Six-DOF motion testing and motion parameter decoupling method for rotors based on shaft-disk

Abstract

A six-DOF motion testing and motion parameter decoupling method for rotors based on shaft-disk is proposed, which includes a displacement sensor tooling and a precision shaft-disk fixed on the rotor where three measuring points are arranged on the surface of disk to measure the axial motion of the rotor, two measuring points on the shaft to measure the radial motion, and the angle encoder at the shaft shoulder to measure the rotation motion. The tooling guarantees the accuracy of displacement sensors. The fixed coordinate system and the shaft-disk moving coordinate system are set, and the measured values of the displacement sensors and the encoder are represented by vectors to establish the relationship between the six-DOF motion of the shaft-disk axis and the measured values of sensors. Thus, the six-DOF motion of the rotor/shaft-disk can be determined by the measured data.

Claims

1. A six-DOF motion testing and motion parameter decoupling method for rotors based on shaft-disk, wherein comprising the following steps: step 1: a shaft-disk and a displacement sensor tooling are prepared, and the shaft disk is an integral body including a standard shaft, a disk and a shaft shoulder; the standard shaft is located between the disk and the shaft shoulder, whose axis is perpendicular to the disk surface and concentric with those of the disk and shaft shoulder; the displacement sensor tooling includes sensor mounting holes and threaded holes for the installation of the displacement sensors; the tolerance of flatness, cylindricity, verticality and position of the shaft-disk and displacement sensor tooling should be one order of magnitude higher than the motion accuracy of the rotor; step 2: two radial displacement sensors A.sub.1 and A.sub.2 are orthogonally arranged on the cylindrical surface of the shaft, and three axial displacement sensors A.sub.3, A.sub.4 and A.sub.5 are uniformly arranged on the surface of disk, and the angle encoder is installed at shaft shoulder; the five displacement sensors are all fixed on the displacement sensor tooling which ensures the accuracy of measuring position of the displacement sensors; step 3: the non-measured surface of the disk is fixed on the rotor; the fixed coordinate system S.sub.f{O.sub.f; X.sub.f, Y.sub.f, Z.sub.f} of displacement sensor tooling and the shaft-disk moving coordinate system S.sub.m{O.sub.m; X.sub.m, Y.sub.m, Z.sub.m} are established, of which the O.sub.f and O.sub.m are the center of displacement sensor tooling and shaft-disk respectively, X.sub.f, Y.sub.f and Z.sub.f are parallel to the direction of radial and axial displacement sensors respectively, O.sub.m−X.sub.mY.sub.m is coincident with the disk surface of the shaft-disk, and Z.sub.m is coincident with the axis of shaft; the coordinate axes of S.sub.f and S.sub.m are parallel at the initial moment; step 4: the six-DOF motion parameters of the rotor are described by the translational motion parameters (x,y,z) and rotational motion parameters (θ.sub.x,θ.sub.y,θ.sub.z) in three directions of the axes of the disk-shaft coordinate system S.sub.m relative to the fixed coordinate system S.sub.f, the transformation relationship between the position vector r.sub.pf and r.sub.pm of any point P on the rotor in the fixed coordinate system and the moving coordinate system is:
r.sub.Pf=r.sub.om+r.sub.Pm=r.sub.om+R.sub.fmr.sub.Pm  (1) where, r.sub.om is the translation transformation matrix, r.sub.om=(x,y,z).sup.T, R.sub.fm is the rotation transformation $R_{\mathrm{fm}}=\left[\begin{array}{ccc}c{\theta }_{y}c{\theta }_z& s{\theta }_{x}s{\theta }_{y}c{\theta }_z-c{\theta }_{x}s{\theta }_z& c{\theta }_{x}s{\theta }_{y}c{\theta }_z+s{\theta }_{x}s{\theta }_z\\ c{\theta }_{y}s{\theta }_z& s{\theta }_{x}s{\theta }_{y}s{\theta }_z+c{\theta }_{x}c{\theta }_z& c{\theta }_{x}s{\theta }_{y}s{\theta }_z-s{\theta }_{x}c{\theta }_z\\ -s{\theta }_y& s{\theta }_{x}c{\theta }_y& c{\theta }_{x}c{\theta }_y\end{array}\right],$ matrix, c and s are the abbreviations for cos and sin respectively; step 5: the position of the end points of the displacement sensors and the measured values are represented by vectors, and the relationship between the six-DOF motion parameters of the rotor and the measured values is established; the measuring direction of radial displacement sensors A.sub.1 and A.sub.2 intersects the standard shaft at points Q.sub.1 and Q.sub.2; make the lines vertical to the axis of shaft through Q.sub.1 and Q.sub.2 which intersect the axis at P.sub.1 and P.sub.2 respectively; the closed loop vector equations of rigid body kinematics is established for any motion position j of the rotor: $\begin{array}{cc}\{\begin{array}{cc}{r}_{\mathrm{Pi}}^{\left(j\right)}+d_{\mathrm{Ai}}^{\left(j\right)}=r_{\mathrm{Ai}}+S_{\mathrm{Ai}}^{\left(j\right)}& i=1,2\\ r_{\mathrm{Om}}^{\left(j\right)}+d_{\mathrm{Ai}}^{\left(j\right)}=r_{\mathrm{Ai}}+S_{\mathrm{Ai}}^{\left(j\right)}& i=3,4,5\\ .Math.d_{\mathrm{Ai}}^{\left(j\right)}.Math.=d\text{/}2& i=1,2\end{array}& \left(2\right)\end{array}$ where, d is the diameter of the standard shaft r.sub.Ai the position vector of the end point of each sensor which is a known quantity, S.sub.Ai.sup.(j) is the vector from the end point of each displacement sensor to the measured point of the shaft or disk surface which is the measured value, r.sub.Pi.sup.(j)=R.sub.fm.sup.(j) (0,0,z.sub.pi.sup.(j)).sup.T+r.sub.Om.sup.(j) is the vector of P.sub.1 or P.sub.2 in the fixed coordinate system, R.sub.fm.sup.(j) is the rotation transformation matrix including three rotational motion parameters, d.sub.Ai.sup.(j) is the vector vertical to the Z.sub.m in the moving coordinate system, r.sub.Om.sup.(j) is the translation of the moving coordinate system relative to the fixed coordinate system, including three translational motion parameters; there are 18 undetermined parameters including r.sub.Om.sup.(j), R.sub.fm.sup.(j), z.sub.pi.sup.(j), d.sub.Ai.sup.(j), and 17 scalar equations; combined with the condition of the rotation angle measured by angle encoder, the six-DOF motion parameters of the rotor including x, y, z, θ.sub.x,θ.sub.y and θ.sub.z can be decoupled, and the trajectory of any point or line of the rotor can be determined to evaluate the motion performance of the rotor.

