WO2020211032A1 - 基于轴盘的转子六自由度运动测试及其运动参数解耦方法 - Google Patents

基于轴盘的转子六自由度运动测试及其运动参数解耦方法 Download PDF

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WO2020211032A1
WO2020211032A1 PCT/CN2019/083171 CN2019083171W WO2020211032A1 WO 2020211032 A1 WO2020211032 A1 WO 2020211032A1 CN 2019083171 W CN2019083171 W CN 2019083171W WO 2020211032 A1 WO2020211032 A1 WO 2020211032A1
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shaft
motion
rotor
vector
displacement sensor
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PCT/CN2019/083171
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English (en)
French (fr)
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董惠敏
张楚
王德伦
邱俊
王智
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大连理工大学
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Priority to PCT/CN2019/083171 priority Critical patent/WO2020211032A1/zh
Priority to US16/969,849 priority patent/US11181442B2/en
Publication of WO2020211032A1 publication Critical patent/WO2020211032A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G01M13/025—Test-benches with rotational drive means and loading means; Load or drive simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M1/00—Testing static or dynamic balance of machines or structures
    • G01M1/14—Determining imbalance
    • G01M1/16—Determining imbalance by oscillating or rotating the body to be tested
    • G01M1/24—Performing balancing on elastic shafts, e.g. for crankshafts

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  • the invention belongs to the technical field of rotor movement accuracy testing, and relates to a rotor six-degree-of-freedom movement test based on a shaft disk and a method for decoupling its movement parameters.
  • the real movement of the rotor is a key indicator to measure the quality of the transmission system movement and power transmission, which directly affects the precision characteristics of precision machine tools, instrument turntables, gear transmissions and other mechanical equipment.
  • the ideal movement of the rotor is a single-degree-of-freedom rotational movement, and the other five degrees of freedom are subject to rigid constraints.
  • the real movement of the rotor presents a six-degree-of-freedom spatial movement, which requires movement testing and six degrees of freedom.
  • the degree of freedom decoupling method evaluates the accuracy characteristics of the rotor movement.
  • Rotor movement test first used unidirectional measurement and bidirectional measurement method to test the radial movement of the rotor; then adopted the method of combining radial movement test and shaft system movement test, installed displacement sensors in three directions of the direct coordinate system,
  • the standard rod on the rotor can be tested to test the radial and shaft movement of the rotor; the movement of the rotor in the inclination angle direction can be tested by multiple cross-section displacement sensors; the above test methods can only test part of the rotor movement parameters (radial , Axial or inclination).
  • the American Lion Company adopted the double-standard ball five-point method, combined with the encoder to test the real movement of the rotor, which can realize the six-degree-of-freedom movement test of the rotor, but the processing of the double-standard ball is very difficult and the use conditions for testing the rotor movement are very harsh.
  • the axial test requires high rotor structure and space, and it is difficult to apply to all rotor motion tests.
  • Four displacement sensors measure the radial movement of the two sections of the standard rod, and one displacement sensor measures the axial movement. It is easy to test the six-degree-of-freedom movement of the rotor. However, this test solution takes up a lot of space and the axial displacement sensor is closed.
  • test surface of the displacement sensor is a cylindrical surface (aspherical surface)—that is, the position of the vertical foot from the measuring point of the rotor movement to the rotor axis always changes, and the six freedoms can be decoupled by assuming that the position of the vertical foot remains unchanged.
  • measurement principle error is introduced, which makes the decoupled motion parameters inaccurate and difficult to meet the motion test requirements of precision equipment.
  • the present invention proposes a six-degree-of-freedom motion test of the rotor based on a shaft disk and its motion parameter decoupling method.
  • Replace the double standard ball with the high-precision "shaft disk” test piece consolidate the shaft disk on the rotor, arrange three measuring points on the disc surface, two measuring points on the cylindrical surface of the standard shaft, and the installation angle on the shaft shoulder
  • the encoder tests the rotor movement.
  • the sensors at five measuring points are fixed on the displacement sensor tooling. Based on the principle of rigid body movement geometry, the rotor movement test plan is formulated.
  • the displacement sensor and angle encoder are used to discrete test data to decouple each rotor.
  • An instantaneous six-degree-of-freedom movement This solves the versatility of the six-degree-of-freedom motion test of the rotor and the precise decoupling of six-degree-of-freedom motion parameters, and provides motion test and six-degree-of-freedom decoupling methods for precision equipment accuracy evaluation, error compensation and fault diagnosis.
