FIRST CYCLE, 15 CREDITS STOCKHOLM SWEDEN 2018,
Consequences of Magnetic
Properties in Stainless Steel for a High-efficiency Wave Power
Generator
MOHAMED SHEIKH ABDI YOSEF GEBRESILASSIE
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT
Abstract—A new kind of wave power generator is being developed at KTH Royal Institute of Technology which potentially can reach an efficiency of 98 %. However, this generator’s small air gap sets strict requirements on the stiffness of the structure to withstand the large magnetic forces. The structure, therefore, need to be both stiff and non-magnetic. To tackle that problem austenitic stainless steel will be used. Then again, austenitic stainless steel tends to become slightly magnetic because of impurities and mechanical stress. The purpose of this report is to study the magnetic properties of the austenitic stainless steel and observe how mechanical stress can change their properties. Moreover, economic and environmental aspects considering the use and production of the steel are studied. Two experiments were applied to measure the magnetic properties, using an LCR-meter and an electrical circuit with a current amplifier. Both methods showed that mechanical stress will result in changing the magnetic property of austenitic stainless steel. Some steel types were less affected by the mechanical stress applied leading to the conclusion that they are more effective when placed near the generator’s air gap. Regarding sustainable development, it is uncertain to determine the impact the generator has on the environment, mainly because of the steel types manufacturing process is unknown. On the contrary, the maintenance costs of the generator are predicted to be low and if the prototype fulfills the efficiency expectations it will have a huge impact on the future of wave power technology.
Sammanfattning— En ny typ av vågkraftsgenerator utvecklas på KTH som potentiellt kan uppnå en verkningsgrad på 98%. Denna generators lilla luftgap ställer dock strikta krav på strukturens styvhet för att stå emot de stora magnetiska krafterna. Strukturen måste därför vara både styv och icke-magnetisk. För att ta itu med det problemet kommer austenitiskt rostfritt stål att användas.
Sedan tenderar austenitiskt rostfritt stål att bli något magnetiskt på grund av föroreningar och mekanisk stress. Syftet med denna rapport är att studera austenitiskt rostfritt ståls magnetiska egenskaper och observera hur mekanisk stress kan förändra deras egenskaper. Dessutom studeras ekonomiska och miljömässiga aspekter som beaktar stålets användning och produktion. Två experiment utfördes för att mäta de magnetiska egenskaperna, med användning av en LCR-mätare och en elektrisk krets med en strömförstärkare. Båda metoderna visade att mekanisk stress kommer att leda till förändring av den magnetiska egenskapen hos austenitiskt rostfritt stål. Vissa ståltyper påverkades mindre av den mekaniska påfrestningen som ledde till slutsatsen att de är mer effektiva när de placeras nära generatorns luftgap. När det gäller hållbar utveckling är det osäkert att bestämma vilken påverkan generatorn har på miljön, främst på grund av att det
rostfria stålets tillverkningsprocess är okänd. Tvärtom förmodas att underhållskostnaderna för generatorn komme vara låga och om prototypen uppfyller effektivitetsförväntningarna kommer det att ha en stor inverkan på framtiden för vågkrafttekniken.
I. INTRODUCTION
LOBAL warming is a tremendous challenge we are facing today. The emissions of greenhouse gases such as carbon dioxide (CO2) and methane (CH4) is the leading cause of global warming and climate change. The reduction of greenhouse gases has been a central debate for a long time and was discussed in the Paris Agreement 2015 where 194 countries agreed to keep the global temperature below 2℃ and also support countries who are being affected by the causes of climate change[5]. The emissions of greenhouse gases come from combustion of fossil fuels such as coal and oil to fill our energy needs[6]. Global warming and climate change will affect our environment and ecosystem heavily. Fossil fuels are also a limited source of energy and will run out in the future.
Therefore, it is important that we meet our energy needs in other ways. There are renewable energy sources that have less impact on the environment such as solar power, hydro power, and wind power. The ideal energy supply in the world should consist of renewable energy sources to get on the path of a sustainable development. Another renewable energy source is wave power, where a generator converts the kinetic energy from the waves into electricity[7]. The difference from the other renewable energy sources mentioned earlier is that wave power is not a commercial energy source and is used to a lesser extent.
The biggest problems with wave power are the ineffective energy conversion and the complications with the marine environment[4].
A new type of wave power generator is being developed at KTH Royal Institute of Technology that will reach new levels of efficiency compared to the wave power generators today.
