CN112729682A - Method for obtaining equivalent unbalance amount of rotor and method for improving critical rotating speed vibration response of rotor - Google Patents

Method for obtaining equivalent unbalance amount of rotor and method for improving critical rotating speed vibration response of rotor Download PDF

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CN112729682A
CN112729682A CN202011555396.8A CN202011555396A CN112729682A CN 112729682 A CN112729682 A CN 112729682A CN 202011555396 A CN202011555396 A CN 202011555396A CN 112729682 A CN112729682 A CN 112729682A
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rotor
sensor
unbalance
balance
adjustment
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罗华耿
邓振鸿
吴太欢
张保强
冯吴俊
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Xiamen University
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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
    • 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

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Abstract

The method for obtaining the equivalent unbalance of the rotor comprises the steps of selecting balance surfaces on the rotor, arranging sensors with the number equal to or more than that of the balance surfaces, and measuring the vibration response Y below the critical speedq(ω) and then by means of a complex parameter P related to each sensor and not to the speed of rotationqAnd PqrAs a bridge, obtaining the equivalent unbalance U on each balance surface by using an influence coefficient methodnThe method can obtain the equivalent unbalance amount of the rotor under the test condition of the rotation speed lower than the critical rotation speed, thereby reducing the requirement on a balance measuring instrument. The method for improving the vibration response of the critical rotating speed of the rotor adjusts the rotor on the corresponding balance surface according to the equivalent unbalance obtained by the method, so that the vibration response of the critical rotating speed of the rotor is improved.

Description

Method for obtaining equivalent unbalance amount of rotor and method for improving critical rotating speed vibration response of rotor
Technical Field
The application relates to the field of rotor critical speed vibration response, in particular to a method for obtaining equivalent unbalance of a rotor and a method for improving rotor critical speed vibration response.
Background
In a rotary machine, due to errors in manufacturing and processing of a rotating member (hereinafter referred to as a rotor) or due to material unevenness, the mass distribution of the rotating member is not completely symmetrical with respect to the center of rotation, and a certain eccentric unbalance amount (hereinafter referred to as an unbalance amount) is formed. During the rotation of the rotor, the unbalance causes the vibration of the support system (unbalance vibration) due to the centrifugal force, thus destroying the mechanical performance of the system, therefore, the rotor needs to be balanced and calibrated to reduce or eliminate the vibration generated by the unbalance.
If the rotor is designed to run at or above its first critical speed, it should be classified as a flexible rotor (one cannot ignore the amount of unbalance). The traditional dynamic balancing method of the flexible rotor mainly comprises a modal balancing method and a field dynamic balancing method, and the two methods both need vibration information of the rotor at the critical speed or higher. However, in most cases, it is difficult to operate to the supercritical speed of the rotor due to the structural constraints of the dynamic balancer. The field dynamic balance belongs to a dynamic balance method based on trial weight, although the response of the rotor in high-speed operation can be obtained, a large amount of workload is brought, and the field dynamic balance is generally avoided as much as possible except for the stages of installation, trial run and maintenance. Therefore, how to realize the high-speed dynamic balance of the rotor under the condition of low-speed operation of the rotor, namely, the suppression of the vibration of the rotor under the critical and supercritical operation conditions is an urgent problem to be solved.
Disclosure of Invention
The present application is directed to overcoming the above-mentioned drawbacks and problems in the prior art, and providing a method for obtaining an equivalent unbalance amount of a rotor and a method for improving a critical rotational speed vibration response of the rotor, which can obtain the equivalent unbalance amount of the rotor under a test condition below a critical rotational speed, and accordingly improve the critical rotational speed vibration response of the rotor.