  • the six-degree-of-freedom motion test of the rotor based on the shaft disk and its motion parameter decoupling method include the following steps:
  • Step 1 Prepare a shaft disc and displacement sensor tooling.
  • the shaft disc is an integrated structure including a standard shaft, a disc and a shoulder.
  • the standard shaft is located between the disc and the shoulder, and the axis of the standard shaft is perpendicular to the disc surface , And concentric with the disc surface and the shaft shoulder;
  • the displacement sensor tooling includes sensor mounting holes and threaded holes for the installation and positioning of the displacement sensor; the flatness, cylindricity, perpendicularity, and position of the shaft disc and the displacement sensor
  • the tolerance requirement is one order of magnitude higher than the rotor movement accuracy;
  • Step 2 Arrange two radial displacement sensors A 1 , A 2 orthogonally on the cylindrical surface of the standard shaft, and arrange three axial displacement sensors A 3 , A 4 , A 5 evenly on the disc surface. All displacement sensors are fixed on the displacement sensor tooling; an angle encoder is installed at the shaft shoulder; the displacement sensor tooling ensures the accuracy of the displacement sensor's measuring position;
  • Step 3 Fix the non-measurement surface of the shaft disk on the rotor, and establish the fixed coordinate system S f ⁇ O f ; X f , Y f , Z f ⁇ of the displacement sensor tool and the motion coordinate system S m of the shaft disk ⁇ O m ; X m , Y m , Z m ⁇ , O f and O m are the displacement sensor tooling and the center of the shaft disk respectively, X f , Y f , Z f are respectively parallel to the radial and axial directions of the displacement sensor, O m -X m Y m coincides with the disc surface of the shaft disk, Z m coincides with the axis of the shaft disk, and the coordinate axes of S f and S m are parallel at the initial time;
  • Step 4 The translational degrees of freedom (x, y, z) in the three directions of the axis disk motion coordinate system S m relative to the fixed coordinate system S f and the rotational degrees of freedom in the three directions ( ⁇ x , ⁇ y , ⁇ z ) Describe the six-degree-of-freedom motion parameters of the rotor.
  • the transformation relationship between the position vectors r Pf and r Pm in the fixed coordinate system and the motion coordinate system is:
  • rom is the translation transformation matrix
  • rom (x,y,z) T
  • R fm is the rotation transformation matrix
  • c and s are the abbreviations of cos and sin;
  • Step 5 Express the position and measured value of the displacement sensor's end point as a vector, and establish the relationship model between the axis motion vector of the shaft disk and the test vector;
  • the measuring directions of radial displacement sensors A 1 and A 2 cross the standard axis at Q 1 , Q 2 points, and cross Q 1 , Q 2 to make the perpendicular to the standard axis axis, and cross at P 1 , P 2 , for any movement position of the shaft system j, establish the closed-loop vector equation of rigid body motion geometry:
  • r Ai is the position vector (known) of each sensor endpoint, Is the vector (measured) from the end point of each displacement sensor to the measured point on the standard axis or disk surface, Is the vector radius of points P 1 and P 2 in a fixed coordinate system, where Is the rotation transformation matrix, including three rotation motion parameters; Is a vector perpendicular to the dynamic coordinate system Z m ; Is the translation amount of the motion coordinate system relative to the fixed coordinate system, including three translation motion parameters; 18 undetermined parameters, 17 scalar equations, combined with the encoder to measure the rotation angle condition, decouple the rotor's six-degree-of-freedom motion parameters x, y, z, ⁇ x , ⁇ y , ⁇ z , and solve the rigid body through the rigid body motion transformation relationship Evaluate the movement characteristics of the rotor for any point or straight line movement track.
