1. Introduction
As a crucial part of the rotor–stator system, stator frame is not only a mechanical load-bearing component but also a carrier of the electric generator, which means that it will be affected by multiple factors such as electromagnetic force from the rotating rotor, outward thermal expansion force from the stator core, hydraulic turbulence from the base and structural gravity simultaneously during the practical operation. Therefore, the study of vibration of stator frame is a complex multi-field coupling problem. Many studies have been done to investigate the vibration of stator in the past decades, which can be classified into two categories: theoretical research and engineering application. Theoretical research mainly includes mathematical modeling, structure characteristic calculation, and dynamic response predicting using analytic or numerical method [
1,
2,
3]. Engineering application mainly focuses on the vibration analysis technique, fault diagnosis technology and elimination solution [
4,
5,
6]. These studies show that the excessive vibration of stator frame caused by assembly error, improper design, manufacturing deviation or other reasons can result in structural noise, fatigue damage, even bolt cutting and other negative effects, which would seriously threaten the safety of the unit.
With the development of large scale hydropower generator, higher requirement of security and stability are proposed. A novel stator frame with fixed base and oblique-studs was wildly adopted in large capacity and low speed unit for its low production costs and the advantage of using elastic deformation to counteract external forces, and the features of the stator frame can be characterized by large elasticity and small rigidity. The authors, to investigate the abnormal vibration occurred on the oblique-stud stator frame in a 250 MW hydropower generator, have carried out the experimental test under various operating conditions, and to further study the impact of the electromagnetic factors on vibration, a finite element (FE) analysis was performed.
The calculation of electromagnetic force is of key importance in the simulation. Lots of studies are by means of analytical method which is relied on an accurate result of the magnetic field. For example, Smith et al. described a method for predicting the static and pulsating unbalanced magnetic pull (UMP) in a three-phase, induction motor with an eccentric rotor [
7,
8]. Guo et al. [
9] obtained an analytical expression of electromagnetic forces by expressing the air gap permeance as a Fourier series, but these methods are suitable for the initial design and optimization. When it comes to structure adjustment and dynamic response study, FE method is a better choice because it can provide more accurate result of the magnetic field by taking the saturation and complex structures into account. With the advent of the increased computational power, FE method has been widely used in engineering practice in the past several decades. However, there would be two big challenges for FE analysis of the stator frame in a large scale hydropower generator. Firstly, when investigating the electromagnetic effect of a rotating machine, eccentricity must be considered. The eccentricity would ruin the symmetry and periodicity of the structure, hence the conventional method that utilizing the symmetry and periodicity to simplify the computational model could no longer be used. Considering there are 64 magnetic poles, 528 coil slots and thousands of current sources in the studied stator model, the calculation would be very time-consuming. Secondly, it is difficult to find a coupling method of electromagnetic field and mechanical field with both high accuracy and acceptable calculating time. Fonteyn et al. proposed an approach which is referred as directly coupling method that is to solve the 2D magnetic field and calculate the displacement simultaneously without using the common “equivalent forces” approach, as in [
10]. Lin and Arkkio [
11] investigated the vibration of the end-windings on the stator by using an approach which is known as weakly coupling method: solving the electromagnetic field firstly and then utilizing the generated magnetic stress tensor as the boundary condition for the mechanical equations. To cut down the unacceptable computational time brought by the huge number of DOFs, Xu et al. [
12] obtained the electromagnetic force by means of a simple analytical method that employed the no-load characteristic curve of an electrical machine, and then developed a FE rotor model of a large hydro-turbine generator unit to investigate the influence of UMP on radial vibrations. Matinez et al. [
1] presented a 2D-magnetic and 3D-mechanical coupled FE model which is the most suitable method for the vibration study in the stator of induction motors, but it only focused on steady-state and the eccentric situation was not considered. Inspired by the work of [
1], a 2D-magnetic and 3D-mechanical coupled FE model was developed in this paper. With different mechanical models, eccentricity and radial-stud structure were considered.