2. The six-DOF motion testing and motion parameter decoupling method for rotor based on shaft-disk according to claim 1, wherein, step 5: the position of the end points of the displacement sensors and the measured values are represented by vectors, and the relationship between the six-DOF motion parameters of the rotor and the measured values is established; the measuring direction of radial displacement sensors A.sub.1 and A.sub.2 intersects the standard shaft at points Q.sub.i and Q.sub.2; make the lines vertical to the axis of shaft through Q.sub.1 and Q.sub.2 which intersect the axis at P.sub.1 and P.sub.2 respectively; the closed loop vector equations of rigid body kinematics is established for any motion position j of the rotor: $\begin{array}{cc}\{\begin{array}{cc}{r}_{\mathrm{Pi}}^{\left(j\right)}+d_{\mathrm{Ai}}^{\left(j\right)}=r_{\mathrm{Ai}}+S_{\mathrm{Ai}}^{\left(j\right)}& i=1,2\\ r_{\mathrm{Om}}^{\left(j\right)}+d_{\mathrm{Ai}}^{\left(j\right)}=r_{\mathrm{Ai}}+S_{\mathrm{Ai}}^{\left(j\right)}& i=3,4,5\\ \left(r_{P1}^{\left(j\right)}-r_{\mathrm{Om}}^{\left(j\right)}\right)\times \left(r_{P2}^{\left(j\right)}-r_{\mathrm{Om}}^{\left(j\right)}\right)=0& \\ .Math.d_{\mathrm{Ai}}^{\left(j\right)}.Math.=d\text{/}2& i=1,2\\ d_{\mathrm{Ai}}^{\left(j\right)}.Math.\left(r_{P1}^{\left(j\right)}-r_{\mathrm{Om}}^{\left(j\right)}\right)=0& i=1,2,\mathrm{.Math.},5\end{array}& \left(3\right)\end{array}$ where, d is the diameter of the standard shaft, r.sub.Ai, is the position vector of the end point of each sensor which is a known quantity, S.sub.Ai.sup.(j) is the vector from the end point of each displacement sensor to the measured point of shaft or disk surface which is the measured value, r.sub.P1.sup.(j), r.sub.P2.sup.(j) and r.sub.Om.sup.(j) are the vector of P.sub.1, P.sub.2 and O.sub.m from the origin O.sub.f of the fixed coordinate system, d.sub.Ai.sup.(j) is the vector from P.sub.i or O.sub.m to Q.sub.i; there are 24 undetermined parameters including r.sub.P1.sup.(j), r.sub.P2.sup.(j), r.sub.Om.sup.(j), d.sub.Ai.sup.(j), and 24 scalar equations to solve the direction vector of the axis k.sub.m=(r.sub.P1.sup.(j)−r.sub.Om.sup.(j))/|r.sub.P1.sup.(j)−r.sub.Om.sup.(j)|; the direction vector of the rotor axis can be obtained without the condition of the rotation angle measured by angle encoder, including x, y, z, θ.sub.x and θ.sub.y, combined with the rotation angle θ, measured by angle encoder, the trajectory of any point or line of the rotor can be determined to evaluate the motion performance of the rotor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of the shaft-disk in a specific implementation of the invention.

(2) FIG. 2 is a schematic diagram of the displacement sensor tooling in a specific implementation of the invention.

(3) FIG. 3 is a schematic diagram of the measuring point layout of shaft-disk in a specific implementation of the invention.

