Flow, thermal, and vibration analysis using three dimensional finite element analysis for a flux reversal generator

Abstract

This paper presents the simulation of major mechanical properties of a flux reversal generator (FRG) viz., computational fluid dynamic (CFD), thermal, and vibration. A three-dimensional finite element analysis (FEA) based CFD technique for finding the spread of pressure and air velocity in air regions of the FRG is described. The results of CFD are mainly obtained to fine tune the thermal analysis. Thus, in this focus, a flow analysis assisted thermal analysis is presented to predict the steady state temperature distribution inside FRG. The heat transfer coefficient of all the heat producing inner walls of the machine are evaluated from CFD analysis, which forms the main factor for the prediction of accurate heat distribution. The vibration analysis is illustrated. Major vibration sources such as mechanical, magnetic and applied loads are covered elaborately which consists of a 3D modal analysis to find the natural frequency of FRG, a 3D static stress analysis to predict the deformation of the stator, rotor and shaft for different speeds, and an unbalanced rotor harmonic analysis to find eccentricity of rotor to make sure that the vibration of the rotor is within the acceptable limits. Harmonic analysis such as sine sweep analysis to identify the range of speeds causing high vibrations and steady state vibration at a mode frequency of 1500 Hz is presented. The vibration analysis investigates the vibration of the FRG as a whole, which forms the contribution of this paper in the FRG literature.

Keywords

flux reversal generator / air velocity / computation fluid dynamics / thermal analysis / vibration analysis / finite element analysis

Introduction

The flux reversal machine (FRM) was developed by combining the advantages of the switched reluctance machine (SRM) (simple construction, fault tolerance, mechanical robustness) and the doubly salient permanent magnet machine (DSPMM) (high energy magnets placed in a stator back iron) way back in 1996. It is a doubly salient machine. It has projecting stator poles. Each pole has two different excitation setups. Each of the stator pole has a concentrated AC winding which is called the main excitation winding. Permanent magnets (PM) are pasted on the stator pole shoe in opposite polarities, which also provides excitation. This arrangement of opposite polarities in stator PM causes reverse flux [ 1]. This along with winding excitation makes the induced EMF of each coil to go twice as high as that of other doubly salient machines. So FR machines offer high power density, torque and high speed capability. The rotor has no winding (or) magnets. In the recent past, the PM alternators are slowly replaced by FRM. A detailed research [ 1] has been conducted to declare that FRM has a better performance than the other special electrical machines such as SRM, DSPMM, and brushless DC machine (BLDCM). It has more advantages such as low inductance, low electrical time constant, low rotor inertia, simple construction, high power density, and fault tolerance capability. This superiority makes FRM suitable particularly for high speed aerospace and vehicle applications.

The cross sectional view of the FRG under investigation is shown in Fig. 1. It is a 8/6 rotor-stator pole combination generator and PMs are placed on the pole faces of stator poles. PMs are made up of high energy density material neodium iron boron (NdFeb). The stator and rotor are laminated by steel.

The main coil in the stator pole consists of two coils. These coils run on diametrically opposite stator poles. Each of these coil is connected in series or parallel to form ‘a phase’ of the machine [ 2]. These coils are connected to the load. The rotor speed is increased with the help of the prime mover which induces a magnetic field in the stator coils.

When the rotor rotates at a high speed, it creates an unbalanced centrifugal force in the components, which leads to vibrations and excessive heat in the machine parts. Besides, the air flow is highly turbulent inside the machine, which results in an air friction loss in the rotor. As the disadvantages of vibration and heat distribution are air velocity dependent, the analysis of both these aspects incorporating the knowledge of air velocity distribution will be a realistic one. Thus, the aim of this paper is to find the velocity of air, pressure and temperature in the interpolar air regions of the machine for a more real vibration and thermal analyses which are systematically documented below.

