Modal Based Predictive Design and Analysis of Electric Motors M. A. NASSER Visiting Researcher, Mechanical Engineering Department, University of Dundee, Dundee, DD1 4HN, Scotland, UK, [email protected]. (Associate Professor, Production Engineering & Mechanical Design Department, Faculty of Engineering, Menoufia University, Shebin El Kom, Egypt) ABSTRACT: Electric motors are critical elements in all or most energy applications. A good design of electric motors is that it should be light, small and stable. Moreover, the product should be low maintenance, have less scrap rates and have lower vibration levels and acoustic noise. To achieve these goals, a predictive engineering “design and analysis” process was proposed and applied to an electric motor. The predictive engineering process steps were; defining the concept of design, modelling, simulation, analysis and a results review. Both a finite element and an experimental modal analyses were used in re-rating a simple structure electric motor to validate the proposed process. The finite element was used in modelling, simulation, analysis and the result review, while the experimental modal analysis was used in model validation and verification. The component re-modelling was done first and then the model validation and design modification were achieved. Soon after this the full motor structure was assembled based on a component mode synthesis and then analysed to review its dynamic behaviour in both modal and frequency domains. The results revealed that the components imperfections and an unbalanced magnetic pull could produce serious rotor/stator interference as well as downward the mode frequencies. Results also indicated that the added radial and axial ribs on the motor casing as well as the radial ribs to both the front and rear end shields were efficient techniques to stiffen the structure and improve the mode shapes and consequently reduce the vibration and radiated noise from them. Moreover, components and full motor structure modifications can be carried out quickly and easily. In addition, rotor/stator interference can be defined at any mode of vibration. The predictive engineering process is an efficient global design and analysis technique. NOMENCLATURE: K M , : Analytical mass and stiffness matrices. I : unit matrix. x :vector of position. o B :influence matrix. () t u :vector of applied forces. Ψ :mode shape. [ ] M , : modal mass and stiffness matrices. [K ] Φ :mass normalized mode shape. q :generalized coordinate. ω : natural frequency. T : transformation. e : rotor stator eccentricity. m δ : ideal air gap. ϕ δ : real air gap. ϕ : angle. C : magnetic flux. F :force. ϕ B : magnetic flux density. 1. INTRODUCTION: Manufacturers of equipment in most industries are increasingly urged to reduce the mechanical vibrations and acoustic noise produced by their products. This development is now increasingly required by the market and by
Transcript
Modal Based Predictive Design and Analysis of Electric Motors
M. A. NASSER Visiting Researcher, Mechanical Engineering Department, University of Dundee, Dundee, DD1 4HN,
Scotland, UK, [email protected]. (Associate Professor, Production Engineering & Mechanical Design Department, Faculty of
Engineering, Menoufia University, Shebin El Kom, Egypt) ABSTRACT: Electric motors are critical elements in all or most energy applications. A good design of electric motors is that it should be light, small and stable. Moreover, the product should be low maintenance, have less scrap rates and have lower vibration levels and acoustic noise. To achieve these goals, a predictive engineering “design and analysis” process was proposed and applied to an electric motor. The predictive engineering process steps were; defining the concept of design, modelling, simulation, analysis and a results review. Both a finite element and an experimental modal analyses were used in re-rating a simple structure electric motor to validate the proposed process. The finite element was used in modelling, simulation, analysis and the result review, while the experimental modal analysis was used in model validation and verification. The component re-modelling was done first and then the model validation and design modification were achieved. Soon after this the full motor structure was assembled based on a component mode synthesis and then analysed to review its dynamic behaviour in both modal and frequency domains. The results revealed that the components imperfections and an unbalanced magnetic pull could produce serious rotor/stator interference as well as downward the mode frequencies. Results also indicated that the added radial and axial ribs on the motor casing as well as the radial ribs to both the front and rear end shields were efficient techniques to stiffen the structure and improve the mode shapes and consequently reduce the vibration and radiated noise from them. Moreover, components and full motor structure modifications can be carried out quickly and easily. In addition, rotor/stator interference can be defined at any mode of vibration. The predictive engineering process is an efficient global design and analysis technique. NOMENCLATURE: KM , : Analytical mass and stiffness matrices.
I : unit matrix. x :vector of position.
oB :influence matrix.
( )tu :vector of applied forces. Ψ :mode shape. [ ]M , : modal mass and stiffness matrices. [K ]Φ :mass normalized mode shape. q :generalized coordinate. ω : natural frequency. T : transformation. e : rotor stator eccentricity.
mδ : ideal air gap.
ϕδ : real air gap. ϕ : angle. C : magnetic flux. F :force.