In order to achieve the purpose, the following technical scheme is adopted:
method for obtaining equivalent unbalance of rotor supported by support systemThe first shaft rotates, and the dynamic modal parameter of the rotor comprises critical speed omega0And damping ratio ζ0The method comprises the following steps of (1) knowing; it includes: selecting s balance surfaces perpendicular to a first axis on a rotor, and arranging t sensors on a supporting system along the first axis to obtain vibration response in a single direction, wherein s is a natural number greater than or equal to 1, and t is a natural number greater than or equal to s; the method comprises the following steps: measuring the vibration response Y of each sensor at different rotation speeds in a range below the critical rotation speedq(ω), wherein q is the sensor number, whose value ranges from 1 to t; definition of
Figure BDA0002857263130000021
Wherein ω is the rotational speed of the rotor; x is a constant, x is 2 when measuring vibration displacement, x is 3 when measuring vibration speed, and x is 4 when measuring vibration acceleration; j is a symbol of a complex number,
Figure BDA0002857263130000022
defining complex parameters associated with a sensor
Figure BDA0002857263130000023
Obtaining P of each sensor by fittingq(ii) a Step two: adjusting unbalance amount for each balance surface at least once, and measuring vibration response Y at different rotation speeds after each adjustment in the range below the critical rotation speedqr(ω), where r is the number corresponding to each adjustment; defining a complex function of the adjusted respective serial numbers associated with the sensors for the respective serial numbers
Figure BDA0002857263130000024
Figure BDA0002857263130000025
Obtaining P of each sensor after each adjustment through fittingqr(ii) a Step three: due to the fact that
Figure BDA0002857263130000026
And is
Figure BDA0002857263130000027
Figure BDA0002857263130000028
Wherein n is the serial number of the balance surface, and the numeric area of n is a natural number from 1 to s; h isnqThe mechanical transmission rate from the sensor with the corresponding serial number to the balance surface with the corresponding serial number; u shapenThe equivalent unbalance amount of the rotor on the balance surface with the corresponding serial number is obtained; u shapenrFor the unbalance amount on the balance surface of the corresponding serial number after the adjustment of the corresponding serial number, if the balance surface is adjusted in the adjustment, U is determinednr＝Un+Ur', wherein Ur' is the amount of unbalance of the adjustment of the balance surface in the adjustment, if the balance surface is not adjusted in the adjustment, Unr＝Un(ii) a Thus, according to Ur′、PqAnd PqrSolving the unbalance U on each balance surface by using an influence coefficient methodn。
Further, s ≧ 2.
Further, s is 2 and t is 2.
A method for improving the critical speed vibration response of the rotor adopts the method for obtaining the equivalent unbalance amount of the rotor to obtain the equivalent unbalance amount U on each balance surfacenAnd according to the equivalent unbalance U on each balance surfacenThe rotor is adjusted on the corresponding balancing plane.
Compared with the prior art, the scheme has the following beneficial effects:
in the technical scheme of the application, the complex parameter P related to each sensor and unrelated to the rotating speed is usedqAnd PqrAs a bridge, solving and obtaining the equivalent unbalance U on each balance surface by using an influence coefficient methodnThus obtaining the equivalent unbalance amount U on each balance surfacenTherefore, the technical scheme of the application can achieve the purpose of obtaining the equivalent unbalance amount of the rotor under the test condition of the rotation speed lower than the critical rotation speed, reduces the requirements on a balance measuring instrument, and can also avoid the damage to some special bearings caused by excessive heat generated by the friction of the bearings in the air. By applying the present applicationThe technical scheme of (2) does not need on-site high-speed dynamic balance, thereby avoiding a large amount of workload caused by trial weight.
Now, the following is described in detail:
in the prior art, it is known that the synchronous vibration response Y (ω) of the rotor follows the following law, where U is the amount of unbalance.
Figure BDA0002857263130000029
Wherein x is a constant, x is 2 when measuring the vibration displacement, x is 3 when measuring the vibration speed, and x is 4 when measuring the vibration acceleration;
the application sets an equivalent unbalanced surface and a sensor and defines hnpFor the mechanical transmission efficiency between a specific equivalent unbalanced surface and a specific sensor (related to the position of the sensor and the position of the equivalent unbalanced surface only), the vibration response Y at the sensor is obtained by applying the above ruleq(ω) can be expressed as:
Figure BDA0002857263130000031
definition of
Figure BDA0002857263130000032
And
Figure BDA0002857263130000033
after that, the air conditioner is started to work,
Yq(ω)＝PqZ(ω)
thus, PqComplex parameters related to the sensor and unrelated to the rotating speed are formed, and further U can be solved by adjusting the unbalance amount on each balance surface and utilizing an influence coefficient methodn。
The above unbalance amount UnAlthough the method is obtained under the condition of low-speed measurement, the critical rotating speed vibration response of the rotor can be well improved by adjusting the rotor according to the method.
