WO2020051793A1 - 一种基于端跳测量计算转子装配轴线偏斜的方法 - Google Patents

一种基于端跳测量计算转子装配轴线偏斜的方法 Download PDF

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WO2020051793A1
WO2020051793A1 PCT/CN2018/105195 CN2018105195W WO2020051793A1 WO 2020051793 A1 WO2020051793 A1 WO 2020051793A1 CN 2018105195 W CN2018105195 W CN 2018105195W WO 2020051793 A1 WO2020051793 A1 WO 2020051793A1
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contact
points
point
rotor
triangle
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PCT/CN2018/105195
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English (en)
French (fr)
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孙清超
刘鑫
高一超
汪云龙
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大连理工大学
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Priority to US16/652,838 priority Critical patent/US11093582B2/en
Priority to PCT/CN2018/105195 priority patent/WO2020051793A1/zh
Publication of WO2020051793A1 publication Critical patent/WO2020051793A1/zh

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    • 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
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03D—WIND MOTORS
    • F03D17/00—Monitoring or testing of wind motors, e.g. diagnostics
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03D—WIND MOTORS
    • F03D13/00—Assembly, mounting or commissioning of wind motors; Arrangements specially adapted for transporting wind motor components
    • F03D13/10—Assembly of wind motors; Arrangements for erecting wind motors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2230/00—Manufacture
    • F05B2230/60—Assembly methods
    • F05B2230/604—Assembly methods using positioning or alignment devices for aligning or centering, e.g. pins
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2260/00—Function
    • F05B2260/82—Forecasts
    • F05B2260/821—Parameter estimation or prediction
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05B—INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
    • F05B2260/00—Function
    • F05B2260/96—Preventing, counteracting or reducing vibration or noise
    • F05B2260/966—Preventing, counteracting or reducing vibration or noise by correcting static or dynamic imbalance
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
    • Y02P70/50—Manufacturing or production processes characterised by the final manufactured product

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  • the invention belongs to the calculation method of rotor assembly axis deflection, and can be applied to the process of axis prediction, assembly phase optimization, and assembly guidance in the assembly process of important components such as aero engine high-pressure compressor rotor, high-pressure turbine disc, and low-pressure rotor assembly.
  • the measurement of rotor assembly axis skew is an important step in the optimization of assembly phase prediction.
  • the fitting plane method is a method of performing least square fitting based on measured rotor end-face runout data, and calculating the assembly stacking skew by fitting the plane equation.
  • This processing algorithm program is simple and can grasp the two joint surfaces as a whole. Topographical features, but for rotor joints with "double highs" or irregular topography, the error between the fitting plane and the source data is large, and the accuracy of the predicted axis deviation is difficult to guarantee; the actual center of rotation method It is the axial skew prediction method adopted by Axiam.
  • the essence is to measure the actual surface rotation axis generated after assembly by measuring the morphological data of the end faces of the disks at various levels, and adjust and optimize the assembly phase based on this axis.
  • This method is mainly used in foreign countries.
  • the key technology has not yet been introduced in China and has high prediction accuracy.
  • the phenomenon of out-of-tolerance parts is common.
  • the tilting process is difficult to adapt to the production and assembly process of China's aero engine rotor.
  • the invention is based on the measurement of the end-face runout of the flange joint surface before the rotor is assembled, and does not consider the normal elastic deformation, and proposes a calculation method for the axis deviation after assembly. It is of great practical significance to predict the skew of the axis of the disc, and then further optimize and adjust the assembly phase.
  • the invention proposes a calculation method for calculating the assembly skew between different levels based on the measured runout data of each single-stage disk of the rotor part in combination with engineering practice.
  • the core of this method is to find the three initial contact points of the two-stage disc under rigid conditions, and determine the deflection amount of the upper-stage disc from the next-stage disc through these three points.
  • the surface topography of the part has the feature of "macro continuity"-that is, although the measured bounce values of adjacent measuring points are discrete, the measuring points within a small range fluctuate. Smaller, continuous features on a larger scale—thus the three points found can characterize the location of the actual initial contact point under rigid contact.
  • the roundness tester is firstly used to measure the end-face runout of the flange joint surfaces of the disks at each level, and then the end-hop data of each adjacent two-level disk is used as the input parameter.