ϕB : magnetic flux density. 1. INTRODUCTION: Manufacturers of equipment in most industries are increasingly urged to reduce the mechanical vibrations and acoustic noise produced by their products. This development is now increasingly required by the market and by
governmental regulations. The objective of this study is to provide the designers and vibration and noise engineers with tools that enable them to efficiently predict the influence of machine components and substructures on the dynamic behaviour of the associated machine. With the help of these tools engineers can find solutions to several design, manufacturing and maintenance related topics such as the perception of vibrations and acoustic noise at the periphery of the electric motors. As experienced and noted the faults of the motor cause mechanical vibrations and an Unbalanced Magnetic Pull (UMP). The electromagnetic forces are centripetal forces that cause vibration in the motor and transmit it to the load and the mountings. Vibrations also increase noise levels. Vibration of the motor can causes rotor/stator interaction instigating collapse or rubbing of the rotor and/or stator. Moreover, vibrations loosen screws, increase bearing loads, and cause fatigue cracking in structural members, bearings and unsupported wires. In addition, they cause springs to disengage, attention to the resonant frequencies and reduce the bearings from working smoothly. Electric motors and their components receive attention in literature. Timar et. Al. [1], Ozturk et. al. [2], Eis [3], Costello [4] and Finley [5], Finley et. al. [6], handled noise and vibrations in electrical machines with causes, results and diagnosis. Cameron [7], used vibration and current monitoring for detecting air gap eccentricity in induction motors, whereas Dorrell et. al. [8], used these parameters and flux for the same purpose. Utecht [9], used finite elements to predict the eigenvalues of large-scale electric motors. Rotor and stator as the main parts of electric motors play an important part in their dynamic behavior. Rotordynamics phenomena, modeling and analysis have also been studied. Childs [10], Wang and Williams [11], Girgis and Verma [12], Verma and Balan [13], Verma et. al. [14,15] and Singal et. al. [16], studied analytically and experimentally the vibrations of induction motors stators and concluded that the modes shapes at lower frequencies are not very different from sinusoidal shapes. The dynamic behavior of a ball bearing as the critical path of vibrations between the rotor and stator has a significant effect on the dynamics of the rotating machines. Different aspects like geometrical imperfections, the effect of lubrication, the cage, the flexibility of the application and the flexibility of the outer ring are accounted for theoretically and experimentally by Su et. al. [17], Hendrikx et. al. [18], Wensing [19] and Meeks et. al. [20], while the rotor/stator assembly was studied by Glasgow and Nelson [21]. The housing of the motor is a hollow cylinder with radial reinforcement. The structural dynamics of the hollow cylinders were investigated extensively by Leissa and So [22], So and Leissa [23], Liew et. al. [24], Smith and Haft [25], Takahashi and Hirano [26], Yuan and Dickinson [27], Cheng and Nicolas [28], Girgis and Verma [29], and Tzou [30]. The front and rear endshields of the motor are circular plates with a bearing housing hub or “short cylinder”. Dynamics of circular plates were investigated by Tseng and Wickert [31], and Parker and Mote [32]. From the literature review, there seems to be no global engineering procedure that covers the majority of both design and analysis aspects and concepts. A global design concept is required to challenge the new market needs at a lower investment risk, in which vibration, acoustic noise and shock are not only considered as environment parameters but also as important design parameters. To achieve these goals, a predictive engineering “design and analysis” process was proposed and applied to an electric motor at both component and full motor structure levels. The predictive engineering process steps are as follows; defining the concept of design, modelling, simulation, analysis and a results review. This procedure gives engineers and designers the power to quickly improve products by identifying design flaws early in the process. It can analyze the stress, vibration, dynamics, nonlinear characteristics of mechanical components, machines and structures. For an efficient design process, mechanical structures are often subdivided into substructures or components. The components are usually connected to each other with well-defined interfaces. Component mode synthesis approach enables designers to conduct the dynamic performance of individual components accurately, quickly, easily, and cheaply as well as conducting the design modifications more efficiently. Regardless of the complexity of the structure the modeling and analyses at the component mode level can be modeled once and left to subcontractors. Experimental testing of a complete structure can be very complicated and expensive and even impossible in structural modification. Consequently, testing at the component level is the only logical option. Testing at the component level can be used for either design verification or to define the dynamic properties of components which are difficult to model. Component mode methods are either based on constraint modes and fixed-interface modes “Hurty [33], Craig and Bampton [34], Craig and Hale [35], Bennighof et. al. [36]”, or attachment modes and free-interface modes “MacNeal Method [37], Rubin Method [38], Hintz [39], Craig and Chang [40,41]”. In this paper a 250 watt, 4-pole, single-phase alternating current (AC) 220 V., 50Hz. induction motor that operates at 1450 rpm (24.167 Hz) of very simple geometrical structure was selected and used. Simple geometry makes finite element and experimental modal analyses easier. The motor consists of the rotor, rotor shaft, bearings, stator, housing, rear endshield and front endshield. The motor components, substructures and full motor structure were all modelled in Ansys. The motor was disassembled and experimental modal analyses, Ewins [42], were carried out on components, substructures and at full motor structure levels for validation and verification. The predictive engineering process was first applied to the component level.
Modification scenarios of stiffening the casing and front and rear endshields were carried out and their best designs were defined. Moreover, the loose fits between the bearing “fixed on the rotor” and bearing housing were studied. A component mode synthesis (CMS), which was carried out by using Matlab was used to study the full motor structure based on the models of its components and substructures. The results indicated the efficiency of predictive engineering process. 2. ANALYSIS The predictive engineering process steps are; the defining of the concept of design, modelling, simulation, analysis and a results review. A component mode synthesis technique was used to analyze the full motor structure. The analysis started with a normal mode analysis of the system components. Figure (1) presents the conceptual procedure of the design process. This procedure was applied on an electric motor shown in Figure (2). For an undamped multi-degree-of-freedom system, the governing equations of motion can be expressed as:
)(0 tuBKxxM =+&& (1) In order to determine the free vibration solution, the applied force can be set to zero. The homogenous solution for Equation (1) can be assumed as
tjetx ωΨ=)( (2) Substituting Equation (2) into Equation (1) yield the undamped eigenproblem, ( ) tjeMK ωω Ψ− 2 (3) for which the non-trivial solution is defined by
( ) 0det 2 =− MK ω (4) The most important property of mode shapes is the orthogonality property. It can be expressed as
[MMT =ΨΨ ] ] and (5) [KKT =ΨΨThe mass normalized mode shape Φ have the following particular properties
[ ]IMT =ΦΦ and [ ]2ω=ΦKTΦ (6)
The relationship between the mass normalized mode shape for mode and its more general form rthr Φ, Ψ is
rr
r mΨ=Φ
1 (7)
Using the mass normalized property, the following transformation can be achieved ( ) ( )tqtx Φ= (8)
Applying the transformation in Equation (8) to Equation (1), the modal equations of motion can be written as ( )tfqq T
iiii Φ=+ 2ω&& where (9) ni ,....,2,1=Equation (9) represents a set of single DOF equations and can be easily solved. The physical displacement of the nodal points can be estimated from the modal results and the exiting force from the relationship: { } [ ]{ }qx φ= (10) The general procedure of component mode synthesis mainly consists of two major steps. The first step defines for each substructure the transformation that will reduce the original physical degrees of freedom into a reduced set of generalized coordinates. Model reduction was performed by partitioning the mass, damping, and stiffness matrices into an “a ”-set (analysis) and an “o ”-set (omitted) as
=
=
oooa
aoaa
oooa
aoaa
KKKK
KMMMM
M , (11)
Typically, the -set partition corresponds to DOFs that are measured on the test structure. The reduction transformation can be expressed as
a
aro
a xTI
xx
=
(12)
Applying the above transformation to each of the property matrices, the results are ( )roooa
Trraoaar TMMTTMMM +++= and ( )roooa
Trraoaar TKKTTKKK +++= (13)
Guyan model reduction technique was used. To determine the Guyan transformation T . The static problem can be written as G
=
0a
o
a
oooa
aoaa fxx
KKKK
(14)
Through matrix manipulation, the transformation that relates to can be determined as ax ox
aGaoaooo xTxKKx =−= −1 (15) Applying the Guyan transformation, the reduced stiff ess and mass matrices can be written as n
Gaoaar TKKK += and ( )GMoaTGGaoaar TMTTMMM
oo+++= (16) The Craig-Bampton reduction technique produced a hybrid reduced model using the following transformation
Φ
=CG
Cb TI
T0
(17)
where Φ are modes computed with the interface points constrained. C
The second step component mode synthesis CMS was built together all these component reduced models into one assembly. This assembly was then solved and the solution was back-transformed to the reduced physical degrees of freedom of interest. The principle of component mode synthesis CMS is to transform the physical degrees of freedom of each substructure into a reduced number of the generalized coordinates
{ }x{ }q :
{ } [ ] { }qTx T= (18) Imperfections caused by improper tolerances of dimensions at the component level lead to loose fits between those parts which lowers the substructures and full motor structure mode frequencies and dissymmetric the air gap between the rotor and stator. The dissymmetrical air gap increases the possibility of rotor/stator interaction. An unbalanced magnetic pull is initiated and continued from the displacements of different parts of the rotor and stator. Unbalanced magnetic pull results in the case of eccentric air gap between the rotor and stator.
