# Finite Element Methods in CAD: Electrical and Magnetic Fields

Each failure has other symptoms other vibration frequencies, direction, size, etc. This makes it possible to determine the type of failure based on long-term tracking. In order to be able to identify in a timely manner, the type of malfunction that arises, it is necessary to know the manifestations of the individual faults. In earlier times, the only possibility of tracking and measuring the development of malfunctions was done on real machines. On the basis of this experience, the same foreseeability disturbances could be assumed in other machines.

This process has been simplified with the onset of computing and finite element utilization. It is now possible to simulate the physical models in electrical machines in full extent. It is possible to interface individual types of models mechanical, electromagnetic, thermal and then achieve very accurate results. The Ansys program is a program that allows to solve physical phenomena in electrical machines. Thanks to the individual modules, it is possible to make electromagnetic, thermal and mechanical design of any electrical machine and then simulate its behavior in different operating states.

Especially today, when using many types of inverters, it is a great advantage to connect a model to an electrical circuit. It allows to solve the influence of different methods of power supply on electric machine. For example, what effect the vibrations of the electric machine will have on higher harmonic generated inverter. The problem of calculating vibrations in electrical machines is very complex due to the number of physical phenomena, and it is necessary to handle a large amount of information from many areas mechanics, magnetism, etc. For this reason, this chapter focuses on a basic approach to solution issues.

In solving a particular problem, it is necessary to take into account the time requirement of individual calculations and to perform a sufficient amount of calculation simplifications which are based on the results requirements analysis. Simplification may involve adjustments to a particular model that is used for the calculations. Another simplification may be the neglect of some of the vibration sources that operate in the electric machine, and so on. The main requirement is that the simplification of the model does not cause the error to be calculated.

Therefore, it is necessary to familiarize themselves with the construction of the simulated machine, the sources of vibration, the functions of individual parts and their effect on the propagation of vibrations [ 1 , 2 ]. Vibrations are a mechanical phenomenon. It can be said that this is the movement of a flexible body or environment whose individual body vibrates around the equilibrium position. The forces acting on any system create the oscillation itself. In a simple case, the oscillation has a harmonic character. This occurs when system is exposed to a single source with a constant exciting force.

For the description of harmonic oscillation, the relationship is used:. This relationship applies to very simple oscillations. There are a number of sources and influences in electric machines that affect the vibration generation. The actual course of vibration displacement is, therefore, the sum of forces that change over time with different frequencies.

For the calculation of vibrations in electrical machines, it is necessary to get basic information about their basic construction. The electric machine consists of a magnetic circuit. The magnetic circuit focuses most of the magnetic field into a defined area. The magnetic circuit itself is made of steel plates connected to the stator, respectively into the rotor.

There are grooves cut on the internal circumference of the stator, into which the winding is inserted. The winding itself is one of the most important parts of electric machines. In some applications, aluminum alloy of similar purity is used as a material. All electric motors have many other mechanical parts.

These include a shaft on which the rotor plates are mounted. Although the shaft is, in most cases, a simple component that is made of a machined steel rod, it can have a great effect on the vibration of the machine. The main parameter that can affect the vibration is the quality of the processing and the quality of the whole rotor balancing.

Due to the possible inhomogeneity of the material, the so-called mass unbalance can occur, causing the unwanted vibrations generated by the machine. The vibration level and frequency depend on the rotation speed of the rotor itself. Rotors are balancing in production to reduce this phenomenon. Another important part of electrical machines is bearings. Many types of bearings are used in electrical machines. Ball bearing or roller bearings are commonly used. Nowadays, electromagnetic bearings are also used in special applications.

From the vibration point of view, two separate phenomena occur in the bearings. The first is generating vibrations. This is in trouble-free condition caused, for example, by skipping the balls. The fault condition is the result of a missing lubricant.

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Failures can also be caused by poor quality lubricants. The second factor that affects the vibration of the electric machine is transmission between the rotor and the stator. Depending on the design of the bearings, they are partially damped. The bearings are located in a bearing shield that is attached to the frame of the electric machine. A stator of the electric machine is also placed in the frame. There are several types of frames. The most commonly used are foot frame or flanges frame. Based on the type of frame, the machine is mechanically connected to the device.

Again, the method of attachment of the machine affects the propagation or, respectively, vibration damping in the electrical machine. A terminal box is also attached to the frame and it serves to connect the power supply. The power supply method of the electric machine is another important factor. Electric machines are divided according to the following types of power supply: Asynchronous: Electric machines powered by AC voltage, either in one or in three phases. These are the most commonly used machines in the industry. They have different rotations of the magnetic field in the stator and the rotor.

Synchronous: Electrical machine whose rotating speed is proportional to the frequency of the alternating current supply and independent of the load. Synchronous machines are very often used as a generator. DC machines: Electrical machine powered by direct current.