  • two adjacent levels are obtained.
  • Relative skew matrix of disks multiply the skew matrix of each adjacent two-stage disks to get the total skew matrix reflecting the coaxiality of the assembly; it should be noted that adjusting different assembly phases will result in different skews A skewed matrix, but the assembly phase of two adjacent discs is limited by the number of bolt holes and positioning holes.
  • the optimal assembly phase can be sought before assembly, greatly reducing the number of repeated disassembly and assembly, and improving the qualification rate of one assembly.
  • Figure 1 is a schematic diagram of the impact of end-face runout on assembly skew.
  • FIG. 2 is a schematic diagram of a homogeneous coordinate transformation matrix.
  • a method for calculating the skew of the rotor assembly axis based on end-hop measurements the steps are as follows:
  • Step A The upper and lower centers of the rotor A and the rotor B are A O2 and A O1 , and the upper and lower centers of the rotor B are B O2 and B O1 respectively .
  • the mating surfaces of the two rotors are the upper end A of the rotor A. 2 and the lower end surface B 1 of the rotor B.
  • the two contact surfaces A 2 and B 1 are characterized by a matrix.
  • the data is in the form of a circle, which is A ( ⁇ , z) and B ( ⁇ , z), and the beating value z of a point at ⁇ is represented by polar coordinates.
  • the position of the center of the circle O in the global coordinate system is O (0,0), the rotor radius R is known; With the upper end surface A 2 of the rotor A as the base surface, find the lower end surface B 1 of the rotor B when it is in contact with A 2 at three points Three points of, which determine the plane after contact;
  • Step B Calculate the first contact point: the lower rotor A is fixed, and the upper rotor B is gradually translated and approached, that is, the lower end B 1 of the rotor B is translated to approach the upper end A 2 of the rotor A, assuming that the translation distance is d.
  • the first contact point c 1 then c 1 is the two points closest to the actual distance between the two ends. It should be noted here that c 1 is the first two points of contact, and may not be one of the final three points of contact;
  • the input is the jump data of the upper end A 2 and the lower end B 1 , A ( ⁇ , z) and B ( ⁇ , z ′).
  • the point corresponding to the end jump and the maximum value is the first contact point, that is, the ⁇ corresponding to z''maximum z '' max is the first contact point c 1 ( ⁇ );
  • Step C Calculate the second contact point: Rotate the lower end face B 1 of the rotor B around the point c 1 to continue to approach the upper end face A 2 of the rotor A, and the rotation direction is the direction of the line c 1 and the center O of the lower end face B 1 to rotate. After a certain angle ⁇ 1 , a second contact point c 2 is generated;
  • This stage is a single-point rotating contact process.
  • the inputs are: the maximum distance z '' max , the first contact point c 1 ( ⁇ ), the end jump data of the upper end A 2 and the lower end B 1 , A ( ⁇ , z) And B ( ⁇ , z ′).
  • the rotation direction is the connection direction between the contact point c 1 ( ⁇ ) and the circle center O ′ of the lower end surface B 1 , and the rotation is directed toward the circle center O ′.
  • a ( ⁇ , z) and B ( ⁇ , z ′) can calculate the The angle ⁇ i corresponding to the remaining contact distance is projected in the rotation direction to find the minimum value of ⁇ i The corresponding point, which is the second contact point c 2 ( ⁇ 2 );
  • Step D Calculate the third contact point: the lower end surface B 1 is about the perpendicular bisector of the line connecting the point c 1 and the point c 2 , and rotates toward the center O, and continues to approach the upper end A 2 , and rotates a certain angle ⁇ 2 to produce The third contact point c 3 ;
  • This stage is the process of wire rotation contact.
  • the input is: ⁇ i minimum Second contact point c 2 ( ⁇ 2 ), maximum distance z '' max , first contact point c 1 ( ⁇ ), upper end face A 2 and lower end face B 1 end jump data A ( ⁇ , z), B ( ⁇ , z ′).
  • the rotation direction can be determined as the line of the contact points c 1 ( ⁇ ) and c 2 ( ⁇ 2 ) perpendicular to the direction of the bisector. Rotation Toward the center O ".