)cos1()( ϕδϕδ em += (19) Neglecting the magnetic saturation, the magnetic energy flux density can be:
)()(
ϕδϕ CB = (20)
The force, which is proportional to the square of the energy flux density:
2)cos1()(
ϕϕ
eCF
+= (21)
If the rotor and stator are concentric, i.e. e , then the magnetic forces are in equilibrium, while for eccentric air gap , the magnetic forces are
0=0≠e
∫ +=∫=
π
ϕϕϕϕϕ
2
0 2)cos1(.cos.)().(
edCdFFmagn (22)
At the same time an unbalanced magnetic force is generated in the air gap. In the narrowed zone the magnetic forces increase and in the widened gap they decrease, instigating an unsteady equilibrium. The magnetic stiffness can be defined on the basis of equation
eF
k magnmagn = (23)
The stability problem can be achieved in electrical machines by: magnmech kk ≥ (24)
where is the mechanical stiffness of the system (rotor/stator). mechkAs a first approximation the rotor can be considered rigid, then:
ukF statormech = (25) If the stator is treated in other cases as a rigid structure the mechanical force of the motor takes the form:
ukF rotormech = (26) The dynamic deformation and/or dimensional tolerances, cause eccentricity in the air gap and thereby generate a resulting magnetic force with the stiffness. The stability measure in this case can be expressed as:
magn
mech
kkS = (27)
If S < 1, then the stator collapses and adheres to the rotor. This case would result in complete destruction of the equipment with huge economic damages. Hence the evaluation of the stability constitutes an important criterion for the design of large electrical machines.
Geometrical Model
Design Result Review
Simulation Model
Analysis
Design Concept
Experimental Modal Tests
System Identification
Test/Analysis Correlation
Figure (1) Predictive design process.
φ75φ50 φ20
70
φ15
50 4332
φ14
2525 7 7
215Dimensions in (mm.)
φ18φ15
30
(a) eccentric air gap
(b) rotor
(c) stator/casing substructure
(d) photo
maxδ minδ
F
e
172
φ128.2
42375043
φ75.4
1.5
Dimensions in (mm.)
φ40 φ132.2
φ75.4φ40
Front endshield
Front bearing
Fan
Rotor
Motor casing Rear
endshield
Rotor shaft
Figure (2) Electric Motor eccentric air gap (a), rotor (b), stator/casing substructure (c) and photo (d). The eigensolution, displacement and interference diagrams of the full motor structure were also obtained and can be used in the design and operation stages of relevant application. Finite element and experimental modal analyses of the motor structure were obtained. A combined matrix of the substructures matrices was assembled and used in the component mode synthesis process. 3. EXPERIMENTAL WORK An impact (impact hammer PCB086CO2) excitation is commonly used in modal analysis to provide a transient excitation of structures. A piezoelectric force transducer in the hammer tip measures the transient force applied by the hammer when it strikes an object. This impulse in the time domain corresponds to broad band excitation in the frequency domain, and can therefore excite many modes simultaneously. Shorter impulses in the time domain excite a broader range of frequencies. Impact location and direction are moved from one measurement point to another measurement point during the data collection process. An accelerometer (B&K 4393) was used to measure the vibratory response of each measurement point on the measured components, substructures and full motor structure, to the applied excitation. An accelerometer oriented in the radial direction to rotor, stator and motor structures, while it was axial in the case of front and rear end shields. The accelerometer was fixed into the test object during the modal test. Wax held the accelerometers firmly in place during data collection. Figure (3) shows a schematic and photo of one of the modal tests. The test objects were meshed as shown in Figure (4). The best suspension and excitation points for hammer excitation were selected. Then the best accelerometer points were selected. The excitation was done and the vibration signals were collected. The
excitation and measurements were made in local coordinates. The transformation, which was needed to obtain the results in a global coordinate system, had been done. The principal response function and reciprocal modal vector were obtained. The first indicates how many measurements were effective and how many were near the signal noise floor, while the second gives the number of modes in a given range. Excitation and response signals from the test were processed using a Dual Channel Dynamic Signal Analyser (HP 35760A) to compute a Frequency Response Function (FRF) for each measurement point. The measured signals were periodic within the sampling (data collection) interval to prevent errors in the Fast Fourier Transformation (FFT) that formed the basis for this calculation. Weighting windows were used to control FFT errors by reducing the signal amplitude to zero at the beginning and end of the sampling interval. Modal test data from the impact test was reduced on a personal computer with modal analysis software (Me’Scope modal plus VT 520) to conduct the experimental modal analysis. Peaks in the acquired frequency response functions indicated the measured component, substructure or full motor structure natural frequencies. The mode shape and modal damping ratio associated with each peak or natural frequency was identified by curve fitting one or more peaks at a time. A polynomial equation for the FRFs were fit in a least-squared-error sense to specified frequency bands of the measurement data. This information was used to build a table containing normalized mode shape amplitude and phase data for each measurement point and direction, and at each mode frequency. Post-processing was done by animating the mode shapes for better understanding the modes.
(a) schematic (b) photo of stator/casing substructure tests
Computer
Dynamic analyzer
Soft spring
Test object
Impact hammer
Accelerometer
Fixed frame
FFT ANALYZER
Computer Test object
Impact Hammer
Accelerometer
Figure (3) Experimental Set-up schematic (a) and photo of stator/casing substructure tests (b).