Flow analysis in FRG

Computational flow analysis

Computational flow analysis is a scientific process applied to resolve the fluid flow related problems like flow velocity, heat and mass transfer by computer based simulation methods [ 3– 5]. For electrical engineering, although the fluid flow analysis is almost nil, the knowledge of air flow inside the electrical machine will help in a great way for understanding the heat distribution in the machine, insulation coordination, and other thermal-insulation dependent issues. Air is treated as fluid and the flow analysis performed. When the rotor rotates, the air flow inside the electrical machine is largely tempestuous. This turbulent air can be captured and effectively used for thermal analysis. It is difficult to solve the air velocity by using the analytical method and hence numerical approach is used for this purpose. The Ansys CFX software has been used in this paper to investigate the effect of rotation of rotor on the air inside the machine. This is done to get the air velocity at all air region inside the machine to predict the thermal characteristics, further more accurately.

At first, the geometry of the air region inside the machine is completely modeled in 3D. The outer diameter of the air region is 75 mm. The diameter of the rotor is 49.40 mm. The stack length is 40 mm. The rotor-stator gap is 0.5 mm. The quadrature model of the FRG showing the machine geometries and the various air portions to be modeled for flow analysis is illustrated in Fig. 2(a), while the 3D model of the inter-polar air region alone is depicted in Fig. 2(b). The material properties required to conduct the CFD simulation have been set as follows: For 300 K ambient air temperature, the (fluid) air density ρ, is 1.086 kg/m³ and kinematic viscosity v, is 1.568 ×10^-5 m²/s.

Boundary conditions and governing equation

The boundary condition is to define the behaviour of air flow on the surfaces. It is applied in Ansys as inlet and outlet of the domain. In the air model of Fig. 2(b), there are two cross-sectional surfaces, one, as shown in Fig. 2(b), and the other on the back side. Any one side of these cross sectional surface is taken as the inlet. The other cross sectional surface will then form as the outlet surface. The outlet is set as 0 pascal average static pressure. A total fluid pressure (P_Total of 1 atmosphere is applied at an inlet, which will require inputting ρ and n. This will calculate the static pressure from the given equation,

(1) P_{\mathrm{Total}}=P_{\mathrm{static}}+ {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\rho {\left|\overline{v}\right|}^{\mathrm{2}}\mathrm{.}

The machine air region wall is set at zero velocity. This is called a no-slip boundary condition. Then, the hexahedral mesh is applied in the fluid region with a maximum mesh size of 3 mm to save the computational time. The steady state model is chosen for the CFD simulation. The air volume around the rotor is configured to rotate at 900 r/min. The solver runs the K-Epsilon model, taking into account the air velocity and mesh size near walls. The shear stress transport (SST) turbulence model is chosen for modeling the turbulent fluid flow to provide closure for the Reynolds-averaged Navier-Stokes (RANS) equations.

The process of establishing the speed of air comprises the fluid flow pattern. A fluid flow situation includes the laws of mass conservation and momentum conservation. The fluid mass conversation equation is given by

(2) {\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial (\rho u)}{\partial x}}+{\displaystyle \frac{\partial (\rho v)}{\partial y}}+{\displaystyle \frac{\partial (\rho w)}{\partial z}}=\mathrm{0},

where ρ is density, t is time, u, v, and w is velocity vector along x, y, and z directions.

The momentum conversation equation, also called the Navier-stoke equation, is described by

(3) $$\begin{gathered} \begin{array}{l}{F}_x-{\displaystyle \frac{\mathrm{1}}{\rho }}{\displaystyle \frac{\partial P}{\partial x}}+U\left({\displaystyle \frac{{\partial }^{\mathrm{2}}u}{\partial x^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}u}{\partial y^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}u}{\partial z^{\mathrm{2}}}}\right)={\displaystyle \frac{\mathrm{d}u}{\mathrm{d}t},}\end{array} \\ {F}_y-{\displaystyle \frac{\mathrm{1}}{\rho }}{\displaystyle \frac{\partial P}{\partial y}}+U\left({\displaystyle \frac{{\partial }^{\mathrm{2}}v}{\partial x^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}v}{\partial y^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}v}{\partial z^{\mathrm{2}}}}\right)=\frac{\mathrm{d}v}{\mathrm{d}t}, \\ {F}_z-{\displaystyle \frac{\mathrm{1}}{\rho }}{\displaystyle \frac{\partial P}{\partial z}}+U\left({\displaystyle \frac{{\partial }^{\mathrm{2}}w}{\partial x^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}w}{\partial y^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}w}{\partial z^{\mathrm{2}}}}\right)=\frac{\mathrm{d}w}{\mathrm{d}t}, \end{gathered}$$

where P is pressure, U is dynamic viscosity, F_x, F_y, and F_z are mass force at x, y, and z direction respectively. The above Navier-stroke equation is solved by the using the FE method for evaluating the velocity vector distribution and pressure with its density ρ.