In most cases, it works with a static field in static machine parts. Permanent magnets may appear in their construction. As can be seen from the brief description of the construction of the electric machine, it is a mechanically and intricately complex device with many variations. Various factors can affect the formation or propagation of vibrations. For this reason, it is always necessary to determine which parameters and structural elements are inserted into the calculation process and which are neglected [ 5 , 6 , 7 , 10 , 11 ].

The generation of vibrations in an electric machine influences several design parameters. The influence on the generation of vibrations is mainly due to components design, mainly their shape and quality of production. With the time of use of the electrical machine in operation, vibration and wear of individual components increase.

Vibration sources are identified in vibration spectrum. Each vibration source takes effect of specific frequency in the spectrum. The amplitude is proportional to the degree of damage. For each source that causes the peaks at corresponding frequencies with increasing deviation, the value of peaks increases [ 2 , 8 ]. Examples of electrical machine faults that can be modeled with finite element method are: Unbalance of the rotor: The unbalance depends on the distribution of the center of gravity of the rotor relative to its axis of rotation. Because of the uneven distribution of matter, the imbalance causes centrifugal force, noise and rotor vibration.

With higher speeds, vibration is increasing. Eccentric rotor: Eccentricity occurs especially when the rotary axis is shifted relative to the geometric axis. Because of the eccentric rotor, there is a variable air gap between the stator and the rotor that generates pulsating vibrations. The greatest vibration reaches the first harmonic component.

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The rotor eccentricity contributes to vibration and noise. It causes an unbalanced pull of magnetic force in the rotor and bending the shaft. Static eccentricity: Situation, when the rotor is deflected from the center of the engine and still rotates around its own axis of rotation. This is because of the static eccentricity.

The size of the air gap is not constant over its entire circumference, resulting in stronger interactions between the stator and rotor magnetic fields in places with a smaller air gap. Dynamic eccentricity: In the latter case, dynamic eccentricity occurs when the rotor rotates in the geometric center of the engine but does not rotate around its own axis of rotation. The way in which computational efficiency can be reached is also discussed.

Examples of application are given in order to illustrate the practical use of the procedure and to validate it by comparisons with available solutions. Volume 37 , Issue The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account.

Institutional Login. Log in to Wiley Online Library. The second factor that affects the vibration of the electric machine is transmission between the rotor and the stator. Depending on the design of the bearings, they are partially damped. The bearings are located in a bearing shield that is attached to the frame of the electric machine. A stator of the electric machine is also placed in the frame. There are several types of frames. The most commonly used are foot frame or flanges frame. Based on the type of frame, the machine is mechanically connected to the device. Again, the method of attachment of the machine affects the propagation or, respectively, vibration damping in the electrical machine.

A terminal box is also attached to the frame and it serves to connect the power supply. The power supply method of the electric machine is another important factor. Electric machines are divided according to the following types of power supply: Asynchronous: Electric machines powered by AC voltage, either in one or in three phases. These are the most commonly used machines in the industry.

They have different rotations of the magnetic field in the stator and the rotor. Synchronous: Electrical machine whose rotating speed is proportional to the frequency of the alternating current supply and independent of the load. Synchronous machines are very often used as a generator. DC machines: Electrical machine powered by direct current. In most cases, it works with a static field in static machine parts. Permanent magnets may appear in their construction.

## List of finite element software packages - Wikipedia

As can be seen from the brief description of the construction of the electric machine, it is a mechanically and intricately complex device with many variations. Various factors can affect the formation or propagation of vibrations. For this reason, it is always necessary to determine which parameters and structural elements are inserted into the calculation process and which are neglected [ 5 , 6 , 7 , 10 , 11 ]. The generation of vibrations in an electric machine influences several design parameters.

The influence on the generation of vibrations is mainly due to components design, mainly their shape and quality of production. With the time of use of the electrical machine in operation, vibration and wear of individual components increase. Vibration sources are identified in vibration spectrum.

Each vibration source takes effect of specific frequency in the spectrum. The amplitude is proportional to the degree of damage. For each source that causes the peaks at corresponding frequencies with increasing deviation, the value of peaks increases [ 2 , 8 ]. Examples of electrical machine faults that can be modeled with finite element method are: Unbalance of the rotor: The unbalance depends on the distribution of the center of gravity of the rotor relative to its axis of rotation. Because of the uneven distribution of matter, the imbalance causes centrifugal force, noise and rotor vibration.

With higher speeds, vibration is increasing. Eccentric rotor: Eccentricity occurs especially when the rotary axis is shifted relative to the geometric axis. Because of the eccentric rotor, there is a variable air gap between the stator and the rotor that generates pulsating vibrations. The greatest vibration reaches the first harmonic component. The rotor eccentricity contributes to vibration and noise. It causes an unbalanced pull of magnetic force in the rotor and bending the shaft. Static eccentricity: Situation, when the rotor is deflected from the center of the engine and still rotates around its own axis of rotation.