(a) rotor/bearing substructure
(b) stator/casing substructure
(c) motor
Figure (4) The meshes of the rotor/bearing substructure (a), stator/casing substructure (b) and motor (c). 4. RESULTS and DISCUSSION In component mode synthesis, the natural frequencies and the normal modes were first calculated at the component level. For an efficient design process, the mechanical structure of the motor was subdivided into components or substructures. The components were connected to each other with well-defined interface couplings. The rotating “rotor, fan”, stationary “stator, casing, front and rear endshields” and rotating/stationary “bearings” parts were disassembled, re-modeled, analyzed and modified. Two steel (elastic modulus=2.068e11N/m², density=7830kg/m³, poission ratio=0.3) cooling fans were riveted to the rotor front and rear faces as shown in Figure (2). The fan is a hollow cylinder of 0.7 cm depth, and 2.5 and 3.75 cm inner and outer diameters respectively with eight solid blades of 0.35x1.25x2.5 cm. The fan was modelled in Ansys using a solid “solid element-92 10 nodes used in meshing process” model method. Simulations of the unconstrained and constrained fans were obtained. The results indicated that the fans natural frequencies were very high and most mode shapes are concerned with the blades, which are of local effect as can be seen from Table (1) and Figure (3). From the obtained results of cooling fans, fan blades can
be neglected in the modeling process because of their higher frequencies and local modes. This assumption results in simplicity in modelling, a smaller model size, computing memory and time. A finite element model of the rotor integrated with the front and rear cooling fans was also built with solid elements. Blades of the cooling fans were neglected because of their local effects. The rotor was an axisymmetric structure, in which a doublet mode, having repeated natural frequencies, is denoted (n), where n is the number of nodal points. As periodic features would be gradually added, axisymmetry is lost, and the doublets are classified as being either repeated or split in frequency. Because of symmetry, there are ten natural frequencies of the rotor that are accompanied by five sets of two similar normal modes, which can only be distinguished by a phase shift in the spatial domain. As a result, the natural vibrations of the rotor can be described by any linear combination of the two modes. Table (2) presents the undamped natural frequencies and modes description of the rotor. Figure (4) shows some normal modes and natural frequencies of the unconstrained rotor.
Freq. (Hz.)
Normal mode
6493.0(8x) blade 1st bending mode 15670(8x) global blade bending 21073(8x) blade twisting 36420. (8x) 2nd bending mode of blades
Table (1) Undamped natural frequencies (Hz) and mode shapes of the fan.
Freq. (Hz.)
Normal mode
Freq. (Hz.)
Normal mode
0 (6x) rigid body mode 11049 rotation of front shaft about y-axis 2012 (2x) bending mode, n=0 12548 (2x) bending mode n=3 2997 (2x) bending mode n=1 15241 1st axial mode 8643 (2x) bending mode n=2 16475 2nd axial mode as rigid 10972 rotation of rear shaft about y-axis 20662(2x) bending mode n=4
Table (2) undamped natural frequencies (Hz) and mode shapes of the rotor.
Table (3) Undamped natural frequencies (Hz) and mode shapes of the unconstrained and fixed inner race bearings.
A finite element model of the ball bearing (SKF 6202) is built with solid brick elements. As seen in Table (3) there are 60 rigid body modes for the unconstrained undamped ball bearings, “10 elements x 6 degrees of freedom/element”. The modes are denoted by (n), where n is the number of nodal diameters. Because of symmetry, the fourteen natural frequencies of the bearing are accompanied by seven sets of two similar normal modes, which can only be distinguished by a phase shift in the spatial domain. Again as a result, the natural vibrations of the bearing can be described by any linear combination of the two modes. Figure (5) shows some normal modes and natural frequencies of the unconstrained ball bearings. The bearing together with the rotor is treated as a single substructure. The interface between them was considered as rigid coupling. Three scenarios were modelled to this substructure. In the first scenario, the outer rings of the front and rear ball bearings were fixed, whereas the outer ring of the front and rear ball bearings were fixed in the second and third scenarios simulating the loose fit between the bearings and bearing housings in the front and rear sides respectively. Figures (6-7) show some finite element and experimental mode shapes of the rotor/bearing substructure respectively. The finite element and experimental mode frequencies and shapes are consistent. In addition, finite element could offer more accurate modes and nodal
details than experimental modal analysis. Tables (4-6) represent the mode frequencies and description, while some finite element mode shapes are shown in Figures (6, 8, 9) in the case of the three scenarios.
#5 6493 Hz. #10 15670 Hz. #22 21073 Hz. Figure (3) Normal modes and natural frequencies (Hz) of the constrained fan.
#2 2012 Hz. #4 2997 Hz. #6 8643 Hz. Figure (4) Normal modes and natural frequencies (Hz) of the unconstrained rotor.
#1 12040 Hz. #2 12349 Hz. #3 19579 Hz. Figure (5) Normal modes and natural frequencies (Hz) of the constrained bearing.
The loose fit at the front or rear ends significantly reduce the mode frequencies and completely changed the mode shapes compared with those of the first scenario, “shrinking fit”. In addition, the loose fit between the bearing and bearing housing in the front and rear directions can cause an eccentric rotor/stator relationship “air gap”, which means that the rotor axial is not concentric with the stator, creating an area of minimum air gap which will rotate with the rotor orbitally at one times rotational frequency. The eccentricity in the air gap causes an unbalanced magnetic pull, which increases the motor vibration and vice versa. In other words, the loose fits make rotors act as cantilevers rather than fixed-fixed beams instigating non-symmetric air gaps, which increases the possibility of rotor/stator interactions as stated earlier. This reduction in mode frequencies ensures their presence in the critical effective frequency range of the human ear (≤4K Hz). As can be seen in Table (7) the loose fits between the bearing and bearing housing in the front and rear bearings lower the natural frequencies of the rotor/bearing substructure. The reduction in mode frequencies in the first twenty modes varies from 80% (at mode number two) to 9% (at mode number sixteen) of the front endshield. Similar reductions in mode frequencies were achieved by the loose fit between the bearing and bearing housing in the rear end shield (82% at mode number two to 6% at mode number twenty). Moreover, the total number of mode shapes in the frequency range 0-20 kHz, was increased with the loose fits. Repeated impacts between the outer ring of the ball bearing assembled under loose fits and its associated bearing housing in both radial and axial directions in the front or rear sides can take place. The impact location and intensity are dependent on the associated mode. The experimental modal analysis verifies the finite element mode frequencies and shapes. There is a good agreement between both.
# Freq. (Hz.) E
Normal mode # Freq. Normal mode xp, FE (Hz.)