Determination of air velocity and pressure

The 3D CFD analysis is performed for evaluating the air velocity and pressure in the whole air region of FRG. The CFD results obtained by solving Eq. (3) are demonstrated in Fig. 3. From the simulation results, it is observed that, at 900 r/min, the surface air velocity varies from 3.39 m/s to 6.78 m/s and the velocity in the mid portion of air region varies from 1.48 m/s to 3.39 m/s, which is highlighted in colour distinctions. Here, these are shown in green and blue colours of velocity streamline plot (Fig. 3(b)). The pressure inside the air region is 4.629 Pa. For the simulation of thermal analysis, the accurate prediction of heat transfer coefficient is always good, and this is achieved only through the knowledge of air flow distribution.

Generally the required limit of the air velocity for the electrical machine is 2–7 m/s. From the above results, it is inferred that on the surface the air velocity lies within this limit. The air velocity depends on the pressure drop. Therefore, it is necessary to estimate the pressure drop in the generator. In electrical machines, the primary heat generation starts from the stator, and the highest temperature of the stator occurres at the central position of the machine. The pressure is inversely proportional to the velocity. From the above plot, it is found that the pressure at the centre position of the generator is higher, but the velocity at the same position exhibits less value. In the surface area, the flow rate is higher but the pressure is lower. Hence, from the obtained air velocity and pressure, it can be inferred that the heat distribution inside the generator is nominal.

Thermal analysis of FRG

This section presents the prediction of steady state thermal characteristics of FRG using three dimensional finite element analyses. At first, the heat convection coefficients in the inner surfaces of the machine are evaluated. Usually, a lumped number is used as a constant velocity in the evaluation of convection coefficients. This single value of convection coefficient is assumed every where inside the machine. But practically the velocity is not constant. It varies turbulently and hence assuming it to be a constant will cause a big approximation [ 4– 6]. To avoid this limitation only, the air velocity at various inner walls is calculated using CFD, which fine tunes the thermal analysis.

Modelling procedure

Thermal analysis of FRG is performed in the Ansys platform. The geometry is modeled using key points, lines, arcs, and curves. The modeling has been conducted by taking three dimensional solid elements. The height and width of the stator pole are created using the main command menu-pre-processor-create-rectangle. Initially, a quarter model of the stator pole is created, and then it is rotated and copied for every 90 degrees to form a stator. Similarly, a rotor pole pitch is created as per dimensions and a 0.5 mm air gap is maintained between the stator and the rotor. The generator is mounted on the footage with a height of 22.19 mm. This completes the modeling stage of FRG. The 3D model of FRG is displayed in Fig. 4(a) and (b).

The major material properties of various parts are thermal conductivity, resistivity, density, specific heat, and Poisson’s ratio. Steel has been chosen for stator, rotor and footage material. The NdFeb material is used for permanent magnets. The assigned material properties are listed in Table 1.

The initial ambient temperature is set at 298 K. After assigning the material properties, the model is meshed, using the main command menu-pre-processor-mesh-free. The meshed model is demonstrated in Fig. 4(c).

Governing equation and boundary conditions

The electromagnetic analysis for FRG is performed approximately at 900 r/min and the losses are found out using the MagNetv7 FEA software. The total loss value is 5.42 W including copper and eddy current losses. These losses are the main source of heat production in electric machines. The value of heat flow rate Q is evaluated as the total loss in watts per square meter of the surface. All the four sides of a stator pole surface is selected and the calculated heat flow rate Q is applied, as these are the sides to which the heat producing winding is tightly wound. The developed heat is dissipated through the bottom pole shoe surface by natural convection process.