  • the minimum value of ⁇ i For the second contact point c 2 ( ⁇ 2 ), the angle ⁇ i2 corresponding to the projection of the remaining contact distance of each group in the rotation direction can be calculated to find the minimum value of ⁇ i2 The corresponding point, which is the third contact point c 3 ( ⁇ 3 );
  • Step E Triangle determination: It is determined whether the three contact points meet the triangle determination criterion according to the obtained three points c 1 , c 2 , and c 3 . If so, the triangle determination process ends and three contact points are obtained. If not, proceed to the next step;
  • the triangle judgment criterion explains: The validity of the three points can be determined according to whether the triangle formed by the three points in the local coordinate system contains a circle center. If the circle center is within the triangle, the triangle must be an acute triangle; the significance of the triangle judgment criterion is to avoid Due to the high (or low) concentration of the measurement points in a small area, the three contact points are very close. This situation does not meet the contact stability under the rigid assumption. In actual contact, the three points The point in the middle of the structural arc (also the point corresponding to the obtuse angle) is out of contact, which is not in line with the actual situation, and it also indicates that the selected assembly phase is inappropriate;
  • Calculation method It can be judged according to the internal angle of the three-point connecting triangle of c 1 , c 2 , and c 3 : If the three internal angles are all acute angles, then O "is within the triangle, the three points meet the actual situation, and the coordinates of the three contact points are sufficient. OK; otherwise, O "is not in the triangle, you need to discard the middle point of the inferior arc formed by the three points, re-find the contact point, and perform step F;
  • Step F This stage is the stage of re-finding the third contact point.
  • the input amount at this stage is: the first contact point c 1 ( ⁇ ), the second contact point c 2 ( ⁇ 2 ), and the third contact point c 3 ( ⁇ 3 ).