1124 21255 nd
2 1389 1415 x -bending n=0 12 22824 y –3rd axial rotor 3 1486 1451 z - bending n=0 13 25089 z -bending n=4 4 3053 3362 x -bending n=1 14 25116 x -bending n=4 5 3120 3406 z - bending n=1 15 25275 free end twisting 6 4187 3951 y – 1 axial rotor st 16 26710 twisting rear shaft 7 5465 5910 x - bending n=2 17 28422 rotor twisting 8 5682 5935 z - bending n=2 18 29102 rotor twist about z-axis 9 ar shaft 13459 y - extensional re 19 29611 z -bending n=5 10 13801 z - bending n=3 20 30320 x -bending n=5
tal an ampe natural freq (Hz and mode shapes of the assembled rotor and
1 1098 y - axial rotor 11 y – 2 axial front shaft
Table (4) Experimen d und d uencies )
# Freq. Normal mode # Freq. Normal mode
bearings.
(Hz.) (Hz.)
2 284.059 x -Bending n=0 12 12708 z -bending n=4 3 755.648 rotation about y-axis 13 12777 x -bending n=4 4 2068 x -bending n=1 14 13225 y - 2nd axial rotor 5 2083 z -bending n=1 15 21311 3rd axial rotor 6 2734 y – 1st axial rotor 5 16 24315 z -bending n=7 3729 x -bending n=2 17 24395 x -bending n=5 8 3754 z -bending n=2 18 25077 z -bending n=6 9 5911 x -bending n=3 19 25107 x -bending n=6
10 5934 z -bending n=3 20 25275 rotor twisting equencie Hz) and mod pes of the assembled
1 283.574 z -bending n=0 11 8900 rotation about x-axis
Table (5) Undamped natural fr s ( e sha rotor and bearings with the loose
# Freq. Normal mode # Freq. Normal mode
front endshield.
(Hz.) (Hz.) 1 2 z - z3 4.661 bending n=0 11 9220 -bending n=3 2 249.424 x -bending n=0 12 13460 z -bending n=4 3 823.083 rotation about y-axis 13 13800 x -bending n=4 4 1836 x -bending n=1 14 14711 y - 2nd axial rotor 5 1871 z -bending n=2 15 19460 z -bending n=5 6 2647 y – 1 axial rotorst 16 19516 z -bending n=5 7 3226 x -bending n=2 17 22788 3 Axially rotor rd
8 3265 z -bending n=2 18 26710 shaft twisting 9 8679 rotation about x-axis g 19 27157 free end twistin
10 9150 x -bending n=3 20 28438 rotor love mode equencie z) and mode pes of the ssembled rotoTable (6) Undamped natural fr s (H sha a r and bearings with the loose
Figure (7) structure.
rear endshield.
#3 1451 Hz. re (6) Normal modes a
#5 3406 Hz. requencies of the asse
#10 13801 Hz. nd bearings. Figu nd natural f mbled rotor a
#1 1098 Hz al mode shape#1 of the rotor/bearing sub
10 57 34 20 17 6 Deteriora n in he n quTable (7) tio t atural fre encies (%)
he stator of the selected motor is an octagonal block of 12.82 cm outer diameter, 5 cm length, with hollow
Tabl tural freq s (H pes
Freq. Normal mode Freq. Normal mode
of the front and rear loose end rotors.
Tcylinder of 3.77 cm radius. It has 32 teeth to fix the stator coils. It is also attached to the housing through a press fit. This fit is accomplished by rounding the eight corners of the stator to a slightly larger radius than the inner radius of the housing. The stator plays an important part in the rotor/stator relationship. This part vibrates as a ring or thick short cylinder when excited. Depending on the exciting frequency and exciting force distribution, the stator vibrates in its modal regime. The stator was first modelled and the mode frequencies and mode shapes were obtained. The undamped natural frequencies of the unconstrained stator are given in Table (8), while those for the constrained stator are given in Table (9). Modes of the stator are denoted by (n), where n is the number of nodal diameters. All mode shapes of the stator will affect on the symmetry of the air gap of the motor, regardless of whether they are symmetric, antisymmetric or axisymmetric. These effects may cause rotor/stator interaction with a rub between them, generating acoustic noise, and causing poor motor performance and/or completely damaging the motor.
FiAs can be seen from Tables (8, 9) and Figure (10), the octagonal shape of a stator significantly contributes to their dynamic behavior by increasing their mode frequencies and modal rank.
#1 1154
#4 2714 #6 3081 (a) uncon
#2 7091 #1 6407 ained.
#6 10359 (b) constr
natural fre constraineFigure (10) Some
Athe motor casing. The casing part is a path of vibrations between rotor and stator. Also, it is a noise radiator. To reduce the mechanical vibrations and acoustic noise of systems, it is essential to avoid coincidence between excitation and the natural behavior of the structure (frequencies and shapes). Therefore, it is necessary to determine its natural frequencies and mode shapes and avoid their coincidence with exciting frequencies or load distribution. Normal modes of this cylindrical tubular part can be described by the node number “spatial rank”, and its frequency “time rank”. Where n=0 is a purely extensional mode in which the deformation is principally due to extension, n=1 is a rigid body motion, without deformation, and n=2 flexion, and for n>2 flexural modes. Table (10) and Figure (11) show some mode shapes of the cylindrical casing only without any reinforcement. Athe casing cylinder at 43 mm from its rear end as a reinforcement rib. The mode natural frequencies have been increased by values varing from 17% at the first and second modes reaching its maximum increase of 107% at the third and forth modes in comparison with the original casing, “without radial reinforcement”. Moreover, axial ribs (1.41x3.5x0.15 cm) were proposed to be added at the rear end of the casing reinforced with the annular plate. Table (10) gives the undamped natural frequencies and mode shapes of the constrained annular rib. The annular rib is an axisymmetric structure, in which a doublet mode, having repeated natural frequencies, is denoted (m,n), where m is the number of nodal circles and n is the number of nodal diameters.
Frequency Normal mode Frequency Normal mode shape (Hz.) shape (Hz.)
s periodic features would be gradually added, axisymmetry is lost, and the doublets are classified as being
Casing without reinforcement Casing with annular reinforcement
of the constrained annular rib.