It is worth noting that the machine develops 1 kW at 5000 r/min and 50 W at 900 r/min. This is the reason for a total loss of 5.42 W at 900 r/min. As the total copper loss in any machine is about 10% of the power developed, the obtain loss of 5.42 W at 50 W output is justified. The governing equation for three dimensional finite element thermal analyses involving these heat dissipation is given by [ 7]

(4) \{K_{xx}{\displaystyle \frac{{\partial }^{\mathrm{2}}T}{\partial x^{\mathrm{2}}}}+K_{yy}{\displaystyle \frac{{\partial }^{\mathrm{2}}T}{\partial y^{\mathrm{2}}}}+K_{zz}{\displaystyle \frac{{\partial }^{\mathrm{2}}T}{\partial z^{\mathrm{2}}}}\}+ h_{\mathrm{cv}}(T-T_{\mathrm{amb}})=-Q,

where T is the unknown temperature distributed in Kelvin, K is the thermal conductivity (K/m²), Q is the heat source (W/m²), h_CV is the heat transfer co-efficient, and T_amb is the ambient temperature (K).

The evaluation of convection coefficients inside the walls of the machines helps to refine thermal related studies. Even though the conduction, convection and radiation modes of heat dissipations play a role in the heating and cooling process of systems, the convection mode usually takes a prominent part, and hence the conduction and radiation are ignored. The convection heat transfer co-efficient for the inner surface [ 6, 7] is given by

(5) {{\displaystyle h}}_{\mathrm{c}\mathrm{v}}={\displaystyle \frac{K}{D}}(\mathrm{0.11}){[\mathrm{0.5}{\mathit{Re}}^{\mathrm{2}}+{{\displaystyle G}}_{\mathrm{r}\mathrm{D}}Pr]}^{\mathrm{0.35}},

where D is the diameter of the stator up to the stator pole arc (m); Re (= (\rho V^{\mathrm{2}})/\left({\displaystyle \frac{UV}{D}}\right) ) is the Reynold’s number, shearing stress= \left({\displaystyle \frac{UV}{D}}\right) , V is the velocity of air (m/s), ρ is the density of air (kg/m³), U is the dynamic viscosity (kg/ms); Pr is the Prandtl number; G_{\mathrm{rD}}={\displaystyle \frac{g\beta D^{\mathrm{3}}\Delta T}{v^{\mathrm{2}}}} , v is the kinematic viscosity (m²/s), β is air thermal expansion co-efficient, \beta =\mathrm{1}/T_{\mathrm{f}} , T_{\mathrm{f}}={\displaystyle \frac{T_{\mathrm{amb}}+T_{\mathrm{wall}}}{\mathrm{2}}} and \Delta T=T_{\mathrm{amb}}\cong T_{\mathrm{wall}} .

The values of the above data for dry air are given in Table 2.

The heat transfer co-efficient on the inner surfaces depends on the velocity of air with which they are in contact. This contact velocity varies and hence the Renold’s number (Re) accordingly varies. Reynold’s number is between 15010 and 21793. If Re is above 4000, the whirl of air is considered as turbulent, and hence the flow of air is turbulent in this machine. This when substituted in Eq. (5), the respective values of heat convection co-efficient h_CV are found out. In the inner surface h_CV is between 23.14 W/(m²·K) and 46.51 W/(m²·K) at the respective air velocities. This heat convection coefficients are set respective as boundary conditions for accurate thermal analysis.

It is to be noted that if the h_CV is evaluated at the velocity of the operating speed, it will be a single lumped approximated value; now, as the h_CV is found out in every inner wall portions of the machine at the respective varying air velocities, the simulation of heat distribution becomes more accurate and realistic. The static and dynamic heat distribution inside the machine can be effectively calculated now with the CFD results. The respective heat convection coefficients are specified at these surfaces. The FRG model with boundary condition applied is shown in Fig. 4(d).

Complete simulation of steady state thermal analysis

The heat flow rate Q (Section 3.2) and the convection heat transfer co-efficient at the inner surfaces are specified. The ambient temperature is set at 35°C and a finite element thermal analysis is conducted at 900 r/min. The results of heat distribution and heat flux, under steady-state condition are exhibited in Fig. 5. The heat flux is the total heat energy transferred through the given surface per unit time. From Fig. 5, it is observed that the steady state temperature is increased up to 66°C at full load and 900 r/min. Thus the maximum temperature of FRG is about 66°C.