This is because of the static eccentricity. The size of the air gap is not constant over its entire circumference, resulting in stronger interactions between the stator and rotor magnetic fields in places with a smaller air gap. Dynamic eccentricity: In the latter case, dynamic eccentricity occurs when the rotor rotates in the geometric center of the engine but does not rotate around its own axis of rotation. The air gap is a function of both position and time. The variable air gap rotates at a frequency equivalent to the rotational speed of the rotor.

Bent shaft: The cause of the shaft deformation is the difference between the geometric axis and the axis of rotation. The geometric axis of the bent shaft has the shape of a curve. If the axis of rotation is not a straight line, it is a bend shaft. If the center of gravity does not lie on the rotary axis, the rotor is unbalanced [ 2 , 8 ].

For any calculation of the vibration level, it is necessary to become familiar with the various sources that generate these vibrations in electric machines. According to the physical principle, sources of vibration can be divided into several groups: Electromagnetic sources. Vibrations of electromagnetic and mechanical origin occur in all rotating electric machines. As a source of aerodynamic origin, it is usually a fan.

Fan is often not a part of the construction of electric machines. For this reason, this chapter does not deal with the problem of calculating the vibrations thus generated [ 1 ]. Part of the vibration of electric machines is of electromagnetic origin. Their cause is the oscillation of the machine frame and its parts caused by electromagnetic forces.

These forces are due to higher harmonics of the supply current, magnetic saturation, phase asymmetry, magnetostriction or disturbances in the magnetic circuit or electrical component of the machine. The frequency spectrum of these vibrations has discrete character. Vibrations caused by the electrical causes occur mainly in the radial direction. Vibrations are occurred in the case of more varied air gap size in the axial direction, for example, due to non-symmetrical rotor mounting [ 1 ]. Mechanical vibrations are mainly caused by bearings, rotor balancing, machining of rotating parts and rotor mounting.

Mechanical vibrations produced into electrical machines are also caused by connected devices. These external vibration sources include clutch misalignment or gearing, wedge gears or vibrations caused by connected loads [ 1 ]. The basic aerodynamic source of vibration is the fan in electric machine. Any obstruction that is exposed to air flow can generate vibration.

The main cause of fan noise is the formation of turbulent airflow around the fan blades [ 1 , 2 , 4 ]. As already indicated in the previous sections of the chapter, the vibration of electric machines is a phenomenon that interferes with several physical areas mechanics, electromagnetism, etc. Therefore, the entire calculation process needs to be divided into several parts: Determining Vibration Sources: at first, it is necessary to decide which resources to count.

In the case of this chapter, the calculation is simplified only for the occurrence of vibrations by the effect of a time-dependent electromagnetic field. For this reason, it is possible to use Maxwell 2D or Maxwell 3D. This module allows to calculate the time-varying effect of the force in the magnetic circuit depending on the change of the electric current.

The use of this program also allows to connect to a simulator of electrical circuits program Simplorer. After connecting the supply current to the Maxwell model on the simpler electric circuit, it is possible to calculate the changes in the magnetic circuit caused by the control logic, that is, speed control. Model creation: creating a model of an electric machine is one of the most important parts of the calculation itself.

The user must choose between 2D and 3D model. The 2D model is much simpler, and therefore, the calculation itself takes a very short time.

On the other hand, this is a great simplification of the calculation. The 3D model will allow for a more accurate calculation and consideration of the more influences affecting the calculation. However, the calculation of 3D models is considerably more demanding for computational power, and therefore, the calculation time is considerably longer.

Calculation of forces caused by selected sources: the next step is to determine the forces that act on the electrical machine. In this chapter, this is defined as a force of electromagnetic origin. The Maxwell program is used to determine them. These calculations can be supplemented by the calculation of the actual frequencies of the electric machine and also by external influences such as asymmetry, etc.

An important factor is determining the right time step. The model of an electric machine can be made in several ways. One of them is the use of modern CAD systems to create geometry and its subsequent import into the computing environment. Another option is to create a model directly in the Ansys using DesignModeler.

Another choice is to use the RMxprt environment. This module is primarily designed for rapid calculations of electrical machines. It features an environment for fast input of electrical machine dimensions. At the beginning of the job, the user selects a template that matches the specific machine type.

The user then enters the main machine dimensions, slot size and slot type, and other parameters using simple tables. RMxprt contains the following electrical machine templates: Synchronous machine. User needs to know a lot of information to create a model in RMXprt.

Finite Element Methods in CAD: Electrical and Magnetic Fields
Finite Element Methods in CAD: Electrical and Magnetic Fields
Finite Element Methods in CAD: Electrical and Magnetic Fields
Finite Element Methods in CAD: Electrical and Magnetic Fields
Finite Element Methods in CAD: Electrical and Magnetic Fields
Finite Element Methods in CAD: Electrical and Magnetic Fields
Finite Element Methods in CAD: Electrical and Magnetic Fields

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