  • step 5 adopt another scheme to express the end position and measurement value of the displacement sensor in vector, and establish the relationship model between the axis motion vector of the shaft disk and the test vector;
  • the measuring directions of radial displacement sensors A 1 and A 2 cross the standard axis at Q 1 , Q 2 points, and cross Q 1 , Q 2 to make the perpendicular to the standard axis axis, and cross at P 1 , P 2 , for any movement position of the shaft system j, establish the closed-loop vector equation of rigid body motion geometry:
  • r Ai is the position vector (known) of each sensor endpoint, Is the vector (measured) from the end point of each displacement sensor to the measured point on the standard axis or disk surface, Is the vector radius of points P 1 , P 2 , O m in a fixed coordinate system, Is the vector connecting Pi or O m and Q i , sharing 24 undetermined parameters, 24 scalar equations, solving the direction vector of axis movement
  • the direction vector of the rotor axis can be obtained without the need of an encoder to measure the rotation angle, including five motion parameters x, y, z, ⁇ x , ⁇ y , combined with the rotation angle ⁇ z measured by the angle encoder and the rigid body motion transformation relationship to solve
  • the motion trajectory of any point or straight line of a rigid body is used to evaluate the motion characteristics of the rotor.
  • the shaft disk is used to test the rotor movement, which facilitates the arrangement of displacement sensors and reduces the space occupied by the movement test. Based on the rigid body movement geometry principle, the problem of precise decoupling of the rotor six degrees of freedom movement parameters is solved.
  • Fig. 1 is a schematic diagram of a shaft disk in a specific embodiment of the present invention.
  • Fig. 2 is a schematic diagram of a displacement sensor tooling in a specific embodiment of the present invention.
  • Fig. 3 is a schematic diagram of the arrangement of measuring points for the movement of the shaft disk in a specific embodiment of the present invention.
  • Fig. 4 is the definition of the rotor motion test coordinate system and the closed-loop vector diagram in a specific embodiment of the present invention.
  • Fig. 5 is a decoupling curve diagram in a specific embodiment of the present invention.
  • Figure 6 is a schematic diagram of the rotor motion test structure of the present invention.
  • the goal of this implementation case is to test the six-degree-of-freedom motion of the rotor and decouple the six-degree-of-freedom motion parameters through the shaft disk, displacement sensor and angle encoder.
  • Step 1 Prepare a shaft disk and displacement sensor tooling, as shown in Figure 1 and Figure 2, which meets the parameters in the rotor motion test plan in Table 1.
  • the shaft disk is an integrated structure including a standard shaft, a disc and a shaft shoulder.
  • the standard shaft is located between the disc and the shaft shoulder.
  • the axis of the standard shaft is perpendicular to the disc surface and concentric with the disc surface and the shaft shoulder;
  • the displacement sensor tooling includes sensor mounting holes and threaded holes for the installation of the displacement sensor And positioning; the accuracy of the flatness, cylindricity, perpendicularity, and position of the shaft plate and displacement sensor is one order of magnitude higher than the accuracy of the rotor movement.
  • Step 2 Arrange two radial displacement sensors A 1 , A 2 orthogonally on the cylindrical surface of the standard shaft, and arrange three axial displacement sensors A 3 , A 4 , A 5 evenly on the disc surface. All displacement sensors are fixed on the displacement sensor tooling; an angle encoder is installed at the shaft shoulder; the displacement sensor tooling is used to ensure the accuracy of the displacement sensor measurement position; the test plan is shown in Figure 3.
  • Step 3 Fix the non-measurement surface of the shaft disk on the rotor, and establish the fixed coordinate system S f ⁇ O f ; X f , Y f , Z f ⁇ and the movement of the shaft disk for the displacement sensor tooling (frame)
  • the coordinate system S m ⁇ O m ; X m , Y m , Z m ⁇ , O and O 1 are the centers of the displacement sensor tooling and the shaft disk respectively, and X, Y, and Z are respectively parallel to the radial and axial directions of the displacement sensor, O 1 -X 1 Y 1 coincides with the disc surface of the shaft disk, Z 1 coincides with the axis of the shaft disk, and the coordinate axes of the initial time S and S 1 are parallel.
  • the coordinate system definition is shown in Fig. 4.
  • Step 4 The translational degrees of freedom (x, y, z) in the three directions of the axis disk motion coordinate system S m relative to the fixed coordinate system S f and the rotational degrees of freedom in the three directions ( ⁇ x , ⁇ y , ⁇ z ) Describes the six-degree-of-freedom motion parameters of the rotor.
  • Step 5 Express the end position and measured value of the displacement sensor as a vector.