Since the F class insulation is used, the machine can withstand a temperature of up to 155°C, and hence the FRG is in the thermal safety region. It is predicted that the inside temperature is nominal, and compared to the lower part, the upper part of the generator has an intense heat distribution. This is because of the fact that the lower part is grounded through the footage at a temperature of 40°C.

When the heat flux results are considered with the help of Fig. 5(d) and (e), the obtained heat flux distribution at the stator is 28.6 kW/m² and the rotor is 1.46 kW/m². It is directly proportional to temperature difference and heat coefficient. It measures the heat transfer rate by measuring the temperature difference across a thermal barrier.

Demagnetization analysis of permanent magnet

The retentivity of permanent magnet is temperature dependent. The magnetization is retained in full up to the threshold temperature of the permanent magnet, beyond which it will start losing its magnetic retentivity. The permanent magnet will then start demagnetizing.

Figure 6 shows the generalized demagnetization curve of the permanent magnet material, describing the magnet performance. The linear portion of this curve (load line P₁, P₂) has a slope called the recoil permeability. A load line has been drawn from zero to the permeance coefficient of the magnet. For the NdFeb magnet, the permeance coefficient is 1.05. The intersection of the load line and normal curve describes the single operating point (P₁). When the operating point P₁ moves to P₂ due to a external demagnetization field, the residual flux density B_r is decreased to {B^{\prime }}_{\mathrm{r}} and magnet demagnetization occurs [ 8]. As a result, the magnetization M of the magnet is also decreased. The magnetization M is derived as

(6) M=B-{\mu }_{\mathrm{0}}H=B-{\mu }_{\mathrm{0}}f(B),

where μ₀ is permeability. Equation (6) means that the magnetization M of a magnet is a function of flux density B; H=f(B).

In this paper, an attempt is made to address this issue of the capacity of permanent magnets employed to retain their magnetic strength, through thermal analysis.

Figures 7 and 8 depict the demagnetization in the permanent magnets at various locations in it. This is done at different temperatures. There is an option available in the MagNet software for studying the demagnetization of permanent magnet for different temperatures. It is a demagnetization versus temperature study option. The permanent magnet is set with varying temperatures and this study is undertaken for every such set of temperatures. The results show that the permanent magnets of this machine start to loose their retentivity and start to demagnetize at a temperature of 80°C. This demagnetization of permanent magnets becomes worst at about 120°C.

This result suggests that the proposed FRG has to be operated at a temperature of up to 80°C to avoid demagnetization of permanent magnets. This is a safer limit because it is unlikely for a machines to reach 80°C at a continuous rating.

Windage (or) air friction loss calculation

Windage loss calculation is the other application of flow analysis. The air flow inside the generator is highly turbulent when the rotor rotates. This results in an air friction loss in the rotor. So it will add value for efficiency calculations to know the air friction loss in the design of a high speed generator. The air friction loss or windage loss can be expressed as [ 9]

(7) P_{\mathrm{loss}}=C_{\mathrm{f}}\pi \rho {\omega }^{\mathrm{3}}{r}^{\mathrm{4}}l ,

where ρ is the air density in kg/m³, ω is the angular velocity in rad/s, r is the radius of the rotor in mm, and l is the length of the generator in mm. The air friction coefficient is the only unknown variable. This is expressed as

(8) C_{\mathrm{f}}={\displaystyle \frac{\tau }{{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\rho V^{\mathrm{2}}}} ,

where τ is the shear stress on the rotor surface, and V is the velocity of airflow. From Eqs. (7) and (8), it is found that the air friction loss depends on the velocity of the air. Using the result of CFD analysis, the calculated value of air friction coefficient is between 0.4 and 0.6 and the windage loss is between 0.012 to 0.03 W , at a 900 r/min operating condition. The winding loss will be low and is usually assumed to be negligible.

Vibration analysis of FRG

This machine has combined the advantages of SRM and the doubly salient pole permanent magnet (DSPPM). The attraction and repulsion cycle caused by permanent magnets and the salient rotor during the energy transformation leads to the vibration and noise in the FRM [ 9, 10], which can become destructive. To identify the frequencies of the vibration which can cause the severe vibrations, a vibration analysis has to be done. The results of the vibration analysis will list the frequencies (or speeds) to be skipped to prevent any structural damage which occurs when the frequency of the machine coincides with the natural frequency. This is called the modal study which will ensure a quiet operation of the machine.

