Method for calculating eccentricity of rotor assembly axis based on radial runout measurement

Abstract

A method for calculating eccentricity of rotor assembly axis based on radial runout measurement comprises matrix characterization of data and calculation of relative runout value at each point, establishment of a spring equivalent model and calculation of contact force, eccentric direction and magnitude; calculation of relative runout value; establishment of a spring equivalent model to analyze the relationship between force and displacement in each phase of a contact process, and then an uneven contact force at each point is obtained; and determination of eccentricity is to determine the magnitude of eccentricity. Based on the measured radial runout data in production practice, this method realizes the prediction of eccentricity of axis before assembly, improves the coaxiality of rotors after assembly, and has important practical guiding significance for axis prediction as well as assembly phase adjustment and optimization in the assembly process of aero-engine rotor pieces.

Claims

1. A method for calculating eccentricity of rotor assembly axis based on radial runout measurement, wherein comprising the following steps: step A, for two adjacent stage disks, positioning the joint of a lower stage rotor A and an upper stage rotor B by a spigot interference fit, then the centers of surfaces from the bottom up are respectively A.sub.O1, A.sub.O2, B.sub.O1, B.sub.O2; accessing the measured radial runout values of the spigot joint surfaces of the two rotors and characterizing the values by a matrix, with the data in the form of a circle, using a polar coordinate representation method for characterization, then the radial runout data of a lower end surface of an upper end piece B is expressed as: B.sub.O1(α,z.sub.b1), and the radial runout data of an upper end surface of a lower end piece A is expressed as: A.sub.O2(α,z.sub.a2); α refers to the measurement angle, Z.sub.b1 and Z.sub.a2 refer to the radial runout value when the measurement angle is α; a coordinate of a reference circle center is O(0,0), and the fit spigot radius R is given, R is the radius of the reference circle; step B, calculating the relative runout value at each point of the upper end surface and the lower end surface are in an interference fit state; the formed “burr” means that in a part manufacturing process, due to the existence of a machining error, the actual diameter of a rotor at a fit spigot is randomly generated within the range of the machining error, wherein, the radius value of each point relative to center of the reference circle is also randomly generated, and the burr dimension is the distance of each point relative to the reference circle; step C, due to the existence of spigots interference amount, uneven elastic forces directing to the center of the reference circle are generated around both spigots of the rotor A and the rotor B when the two rotors are assembled; in order to calculate the elastic force at each measuring point, the burr dimension at each measuring point needs to be calculated; the rigidity of the burr is negligible compared with the reference circle, and the relative position of the center of the reference circle is temporarily assumed to be unchanged in the assembly process; a force caused the burr portion is equivalent to a elastic force of a spring, assuming that the burr rigidity function is k.sub.1(n), where n is the burr width; the reference circle rigidity is k.sub.2(y), where y is the distance from the surface of the reference circle; h.sub.1 is the burr dimension of B.sub.1 at one point, h.sub.2 is the burr dimension of A.sub.2 at another point; if h.sub.2>h.sub.1, x represents a displacement distance, and {circle around (1)} represents the first phase of two springs being compressed at the same time; {circle around (2)} represents the second phase of h.sub.1 spring being compressed; {circle around (3)} represents the third phase of the reference circle compression phase; F represents the suffered elastic force; the relationship between force and displacement in each phase is as follows: in the first phase: $\begin{array}{cc}F=k_1\left(n\right)\frac{x}{2}& \left(1\right)\end{array}$ in the second phase:
F=k.sub.1(n)h.sub.2+k.sub.1(n)(x−2h.sub.2)  (2) in the third phase:
F=k.sub.2(y)(x−h.sub.1−h.sub.2)+k.sub.1(n)h.sub.2+k.sub.1(n)(h.sub.1−h.sub.2)  (3) if h.sub.2<h.sub.1, it is obtained in a similar way that: in the first phase: $\begin{array}{cc}F=k_1\left(n\right)\frac{x}{2}& \left(4\right)\end{array}$ in the second phase:
F=k.sub.1(n)h.sub.1+k.sub.1(n)(x−2h.sub.1)  (5) in the third phase:
F=k.sub.2(y)(x−h.sub.1−h.sub.2)+k.sub.1(n)h.sub.1+k.sub.1(n)(h.sub.2−h.sub.1)  (6) step D, calculating the contact force at each point in an ideal state, includes: considering the contact surfaces of spigot of the rotor A and spigot of the rotor B as springs, the uneven radial runout values of the two spigots are equivalent to uneven elastic forces, and the solid portion of a base body is regarded as a rigid body without deformation; calculating the elastic force at each point in the case where the centers of the two joint surfaces coincides with each other in the ideal state first according to formulas (1) to (6); the formulas are the same as formulas (1) to (6); step E, calculating resultant force vector, includes: combining the spring force of each measuring point at the center of the reference circle, and obtaining a resultant force F.sub.n;
F.sub.n=Σ.sub.1.sup.nF.sub.i  (7) where, i represents the number of measuring points; step F, calculating eccentricity e: the offset direction of the actual centroid relative to the center of the reference circle, wherein, the direction of eccentricity is the direction of the resultant force F.sub.n; when the relative positions of the centers of the reference circle of the two rotors are moved in F.sub.n direction, the contact portions of each pair of measuring points are changed, and the elastic force of each measuring point is changed until the force is balanced and an equilibrium state is achieved; the centroid offset amount and eccentric angle are calculated according to this principle; since the center of the reference circle is moved by a certain distance, the displacement distance of each point is different; e is the eccentricity, O is the center of the reference circle, O.sub.2 is the center of an eccentric circle, r is the radius of the reference circle of the rotors, d is the displacement of a measuring point, θ is the eccentric angle, θ.sub.2 is the angle corresponding to the measuring point, and γ is the angle corresponding to a triangle; it is obtained according to the geometrical relationship that: $\begin{array}{cc}\{\begin{array}{c}{r}^2=e^2+l_2^2-2{\mathrm{el}}_2\cos \gamma \\ d=r-l_2\end{array}& \left(8\right)\end{array}$ the relationship between eccentricity and the displacement of the measuring point is obtained from formula (8), and the resultant force is obtained by vector force combination at the center of the reference circle; when the equilibrium state is reached, it is obtained that: $\begin{array}{cc}\{\begin{array}{c}{F}_i^{\prime }=F_i\pi \left(d\right)\\ F_n={.Math.}_1^n{F}_i^{\prime }\\ F_n=0\end{array}& \left(9\right)\end{array}$ the eccentricity e is obtained by solving formula (9).