If s ≧ 2 is set, the rotor having a certain length in the rotation axis direction can be effectively adjusted.
By setting s to 2 and t to 2, efficient adjustment can be achieved with a minimum measurement effort unless the rotor is particularly long in the direction of the rotation axis.
Drawings
In order to more clearly illustrate the technical solution of the embodiments, the drawings needed to be used are briefly described as follows:
FIG. 1 is a schematic view of a measurement system;
FIG. 2 is a schematic view of the amount of unbalance on the balance plane;
FIG. 3 is a vibration acceleration response of the first sensor measured in a low velocity region;
FIG. 4 is a vibration acceleration response measured by the second sensor in a low velocity region;
FIG. 5 is a comparison of the measured vibration acceleration response of the first sensor at various rotational speeds before and after adjustment;
FIG. 6 is a comparison of the measured vibration acceleration responses of the second sensor at various rotational speeds before and after adjustment;
description of the main reference numerals:
a measurement system 10;
rotor 1, shaft 11, shaft key phase mark 111, first disk 12, first balance surface 121, second disk 13, second balance surface 131;
a variable speed motor 2;
support system 3, first bearing 31, second bearing 32;
a first sensor 41, a second sensor 42, a phase sensor 43;
a data acquisition module 51 and a data processing module 52.
Detailed Description
In the claims and specification, unless otherwise specified the terms "first", "second" or "third", etc., are used to distinguish between different items and are not used to describe a particular order.
In the claims and specification, unless otherwise defined, the terms "comprising", "having" and variations thereof mean "including but not limited to".
The technical solution in the embodiments will be clearly and completely described below with reference to the accompanying drawings.
Referring to fig. 1, fig. 1 shows the structure of a measurement system 10. As shown in fig. 1, the measurement system 10 includes a rotor 1, a variable speed motor 2, a support system 3, a first sensor 41, a second sensor 42, a phase sensor 43, a data acquisition module 51, and a data processing module 52.
Wherein the rotor 1 comprises a shaft 11, a first disc 12 and a second disc 13, which are fixedly connected to each other. A shaft key phase mark 111 is provided on the shaft 11, and two surfaces of the first disk 12 and the second disk 13 which are opposite to each other and perpendicular to the extending direction of the shaft 11 are a first balance surface 121 and a second balance surface 131 in the embodiment. Both the first 121 and the second 131 balancing surfaces may be used for attaching a mass to change the amount of unbalance on the respective balancing surfaces.
In the present embodiment, the dynamic modal parameters of the rotor 1 include the critical speed ω0And damping ratio ζ0It can be obtained in advance through numerical calculation or experimental analysis (such as finite element simulation and modal experiment) in the prior art. In this embodiment, the critical speed ω of the rotor0At 6000RPM, the first critical damping ratio ζ0About 0.1.
The variable speed motor 2 is coupled with the shaft 11 to drive the rotor 1 to rotate around the first shaft, and the rotating speed is controllable and adjustable.
The support system 3 comprises a first bearing 31 and a second bearing 32, wherein the first bearing 31 and the second bearing 32 are respectively arranged at the outer sides of the first disc 12 and the second disc 13 to support the rotor 1 to rotate around the first shaft.
The first sensor 41 and the second sensor 42 are arranged on the bearing seat of the first bearing 31 and the bearing seat of the second bearing 32, respectively, but may of course be arranged elsewhere in the support system. In the present embodiment, the first sensor 41 and the second sensor 42 are both acceleration sensors and are respectively used for measuring the vibration acceleration in the first direction parallel to each other and in the first axial radial direction, and the directions measured by the first sensor 41 and the second sensor 42 may be different, but need to be changed in the following calculation.