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  • General Physics & Mathematics (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)
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Abstract

一种基于轴盘的转子六自由度运动测试及其运动参数解耦方法，该方法先制备一个高精度的轴盘测试件（7）和位移传感器工装（6）；将轴盘测试件（7）固结在转子上；在轴盘测试件（7）的圆盘面（1）上布置三个测点(测轴向运动)，标准轴圆柱面（2）上布置两个测点(测径向运动)，轴肩（3）处布置角度编码器（8）(测回转运动)，通过工装保证位移传感器（4）测量位置的准确性；建立固定坐标系与轴盘测试件（7）的动坐标系，将位移传感器（4）和角度编码器（8）的测量值以矢量表示，建立轴盘测试件（7）的轴线六自由度运动矢量与测试矢量的关系模型；以位移传感器（4）和角度编码器（8）的离散测量数据为已知量，求解转子/轴盘测试件（7）轴线的六自由度运动。应用该方法可解耦转子每个瞬时的六自由度运动。

Description

基于轴盘的转子六自由度运动测试及其运动参数解耦方法 技术领域
本发明属于转子运动精度测试技术领域，涉及一种基于轴盘的转子六自由度运动测试及其运动参数解耦方法。
背景技术
转子真实运动是衡量传动系统运动和动力传递质量的关键指标，直接影响精密机床、仪器转台、齿轮传动装置等机械设备的精度特性。转子的理想运动为单自由度的回转运动，其它五个自由度受刚性约束，然而由于各零件的制造误差和弹性变形，转子的真实运动呈现六自由度的空间运动，需要通过运动测试和六自由度解耦方法评价转子运动的精度特性。早在上世纪70年代，国际机械生产技术研究协会发表了“关于回转轴性能和误差运动测定”的统一文件，对回转轴线等术语进行了统一的定义，推动了转子运动测试的研究。现今，转子运动测试广泛应用于精密装备的精度评价、误差补偿和故障诊断当中，随着机械装备的精度需求不断提高，转子六自由度运动测试及其运动参数精确解耦问题日益凸显，已经成为转子运动特性评价、补偿和故障诊断的主要问题。
转子运动测试最早采用单向测量和双向测量方法测试转子的径向运动；随后采用径向运动测试和轴系运动测试相结合的方法，在直接坐标系三个方向安装位移传感器，对固结在转子上的标准棒进行检测，可测试转子的径向和轴系运动；转子倾角方向的运动可通过多个截面布置位移传感器进行测试；以上的测试方法仅能测试转子的部分运动参数(径向、轴向或倾角)。1992年美国雄狮公司采用双标准球五点法，结合编码器测试转子的真实运动，可实现转子六自由度运动测试，但双标准球的加工难度很大且测试转子运动的使用条件十分苛刻，尤其轴向测试对转子结构和空间要求很高，难以适用于所有转子的运动测试当中。通过四个位移传感器测量标准棒两个截面径向运动、一个位移传感器测量轴向运动，可简单地测试转子的六自由度运动，但该种测试方案占用空间较大、轴向位移传感 器在闭式传动链中难以布置，并且由于位移传感器测试表面为圆柱面(非球面)—即随转子运动测点到转子轴线的垂足位置始终变化，通过假设该垂足位置不变可解耦六自由度运动参数，但引入了测量原理误差，使解耦的运动参数不准确，难以满足精密设备的运动测试要求。
发明内容
为了克服现有技术中存在的转子六自由度运动测试的通用性以及六自由度运动参数精确解耦问题，本发明提出了基于轴盘的转子六自由度运动测试及其运动参数解耦方法，以高精度“轴盘”测试件代替双标准球，将轴盘固结在转子上，通过圆盘面上布置三个测点、标准轴圆柱面上布置两个测点、轴肩上安装角度编码器对转子运动进行测试，五个测点的传感器固定于位移传感器工装上，并基于刚体运动几何学原理，制定转子运动测试方案，通过位移传感器和角度编码器离散测试数据，解耦转子每个瞬时的六自由度运动。由此解决了转子六自由度运动测试的通用性以及六自由度运动参数的精确解耦问题，为精密装备精度评价、误差补偿和故障诊断提供运动测试和六自由度解耦方法。
本发明的具体技术方案为：
基于轴盘的转子六自由度运动测试及其运动参数解耦方法，包括步骤如下：