  • the circle center O is not in the triangle formed by the three points c 1 , c 2 , and c 3 , the upper end piece B cannot be stabilized and will continue to tilt to find another point. At the same time, there will be one point among the three contact points.
  • disengagement i.e., three out of contact intermediate point
  • Step G After the three contact points are determined, the axis deflection is the vector multiplication of the two axis tilts of the rotor B when the second and third contact points are calculated in steps C and D.
  • the skew matrix in step E when calculating the overall axis skew, the skew matrix in step E must be substituted into the multiplication each time; as shown in Figure 2, the homogeneous coordinate transformation matrix of the measurement surface can be expressed as:
  • u and v are translations
  • z is the cross-sectional height
  • ⁇ and ⁇ are equivalent to A and B in the plane normal vector (-A, -B, 1).
  • the -A component is about the y axis. corner, -B angle about the x axis component of the negative;
  • formula (6) calculated in step C, D, F in each skew axis coordinate transformation matrix H i indicates, should the entire process results n coordinate transformations, then these coordinate transformation matrices are multiplied according to the transformation order corresponding to the execution steps to obtain the overall axis skew transformation matrix:
  • the overall axis skew transformation matrix H can be converted into two parameters of the axis deviation direction and the magnitude of the skew according to formula (6), which is the final result.

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Abstract

一种基于端跳测量计算转子装配轴线偏斜的方法，包括三接触点的计算、三角形判定准则和偏斜矩阵齐次坐标变换算法三部分；三点接触计算主要包括初始测量数据的表征、接触点的确定、偏转方向的确定及表征方法；三角形判定准则用于判定所得三点是否符合实际，详细描述了判定原则、计算方法与舍弃点的确定过程；偏斜矩阵齐次坐标变换算法包括倾角方向及大小的矩阵表征，最终装配结果整体轴线偏斜的计算方法与矩阵表示方法等。本方法基于生产实际中的实测端跳数据，实现了在装配前对轴线偏斜的预测，提高了装配后的转子同轴度，同时大大提高了一次装配通过率，对航空发动机转子件装配过程中的轴线预测、装配相位调整与优化有着重要的现实指导意义。

Description

一种基于端跳测量计算转子装配轴线偏斜的方法 技术领域
本发明属于转子装配轴线偏斜计算方法，可应用于如航空发动机高压压气机转子、高压涡轮盘、低压转子组件等重要零组件装配过程中的轴线预测、装配相位优化、装配指导过程之中。
背景技术
在装备制造过程中，装配作为一个十分重要的环节，对产品的性能及可靠性有着直接影响。而对于航空发动机转子组件而言，保证其装配后的同轴度满足要求非常重要，为了降低由于“试错”装配产生的时间和人力成本，提高装配后的同轴度，装配相位的预测及优化至关重要，而要提高一次装配通过率、降低反复拆装中产生的零件磨损及时间成本，就需要结合工厂实际装配流程，寻求各级盘在装配前端面的形貌与装配后所产生的轴线偏斜之间的关系。