A third sensor 43 is located opposite the shaft key phase mark 111 for identifying the number of rotations of the shaft 11 and for referencing the vibration response phase value.
The data acquisition module 51 is electrically connected to the first sensor 41, the second sensor 42 and the third sensor 43, respectively, to acquire electrical signals or data transmitted by the three sensors.
The data processing module 52 is in signal connection with the data acquisition module 51, and is configured to calculate an equivalent unbalance amount U on the first balance surface 121 and the second balance surface 131 according to the data acquired by the data acquisition module 511And U2。
The method for acquiring the equivalent unbalance amount of the rotor by adopting the measuring system 10 comprises the following steps:
the method comprises the following steps:
measuring the vibration response Y of each sensor at different rotation speeds in a range below the critical rotation speedq(ω), where q is the number of sensors and is a natural number ranging from 1 to t (where t is the number of sensors and should be a natural number greater than or equal to s, and s is the number of selected balance planes and is a natural number greater than or equal to 1, in this example of substance, s is 2 and t is 2). In this embodiment, the vibration acceleration response Y of the first sensor 41 is measured continuously in the range of 600RPM to 2000RPM1(ω) and the vibration acceleration response Y of the second sensor 422(ω). FIGS. 3 and 4 show Y respectively1(omega) and Y2(ω) curve.
Definition of
Figure BDA0002857263130000051
Where ω is the rotation speed of the rotor, x is a constant, x is 2 when measuring the vibration displacement, x is 3 when measuring the vibration speed, and x is 4 when measuring the vibration acceleration, in this embodiment, since the vibration acceleration is measured, x is 4; j is a symbol of a complex number,
Figure BDA0002857263130000052
defining complex parameters associated with a sensor
Figure BDA0002857263130000053
Wherein q is the serial number of the sensor, and the value range thereof is 1 and 2 in the embodiment; it is to be noted that PqThe value is not dependent on the rotational speed, but is dependent on the sensor position, the position of the balancing surface and the equivalent unbalance of the balancing surface.
Obtaining P of each sensor by fittingqIn this embodiment, P1And P2。P1And P2See table 1 below.
Step two:
adjusting unbalance amount for each balance surface at least once, and measuring vibration acceleration response Y at different rotation speeds after each adjustment in the range below the critical rotation speedqrAnd (omega), wherein r is a corresponding serial number of each adjustment. In this embodiment, two adjustments are made, the first adjustment is to add a weight U to the first balance surface 1211' (mass 5g, mounting radius 75mm, angle 0 deg.). The second adjustment is to take off the counterweight U added in the first adjustment1' thereafter, a weight U is added to the second balance surface 1312' (5 grams in mass, 75mm in radius of fit, 0 degree angle). After each adjustment, the vibratory acceleration response Y of the first sensor 41 is continuously measured over a range of 600RPM to 2000RPM11(ω)、Y12(ω) and the vibration acceleration response Y of the second sensor 4221(ω)、Y22(ω). Thus, Y can be obtained11(ω)、Y12(ω)、Y21(ω)、Y22(ω) curve.
Defining adjusted sensor-related complex functions for respective serial numbers
Figure BDA0002857263130000054
From this we find the P of each sensor by fittingqrIn this embodiment, P will be obtained11、P12、P21、P22As shown in table 1:
table 1: p1、P2、P11、P12、P21、P22Calculated result after fitting
Figure BDA0002857263130000061
Step three:
in the prior art, it is known that the synchronous vibration acceleration response Y (ω) of the rotor follows the following law, where U is the amount of unbalance.