步骤1：制备一个轴盘和位移传感器工装，所述轴盘是包括标准轴、圆盘和轴肩的一体结构，标准轴位于圆盘和轴肩之间，标准轴的轴线垂直于圆盘面，并与圆盘面和轴肩同心；所述位移传感器工装包括传感器安装孔和螺纹孔，用于位移传感器的安装和定位；轴盘和位移传感器的平面度、圆柱度、垂直度、位置度公差要求高于转子运动精度一个数量级；
步骤2：在标准轴的圆柱面上正交布置两个径向位移传感器A 1、A 2，在圆盘面上均匀布置三个轴向位移传感器A 3、A 4、A 5，所述五个位移传感器皆固定于位移传感器工装上；在轴肩处安装角度编码器；通过位移传感器工装保证位移传感器测量位置的准确性；
步骤3：将轴盘的圆盘非测量面固结在转子上，建立位移传感器工装的固定坐标系S f{O f；X f,Y f,Z f}和轴盘的运动坐标系S m{O m；X m,Y m,Z m}，O f与O m分别为位移传感器工装和轴盘的中心，X f、Y f、Z f分别与径向和轴向位移传感器方向平行，O m-X mY m与轴盘的圆盘面重合，Z m与轴盘的轴线重合，初始时刻S f与S m的各坐标轴平行；
步骤4：以轴盘运动坐标系S m相对于固定坐标系S f的三个方向的平移自由度(x,y,z)和三个方向的旋转自由度(θ x,θ y,θ z)描述转子六自由度运动参数，转子上任意一点P，在固定坐标系和运动坐标系下的位置矢量r Pf和r Pm的变换关系为：
r Pf＝r om+r Pm＝r om+R fmr Pm       (1)
其中，r om为平移变换矩阵，r om＝(x,y,z) T，R fm为旋转变换矩阵，
Figure PCTCN2019083171-appb-000001
c和s为cos和sin的缩写；
步骤5：将位移传感器端点位置、测量值以矢量表示，建立轴盘的轴线运动矢量与测试矢量的关系模型；
径向位移传感器A 1、A 2测量方向交标准轴于Q 1、Q 2点，过Q 1、Q 2做标准轴轴线的垂线，交于P 1、P 2，对于轴系任意运动位置j，建立刚体运动几何学的闭环矢量方程：
Figure PCTCN2019083171-appb-000002
其中，r Ai为各传感器端点的位置矢量(已知)，
Figure PCTCN2019083171-appb-000003
为各位移传感器端点到标准轴或圆盘面被测点的矢量(被测量)，
Figure PCTCN2019083171-appb-000004
为P 1、P 2点在固定坐标系下的矢径，其中
Figure PCTCN2019083171-appb-000005
为旋转变换矩阵，包含三个旋转运动参数；
Figure PCTCN2019083171-appb-000006
为垂直于动坐标系Z m的矢量；
Figure PCTCN2019083171-appb-000007
为运动坐标系相对于固定坐标系的平移量，包含三 个平移运动参数；共有
Figure PCTCN2019083171-appb-000008
18个待定参数，17个标量方程，结合编码器测得回转角条件解耦转子的六自由度运动参数x,y,z,θ x,θ y,θ z，通过刚体运动变换关系，求解刚体任一点或直线的运动轨迹，评价转子运动特性。
上述步骤5：采用另一种方案将位移传感器端点位置、测量值以矢量表示，建立轴盘的轴线运动矢量与测试矢量的关系模型；
径向位移传感器A 1、A 2测量方向交标准轴于Q 1、Q 2点，过Q 1、Q 2做标准轴轴线的垂线，交于P 1、P 2，对于轴系任意运动位置j，建立刚体运动几何学的闭环矢量方程：
Figure PCTCN2019083171-appb-000009
其中，r Ai为各传感器端点的位置矢量(已知)，
Figure PCTCN2019083171-appb-000010
为各位移传感器端点到标准轴或圆盘面被测点的矢量(被测量)，
Figure PCTCN2019083171-appb-000011
为P 1、P 2、O m点在固定坐标系下的矢径，
Figure PCTCN2019083171-appb-000012
为P i或O m与Q i连线的矢量，共有
Figure PCTCN2019083171-appb-000013
24个待定参数，24个标量方程，求解轴线运动的方向矢量
Figure PCTCN2019083171-appb-000014
无需编码器测回转角即可得到转子轴线的方向矢量，包含五个运动参数x,y,z,θ x,θ y，结合角度编码器测得的回转角θ z以及刚体运动变换关系，求解刚体任一点或直线的运动轨迹，评价转子运动特性。