转子装配轴线偏斜的测定是应用于装配相位预测优化中的重要步骤。拟合平面法是一种基于所测转子端面跳动数据进行最小二乘拟合，通过拟合平面方程计算装配堆叠偏斜的方法，这种处理算法程序简单，能够从整体上把握两结合面的形貌特征，但对于具有“双高点”或不规则形貌的转子结合面，其拟合平面与源数据间误差较大，所预测轴线偏斜的精度也难以保证；实际回转中心线法是Axiam公司所采用的轴线偏斜预测方法，其本质是通过对各级盘端面形貌跳动数据的测量，探求其装配后产生的实际回转轴线，并基于此轴线进行装配相位的调整与优化，此方法主要应用于国外，关键技术尚未引进国内，具有较高的预测准确度，但受我国高端零部件制造水平限制，零件超差现象普遍存在，本方法应用过程中没有圆度仪基本的调心调倾过程，较难适应于我国航空发动机转子的生产装配过程中。
本发明是基于对转子装配前的法兰盘结合面端面跳动的测量，不考虑法向弹性变形，提出了一种装配后轴线偏斜的计算方法，该方法可以实现对某一装配相位下各级盘的轴线偏斜预测，而后可以进一步实现装配相位的优化调整，具有重要的现实意义。
发明内容
为满足航空发动机转子件装配过程中的同轴度要求，本发明结合工程实践，基于转子件各单级盘实测跳动数据，提出了一种计算各级间装配偏斜的计算方法。
本方法的计算原理如下：
在刚性假设下，考虑两级盘装配中某一确定的安装相位，计算端面跳动与偏斜量的关系。由于不共线的三点确定一个平面，本方法的核心在于找到刚性条件下两级盘的三个初始接触点，通过这三点确定上一级盘相对下一级盘的偏斜量。需要指出的是，由于机械加工过程使得零件的表面形貌具有“宏观连续性”的特征——即虽然相邻测点测得的跳动值是离散的，但在小范围内的各测点波动较小，在较大尺度上来看是连续的的特征——因而所找出的三个点可以表征刚性接触下的实际初始接触点的位置。
本方法需首先采用圆度仪对各级盘法兰结合面的端面跳动进行测量，而后以每相邻两级盘的端跳数据为输入参数，通过本算法的计算，得出相邻两级盘的相对偏斜矩阵；将每相邻两级盘的偏斜矩阵叠乘，即可得到反映装配体同轴度的总偏斜矩阵；需要指出的是调整不同的装配相位会得到不同的偏斜矩阵，但相邻两级盘的装配相位受螺栓孔、定位孔等的限制是有限的个数。以运用本方法计算出的总偏斜矩阵作为评定参数，可在装配前寻求最优装配相位，大大降低反复拆装次数，提高一次装配合格率。
附图说明
图1是端面跳动对装配偏斜影响示意图。
图1中：转子A的上、下端面分别为A O2、A O1；转子B上下端面分别为B O2、B O1；装配过程中由于两接触面A O2、B O1表面不平所引起的转子B相对转子A的轴线偏斜如图所示；
图2是齐次坐标变换矩阵示意图。
具体实施方式
以下结合附图和技术方案，进一步说明本方法的具体计算方式。
实施例
一种基于端跳测量计算转子装配轴线偏斜的方法，步骤如下：
步骤A：相邻两级盘，转子A、转子B的上下面中心分别为A O2、A O1，转子B上下面中心分别为：B O2、B O1，两转子配合面为转子A上端面A 2及转子B下端面B 1。两接触面A 2、B 1用矩阵表征，数据的形式是一个圆环，分别为A(α,z)及B(α,z)，用极坐标表示法表征α处某点的跳动值z；圆心O在全局坐标系中的位置为O(0,0),已知转子半径R；以转子A上端面A 2为基面，找到转子B下端面B 1在与A 2三点接触时的三点，此三点可确定接触后的平面；
步骤B：计算第一接触点：下端转子A固定不动，上端转子B逐渐向下平移逼近，即转子B的下端面B 1平移逼近转子A的上端面A 2，假设平移距离为d后产生第一个接触点c 1，则c 1即为两端面实际距离最近的两点。此处需指出c 1为最先接触的两点，未必是最终的三个接触点之一；
此阶段为平移接触过程，输入为上端面A 2及下端面B 1的端跳数据，A(α,z)及B(α,z′)。找出相距最近的两点，即第一个接触点c 1，在此对两组端跳数据求和， 获得求和后的数据矩阵SUM(α,z‘’)，找出数据矩阵SUM(α,z‘’)端跳和最大值对应的点即为第一个接触点，即z‘’最大值z‘’ max对应的α，即为第一个接触点c 1(α)；
计算式：z‘’＝z+z′；            (1)
步骤C：计算第二接触点：使转子B的下端面B 1绕点c 1旋转继续与转子A的上端面A 2靠近，旋转方向为c 1与下端面B 1圆心O连线方向，旋转一定角度θ 1后，产生第二个接触点c 2；
此阶段为单点旋转接触过程，输入为：最大距离z‘’ max、第一个接触点c 1(α)、上端面A 2及下端面B 1的端跳数据，A(α,z)及B(α,z′)。根据第一阶段得出的接触点c 1(α)，可确定旋转方向为接触点c 1(α)与下端面B 1圆心O′的连线方向，旋转朝向圆心O′。根据第一阶段得出的最大距离z‘’ max及上端面A 2及下端面B 1的端跳数据，A(α,z)及B(α,z′)可以计算出每一组点的接触剩余距离在旋转方向上投影所对应的角度θ i，找出θ i最小值
Figure PCTCN2018105195-appb-000001
所对应的点，此点即为第二个接触点c 2(α 2)；
计算式：d＝z‘’ max-z-z′；        (2)