Figure BDA0002857263130000062
In the embodiment, an equivalent unbalanced surface and a sensor are arranged, and h is definednpFor the mechanical transmission efficiency between a specific equivalent unbalanced surface and a specific sensor (only related to the position of the sensor and the position of the equivalent unbalanced surface), the acceleration vibration response Y at the sensor is obtained by applying the above ruleq(ω) can be expressed as:
Figure BDA0002857263130000063
because of the fact that
Figure BDA0002857263130000064
Then
Figure BDA0002857263130000065
In the same way
Figure BDA0002857263130000066
Wherein n is the serial number of the balance surface, and the numeric area of n is a natural number from 1 to s; h isqnThe mechanical transmission rate from the sensor with the corresponding serial number to the balance surface with the corresponding serial number; u shapenThe equivalent unbalance amount of the rotor on the balance surface with the corresponding serial number is obtained; u shapenrFor the balance surface of the adjusted corresponding serial numberIf the balance surface is adjusted in the adjustment, U is determinednr＝Un+Ur', wherein Ur' is the amount of unbalance of the adjustment of the balance surface in the adjustment, if the balance surface is not adjusted in the adjustment, Unr＝Un；
In this embodiment, there are:
Figure BDA0002857263130000067
written in matrix form, then there are:
Figure BDA0002857263130000071
the same principle is that:
Figure BDA0002857263130000072
Figure BDA0002857263130000073
where [ H ] represents an influence coefficient matrix.
The following examples illustrate how to solve for h by the influence coefficient methodqnAnd further obtain the equivalent unbalance amount U1And U2The description is as follows:
first, solving an influence coefficient matrix [ H ]:
Figure BDA0002857263130000074
Figure BDA0002857263130000075
further identifying the equivalent unbalance amount U1And U2：
Figure BDA0002857263130000076
In this embodiment, the result of identifying the equivalent unbalance amount on each balance surface is shown in table 2:
table 2: identification result of equivalent unbalance amount on each balance surface
Figure BDA0002857263130000077
Thus, the embodiment realizes the aim of Y in the range lower than the critical rotating speedq(omega) and Yqr(omega) is measured, and then the equivalent unbalance U on each balance surface is obtainednThe effect of (1). Therefore, the requirement on the balance measuring instrument is reduced, and damage to some special bearings caused by excessive heat generated by friction of the bearings in the air can be avoided. By adopting the technical scheme in the embodiment, the on-site high-speed dynamic balance is not needed, so that a large amount of workload caused by trial and error is avoided.
Based on the equivalent unbalance amounts identified above, the present embodiment adds counterweights to the first and second balance surfaces 121 and 131 in opposite directions of the equivalent unbalance amount to improve the critical speed vibration response of the rotor according to the method known in the prior art. As illustrated in fig. 2, the unbalance amount added to the first balance surface 121 is represented by the phase θ of the relative axis key phase mark 111 and the off-axis distance reAnd unbalanced mass meAnd (4) forming. In the present embodiment, due to the limitation of the conditions (the hole site to which the weight is added does not extend over the unbalanced surface), the weight is added at a radius of 75mm at the 220 ° (43.8 ° +180 ° ≈ 220 °) position on the first balanced surface 121 with a mass of 0.41g, and the weight is added at a radius of 75mm at the 300 ° (116 ° +180 ° ≈ 300 °) position on the second balanced surface 131 with a mass of 0.64 g. And measuring the vibration acceleration response at each rotation speed before and after the adjustment. The magnitude of the vibrational acceleration response of the first sensor 41 is shown in FIG. 5 and the magnitude of the vibrational acceleration response of the second sensor 42 is shown in FIG. 6. As can be seen, after the adjustment, the first order threshold is reachedNear 6000RPM, the magnitude of the vibratory acceleration response is significantly improved.
Therefore, the solution provided by the embodiment achieves the aim of improving the vibration response of the critical rotating speed of the rotor.
The embodiment is only one embodiment of the method disclosed in the present application, and those skilled in the art can conclusively derive from the technical content disclosed in the present embodiment that, for a sheet-like rotor, only one balancing surface needs to be introduced, and an equivalent unbalance amount on the balancing surface can be obtained by performing one adjustment through one sensor. For some rotors with longer axial length, three or more balance surfaces can be introduced, and the equivalent unbalance amount on the balance surfaces can be obtained by three or more adjustments through three or more sensors, so that the adjustment is carried out on the balance surfaces. And will not be described in detail herein.