本发明的有益效果为，采用轴盘对转子运动进行测试，便于布置位移传感器以及减少运动测试占用的空间，并基于刚体运动几何学原理，解决了转子六自由度运动参数的精确解耦问题。
附图说明
图1是本发明具体实施例中的轴盘示意图。
图2是本发明具体实施例中的位移传感器工装示意图。
图3是本发明具体实施例中的轴盘运动测点布置示意图。
图4是本发明具体实施例中的转子运动测试坐标系定义和闭环矢量图。
图5是本发明具体实施例中的解耦曲线图。(a)平移运动参数与回转角的关系图(b)角摆运动参数与回转角的关系图。
图6是本发明的转子运动测试结构示意图。
图中：1圆盘面；2标准轴圆柱面；3轴肩；4位移传感器；5夹紧螺钉；6传感器工装；7轴盘测试件；8角度编码器。
具体实施方式
为了更好的说明本发明的技术方案，下面结合附图和具体实施案例，对本发明做进一步说明。
本实施案例的目标是通过轴盘、位移传感器和角度编码器测试转子的六自由度运动并解耦六自由度运动参数。
转子运动测试的相关参数示意图如图3所示，参数值见表1。
表1 转子运动测试方案中的参数
d D l θ 1 θ 2 θ 3
33mm 114mm 29mm 30° 120° 120°
基于轴盘的转子六自由度运动测试及其运动参数解耦方法，具体实现步骤如下：
步骤1：制备一个轴盘和位移传感器工装，如图1和图2所示，满足表1转子运动测试方案中的参数，所述轴盘是包括标准轴、圆盘和轴肩的一体结构，标准轴位于圆盘和轴肩之间，标准轴的轴线垂直于圆盘面，并与圆盘面和轴肩同心；所述位移传感器工装包括传感器安装孔和螺纹孔，用于位移传感器的安装和定位；轴盘和位移传感器的平面度、圆柱度、垂直度、位置度的精度高于转子运动精度一个数量级。
步骤2：在标准轴的圆柱面上正交布置两个径向位移传感器A 1、A 2，在圆盘面上均匀布置三个轴向位移传感器A 3、A 4、A 5，所述五个位移传感器皆固定于位 移传感器工装上；在轴肩处安装角度编码器；通过位移传感器工装保证位移传感器测量位置的准确性；测试方案如图3所示。
步骤3：将轴盘的圆盘非测量面固结在转子上，建立位移传感器工装(机架)的固定坐标系S f{O f；X f,Y f,Z f}和轴盘的运动坐标系S m{O m；X m,Y m,Z m}，O与O 1分别为位移传感器工装和轴盘的中心，X、Y、Z分别与径向和轴向位移传感器方向平行，O 1-X 1Y 1与轴盘的圆盘面重合，Z 1与轴盘的轴线重合，初始时刻S与S 1的各坐标轴平行，坐标系定义如图4所示。
步骤4：以轴盘运动坐标系S m相对于固定坐标系S f的三个方向的平移自由度(x,y,z)和三个方向的旋转自由度(θ x,θ y,θ z)描述转子六自由度运动参数，变换关系如式(1)。
步骤5：将位移传感器端点位置、测量值以矢量表示，各位移传感器的端点位置矢量为r A1＝(0,16.5,0) T，r A2＝(-16.5,0,0) T，r A3＝(0,-57,-29) T，r A4＝(-49.36,28.5,-29) T，r A5＝(49.36,28.5,-29) T，在转子运动过程中记录各位移传感器读数，测量值矢量分别为
Figure PCTCN2019083171-appb-000015
Figure PCTCN2019083171-appb-000016
其中
Figure PCTCN2019083171-appb-000017
为各位移传感器读数。按公式(2)或公式(3)，以位移传感器和角度编码器的离散测量数据为已知量，解耦转子轴线的六自由度运动，即x,y,z,θ x,θ y,θ z，如图5所示。

Claims (2)

  1. 基于轴盘的转子六自由度运动测试及其运动参数解耦方法，其特征在于，包括步骤如下：
    步骤1：制备一个轴盘和位移传感器工装，所述轴盘是包括标准轴、圆盘和轴肩的一体结构，标准轴位于圆盘和轴肩之间，标准轴的轴线垂直于圆盘面，并与圆盘面和轴肩同心；所述位移传感器工装包括传感器安装孔和螺纹孔，用于位移传感器的安装和定位；轴盘和位移传感器的平面度、圆柱度、垂直度、位置度公差要求高于转子运动精度一个数量级；
    步骤2：在标准轴的圆柱面上正交布置两个径向位移传感器A 1、A 2，在圆盘面上均匀布置三个轴向位移传感器A 3、A 4、A 5，所述五个位移传感器皆固定于位移传感器工装上；在轴肩处安装角度编码器；通过位移传感器工装保证位移传感器测量位置的准确性；