#1 240.501 Hz. Figure (11
#4 294.59 Hz. shapes of the casing
# 6 689.289 Hz. ) Some mode cylinder.
Aeither repeated or split in frequency. The added annular rib increased the mass of the casing by 16.6%, while the adding of three, four, six and eight ribs increased the mass by 2.1%, 2.8%, 4.3% and 5.7% respectively. The added axial ribs “beside the annular rib” improved the natural frequencies of this element. This improvement varies with the number of the added ribs. Adding three, four, six and eight ribs “beside the annular rib” improved the natural frequencies with values varing from 20%, 19%, 22% and 22% at the first mode to 186%, 194%, 195% and 202% at mode number eight, respectively as can be seen in Tables (11-14) and Figure (12). The added ribs significantly improved the mode shapes of the casing, which are responsible for acoustic noise radiation from the vibrating casing. Fortunately, the addition of the three ribs gives the most significant increase in mode frequencies and the best mode shape modification at a minimum added mass to this element. Figure (13) shows some mode shapes and frequencies of the casing cylinder and the proposed modification. The stator/casing substructure mode frequencies and shapes were obtained in both finite element and experimental modal analyses. The results showed that the substructure mode shapes became more complicated, and therefore the dominant moving part motion is used to describe the mode shapes. As can be seen in Table (15) and Figures (14), the shrinking fit between the octagonal stator and radial reinforced casing has improved the mode frequencies and shapes of the substructure. A trial was made to use experimental results in the analysis of the internal, inner surface of the stator, parts by focusing the animation of the stator/casing substructure only on this surface. Data from the trial was not reliable enough to have clear picture on the stator behavior when it is a part of stator/casing substructure as can be seen in Figure (15). From the obtained results and as can be seen also in Figures (14, 15) that, unlike the experimental modal analysis the finite element analysis gives more details of the dynamic behavior of the complicated and internal parts of structures. This means that experimental modal analysis could offer very limited information about rotor/stator relationship, “air gap”.
#4 764.449 Hz. (6 axial rib) Figu forth normal modes and equencies of the
casing with one annular and three and six axial ribs.
unconstrained stator/casing substructure constrained stator/casing substructure Experimental FE FE
Freq. (Hz.)
Freq. rmal mode Freq. rmal mode (Hz.)
No(Hz.)
No
x) es 65.8 te bending (0,1) 1078.1 radial plate bending 1908.8(x radial plate bending (1,1)
1871 1930.5 radial plate bending (1,1) 2383.1(x2) casing bending n=0 & stator n=1 2150 2348.2(x2) stator bending n=2 2660.2(x2) stator n=2 2451 2657.3 casing front part bending n=4 ng (3,1) 3222.9(x2) radial plate bendi2778 3032.6(x2) casing front part bending n=5 4003.3 casing twisting 2990 3138.2(x2) casing antisymmetric bending n= 4 2) ng (0,2) 4870.7(x radial plate bendi3054 3197.8(x2) casing rear part of casing bending n= 4 5072.5(x2) radial plate bending (2,2) 3103 3229.6(x2) radial plate bending (2,1) 6080.8(x2) radial plate bending (2,1) 3192 3393.2(x2) casing front part bending n=5 6262.5(x2) stator n=3
3462.9(x2) casing rear part bending n=5 6264.9 stator n=3 3566.9(x2) antisymmetric casing and stator bending n=2 3721.7(x2) casing symmetric bending n=3 4070.6(x2) casing front part bending n=6 Table (15) Ex l lts of unco strained tator/casing substructure
(a) unco
Figur finite elements mode e unconstrained and r/casing substructure.
perimenta and Finite element resu n s
0(6 rigid body mod 10 radial pla1138 (x2) (0,1) 2)
and finite element results of the constrained stator/casing substructure.
5 2350Hz
6 2657Hz
19 3574Hz # # #
nstrained
#5 2398 Hz. (b) constrained
#6 2660 Hz. #18 6265 Hz.
e (14) Some shapes of th constrained stato
3D View STATOR.SHP-(Mode#2 1871Hz) (x,y,z)
Figure (15) Experimental mode shape of the stator/casing substructure. The front endshield is one of the two paths of rotor vibrations to the stator and surrounding environment through the motor casing. The study of the dynamic behavior of this part is important because it affects the rotor, stator and bearings vibrations and vise-versa. The front endshield, especially the throat part, “bearing housing”, modes of vibration directly affect the rotor/stator interaction as well as the bearings. The bending modes of the throat part will induce a non-symmetric air gap between the rotor and stator, while its axial modes will generate a variable air gap length. The front endshield plate is partially a noise radiator, so the control of effective mode shapes in noise generation and radiation is important. An annular steel plate of 131.2 mm outer diameter, and 16 mm inner diameter and 5.5 mm thickness, with a throat of 44 mm outer diameter, 35 mm inner diameter and 11 mm height was used as a front endshield of the electric motor. Different scenarios of structural dynamic behavior were proposed and carried out to achieve the best design of the motor front endshieled, which is responsible for the housing of the front bearing and consequently the rotor/stator assembly. A solid model and finite element were built to define their dynamic characteristics. The front and rear endshields were of axisymmetric structure, in which a doublet mode, having repeated natural frequencies, is denoted (m,n), where m is the number of nodal circles and n is the number of nodal diameters. As periodic features would be gradually added, axisymmetry is lost, and the doublets are classified as being either repeated or split in frequency. Criteria for frequency splitting in slightly asymmetric or periodic structures have been developed through a variety of analytical and experimental means. Modification scenarios including plate thickness and the number and direction of added ribs were done. Plates of 3.5, 4.5 and 5.5 mm with three, four, six and eight radial and circumferential ribs were investigated. Radial ribs “0.4 cm thickness, “triangular shape 1.1x3.8 cm”, were added to the front and rear endshields symmetrically around the throat. The addition of three, four, six and eight ribs increases the mass by 3.2%, 5.2%, 7.7% and 8.6% respectively. Tables (16-20) present the mode frequencies and description of the original front endshield with and without the proposed modifications. From the results it is clear that the mode shapes are positively changed. Moreover the added radial ribs improved the natural frequencies of this element. This improvement varies with the number of the added ribs. Adding three, four, six and eight radial ribs to the plate thickness of 5.5 mm improved the natural frequencies with values varies from “1%, 1%, 2% and 2% at mode number ten” to “12%, 22%, 34% and 41% of that part without ribs at mode number three” respectively as can be seen in Table (20). The added ribs significantly improved the mode shapes of the casing, which are responsible for the rotor/stator relationship as well as the acoustic noise radiation from the motor through this part. The eight ribs reinforcement gives a significant increase in mode frequencies and the best mode shape modification. Figure (16) shows some mode shapes of the unmodified and modified front endshield. As can be seen from the figure, the moving areas and amplitudes in each mode of the modified structures is less than those of the unmodified structures. The higher number of added ribs the lower moving areas and amplitudes.