The description of the above specification and examples is intended to be illustrative of the scope of the present application and is not intended to be limiting.

Claims (4)

1. A method for obtaining an equivalent unbalance of a rotor supported by a support system for rotation about a first axis, the dynamic modal parameters of the rotor including a critical speed ω0And damping ratio ζ0The method comprises the following steps of (1) knowing; the method is characterized by comprising the following steps:
selecting s balance surfaces perpendicular to a first axis on a rotor, and arranging t sensors on a supporting system along the first axis to obtain vibration response in a single direction, wherein s is a natural number greater than or equal to 1, and t is a natural number greater than or equal to s; the method comprises the following steps:
measuring the vibration response Y of each sensor at different rotation speeds in a range below the critical rotation speedq(ω), wherein q is the sensor number, whose value ranges from 1 to t;
definition of
Figure FDA0002857263120000011
Wherein ω is the rotational speed of the rotor;
x is a constant, x is 2 when measuring vibration displacement, x is 3 when measuring vibration speed, and x is 4 when measuring vibration acceleration;
j is a symbol of a complex number,
Figure FDA0002857263120000012
defining complex parameters associated with a sensor
Figure FDA0002857263120000013
Obtaining P of each sensor by fittingq；
Step two:
adjusting unbalance amount for each balance surface at least once, and measuring vibration response Y at different rotation speeds after each adjustment in the range below the critical rotation speedqr(ω), where r is the number corresponding to each adjustment;
defining a complex function of the adjusted respective serial numbers associated with the sensors for the respective serial numbers
Figure FDA0002857263120000014
Obtaining P of each sensor after each adjustment through fittingqr；
Step three:
due to the fact that
Figure FDA0002857263120000015
And is
Figure FDA0002857263120000016
Wherein n is the serial number of the balance surface, and the numeric area of n is a natural number from 1 to s;
hqnthe mechanical transmission rate from the sensor with the corresponding serial number to the balance surface with the corresponding serial number;
Unthe equivalent unbalance amount of the rotor on the balance surface with the corresponding serial number is obtained;
Unrfor the unbalance amount on the balance surface of the corresponding serial number after the adjustment of the corresponding serial number, if the balance surface is adjusted in the adjustment, U is determinednr＝Un+Ur', wherein Ur' is the amount of unbalance of the adjustment of the balance surface in the adjustment, if the balance surface is not adjusted in the adjustment, Unr＝Un；
Thus, according to Ur′、PqAnd PqrSolving the unbalance U on each balance surface by using an influence coefficient methodn。
2. The method for obtaining the equivalent unbalance amount of the rotor as claimed in claim 1, wherein s ≧ 2.
3. A method of obtaining rotor equivalent unbalance as defined in claim 2, characterized in that s-2 and t-2.
4. A method for improving vibration response of rotor at critical speed, characterized in that the method for obtaining rotor equivalent unbalance as claimed in any one of claims 1 to 3 is used to obtain the equivalent unbalance U on each balance surfacenAnd according to the equivalent unbalance U on each balance surfacenThe rotor is adjusted on the corresponding balancing plane.
CN202011555396.8A 2020-12-24 2020-12-24 Method for obtaining equivalent unbalance amount of rotor and method for improving critical rotating speed vibration response of rotor Pending CN112729682A (en)

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CN114018480A (en) * 2021-11-24 2022-02-08 中国科学院重庆绿色智能技术研究院 Real-time diagnosis method for rotor unbalance fault of large-scale rotating machinery
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CN114018480A (en) * 2021-11-24 2022-02-08 中国科学院重庆绿色智能技术研究院 Real-time diagnosis method for rotor unbalance fault of large-scale rotating machinery
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CN114577397A (en) * 2022-03-17 2022-06-03 湖南科技大学 Dynamic balance method and system for high-speed permanent magnet motor rotor
CN114577397B (en) * 2022-03-17 2023-10-13 湖南科技大学 Dynamic balancing method and system for rotor of high-speed permanent magnet motor

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