    步骤3：将轴盘的圆盘非测量面固结在转子上，建立位移传感器工装的固定坐标系S f{O f；X f,Y f,Z f}和轴盘的运动坐标系S m{O m；X m,Y m,Z m}，O f与O m分别为位移传感器工装和轴盘的中心，X f、Y f、Z f分别与径向和轴向位移传感器方向平行，O m-X mY m与轴盘的圆盘面重合，Z m与轴盘的轴线重合，初始时刻S f与S m的各坐标轴平行；
    步骤4：以轴盘运动坐标系S m相对于固定坐标系S f的三个方向的平移自由度(x,y,z)和三个方向的旋转自由度(θ x,θ y,θ z)描述转子六自由度运动参数，转子上任意一点P，在固定坐标系和运动坐标系下的位置矢量r Pf和r Pm的变换关系为：
    r Pf＝r om+r Pm＝r om+R fmr Pm(1)
    其中，r om为平移变换矩阵，r om＝(x,y,z) T，R fm为旋转变换矩阵，
    Figure PCTCN2019083171-appb-100001
    c和s为cos和sin的缩写；
    步骤5：将位移传感器端点位置、测量值以矢量表示，建立轴盘的轴线运动 矢量与测试矢量的关系模型；
    径向位移传感器A 1、A 2测量方向交标准轴于Q 1、Q 2点，过Q 1、Q 2做标准轴轴线的垂线，交于P 1、P 2，对于轴系任意运动位置j，建立刚体运动几何学的闭环矢量方程：
    Figure PCTCN2019083171-appb-100002
    其中，r Ai为各传感器端点的位置矢量，
    Figure PCTCN2019083171-appb-100003
    为各位移传感器端点到标准轴或圆盘面被测点的矢量，
    Figure PCTCN2019083171-appb-100004
    为P 1、P 2点在固定坐标系下的矢径，其中
    Figure PCTCN2019083171-appb-100005
    为旋转变换矩阵，包含三个旋转运动参数；
    Figure PCTCN2019083171-appb-100006
    为垂直于动坐标系Z m的矢量；
    Figure PCTCN2019083171-appb-100007
    为运动坐标系相对于固定坐标系的平移量，包含三个平移运动参数；共有
    Figure PCTCN2019083171-appb-100008
    18个待定参数，17个标量方程，结合编码器测得回转角条件解耦转子的六自由度运动参数x,y,z,θ x,θ y,θ z，通过刚体运动变换关系，求解刚体任一点或直线的运动轨迹，评价转子运动特性。
  2. 权利要求1所述的基于轴盘的转子六自由度运动测试及其运动参数解耦方法，其特征在于，步骤5：将位移传感器端点位置、测量值以矢量表示，建立轴盘的轴线运动矢量与测试矢量的关系模型；
    径向位移传感器A 1、A 2测量方向交标准轴于Q 1、Q 2点，过Q 1、Q 2做标准轴轴线的垂线，交于P 1、P 2，对于轴系任意运动位置j，建立刚体运动几何学的闭环矢量方程：
    Figure PCTCN2019083171-appb-100009
    其中，r Ai为各传感器端点的位置矢量，
    Figure PCTCN2019083171-appb-100010
    为各位移传感器端点到标准轴或圆盘面被测点的矢量，
    Figure PCTCN2019083171-appb-100011
    为P 1、P 2、O m点在固定坐标系下的矢径，
    Figure PCTCN2019083171-appb-100012
    为P i或者O m与Q i连线的矢量，共有
    Figure PCTCN2019083171-appb-100013
    24个待定参数，24个标量方程，求解轴线运动的方向矢量
    Figure PCTCN2019083171-appb-100014
    无需编码器测回转角即可得到转子轴线的方向矢量，包含五个运动参数x,y,z,θ x,θ y，结合角度编码器测得的回转角θ z以及刚体运动变换关系，求解刚体任一点或直线的运动轨迹，评价转子运动特性。
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