In this focus, Section 4.1 describes a 3D modal analysis on FRG including the stator, the rotor, the end shields, the bearings, and the housings. Section 4.2 explains, a 3D static stress analysis to predict the deformation in the generator parts. Section 4.3 records an unbalanced rotor dynamic analysis on FRG, which ensures the vibration of the rotor including the fact that the housing are within the safe limits. This section also reports the harmonic analysis to identify the frequency at which the vibration is maximum and describes the steady state vibration at maximum frequency. All these analyses is a total documentation of vibration study of FRG.

Three dimensional modal analysis

The FRM model under consideration for the vibration study is shown in Fig. 9(a). The length of the stator stack is 40 mm and the end rings are tightly mounted on both sides of the FRG to support the rotor assembly. The thickness of each bearing on the shaft is 5.5 mm. For modal analysis, additional material properties such as Young’s modulus, Poisson’s ratio and mass density are required [ 11]. The mechanical properties used are given in Table 3.

The mechanical coupling is to be modeled separately as there is no provision for readymade selection of this. This modeling is called nodal coupling. The nodal coupling is applied between the shaft and bearing end cover at the bearing location. The nodes are coupled in the U_x, U_y, U_z direction to represent the bearings. Coupling is a way to force a set of nodes to have the same DOF (Degree of Freedom) value. This completed model of coupling is shown in Fig. 9(c).

The foot of the generator is clamped to represent the boundary conditions as shown in Fig. 9(d).

The modal solver makes it possible to evaluate the natural frequency and mode shapes of the structures. The identification of resonant frequency that could create severe vibration and noise is also evaluated.

The three dimensional Laplace equation that is solved to find the modal frequencies is given by

(9) {\displaystyle \frac{ {\partial }^{\mathrm{2}}\varnothing }{\partial x^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}\varnothing }{\partial y^{\mathrm{2}}}}+{\displaystyle \frac{{\partial }^{\mathrm{2}}\varnothing }{\partial z^{\mathrm{2}}}}+{\omega }^{\mathrm{2}}\varnothing =\mathrm{0},

where \varnothing is a modal vector and ω is the frequency of vibration. The solution {\varnothing }_i is the ith mode shape and ω_i is the corresponding natural frequency.

Figure 10 shows the housing vibration mode with foundation. The vibration spreads fully over the housing in three directions viz., horizontal, axial and radial. Figure 10(a) shows the result of vibration in the horizontal direction. This happens at a mode frequency of 1488.62 Hz. Figure 10(b) shows the result of vibration in the axial direction. This occurs at a mode frequency of 1568.78 Hz. Figure 10(c) shows the result of vibration in the radial direction. This takes place at a mode frequency of 4119.94 Hz. At a modal frequency of 3372.43 Hz, the rotor and shaft undergo bending and arresting of the housing, which produce high acoustic noise as shown in Fig.10(d).

Figure 10(e) shows the severe shaft deformation at the modal frequency of 3848.85 Hz. It is observed here that the shaft end vibration does not spread to rotor or housing, but as the pulley and connected loads will be put into vibration, the noise will be high. The natural frequency of various parts of the generator and the vibration value are tabulated in Table 4. The other higher order modal frequencies are given in Table 5. Even though the machine may not be run at these high speeds, a keen listing of modal frequencies indicates the respective speeds to be skipped for a noiseless operation.

Static stress analysis

The static stress analysis is couducted to perform the load test on FRG to monitor the limit violation of stress and deformation at different parts of the machine. Bearing is the additional model required for this analysis and is the element to hold the housing and rotor mass at the shaft location. So, bearing is simulated as four springs attached to the housing from the bearing locations. Four nodes at the housing on x-y axis are selected and joined to a single node at the front bearing location on the shaft. The same procedure is repeated at the back side of the shaft. A spring stiffness of 21000 is assigned and the bearing is modeled [ 6]. The representation of bearing is shown in Fig. 11.

The load component on FRG machine, load is of two components. One is torque resulted from the rotor, while the other is centrifugal load caused by rotating speed.

Under static analysis, the tip of the rotor and inner edge of the stator yoke are coupled in the tangential direction to represent the torque reaction from the rotor to the stator as shown in Fig.12. The load is applied using the following command.