Figure PCTCN2018105195-appb-000002
步骤D：计算第三接触点：下端面B 1绕点c 1与点c 2连线的垂直平分线方向，朝向圆心O方向旋转，继续向上端面A 2靠近，旋转一定角度θ 2后，产生第三个接触点c 3；
此阶段为连线旋转接触过程，输入为：θ i最小值
Figure PCTCN2018105195-appb-000003
第二个接触点c 2(α 2)、最大距离z‘’ max、第一个接触点c 1(α)、上端面A 2及下端面B 1端跳数据A(α,z)、B(α,z′)。根据第二阶段得出的接触点c 1(α)、c 2(α 2)，可确定旋转方向为接触点c 1(α)与c 2(α 2)的连线垂直平分线方向，旋转朝向圆心O"。根据第一阶段得出的最大距离z‘’ max、上端面A 2及下端面B 1的端跳数据，A(α,z)及B(α,z′)、第二阶段得出的θ i最小值
Figure PCTCN2018105195-appb-000004
第二个接触点c 2(α 2)，可以计算出每一组点的接 触剩余距离在旋转方向上投影所对应的角度θ i2，找出θ i2最小值
Figure PCTCN2018105195-appb-000005
所对应的点，此点即为第三个接触点c 3(α 3)；
计算式：d 2＝z‘’ max-z-z′-d×l i/l′；         (4)
Figure PCTCN2018105195-appb-000006
步骤E：三角形判定：根据获得的三点c 1、c 2、c 3判定接触三点是否符合三角判定准则。若符合，三角判定程序结束，获得三接触点。若不符合，则进入下一步骤；
三角形判定准则说明：可根据局部坐标系中的三点所构成的三角形是否包含圆心来判定三点的有效性，若圆心在三角形内，则此三角形必为锐角三角形；三角形判定准则的意义在于避免由于测点在小区域上的集中偏高(或偏低)所导致的三个接触点非常靠近的情况，这种情况不符合刚性假设下的接触稳定性，在实际接触中会使得三点所构劣弧中间的点(同时也是钝角所对应的点)脱离接触，不符合实际情况，同时也说明所选的装配相位不合适；
计算方法：可根据c 1、c 2、c 3三点连线三角形内角来判断：若三个内角均为锐角，则O"在三角形内，三点满足实际情况，三个接触点坐标即可确定；否则，O"不在三角形内，需要舍弃三点所构成的劣弧中间的点，重新寻找接触点，执行步骤F；
步骤F：此阶段为重新寻找第三接触点阶段，此阶段输入量为：第一个接触点c 1(α)、第二个接触点c 2(α 2)、第三个接触点c 3(α 3)。基于实际情况出发，当圆心O"不在三点c 1、c 2、c 3所构三角形内时，上端件B无法稳定，会继续倾斜寻找另一个点，同时三个接触点中会有一个点脱离接触，即三点中间的点脱离接触，可确定旋转方向为另外两点的连线垂直平分线方向，旋转朝向圆心O"，重新执 行步骤D，以未脱离接触两点作为新的c 1(α)、c 2(α 2)接触点进行计算，而后执行步骤E进行三角形判定，直至满足三角形判定准则得出最终接触点。
步骤G：三个接触点确定后，轴线偏斜即为步骤C及步骤D计算第二、第三接触点时转子B的两次轴线倾斜的矢量叠乘；另外若在执行步骤E三角判定时反复执行了步骤F，则在计算整体轴线偏斜时需将每次执行步骤E中的偏斜矩阵都代入叠乘；如图2所示，测量面的齐次坐标变换矩阵可表示为：
Figure PCTCN2018105195-appb-000007
式中，u、v为平移量，z为截面高度，β、α相当于平面法向量(-A,-B,1)中的A、B，从数值上看，-A分量为绕y轴转角，-B分量为绕x轴转角的负值；按式(6)所示计算方法将步骤C、D、F中的每次轴线偏斜用坐标变换矩阵H i表示，如若整个过程产生了n次坐标变换，则将这些坐标变换矩阵按执行步骤对应的变换顺序叠乘即可得到整体轴线偏斜变换矩阵：
Figure PCTCN2018105195-appb-000008
整体轴线偏斜变换矩阵H可按式(6)转化为轴线偏移方向及偏斜大小两个参数，即为最终结果。

Claims (1)

  1. 一种基于端跳测量计算转子装配轴线偏斜的方法，其特征在于，步骤如下：
    步骤A：相邻两级盘，转子A的上下面中心分别为A O2、A O1，转子B上下面中心分别为：B O2、B O1，两转子配合面为转子A上端面A 2及转子B下端面B 1；两接触面A 2、B 1用矩阵表征，数据的形式是一个圆环，分别为A(α,z)及B(α,z)，用极坐标表示法表征α处某点的跳动值z；圆心O在全局坐标系中的位置为O(0,0)，已知转子半径R；以转子A上端面A 2为基面，找到转子B下端面B 1在与A 2三点接触时的三点，此三点确定接触后的平面；
    步骤B：计算第一接触点：下端转子A固定不动，上端转子B逐渐向下平移逼近，即转子B的下端面B 1平移逼近转子A的上端面A 2，假设平移距离为d后产生第一个接触点c 1，则c 1即为两端面实际距离最近的两点；c 1为最先接触的两点，未必是最终的三个接触点之一；
    此阶段为平移接触过程，输入为上端面A 2及下端面B 1的端跳数据，A(α,z)及B(α,z′)；找出相距最近的两点，即第一个接触点c 1，在此对两组端跳数据求和，获得求和后的数据矩阵SUM(α,z‘’)，找出数据矩阵SUM(α,z‘’)端跳和最大值对应的点即为第一个接触点，即z‘’最大值z‘’ max对应的α，即为第一个接触点c 1(α)；