This work focuses on the vibration problem of an oblique-stud stator frame in a large scale hydropower generator. The field experimental tests, including excitation varying test, rotation speed varying test and load varying test, were carried out to find the cause of the undesirable vibration. To do a further mechanism study, a coupled FE model was established, and comparative analyses to reveal the relationship between vibration and structure were performed.
2. Field Experimental Tests
2.1. The Investigated Stator Frame
The stator frame was designed as a plate-like structure composed by rib-plates, annular-plates and oblique-studs (
Figure 1) to dissipate heat and reduce the weight. Unlike the traditional radial-stud structure, this stator frame uses an oblique-stud structure to reduce the deformation caused by thermal expansion. The research object is in a large hydropower generator unit which suffered stator vibration problem since it was put into operation. To find out the cause of the undesired vibration, experimental test and FE analysis were carried out, which is detailed in the following sections.
2.2. Three Sets of Experimental Tests
Since the hydropower unit is a complex hydraulic electromechanical coupling system, it is important to identify the main factor caused stator vibration at the first place. Three sets of field experimental tests were performed and the details are shown as follows:
Excitation varying tests at no-load condition: When the unit speeds up to the rated condition after start-up, a series of excitation with different excitation conditions (An increasing interval of 5% from 50% to 100% of the rated excitation current) are put into operation. When each operation condition turns into steady-state, the vibration data of the stator frame are collected.
Rotating speed varying tests at no-load condition: After the unit starting up to the rated condition, the rotating speed is adjusted to 94.3%, 99%, 102%, and 105% of the rated speed by manually setting the governor frequency. When each operation condition turns into steady-state, the vibration data of the stator frame are collected.
Load varying tests: After started up and installed, the unit is stabilized at different load conditions from the minimum load to the maximum load under the test head (20 MW to 250 MW), and the vibration data of each condition is collected respectively.
The vibration shape of the stator frame is elliptical deformation in the horizontal direction which is presented in
Figure 2. Therefore, it is necessary to place monitoring points in the four directions (+X, −X, +Y, −Y) of the stator frame to measure the maximum amplitude of the vibration. Since the oblique-stud is the crucial supporting component of the stator system and its stiffness is large, eight low-frequency vibration sensors and ICP (VS-TH-DP, Hengyuan Hydropower Equipment Co., Shanxi province, Xi’an, China) acceleration sensors were set on upper portion (top and mid) of oblique-stud to collect the displacement and acceleration data of the structure (
Figure 3). To ensure the accuracy of the experimental test, the sample frequency was set to 2.5 KHz and the sampling time was 89 s.
2.3. Results of the Experimental Tests
Figure 4 demonstrates the peak value of the displacement at the top and the mid of the stator frame in different experimental tests. It can be observed that the amplitude of vibration rises with the increasing excitation current, while it declines slightly with the increase of load, and there is no explicit relationship between vibration and rotation speed. It can also be found that the vibration at the mid part of the stator is obviously stronger than that at the top part.
The spectrum of the vibration at the mid of structure under the no-load and 100% excitation condition is shown in
Figure 5. The dominant frequency of the vibration is the double rotation frequency
f2 (3.125 Hz). The integral multiple of rotation frequency
f1, and
f3–
f6 are also significant in the spectrum, and the influence on vibration caused by these harmonic components decreases with the increase of frequency. The minor-amplitude (
f7 and
f8) and low-frequency component exist due to the hydraulic vibration passing through the base of stator.
From the experimental results, it can be inferred that the main cause of the excessive vibration is electromagnetic factor. There are many methods to measure the air gap of the hydropower unit [
13,
14]. However, most of them need pre-installed special sensor. For the other units without pre-installed special sensor, a FE analysis using a 2D-magnetic and 3D-mechanical coupled model has been performed to put a further research.