Table (19) Undamped natural frequencies (Hz) and mode shapes of the unconstrained front endshield with six and eight radial ribs.
#4 3145 Hz. (0 radial rib) #5 3425 Hz. (6 radial ribs) #4 3443 Hz. (8 radial ribs) Figure (16) Some normal modes and natural frequencies of the unconstrained
front endshield without and with six and eight radial ribs. The rear endshield is the second path of vibration between the rotor and stator, which also is partially responsible for vibration transmission and noise radiation. Its modes frequencies and shapes follow the same trend of those of the front endshield for both original design and proposed modifications. The improvement of mode shapes of both rear and front endshields is very important to keep the rotor/stator relationship “air gap”, in the minimal changes by keeping a stagnant rotor end conditions. As can be seen from Table (21), the reinforcement of the rear end shield improved the natural frequencies from 1%, 2%, 3% & 3% at mode number ten to 12%, 23%, 34% & 42% at the third mode in the case of adding 3, 4, 6 and 8 ribs respectively.
Table (21) Improvement (%) in the undamped natural frequencies of the unconstrained rear endshield with added radial ribs.
The eigensolution, displacements and interference diagrams of the full motor structure were obtained and can be used in the design and operation stages of the relevant application. Experimental modal analyses, finite element and component mode synthesis of the full motor structure were obtained. Experimental modal data of the motor was obtained from the modal test, while finite element and component mode synthesis were obtained as outputs of Ansys and Matlab softwares. The stiffness matrices of the components and substructures were obtained through substructuring analysis on the Ansys, while the assembly process based on component mode synthesis was carried out using Matlab. Figure (17) presents the total combined matrix of the substructures matrices, which was used in component mode synthesis process. Both methods gave almost the same result. Table (22) presents the predictive values of mode frequencies and their corresponding experimental values. The error in these modes is less than 12%. This means that the predictive process can be used as a quality control test of the components, substructures and full motor structure model to ensure the application of total quality assurance in both the design and production stages.
Rotor/bearing substructure
Front and Rear endshield elements
Stator/casing substructure
Figure (17) The total combined matrix of the substructures.
Figures (18, 19) show a frequency response function (FRF) and an experimental mode shape of the electric motor “full structure”. Both finite element and experimental modal analysis gave the similar figures of mode shapes and closely spaced mode frequencies. Unlike experimental modal analysis, the finite element can provide more precise data of the full motor structure of both internal and external components.
Predictive Experimental Predictive Experimental FE CMS FE CMS
Table (22) Predictive and experimental mode frequencies (Hz) of
the full motor structure.
Figure (18) FRF of the full motor structure.
#1 231.908 Hz.
3D View MOTOR.SHP [Mode#1 231.908 Hz] [x,y,z] [mag]
Figure (19) Experimental mode shape#1 of the full motor structure. Experimental and predicted mode shapes of the outer motor casing and rotor shaft give the same results. The mode frequencies and modal shapes are in a good agreement. Moreover, the finite element mode shapes of the internal parts of the motor were obtained and can be used to clarify what is going on inside the electric motor. Mode shapes are important because they give an early indication of the gyroscopic bifurcation of modes for the particular rotor/stator assembly. The designer then has a good insight into whether inertial effects are important in the design, and which modes are more effective in the chosen air gap range. Mode shapes of rotor and stator provide a convenient environment to obtain a detailed understanding of the rotor/stator assembly’s lateral dynamics properties. The unbalanced magnetic pulls were treated as a magnetic-structural coupling in Ansys. Alternatively, it could be treated as the introduction of distributed load of the same value and distribution. This can be accomplished by introducing negative pressure between the rotor and stator on one side and positive at 180º, because the magnetic pull is of a negative stiffness which increases when the air gap is reduced and becomes smaller or positive when the air gap is increased. Since the rotor and stator as well as the unbalanced magnetic pull can be represented with the help of linear-elastic structural elements, the stability analysis can be refined to be a modal analysis problem. Unfortunately, the external force distribution is in the same shape of the first vibration mode in both shrinking and loose fits between the bearings and their relevant housings. As described previously, one of the purposes of the predictive design analysis procedure in this paper was to determine the displacement of the system when subjected to harmonic force inputs characteristic of unbalanced magnetic pulls. The location, magnitude, and frequency of these functions were described in the analysis and Figure (20). In a post processing of magnetic-structural coupling the displacement of the nodes at these locations were obtained, inspected and analyzed. It was decided to examine specific nodes on the outer rotor surface and inner stator surface with respect to displacement. These nodes were located at 0°, 90°, 180° and 270° at five circles along the air gap for both the rotor and stator of the electric motor, as seen in Figure (20-a, b). The harmonic force inputs to the system were applied at the 0° location perpendicular to the shaft axis as shown in Figure (20-a). The nodes at these locations were defined along the entire length of the rotor and stator surfaces by zooming process and their displacements were acquired and analyzed. From the obtained results of 100N harmonic force at the 0° location perpendicular to the shaft axis, it can be deduced that due to the application of the 24.166 Hz forcing functions the rotor remains cylindrical and thus rigid. Its displacement is essentially two-dimensional in the XZ-plane. Thus the rotor shaft behaves as a fixed-fixed beam. In addition, the stator displacement due to the 24.166 Hz force inputs is essentially a two-dimensional problem in the XZ-plane. The rotor and stator displacements due to the 24.166 Hz harmonic force, 100n, input on the rotor and stator are shown in Figures (21) for the 0° and 180° locations. Similarly, the double line
frequency “100 Hz.” problems can be analyzed. However, the obtained results of relatively large unbalanced magnetic pull are between two an three orders of magnitude less than the respective X-axis displacement and therefore may be neglected and the motor is safe from rotor/stator interactions under this range of applied force.
Casing
Stator
StatorFRotorF
Rotor
z
x
o90
o0
o270
o180
circle#1
circle#2
circle#3
circle#4
circle#5
Stator Stator
Rotor
o0o180
xy
(a) forces in the air gap. (b) section at 0°-180°. Figure (20) Schematic of radial forces “unbalanced magnetic pull” and section view along
the motor axis in the air gap length.
-8.00E-06
-7.00E-06
-6.00E-06
-5.00E-06
-4.00E-06
-3.00E-06
-2.00E-06
-1.00E-06
0.00E+00
1.00E-06
2.00E-06
3.00E-06
1 2 3 4 5
Circle#
Dis
plac
emen
t (m
.)
Stator 0? x Stator 0? y Stator 0? z Rotor 0? xRotor 0? y Rotor 0? z Rotor 180? x Rotor 180? y
Rotor 180? z Stator 180? x Stator 180? y Stator 180? z
Figure (21) Rotor and stator displacement at 0˚ and 180˚ due to
100 N unbalanced magnetic pull at 24.166 Hz. In electric motors the minimization of the dynamic stresses produced by fluctuating forces is a primary mechanical design consideration for rotors and stators. Rotors experience fluctuating forces when they pass through a non-uniform air gap from stationary stators and vice versa. The basic criteria that determine the dynamic response levels by the rotors are; proximity to resonance, excitability of the mode and force and damping levels. Evaluation of the interference diagram is the most important step in a rotating machinery vibration analysis. The interference diagram (frequency versus modal number) is used to determine any potentially excitable natural frequencies of the stator and/or rotor. Most motor builders and/or designers take a vibration analysis only far enough to produce a Campbell diagram that covers the first dynamic response criterion. Unlike the Campbell diagram the interference diagram goes further by investigating the mode shapes as the second dynamic response criterion, by determining whether the shape of the exciting force pattern matches the mode shape of the rotor or stator. The interference diagram shows the modal behavior that enables the analyst to avoid rotor/stator combinations that have the possibility of exciting a stator natural frequency. The interference diagram consists of; (a) stator mode shapes, (b) rotor mode shapes and (c) mode frequencies of rotor/ stator and exciting harmonics as can be seen in Figure (22). It also shows the primary and secondary sources of excitation, drawn as straight lines. The primary excitation line is governed by the running speed. The secondary excitation sources include the so-called difference mode “one of the least expected, but one of the strongest excitation sources” and are determined from the running speed, the number of rotating blades, and the number of stator slots. The diagram is valid for both constant and variable speed motors. In constant speed motors, beside the common excitation sources, any substructure vibrate in its natural frequencies can excite other substructures with its vibrating frequency. The intersection of substructures modes is a problem in such conditions. On the other hand in the variable speed motors the rotational speed (rpm) should be added to the chart and its intersections with the rotor and or stator modes is the most dangerous condition. The intersection of an excitation line with an excitation frequency shows points of potential rotor or stator excitation. By combining the stator and rotor mode frequencies, the interference diagram confirms whether a mode number is likely to cause a problem. From the results of octagonal stator, the user of the interference diagram should start with the first mode shape, which takes the rank n=2. Similarly, the Interference diagram can also be used to establish the mode frequencies that should be avoided for a particular
stage design. Depending on the actual configuration, vibration response from dynamic interaction with other motor components must also be considered.
i=0 i=1 i=2 i=3 i=4
j=0 j=2j=1
(a) Stator circumferential and axial nodal pattern.
i=0 i=1 i=2
. . .
. . .
. . .
Rotor axial nodal pattern
Orbital motion of rotor mode#1
(c) Mode frequencies of constrained rotor and stator/casing substructure.
(b) Rotor circumferential and axial nodal pattern.
0
1000
2000
3000
4000
5000
6000
7000
1 2 3 4 5 6 7 8
Mode#
Mod
e fr
eque
ncy
(Hz.
)
stator natural frequency rotor natural frequencymotor r.p.m 2xr.p.mline frequency 2x(line frequency)8Xr.p.m
Figure (22) The interference diagram.
In summary, the design requirements for electric motors are stability, strength and the dynamic behavior in operation stage, which can be achieved by providing an electric motor with a high stiffness, by keeping dimensional tolerances small, and by minimizing the vibration loading in the operation stage. The dynamic forces exerted between the rotors and stators of electric motors are a result of some faults and/or dynamic behavior resulting in more deformation rubbing and possibly interferences. Consequently, rigorous requirements should be placed on the design of electric motors. This applies particularly for the circular form and centering of the rotor and stator, since there are high magnetic tensile forces in the small air gaps. Small deviations in the concentricity generate a high magnetic force, which further increases the magnitude of the deviations. In the case of a higher mechanical stiffness of both rotor and stator, the rotor/stator is able to minimize their deflections and makes the motor work in a stable condition. Moreover, the static or simple estimates are not sufficient to perform a reliable and precise evaluation of the stability of the electric motor. Modal testing can provide valuable information about the dynamic response characteristics of electric motors. This information typically includes the natural frequencies and mode shapes of the simple and outer geometry shapes at room temperature in the absence of unbalanced magnetic pull “centrifugal loading”. While the dynamic response characteristics of electric motors during operation are likely to differ significantly from those measured under the modal test condition. The experimental “zero speed, room temperature” natural frequencies can serve as a valuable quality control test. The most effective methods for identifying potentially resonant conditions and dynamic behavior of electric motors should utilize a combination of modal test and finite element analysis to accurately predict the dynamic response characteristics of the structure under operating conditions. On the other hand, as the accuracy of finite element steady stress predictions has improved in recent years, steady stress and the low cycle fatigue of rotating parts have become more clearly understood. At the same time, vibration-related failures have become more frequent because a parallel development in understanding dynamic responses has not been made. This means that a modal based design and analysis could be used to identify regimes of operation: rigid and flexible rotor and stator modes as well as their assembly in the motor. Moreover it can be used to define the susceptibility of different mode shapes to sources of excitation and to determine the required air gap range to achieve a desired operating condition.
5. CONCLUSIONS 1. A predictive engineering process with access to various analysis and diagnosis tools is a creative and
decision-based process. This is best accomplished through an iterative environment that allows designers to obtain results quickly and efficiently.
2. Predictive design and analysis based on validated finite element and modal testing can provide valuable information about the dynamic response characteristics of electric motors. This information would typically includes the natural frequencies and mode shapes of the rotor, stator, rotor/stator relationship and full motor structure.
3. An accurate prediction of the dynamic response characteristics of the structure under operating conditions can be achieved by utilising a combination of modal test results and finite element analyses as the most effective method for identifying potentially resonant conditions in rotating machines.
4. The dynamic response characteristics of rotating machines from finite elements are likely to differ significantly from those measured under the modal “controlled” test conditions, and can serve as a valuable quality control test.
5. Mechanical vibration problems can vary from a mere nuisance to the indication of imminent motor failure. With a solid knowledge of predictive design and vibration analysis, it is possible to identify the root cause of the problem, and more significantly eliminate or reduce most problems in the design stage in addition, correction, or ascertaining the impact of increased vibrations and noise on motor reliability in the operation stage.
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