    计算式：z‘’＝z+z′；   (1)
    步骤C：计算第二接触点：使转子B的下端面B 1绕点c 1旋转继续与转子A的上端面A 2靠近，旋转方向为c 1与下端面B 1圆心O连线方向，旋转一定角度θ 1后，产生第二个接触点c 2；
    此阶段为单点旋转接触过程，输入为：最大距离z‘’ max、第一个接触点c 1(α)、上端面A 2及下端面B 1的端跳数据，A(α,z)及B(α,z′)；根据第一阶段得出的接触点c 1(α)，确定旋转方向为接触点c 1(α)与下端面B 1圆心O′的连线方向，旋转朝向圆心O′；根据第一阶段得出的最大距离z‘’ max及上端面A 2及下端面B 1的端跳数 据，A(α,z)及B(α,z′)计算出每一组点的接触剩余距离在旋转方向上投影所对应的角度θ i，找出θ i最小值
    Figure PCTCN2018105195-appb-100001
    所对应的点，此点即为第二个接触点c 2(α 2)；
    计算式：d＝z‘’ max-z-z′；  (2)
    Figure PCTCN2018105195-appb-100002
    步骤D：计算第三接触点：下端面B 1绕点c 1与点c 2连线的垂直平分线方向，朝向圆心O方向旋转，继续向上端面A 2靠近，旋转一定角度θ 2后，产生第三个接触点c 3；
    此阶段为连线旋转接触过程，输入为：θ i最小值
    Figure PCTCN2018105195-appb-100003
    第二个接触点c 2(α 2)、最大距离z‘’ max、第一个接触点c 1(α)、上端面A 2及下端面B 1端跳数据A(α,z)、B(α,z′)；根据第二阶段得出的接触点c 1(α)、c 2(α 2)，确定旋转方向为接触点c 1(α)与c 2(α 2)的连线垂直平分线方向，旋转朝向圆心O"；根据第一阶段得出的最大距离z‘’ max、上端面A 2及下端面B 1的端跳数据，A(α,z)及B(α,z′)、第二阶段得出的θ i最小值
    Figure PCTCN2018105195-appb-100004
    第二个接触点c 2(α 2)，计算出每一组点的接触剩余距离在旋转方向上投影所对应的角度θ i2，找出θ i2最小值
    Figure PCTCN2018105195-appb-100005
    所对应的点，此点即为第三个接触点c 3(α 3)；
    计算式：d 2＝z‘’ max-z-z′-d×l i/l′；   (4)
    Figure PCTCN2018105195-appb-100006
    步骤E：三角形判定：根据获得的三点c 1、c 2、c 3判定接触三点是否符合三角判定准则；若符合，三角判定程序结束，获得三接触点；若不符合，则进入下一步骤；
    三角形判定准则说明：根据局部坐标系中的三点所构成的三角形是否包含圆心来判定三点的有效性，若圆心在三角形内，则此三角形必为锐角三角形；
    计算方法：根据c 1、c 2、c 3三点连线三角形内角来判断：若三个内角均为锐角，则O"在三角形内，三点满足实际情况，三个接触点坐标即确定；否则，O"不在三角形内，需要舍弃三点所构成的劣弧中间的点，重新寻找接触点，执行步骤F；
    步骤F：此阶段为重新寻找第三接触点阶段，此阶段输入量为：第一个接触点c 1(α)、第二个接触点c 2(α 2)、第三个接触点c 3(α 3)；基于实际情况出发，当圆心O"不在三点c 1、c 2、c 3所构三角形内时，上端件B无法稳定，继续倾斜寻找另一个点，同时三个接触点中有一个点脱离接触，即三点中间的点脱离接触，确定旋转方向为另外两点的连线垂直平分线方向，旋转朝向圆心O"，重新执行步骤D，以未脱离接触两点作为新的c 1(α)、c 2(α 2)接触点进行计算，而后执行步骤E进行三角形判定，直至满足三角形判定准则得出最终接触点；
    步骤G：三个接触点确定后，轴线偏斜即为步骤C及步骤D计算第二、第三接触点时转子B的两次轴线倾斜的矢量叠乘；另外若在执行步骤E三角判定时反复执行步骤F，则在计算整体轴线偏斜时需将每次执行步骤E中的偏斜矩阵都代入叠乘；测量面的齐次坐标变换矩阵表示为：
    Figure PCTCN2018105195-appb-100007
    式中，u、v为平移量，z为截面高度，β、α相当于平面法向量(-A,-B,1)中的A、B，从数值上看，-A分量为绕y轴转角，-B分量为绕x轴转角的负值；按式(6)所示计算方法将步骤C、D、F中的每次轴线偏斜用坐标变换矩阵H i表示，如若整个过程产生n次坐标变换，则将这些坐标变换矩阵按执行步骤对应的变换顺序叠乘即可得到整体轴线偏斜变换矩阵：
    Figure PCTCN2018105195-appb-100008
    整体轴线偏斜变换矩阵H按式(6)转化为轴线偏移方向及偏斜大小两个参数， 即为最终结果。
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