Description

DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a schematic diagram of joint surfaces of two rotors;

(2) FIG. 2 is a schematic diagram of a relative burr protrusion value;

(3) FIG. 3 is a schematic diagram of fit state of rotors;

(4) FIG. 4 is a schematic diagram of elastic forces in an ideal state;

(5) FIG. 5 is a schematic diagram of resultant force in an ideal state;

(6) FIG. 6 is a schematic diagram of relationship between displacement and eccentricity at each point;

(7) In FIG. 6, e is the eccentricity, O is the initial center of circle, O.sub.2 is the center of an eccentric circle, r is the radius of the reference circle of the rotors, d is the displacement of a measuring point, θ is the eccentric angle, δ.sub.2 is the angle corresponding to the measuring point, and γ is the angle corresponding to a triangle; and

(8) FIG. 7 is a schematic diagram of an equilibrium state.

DETAILED DESCRIPTION

(9) Specific calculation mode of this method is further described below in combination with accompanying drawings and the technical solution.

Embodiment

(10) A method for calculating eccentricity of rotor assembly axis based on radial runout measurement, comprising the following steps:

(11) Step A: for two adjacent stage disks, positioning the joint of a lower stage rotor A and an upper stage rotor B by spigot interference fit, then the centers of surfaces from the bottom up are respectively A.sub.O1 A.sub.O2 B.sub.O1 B.sub.O2, A.sub.O1 A.sub.O2 B.sub.O1 B.sub.O2, A.sub.O1 A.sub.O2 B.sub.O1 B.sub.O2 and A.sub.O1 A.sub.O2 B.sub.O1 B.sub.O2; accessing the measured radial runout values of the spigot joint surfaces of the two rotors and characterizing the values by a matrix, with the data in the form of a circle, then the radial runout data of a lower end surface of an upper end piece B is expressed as: B.sub.O1(α,z.sub.b1), and the radial runout data of an upper end surface of an lower end piece A is expressed as: A.sub.O2(α,z.sub.a2); using a polar coordinate representation method for characterization; the position of the center of circle O in a global coordinate system is O(0,0), and the fit spigot radius R is given;

(12) Step B: calculating the relative runout value at each point. As shown in FIG. 1, the upper end surface and the lower end surface are in an interference fit state; the shown “burr” means that in a part manufacturing process, due to the existence of a machining error, the actual diameter of a rotor at a fit spigot is randomly generated within the range of the machining error, i.e., the radius value of each point relative to an ideal center of circle is also randomly generated, and the burr value is the distance of each point relative to a reference circle;