(4) FIG. 4 is a schematic diagram of the coordinate system definition and closed-loop vector in a specific implementation of the invention.

(5) FIG. 5 is a diagram of the decoupling curves in a specific implementation of the invention.

(6) FIG. 6 is a schematic diagram of the rotor motion test structure in a specific implementation of the invention.

(7) In the figures, 1 is the surface of disk, 2 is the cylindrical surface of standard shaft, 3 is the shaft shoulder, 4 is the displacement sensor, 5 is the clamping screw, 6 is the displacement sensor tooling, 7 is the shaft-disk and 8 is the angle encoder.

DETAILED DESCRIPTION

(8) In order to explain the technical solution of the invention explicitly, the invention is further described in combination with the attached figures and specific implementation cases.

(9) The object of this embodiment is to test the six-DOF motion of a rotor and decouple the six-DOF motion parameters through the shaft-disk, displacement sensors and angle encoder.

(10) The schematic diagram of relevant parameters of rotor motion test is shown in FIG. 3, and the parameter values are shown in Table 1.

(11) TABLE-US-00001 TABLE 1 Parameters of the rotor motion test scheme d D l θ.sub.1 θ.sub.2 θ.sub.3 33 mm 114 mm 29 mm 30° 120° 120°

(12) Upon the six-DOF motion testing and decoupling method for rotors, the specific implementation steps are as follow:

(13) Step 1: A shaft-disk and a displacement sensor tooling are prepared as shown in FIG. 1 and FIG. 2 meeting the parameters in Table 1. The shaft disk is an integral body including a standard shaft, a disk and a shaft shoulder. The standard shaft is located between the disk and the shaft shoulder, whose axis is perpendicular to the disk surface and concentric with those of the disk and shaft shoulder. The displacement sensor tooling includes the sensor mounting holes and threaded holes for the installation of the displacement sensors. The tolerance of flatness, cylindricity, verticality and position of the shaft-disk and displacement sensor tooling should be one order of magnitude higher than the motion accuracy of the rotor.

(14) Step 2: Two radial displacement sensors A.sub.1 and A.sub.2 are orthogonally arranged on the cylindrical surface of the shaft, and three axial displacement sensors A.sub.3, A.sub.4 and A.sub.5 are uniformly arranged on the surface of disk, and the angle encoder is installed at shaft shoulder. The five displacement sensors are all fixed on the displacement sensor tooling which ensures the accuracy of measuring position of the displacement sensors. The testing scheme is shown in FIG. 3.

(15) Step 3: The non-measured surface of the disk is fixed on the rotor. The fixed coordinate system S.sub.f{O.sub.f; X.sub.f, Y.sub.f, Z.sub.f} of displacement sensor tooling and the shaft-disk moving coordinate system S.sub.m{O.sub.m; X.sub.m, Y.sub.m, Z.sub.m} are established of which the O.sub.f and O.sub.m are the center of displacement sensor tooling and shaft-disk respectively, X.sub.f, Y.sub.f and Z.sub.f are parallel to the direction of radial and axial displacement sensors respectively, O.sub.m−X.sub.mY.sub.m is coincident with the disk surface of the shaft-disk, and Z.sub.m is coincident with the axis of shaft. The coordinate axes of S.sub.f and S.sub.m are parallel at the initial moment. The definition of coordinate system is shown in FIG. 4.

(16) Step 4: The six-DOF motion parameters of the rotor are described by the translational motion parameters (x,y,z) and rotational motion parameters (θ.sub.x,θ.sub.y,θ.sub.z) in three directions of the axes of the disk-shaft coordinate system S.sub.m relative to the fixed coordinate system S.sub.f. The transformation relationship is shown in Equation (1).

(17) Step 5: The position of the end points of the displacement sensors and the measured values are represented by vectors. The end points of each displacement sensor are r.sub.A1=(0,16.5,0).sup.T, r.sub.A2=(−16.5,0,0).sup.T, r.sub.A3=(0,−57,−29).sup.T, r.sub.A4=(−49.36,28.5, −29).sup.T and r.sub.A5=(49.36,28.5,−29).sup.T. Record the values of each displacement sensor during the process of the rotor motion, and the measured vectors are S.sub.A1.sup.(j)=(0,−S.sub.A1.sup.(j),0).sup.T, S.sub.A2.sup.(j)=(S.sub.A2.sup.(j), 0,0).sup.T, S.sub.A3.sup.(j)=(0, 0,−S.sub.A3.sup.(j)).sup.T, S.sub.A4.sup.(j)=(0, 0,−S.sub.A4.sup.(j)).sup.T and S.sub.A5.sup.(j)=(0, 0,−S.sub.A5.sup.(j)).sup.T, where S.sub.Ai.sup.(j), i=1, 2, . . . , 5 are the measured values of each displacement sensor. According to the Equation (2) or (3), and the discrete measurement data of displacement sensors and angle encoder, the six-DOF motion parameters of the rotor including x, y, z, θ.sub.x, θ.sub.y and θ.sub.z can be decoupled as shown in FIG. 5.