LOADS:

! ------

OM= 2*PI*rpm/60.0

OMEGA,0,0,OM

T= 102*PWR/OM ! Torque- mkgf

R= 0.0045 ! Shaft radius, m

FOR= T/R ! kgf

ESEL,MAT,3 ! Select element by material

NELE

NSEL,R,LOC,X,4.5 ! Select the node by location

,R,LOC,Z,25,39

NROTA,ALL ! Rotate nodal coordinate systems into the active system

F,ALL,FY,FOR/144! Force, node, label, value

ALLS

The simulation is carried out for different rotating speeds of 900 r/min and 9000 r/min. The different parts of stress and deformation results are shown in Figs.13 to 16. All the deformations are represented in mm. The material considered has a maximum yielding stress of 24 kg/mm². The stress and the deformation in the two cases considered viz., 900 r/min, 9000 r/min are tabulated in Table 6. The factor of safety (FOS) is given by

(10) \mathrm{FOS}={\displaystyle \frac{\mathrm{Yielding}\mathrm{stress}({\sigma }_{yA})}{\mathrm{Maximum}\mathrm{stress}({\sigma }_{\mathrm{1}})}}.

For a safer operation, FOS is to be greater than 2.05.

From Table 6, it is observed that the FOS for all the parts is above 2.05. Thus, FRG can be operated between 900 to 9000 r/min without any mechanical threats.

Unbalanced force dynamics (Harmonic response)

The unbalanced rotor dynamic analysis is to determine the eccentricity of the rotor mass and ensure that the vibration of the rotor is within the limit. The rotor unbalance force is computed assuming a balancing grade (Q) of 2.5 and a damping ratio of 0.02, which are the usual standard values for high-speed machines. The weight of the rotor (w) is 3.23 kg.

Under the operating speeds of 900 and 9000 r/min corresponding to the balancing grade of 2.5 (will vibrate at 2.5 mm/s) the eccentricity e is computed as

(11) e={\displaystyle \frac{V}{\omega }},

where V is the velocity in mm/s, and ω is the angular speed (rad/s).

From Eq. (11), it is obtained that the calculated value of eccentricity is 0.026 mm at 900 r/min and 0.0026 mm at 9000 r/min. As this eccentricity is of negligible value, it is conclusive that the rotor dynamics of the considered FRG is in the acceptable limit.

The unbalanced force is given by

(12) F_U=m{\omega }^{\mathrm{2}}e ,

where m is the mass of the rotor (3.23/9.81=0.33 kg) and e is the eccentricity of the rotor. This gives the unbalanced force of 0.076 N at 900 r/min and 0.76 N at 9000 r/min.

A harmonics frequency analysis is performed to identify whether the vibration of the rotor and housing are within the safe limits. In this paper, the analysis on two different parts, i.e., sine sweep analysis and steady state vibration at 1500 Hz, is presented. The aim is to obtain the structure response of the machine at several frequencies with respect to displacement. Large displacements are identified and plotted as a graph. Stresses and deformations are viewed and tabulated at these frequencies.

Sine sweep analysis

The unbalanced force is applied over a frequency range of 1 to 10000 Hz. This analysis is conducted to identify the possible vibrating and noise producing speed bandwidth which are skipped fast during acceleration. The simulation results of harmonic response of the stator and rotor are shown in Fig. 17. It can be observed that large displacement occurs corresponding to the frequency of 1500 Hz. Since 1488.62 Hz and 1568.78 Hz are predominant, this corresponds to the modes 1 and 2 respectively as shown in Table 4. The critical speeds are identified as 11164 r/min and 11766 r/min. Hence, it is inferred that the FRG should not operate beyond these speeds. These natural frequencies are to be avoided for noiseless operations which protects the machine from the fatigue failure of mechanical parts. So it will not affect the internal organs of human when operating the machines.

Steady state vibration at 1500Hz

From Fig. 17, it is observed that the large displacement (resonance) occurs at the frequency of 1500 Hz. Thus, the harmonic analysis is performed for this frequency to find the stress and deformation and the results are shown in Fig.18. The FOS is calculated for stress and deformation of the housing model, which are given in Table 7. The values of stress and deformations at this frequency are not within the safe limit (FOS<2.05). Thus, the speed limit of FRG is between 900 and 9000 r/min. Above this speed, vibrations are caused, which will damage the mechanical part of the generator.