(13) Step C: as shown in FIG. 2, due to the existence of spigot interference amount, uneven elastic forces directing to the center of circle will be generated around spigots when the two rotors are assembled; in order to calculate the elastic force at each measuring point, the relative burr protrusion value at each point needs to be calculated; the rigidity of the burr is negligible compared with the reference circle, and the relative position of the center of the reference circle is temporarily assumed to be unchanged in the assembly process; the burr portion is equivalent to a spring, assuming that the burr rigidity function is k.sub.1(n), where n is the burr width; the reference circle rigidity is k.sub.2(y), where y is the distance from the surface of the reference circle; as shown in FIG. 3, h.sub.1 is the burr value of B.sub.1 at a certain point, h.sub.2 is the burr value of A.sub.2 at a certain point; if h.sub.2>h.sub.1, x represents a displacement distance, and {circle around (1)} represents the first phase: two springs are compressed at the same time; {circle around (2)} represents the second phase: h.sub.1 spring is compressed; {circle around (3)} represents the third phase: reference circle compression phase; F represents the suffered elastic force; the relationship between force and displacement in each phase is as follows:

(14) In the first phase:

(15) $\begin{array}{cc}F=k_1\left(n\right)\frac{x}{2}& \left(1\right)\end{array}$
In the second phase:
F=k.sub.1(n)h.sub.2+k.sub.1(n)(x−2h.sub.2)  (2)
In the third phase:
F=k.sub.2(y)(x−h.sub.1−h.sub.2)+k.sub.1(n)h.sub.2+k.sub.1(n)(h.sub.1−h.sub.2)  (3)
If h.sub.2<h.sub.1, it can be obtained in a similar way that:
In the first phase:

(16) $\begin{array}{cc}F=k_1\left(n\right)\frac{x}{2}& \left(4\right)\end{array}$
In the second phase:
F=k.sub.1(n)h.sub.1+k.sub.1(n)(x−2h.sub.1)  (5)
In the third phase:
F=k.sub.2(y)(x−h.sub.1−h.sub.2)+k.sub.1(n)h.sub.1+k.sub.1(n)(h.sub.2−h.sub.1)  (6)

(17) Step D: calculating the contact force at each point in an ideal state. Considering the contact surfaces of both spigots of the rotor A and the rotor B as springs, the uneven radial runout values of the two spigots are equivalent to uneven elastic forces, and the solid portion of a base body is regarded as a rigid body without deformation. As shown in FIG. 5, calculating the elastic force at each point in the case where the centers of the two joint surfaces coincides with each other in the ideal state first according to formulas (1) to (6), where i represents the number of measuring points;

(18) The formulas are the same as formulas (1) to (6);

(19) Step E: calculating resultant force vector: as shown in FIG. 6, combining the spring force of each measuring point at the center of circle, and obtaining a resultant force F.sub.n;
F.sub.n=Σ.sub.1.sup.nF.sub.i  (7)

(20) Step F: calculating eccentricity e. The offset direction of the actual centroid relative to the center of circle, i.e., the direction of eccentricity is the direction of the resultant force F.sub.n; when the relative positions of the centers of circle of the two rotors are moved in F.sub.n direction, the contact portions of each pair of measuring points will be changed, and the elastic force of each measuring point is changed until the force is balanced and an equilibrium state is achieved; the centroid offset amount and eccentric angle are calculated according to this principle;

(21) Since the center of circle is moved by a certain distance, the displacement distance of each point is different; as shown in FIG. 6, e is the eccentricity, O is the initial center of circle, O.sub.2 is the center of an eccentric circle, r is the radius of the reference circle of the rotors, d is the displacement of a measuring point, θ is the eccentric angle, θ.sub.2 is the angle corresponding to the measuring point, and γ is the angle corresponding to a triangle.

(22) It can be obtained according to the geometrical relationship that:

(23) $\begin{array}{cc}\{\begin{array}{c}{r}^2=e^2+l_2^2-2{\mathrm{el}}_2\cos \gamma \\ d=r-l_2\end{array}& \left(8\right)\end{array}$

(24) The relationship between eccentricity and the displacement of the measuring point is obtained from formula (8), and as shown in FIG. 7, the resultant force is obtained by vector force combination at the center of circle; when the equilibrium state is reached, it can be obtained that:

(25) $\begin{array}{cc}\{\begin{array}{c}{F}_i^{\prime }=F_i\pi \left(d\right)\\ F_n={.Math.}_1^n{F}_i^{\prime }\\ F_n=0\end{array}& \left(9\right)\end{array}$

(26) The eccentricity e can be obtained by solving formula (9).