对于全局坐标系“0”之间的方向矩阵。它表征着第i个元素所在坐标系的方向转换。具体地，如下定义：
具体地，元素C1l、C2l和C3l是单位向量，表示的是第i元素坐在局部坐标系三坐标相对于全局坐标系“0”三坐标方向的投影向量，它们分别对应x、y和z轴方向。
具体地，是反对称的矩阵，用于表示第i个元素与第n个元素(也即是目标元素)之间的三维距离向量。和可以通过下式进行计算：
具体地，dxi、dyi和dzi是第i个元素所在坐标系相对于全局坐标系在x、y、z方向的距离。通过方向矩阵和距离矩阵之间的乘积，即用来表征偏差在传递过程中的杠杆效应,而RPti是投影矩阵，表示偏差分析方向和公差带之间的投影矩阵。
将式(2)、(3)、(6)带入式(7)中，得到含螺栓连接的机匣装配体雅克比-旋量偏差模型，具体表达式如下：

步骤(4)：考虑法兰面同时受到轮廓度和平行度公差要求，将平行度公差对法兰面角度偏差的限制作用引入到机匣三维尺寸链模型中。
具体地，如图4中连接链的IFE1和IFE2，它们所对应的公差域仅仅是通过轮廓度进行表征的。但机匣法兰面除了受到轮廓度要求外，还受到其他公差的约束。如图2、图3所示，机匣顶部端面同时有轮廓度公差Ts和平行度公差Tpa，因此有必要考虑平行度公差所带来的影响。图7所示轮廓度公差带和平行度公差带。可以看到，平行度公差带Tpa(红色线)在宽度为Ts的范围内可以自由活动，但不能超出轮廓度公差带所确定的边界。实际表面(红色虚线)则在平面度公差带Tpa里可以上下平移和转动。也就是说，轮廓度公差和平行度公差共同组成了复合公差。考虑到平行度公差Tpa对法兰面转动角度的限制，这里需要对法兰面的旋量模型进行修改以满足实际偏差约束条件。相应旋量的表达式如下：

将上式(13)和(14)带入式(11)中，得到含平行度的螺栓连接机匣偏差模型。
步骤(5)：考虑机匣各个公差带边界条件限制，在旋量模型中的角度偏差和平动偏差之间建立约束关系。
具体地，如图8(a)、图8(b)所示法兰面轮廓度Ts的公差带。当w1和β'都取最大值时，红色虚线表示的实际法兰面将有一部分超出Ts的上边界。为了使法兰面处于公差域内，则在w1最大时需要将β'的值变为0才行。这说明平动分量和转动分量之间存在约束关系以满足公差域Ts的边界。
在考虑公差域的边界约束后，旋量TIFE1'中w1和α'、β'之间的关系如下：
与轮廓度公差中的约束类似，TIFE1'中u2、v2和γ'之间也存在约束关系。如图9(a)、图9(b)所示，当u2和v2达到最大值时，中心点位置会超出圆形公差域。只有在v2处于最大值时γ'的值为0才能避免超出边界。相应地，u2、v2和γ'之间的约束关系如下：
步骤(6)：将步骤(5)中角度偏差和平动偏差之间的约束关系代入到机匣三维尺寸链模型中，得到经过修改后的机匣三维偏差传递模型，具体表达式如式(17)。该模型考虑了螺栓连接导致的局部并联尺寸链、法兰面平面度引起的角度偏差约束以及公差带边界约束关系等。
考虑到实际工程中各个偏差大都呈现正态分布，本实施例根据正态分布函数随机生成5000个样本点，从中选取符合公差边界约束条件的偏差，通过所建立的机匣装配体偏差模型计算机匣装配体目标偏差FR的统计学分布。
机匣装配体两侧中心点之间距离偏差FR沿x、y和z方向分量的统计学分布如图10(a)、图10(b)、图10(c)所示。具体地，偏差u、v和w的统计学分布标准差分别是：0.0119mm、0.0115mm和0.0177mm。
通过本实施例所述机匣尺寸链建模方法和所建立的尺寸链模型，将螺栓连接的局部并联尺寸链与机匣串联尺寸链进行了耦合，在此基础上考虑了平行度导致的法兰面复合公差影响以及公差带边界约束条件等。通过该模型，可以计算机匣装配体位置偏差以及目标偏差的统计学分布。
以上实施例只是本发明一部分。实施例所述的公差值和机匣结构几何尺寸仅是一个示例，对于不同的公差值和尺寸，目标偏差的结果也有相应的变化。可以根据实际工程结构和要求，通过该实施例所述的尺寸链建模方法进行偏差的分析。以上所述仅为本发明的具体实施方式而已，对于本领域的技术人员来说，凡在本发明的精神和原则之内，可轻易想到的变化或同等替换、改进等，均应包含在本发明的保护范围之内。因此，本发明的保护范围应以所述权利要求的保护范围为准。并不用于限制本发明。
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。
此外，应当理解，虽然本说明书按照实施方式加以描述，但并非每个实施方式仅包含一个独立的技术方案，说明书的这种叙述方式仅仅是为清楚起见，本领域技术人员应当将说明书作为一个整体，各实施例中的技术方案也可以经适当组合，形成本领域技术人员可以理解的其他实施方式。

Claims (5)

  1. 一种机匣装配偏差建模方法，其特征在于，包括以下步骤：
    步骤(1)：准备好建立机匣尺寸链模型所需的各个关键几何要素的公差要求，如机匣周向尺寸公差、各个法兰匹配面的轮廓度公差值以及螺栓孔位置度公差值；
    步骤(2)：基于小位移旋量理论建立机匣各个关键几何要素偏差的旋量模型；
    步骤(3)：将螺栓连接中偏差的传递和法兰面偏差传递相耦合，得到等效旋量模型；
    步骤(4)：将平行度公差对法兰面角度偏差的限制作用引入到机匣的三维尺寸链模型中；将平行度公差旋量模型中的角度分量替换机匣法兰面轮廓度旋量模型中的角度分量；
    步骤(5)：在旋量模型中的角度偏差和平动偏差之间建立约束关系；
    步骤(6)：将旋量模型中角度偏差和平动偏差之间的约束关系代入到机匣三维尺寸链模型中，得到经过修改后的机匣三维偏差传递模型。
  2. 根据权利要求1所述的机匣装配偏差建模方法，其特征在于，所述步骤(3)具体又分为以下步骤：
    3.1根据实际装配状态，通过交并运算，筛选螺栓孔位置度旋量以及法兰面轮廓度旋量中的有效转动分量；
    3.2根据实际装配状态，通过交并运算，筛选螺栓孔位置度旋量以及法兰面轮廓度旋量中的有效平动分量；
    3.3将法兰面与螺栓孔中有效的平动分量和转动分量耦合在一起，形成机匣法兰面连接处的等效旋量模型；
    3.4将步骤3.3中的等效旋量模型耦合到机匣串联尺寸链中，基于雅克比-旋量理论得到机匣的三维尺寸链模型。
  3. 根据权利要求2所述的机匣装配偏差建模方法，其特征在于，步骤(3)中将法兰面与螺栓孔中有效的平动分量和转动分量耦合在一起，形成机匣法兰面连接处的等效旋量模型，表达式如下：
    TIFE1'＝[u2 v2 w1 α1 β1 γ']T。
  4. 根据权利要求1所述的机匣装配偏差建模方法，其特征在于，步骤(4)中TIFE1'旋量模型中的角度偏差用平行度公差中的角度偏差来代替，表达式如下：
  5. 根据权利要求1所述的机匣装配偏差建模方法，其特征在于，步骤(5)中旋量TIFE1'中w1和α'、β'之间的关系如下：

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