Conclusions

This paper has conducted computation fluid flow analysis, flow-thermal analysis, and vibration analysis using the 3D FEA package ANSYS CFX and Fluent. The air velocity and air pressure profile of a flux reversal generator have been traced out using modelling and simulation of FRG. The steady state temperature distribution analyses inside FRG and the static thermal analysis have been performed. The heat transfer co-efficient has been obtained from the result of flow analysis, and the windage loss has been evaluated from the same flow analysis. Besides, an accurate simulation of thermal analysis has been carried out to specify the heat convection coefficient h_cv at air region, which will approximate the simulation results to a greater extent. The other extension of thermal analysis is to predict the permanent magnet demagnetization. Depending upon the temperature, the reversible and irreversible demagnetization are predicted. It is verified that irreversible demagnization does not occur in the permagnet magnet. While increasing the temperatue under transient state the demagnetization arises at 80°C and reaches the maximum at 120°C. A step-by-step 3D vibration analysis, harmonic analysis and static stress analysis are documented for 6/8 pole FRG. From the vibration analysis, it is observed that vibrations and stresses are under safe limit between 900 and 9000 r/min and the large displacement occurs at the frequency of 1500 Hz. The reported procedures for mechanical characterization of FRG in this paper can be adopted for any pole combinations and dimensions of FRG to thoroughly perform mechanical study in three dimensions. This will help to fine tune the design to be declared for end product. Optimization techniques can be applied to all the procedures reported here, in order to declare a final design sheet, which can be considerd as the future work.

References

[1] Deodhar R P, Andersson S, Boldea I, Miller T J E. Flux reversal machine: a new brushless doubly-salient permanent-magnet machine. IEEE Transactions on Industry Applications, 1997, 33(4): 925–934

[2] Wang C, Nasar S A, Boldea I. Vector control of three-phase flux reversal machine. Electric Machines and Power Systems, 2000, 28: 153–166

[3] Andres U S, Almondoz G, Poza J, Ugalde G, Escalada A J. Radial fan simulations by computational fluid dynamics and experimental validation. In: International Conference on Electrical Machine (ICEM). Berlin, Germany, 2014, 2179–2185

[4] Connor P H, Pickering S J, Gerada C, Eastwick C N, Micallef C. CFD modelling of an entire synchronous generator for improved thermal management. In: 6th IET International Conference of Power Electronics, Machinesand Drives (PEMD 2012). University of Bristol, UK, 2012, 1–6

[5] Chong Y C, Echenique Subiabre E J P, Mueller M A, Chick J, Staton D A, McDonald A S. The ventilation effecton stator convective heat transfer of an axial-flux permanent magnet machine. IEEE Transactions on Industrial Electronics, 2014, 61(8): 4392–4403

[6] Srinivas K N, Arumugam R. Analysis and characterization of switched reluctance motors: Part II—flow, thermal, and vibration analyses. IEEE Transactions on Magnetics, 2005, 41(4): 1321–1332

[7] Srinivas K N, Arumugam R. A novel thermal characterization of switched reluctance motors involving computational fluid dynamics. Electric Power Component and Systems, 2004, 32(9): 855–867

[8] Zhang D, Wang F, Kong X. Air friction loss calculation of high speed permanent magnet machines. In: International Conference on Electrical Machines and System. Wuhan, China, 2008, 320–323

[9] Yan Y, Deng Z, Zhang Q, Wang X. Stator vibration analysis of bearingless witched reluctance motor. In: International Conference on Electrical and Control Engineering. Wuhan, China, 2010, 1993–1996

[10] Gan C, Wu J, Shen M, Yang S, Hu Y, Cao W. Investigation of skewing effects on the vibration reduction of three-phase switched reluctance motors. IEEE Transaction on Magnetic, 2015, 51(9): 8203509

[11] Torregrossa D, Peyraut F, Cirrincione M, Espanet C, Cassat A, Miraoui A. A new passive methodology for reducing the noisein electrical machines: impact of some parameterson the modal analysis. IEEE Transactions on Industry Applications, 2010, 46(5): 1899–1907

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg