Technical LibraryArticle: Paper Introduction
Issue 2 Noise and Vibration Analysis Technology of Electric Motors
In this series, I would like to introduce various papers that present ways of using JMAG while performing electromagnetic field simulation. In this issue, I will introduce eleven pieces (refer to  through  in Reference) of literature that discuss Noise and Vibration analysis technology for electric motors.
In addition, you can search from the Web page of the paper introduced in this corner so please have a look. (http://www.jmag-international.com/cgi-bin/list_search.cgi)
Recently, devices in the world have been switching to electrical operation in order to achieve make improvements in efficiency and functionality. It is normal to see hybrid automobiles and electric vehicles driving around our cities, inside the cars there is also in abundance of electrical appliances and because of this, we understand that our comfortable lives have been attained through motors and solenoids. Because automobiles and home appliances are used close to us, it is easy for us to notice their noise vibration and in order to raise the added value of products, it is necessary to reduce noise vibration.
On the other hand, there is also strong demand for electrical equipment to be reduced in size and weight, improved in efficiency and reduced in cost. Other factors arising from continued reductions in size and weight include reduced device performance, and the difficulty of vibration control, which has the effect of making noise vibration occur more easily.
In order to combine these contradictions, we need to realize from the design stage electrical design that makes vibration less likely to occur and structural design that does not amplify vibration, so simulation tools exert huge power in considering this tradeoff.
The Difficulty of Noise Vibration Simulation
Noise vibration simulation evaluates electromagnetic phenomena with electromagnetic field analysis, and the electromagnetic force obtained there is used to validate vibration phenomena through structural analysis. Compared with electromagnetic field analysis, structural analysis has a longer history and is used in various fields but actually in the validation of electrical equipment, it is possible to say that in compared with electromagnetic field analysis, structural analysis is more difficult in terms of the analysis.
The reason for this is that because electrical equipment is made up several combinations of parts, including laminated core, coils and frames, the contact points cannot be modeled at a small scale. A good example of this is the laminated core. One silicon steel sheet is a 0.35 t or 0.5 t steel plate, but the laminated core punches through this. Just piling it up causes it to move out of alignment so caulking or welding is used to adhere it in place, but vibrational characteristics vary according to how much caulking is used on which parts of the laminated core. Having said that, it is actually impossible to model each single silicon steel sheet if over one hundred have been laminated together so we must use some method to homogenize them.
As we can see in the homogenization method, if the analysis target is changed to an equivalent method, the existing theory alone makes the information insufficient, and there are cases in which it is difficult to model. In such cases, what can be used as a solution is adjusting the analysis model's material properties and constraint method based on the experiment results, and bringing the vibrational characteristics (natural frequencies, mode shapes) closer to the actual measurement. The big drawbacks with this method that can be raised are that because the actual measurement's vibration data is the base point, you cannot run a simulation unless you have the actual measurement results and that if you change the structure a great deal, you will need to take actual measurements again. However, if you accumulate experiments, because you will be able to confirm the relationship between structure and behavior, there are many cases in which this method is used.
One method we can think of to improve the situation by which you cannot run a simulation without experiment results is to gather results from each institute where testing took plus and use them for a paper. By checking papers, it is possible to obtain all kinds of information. The papers we introduce this time are one we checked when running the noise vibration simulation. I hope they will also be of use to those of you when you run noise vibration simulations.
Approaches to These Problems
The papers we will introduce can be divided into four broad themes. Allow us to introduce a paper for each of the themes.
- Modeling laminated core frequently used in electrical equipment
- Handling coils unique to electrical equipment
- The combined relationship of the laminated core and the frame that supports it
- Themes that are not included in the three mentioned already, including ways of thinking about the structure mode of the electromagnetic force mode.
Laminated Steel Core Modeling
Fig. 1 Laminated core (stator)
When dealing with structural analysis of electric motors, the first thing we worry about is modeling the laminated core. We cannot carry out the impossible task of modeling every single structure of the single laminated core, so generally the method to use would be to impart anisotropy in the in-plane direction and direction of the lamination in order to model it. Compared to the entries in the in-plane direction in the laminated core ideally whether or not there are laminations should not have any affect so we can use the Young's modulus as it is in the catalog but as noted already, we need to pay attention to the lamination direction.
With regard to handling the lamination direction, we would think that the compression direction could be as it is in the catalog, but it is actually hard to say that each silicon steel sheet is attached because at the time of punching there was distortion. It is easy for us to get the image that the pulling direction can be connected by caulking and welding, consider that the compression direction has also been connected by caulking and welding, and there are many cases when it is modeled as linear material. In whichever case, there are many reports of the Young's modulus being much lower than the catalog value.
In , we prepared a number of samples that were shrinkage fitted with the cylindrical laminated core as the axis and ran a real eigenmode analysis and from the theoretical equations we extracted a Young's modulus equivalent to the experiment value. Because the sample's outer radius was 100 mm but it had the long axis length of 1 m, the equivalent Young's modulus was reported as 7.34 GPa. The properties of the original materials were that both the axis and core were 206 GPa, so a result is shown that is stops at 3-4%.
In , a Young's modulus of 22 GPa is used in the lamination direction for the finite element method (FEM) analysis results, and 10% of 22 GPa in the in-plane direction.
In  and , we adopted a lamination direction of 21 GPa and an in-plane direction of 210 GPa.
In , we report the results of the experiments we ran, the lamination direction is 70.5 GPa and the in-plane direction is 225 GPa.
We infer that the differences in the lamination direction Young's modulus arise from the relationship between the outer diameter of the laminated core, which can be thought that have changed due to structure, as the smaller the diameter and the smaller the stack length the closer they get to solid geometry, so there is a reduction in the Young's modulus.
Fig. 2 Status of the coil being set in the stator core
The next thing we worry about in modeling structural analysis of electric motors is the coil. The widely used low-capacity distributed winding coils have magnetic wire (copper wire) in the vicinity of 1 mm that can ensure a cross-sectional area, there is also more wire that might be required and is stored in a bundled state in the slot, and in the end it is processed with an insulating varnish. As a result of this, the lamination factor for copper wire in the slot is usually no more than 50%, with the remaining 50% made up of the insulating paper and insulating varnish. As well as the coil end having being arranged, after being fixed, it is processed with insulating varnish so its status is also complex. In this case of both inside the slot and the coil end, the copper is in a completely different state but modeling each strand of copper wire is an even more impossible task than modeling each single laminated steel plate so material properties are allocated that are equivalent to the laminated core.
In , we carried out a trial production of a stator with a different lamination factor and ran a hammering test, and by comparing it to FEM results, we were able to extract the relation nature between the coil lamination factors for in the slot and at its ends and the equivalent longitudinal elastic modulus.
In , the coil ends that have toroidal properties are modeled as an oscillating system, showing an idea that treats the iron core and coil ends as double-degree-of-freedom system.
Combined Structural Modeling
Fig. 3 Status of the stator core being set in the frame
As a rule of thumb, electric motors are made up of four parts which are the laminated core (stator, rotor), coil, frame and rotor axis. In comparison with the fixed side, the natural frequency of the rotation side is high, and because the fixed side can become a cause of noise vibration, there are many cases in which care is taken over the fixed side performing an analysis. As mentioned earlier in this section, there are difficult aspects to modeling each of the parts, and there are also challenges to combined modeling of the laminated core and frame, and the laminated core and coil, and if they share nodes, modeling with a spring has also been reported.
In , press fitting type segment core modeling is introduced, and by reviewing the material properties after considering the nodes of the contact points, the authors report that it is possible to generate a detailed model that will be useful in design validation.
In , in order to model the fitting of the stator and frame, we prepare a two-layer toroidal with a different clearance and run a modal analysis, we extract the relation nature between the eigen frequency changes and the fit pressure.
In , with regard to combining a pocket geometry frame with a core, because frame deformation has made the contact points discontinuous, we suggest that the modeling should be run with the springs in the theta-direction and r-direction. With regard to what spring constant should be used in structural analysis, this has also been modeled based on experiment results.
Until this point, we have introduced papers on the theme of why we should raise the accuracy of structural analysis models but at the end we will introduce papers specializing in vibration noise analysis. To begin with, let's look at the relationship between excitation force and the electromagnetic force mode shape that is the excitation force and the vibration mode shape. Put simply, even if the natural frequencies are the same, if the mode shape of the electromagnetic force and of the vibration are different, they will not lead to large resonance.
In , after considering abstractly the relationship between the vibration response coming from the electromagnetic force mode that is the cause of electromagnetic noise and the structural eigen frequency, we ran a modal analysis and report the usefulness of this logic. Also, we tried two methods to apply electromagnetic force, Multipoint Excitation and Distributed Excitation, and we also conducted experiments on the different relationship nature of the resonating coupled mode for each one, and the points considered make an interesting report.
However, it is merely that the sensitivity of the geometries of the electromagnetic force mode and the eigen frequency mode differ from each other, not that is easy for resonance to occur.
In , we verified that membrane oscillation at the bottom of a motor case is a source of noise vibration, but that an electromagnetic force mode that matches the membrane oscillation mode does not exist. However, because of toroidal electromagnetic force modes such as triangles, cases in which there is a structural connection, the membrane oscillation of case bottoms does not exist, so rather than worrying about whether modes match, there are in cases in which it is better to consider that some resonance will remain.
How were the papers we introduced? I think the information will be useful in electric engine vibration analysis. We may not know, but there are lots of other valuable papers. If we have time, we would like to introduce them, if there are any papers you think "should be read", we would be happy if you would introduce them to us.
 Yoshio IWATA, Hidenori SATO and Yawara MORIOKA
"Natural Frequency of Rotor with Rotor Core"
Transaction of The Japan Society of Mechanical Engineers Series C vol57 No.544 (1991-12)
 Kenzo Tonoki, Shinichi Noda, Makoto Matsushita
"Finite Element Method for Natural Frequency Analysis of Stator Core in Induction Motor (K-Model)"
The National Convention of IEEJ 2005 (5-126)
 Investigating R&D Committee on analysis technology for electromagnetic vibration and acoustic noise of induction machines
"Analysis Technology for Electromagnetic Vibration and Acoustic Noise of Induction Machines"
IEEJ Technical Report No.1048
 Sakashita Yoshiyuki, Tetsuya Hattori, Takashi Yamada, Hiroto Ido, Ryohei Ota, Eri Zeze, Kan Akatsu
"Comparison of Electromagnetic/Vibration Co-Simulation and experimental result for Permanent magnet motor. (The 2nd report)"
IEEJ Technical Meeting of Rotating Machine Technical Committees on Series D (RM-12-126)
 Koki Shiohata, Kanako Nemoto, Yasumasa Nagawa, Shigeru Sakamoto, Takashi Kobayashi, Motoya Ito, Haruo Koharagi
"A Method for analyzing Electromagnetic-Force-Induced Vibration and Noise Analysis"
IEEJ Transaction on Industry Applications vol.118 (1998) No.11
 Ryo KAWASAKI, Kazuyuki YAMAMOTO, Koji MASUMOTO, and Masaharu NISHIMURA
"Noise and Vibration Analysis of Compressor for Air-Conditioning Machine Equipped with a Concentrated Winding Motor with a Press-Fitted Segment Core"
Transaction of The Japan Society of Mechanical Engineers Series C vol77 No.777 (2011-5)
 Kazunobu ITIMI, Shinichi NODA, Isao SUZUKI, Fuminori ISHIBASHI and Hisashi YAMAWAKI
"Young's Modulus of Finite Element Method for Natural Frequencies of Stator Core in Induction Motor"
Transaction of The Japan Society of Mechanical Engineers Series C vol68 No.669 (2002-5)
 Shinichi NODA, Kazunobu ITIMI, Fuminori ISHIBASHI and Katuki IDE
"Contact Pressure and Natural Frequencies on Dual Ring (Experimental Study for Natural Frequencies Stator Core in Induction Motor"
Transaction of The Japan Society of Mechanical Engineers Series C vol65 No.629 (1999-1)
 Kazunobu ITIMI, Shinichi NODA, Isao SUZUKI and Fuminori ISHIBASHI
"Analysis for Natural Frequencies of Stator Core in Induction Motor"
Transaction of The Japan Society of Mechanical Engineers Series C vol64 No.624 (1998-8)
 Shinichi NODA, Isao SUZUKI, Kazunobu ITIMI, Fuminori ISHIBASHI, Sadaaki MORI and Youich IKEDA
"Natural Frequencies of Stator Core with Frame in Induction Motor"
Transaction of The Japan Society of Mechanical Engineers Series C vol61 No.591 (1995-11)
 Shinichi NODA, Fuminori ISHIBASHI and Katuki IDE
"Vibration Response Analysis of Induction Motor Stator Core (Vibration Response of Distributed Excitation and Multipoint Excitation)"
Transaction of The Japan Society of Mechanical Engineers Series C vol59 No.562 (1993-6)
Issue 6 Lesson on Advanced Iron Loss Analysis
Issue 5 For Those Planning to Start Analysis of Large Transformers Part 2
Issue 4 Applications for Induction Heating Phenomena
Issue 3 For Those Planning to Start Analysis of Large Transformers
Issue 2 Noise and Vibration Analysis Technology of Electric Motors
Issue 1 Induction Motor Simulation Technology