This new generator is predicted to be able to convert the energy in low velocity waves with an efficiency of 98 %. Current wave power generators are not capable to reach that level of efficiency due to the low speeds involved[4]. Austenitic stainless steel is being used as structure material to resist the strong magnetic force that appear in the generator’s air gap. In theory, austenitic stainless steel is non-magnetic, but they tend
Consequences of Magnetic Properties in Stainless Steel for a High-efficiency Wave
Power Generator
Mohamed Sheikh Abdi and Yosef Gebresilassie
G
to become slightly magnetic because of impurities and plastic deformation which can affect the performance of the generator [4, 8]. The purpose of this report is to examine how the magnetic properties, especially the relative permeability of austenitic stainless steel affects the wave power generator’s performance. We will also identify the austenitic stainless steels that are most economically profitable from a mass productions perspective and identify problems in these stainless steels types from an ecological and social point of view.
II. THEWAVEPOWERGENERATOR
Our supervisor Anders Hagnestål is currently developing a new type of wave power generator at KTH Royal Institute of Technology that is predicted to have an efficiency of 98 %, much better than the current wave power generators. As mentioned earlier this wave power generator will be able to operate in very low velocities, from 0.7-3 m/s. Current wave power generators either use a hydraulic system or converts the power with an efficiency of 60-90 % when low speeds are involved. The generator mainly consists of a translator which is built of electrical sheets and structure material, and a stator core which is built of electrical sheets, magnets, windings and structure material. The generator will be force-dense, meaning that a shorter winding than usual will be used and the wires in the winding will be made thicker leading to the usage of less material and increased efficiency. The force-density of the generator will also be of an economic benefit since the generator will cost less than usual to construct. To reach an efficiency of 98 % the generator must also be designed to withstand the strong magnetic forces that occur in the generator’s air gap because of the attraction between translator and the stator core[4]. The construction of the wave power generator can be seen in Fig. 1.
In this generator the air gap is unwanted but still unavoidable because of the translator’s movement alongside the stator [9].
The generator must therefore be constructed of material that are stiff and non-magnetic with a low electrical conductivity and good mechanical fatigue properties to resist the magnetic forces
that occurs between the translator and stator. The magnetic flux in the generator will not pass through non-magnetic materials and therefore the losses will be minimized. The austenitic stainless steel will be arranged in different geometrical positions, giving the generator its desired stiff construction[4].
III. THEORY
A. Austenitic Stainless steel and plastic deformation
Austenitic stainless steel is the most common type of stainless steel. There are around 150 different types of austenitic stainless steels that potentially can be a part of the generator in Fig. 1. They are recognized as non-magnetic and easy formable. They can handle a high level of mechanical stress and heat. They are approximately as stiff as ordinary steel. With a high corrosion resistance austenitic stainless steel are very hard to corrode, explaining its great usage [10]. The permeability of austenitic stainless steel ranges from 1.003- 1.005 ideally, more about permeability can be read in the upcoming topic. The most famous types of stainless steels are austenitic, martensitic and ferritic stainless steel with the austenitic ones being the least magnetic and ferritic ones being the most magnetic. When austenitic stainless steel is exposed to plastic deformation, the crystal structure of the stainless steels will be changed, and it might behave martensitic or ferritic, which mean its permeability will increase[4, 11].
B. Permeability
Permeability is a degree of magnetization obtained by a material when it is exposed to a magnetic field. When the medium is linear, isotropic and homogenous, the magnetization vector M is proportional to the magnetic field intensity vector H. The relation between the two can is [12].
𝑴 = 𝜒𝑚𝑯 (1)
χ
m in (1) is the magnetic susceptibility which is a dimensionless quantity. Susceptibility is a microscopic Fig. 2. B-H curves for air, soft and hard magnetic materials [2].Fig. 1. The wave power generator´s structure [4].
magnetic property of a material. Using equation (1), the magnetic flux density B can be obtained and is presented in (2).
𝑩 = µ0(1 + 𝜒𝑚)𝑯 = µ𝑟µ0𝑯 = µ𝑯 (2) The term µ is known as the absolute permeability and µris known as the relative permeability of a specific material. µ0 is the permeability in vacuum with the value 4π*10-7. Material with a µr >1 but still close to 1 are called paramagnetic. On the other hand, material with a µr <1 but also still close to 1 called diamagnetic. Materials with a µr much larger than 1 are called ferromagnetic. Air has a µr equal to 1 [12]. The linear relation in (2) is valid when the magnetic material is below its saturation point which will be discussed in the next topic.
C. Magnetic Materials and Electrical Machines
Soft and hard magnetic materials are commonly used in electrical machines. The relation between B and H of soft and hard magnetic materials can be seen in Fig. 2, also see (2) for further clarification. A specific property of soft magnetic material is that the value of B can easily be changed by applying low values of H, i.e. that the hysteresis effect is small. In contrast, higher values of H are required to obtain a significant change of B in hard magnetic materials. The purpose of using soft magnetic materials in electrical machines is to carry high values of the magnetic flux Φ with low values of power losses.
Φ in a magnetic conductor with a cross-sectional area A and the magnetic flux density B can be seen in (3) [2].
𝛷 = 𝐵𝐴 (3)
The power losses mentioned earlier are hysteresis and eddy- current losses which will be discussed more in detail in the upcoming topics. For an electromagnet the magnetomotive
force (MMF) is simply the number of turns N of a winding through the magnetic conductor multiplied by the magnetization current Im. Im can be described as the current required to obtain a flux in an electromagnet. To obtain the MMF and a flux in a magnetic circuit another unit must be determined which is reluctance Rm[1]. The relation in the magnetic circuit can be seen in (4).
𝑁𝐼
𝑚=
𝛷 𝑅𝑚 ( 4)A magnetic circuit can be compared to an electrical circuit, where NI can be viewed as the voltage, the magnetic flux as the current through the magnetic circuit and the reluctance as the resistance. If the electromagnet has an air gap, the total reluctance Rm,tot of the circuit can be given as the sum of the reluctance of the core Rm,core and reluctance of the air gap Rm,ag.
𝑅𝑚,𝑐𝑜𝑟𝑒= 𝑙𝑐𝑜𝑟𝑒
(µ𝑟µ0𝐴𝑐𝑜𝑟𝑒) (5)
𝑅𝑚,𝑎𝑔 = 𝑙𝑎𝑔
µ0𝐴𝑎𝑔 (6)
In (5), lcore is the path length of the magnetic flux through the core and in (6) lag is the length of the air gap. A magnetic circuit with an air gap is illustrated in Fig. 3 [1].
Depending on what material the core is built of (e.g. iron), there is a limit to B where it reaches a steady value, even if the core is subjected to higher H by allowing higher current flow through the core. When the material reaches that limit, it is saturated and reaches its saturation point, presented for iron in Fig. 4. The B-H curve can be approximated to a linear equation in case the applied magnetic field intensity is low, that will result in the relation in (2). In other words that linear relation is only valid if the material is not saturated.
To obtain maximal efficiency, electrical machines are designed to work tightly under the saturation limit which is presented in Fig. 4. If an electrical machine has its working point under the ideal point, it will lead to an inefficient usage of the machine. Similarly, if the working point is above the ideal point, it will lead to inefficient use of the current.
The lower MMF induced in the electrical machine, the lower will the risk for saturation become. The MMF can be regulated Fig. 3. A magnetic circuit with an air gap [2].
Fig. 4. BH-curve for iron [1]
by the magnetization current Im. Another relation presenting the MMF in an electromagnet without an air gap is seen in (7)[1].
𝑁𝐼 =𝐵𝑙𝑐𝑜𝑟𝑒
µ𝑟µ0 (7)
The magnetic flux path length is lcore. According to the relation (7), materials with high relative permeability can be chosen to reduce the MMF. As a result, the desired magnetic flux is obtained in the magnetic circuit. Material properties such as relative permeability are important in electrical machines specifically for induction and reluctance machines [1].
D. Inductance
In a magnetic circuit the flux linkage Ψ and the magnetization current Im are proportional in case the material is not saturated. The proportionality constant is known as inductance and can be given in (8) and (9).
Ψ = LI (8)
𝐿 =𝑁2 𝑅𝑚
(9)
The relation in (9) is other way of presenting inductance where N is the number of turns and Rm reluctance [13].
E. Hysteresis Losses
One of the power losses mentioned earlier is hysteresis losses. If current varies sinusoidal through an electromagnet it will change the magnetic flux density resulting in a hysteresis curve. Changing the magnetization procedure through the core will cause power losses called for hysteresis losses. The following relation shows that hysteresis losses are proportional to the frequency.
𝑃ℎ = 𝐾ℎ𝑓 𝐵𝑝𝑛 (10)
where Khand n are empirical constants. Approximately, n=2 can often be used. Bp the peak value of magnetic flux density[13].
F. Eddy-current Losses
When a ferromagnetic material is exposed to time-varying magnetic flux density, voltage is induced in the material according to Faraday's law of induction. The relations can be presented in (11) and (12).
∇ × E =∂B
∂t (11)
ԑ = − N dΦ
dt (12)
Equation (12) shows that the time-varying flux density is equal to the rotation of the electric field vector. The second equation presents the induced voltage as the number of turns N times the time derivative of the magnetic flux. The ferromagnetic material has some form of resistance and combined with the induced current it will lead to power losses.
The induced currents are known for eddy-currents and the power loses are called for eddy-current losses. If the magnetic flux density is varying sinusoidal, the eddy-current losses are given as,
P = K𝑓2𝑑2𝐵𝑝2 (13)
here K is a constant, f is the frequency and d is the thickness if the material. To decrease those losses in electrical machines, magnetic materials are divided in small sheets and laminated together. They are also electrically isolated from each other Further, the electric steel contains around 3 % silicon, which increases the electrical resistivity of the iron with about a factor of 4[13].
IV. MATERIALANDMETHOD A. Material
There are 7 different samples of austenitic stainless steels that are being measured for this report. Their dimensions are represented in Table I. Type 5 and Type 7 could not be deformed with a curve radius of 3 cm because of their dimensions. When making the measurements of the relative permeability which will be explained in the upcoming topics, the average value of 3 measurements was used as a result.
B. Methods for measuring permeability
There are several methods for measuring the relative permeability of stainless steel. A Magnetic Permeability Meter Ferromaster can be used. The instrument is relevant to control the quality of stainless steel. The instrument has a probe and by placing the probe in the desired workspace the relative
TABLE I
DIMENSIONS OF THE STAINLESS STEEL TYPES MEASURED Steel Type
Length (cm)
Width
(cm) Height(cm)
1 50,3 0,03 0,035
2 50,3 0,03 0,035
3 50,3 0,03 0,035
4 35 0,03 0,035
5 8,9 0,03 0,035
6 50,3 0,03 0,035
7 27,3 0,03 1,8
permeability can be measured as in fig 5. The equipment has a range for measuring relative permeability between 1,001 and 1,999. Based on the budget for the project, the instruments could not be afforded[3].
Another method for measuring the magnetic permeability is by applying the theory behind a magnetic circuit as discussed earlier. The magnetic circuit can be obtained by building up a magnetic core with steel and copper wire can be used as a winding through the core. This method will be discussed more detailed in the upcoming topic.
C. Construction of a magnetic core with an air gap
As mentioned above a magnetic core with an air gap has been constructed. To avoid eddy-current losses iron sheets has been used. By placing the iron sheets on each other and taping them a desired cross-section area was obtained, which was equal to the cross-section of the air gap. The air gap was dimensioned so it could fit the cross-section area of the stainless steel (0.18 mm2). A copper wire was wound through the core and 32 turns was obtained. The objective of this method was to use the air gap so the steel could be placed there. This can give an opportunity to compare the property of the stainless steel and air. The magnetic core is given in fig 6.
D. Measuring the relative permeability by an LCR-meter The purpose of using an LCR-meter here was to obtain a magnetic circuit by allowing current to flow through the copper winding. The current from the LCR-meter was very low (<1A) which is desired, so the B-H curve of the core is approximately linear. The LCR-meter was connected to both ends of the copper wire and several measurements have been observed which is discussed in the following paragraph.
The first step was to calculate reluctance of the core. The magnetic core was pushed together so that a core without an air gap could be obtained. Using the LCR-meter the inductance of
the circuit was measured. By using relation (9) the reluctance of the core was obtained. The second step was to measure the reluctance of the air gap. By keeping the air gap open with the same dimension as the stainless steel, the inductance was measured. The reluctance was obtained the same way as before.
This experiment is given in fig. 7.
The third step was to evaluate the reluctance of the stainless steel. By placing the stainless steels in the air gap, the inductance was observed and as before the reluctance of the stainless steel and the core was obtained. The reluctance of the stainless steel was obtained by subtracting away the reluctance of the core which is known from the first step.
To examine the impact on the permeability of the stainless steel due to mechanical plastic deformation, some samples of the steels was bended. The stainless steels had the same curvature radius (3cm) and the measurements took place the same way as the non-bended steel. The relative permeability of the stainless steels has been calculated via (14).
Fig. 5. Magnetic Permeability Meter Ferromaster [3].
Fig. 6. Measuring the inductance of the core without an air gap.
Fig. 7. Measuring the inductance of the core with an air gap.
𝑅𝑎𝑔 𝑅𝑠𝑡𝑒𝑒𝑙=
𝑙𝑎𝑔
µ0𝐴𝑎𝑔 𝑙𝑠𝑡𝑒𝑒𝑙
𝜇𝑟𝜇0𝐴𝑠𝑡𝑒𝑒𝑙
= 𝜇𝑟 (14)
E. Measurement by applying a magnetization current This method was based on some calculations to obtain the magnetization current of the magnetic core. The purpose of using the magnetization current was to ensure that the BH-curve of the iron material is linear. In the previous method, the LCR- meter sends out a rather small current to measure the inductance. Thereby, the iron in the core is only weakly magnetized to levels considerably below 0,1 T, where the permeability of the iron is nonlinear. Thereby, the core reluctance can differ significantly between the case where it is measured with no air gap and the cases when the reluctance of the air and stainless steel is measured, since B is expected to be considerably lower in the latter cases due to the higher total reluctance. Thereby, a measurement error is introduced, which may be non-negligible. According to Faraday's induction law by allowing a time varying flux linkage through the inductor a voltage will be induced which is calculated in Table II by using relation (15). The magnetization current that is required can be evaluated by using (16).
𝑢 =2𝜋𝐵𝑝𝑓𝐴𝑓𝑒𝑁
√2 (15)
𝐼𝑚=Ψ L = 𝑢
𝜔∗ 𝑙𝑔 𝑁2𝐴𝑓𝑒𝜇0
= 𝐵𝑝𝑙𝑔
√2 𝑁𝜇0
(16)
HereBp is the desired peak value of the magnetic flux density through the core. Bp is set to 0.3 Tesla, this assumption is based on the saturation point of iron which is approximately between 1.6 -1.8 T. The reluctance of the core is neglected. Other values lower than 1.6 could have been chosen. The relations above are valid when the induced voltage u is sinusoidal. Afe in the
equations above stands for the cross-section area of the core, lag
is the length of the air gap and 𝑤 is the angular frequency (2πf).
The magnetization current Im for different frequencies is evaluated in Table II.
To obtain the magnetization current, a current amplifier was used. The amplifier input was connected to a function generator. The function generator provides a current which is lower than the magnetization current, which is why the amplifier was needed. The output of the amplifier was connected to the copper wire through a fuse to avoid a current above 20 A, for security reasons. A differential probe was connected to the ends of the copper wire and the output of the probe was connected an oscilloscope. Similarly, an AC/DC clamp meter was clamped at one end of a circuit and further connected to the same oscilloscope. The aim of this part was to observe the phase shifts between the voltage over the inductor and the current through it. A multimeter was used to measure the output voltage from amplifier and another one was used to observe the voltage over the inductor. Ideally both multimeters should show the same value and this step was performed to observe if any voltage drop occurs on the other wires of the circuit. The electrical circuit obtained from the description above is presented in Fig. 9.
From the circuit in Fig. 9, a phase diagram can be obtained, as seen in fig. 10. X is the reactance of the copper wire, Iout or i is the output current through the core, u is the voltage over the inductor and R is the resistance of the wire. The resistance was measured by using the LCR-meter in room temperature which was 0.13 ohm, this resistance was chosen as constant during the measurement. The voltage over the fuse was neglected because of its low value. The reactance is given in (17).
𝑋 = 𝜔𝐿 (17)
Fig. 8. Measuring the inductance of the stainless steel and the core.
Fig. 9. Electrical circuit used when applying the magnetization current. Rwire and Lwire is the resistance and inductance of the electromagnet.
TABLE II
VALUES OF THE PARAMETERS NEEDED TO CALCULATE IM
B (T) f (Hz) Afe (m2) N
(turns) U(V) lg (m) Im (A)
0,3 50 0,00018 32 0,38 0,003 15,66
0,3 100 0,00018 32 0,76 0,003 15,66
The first step of the measurement started by applying the magnetization current through the inductor. Similarly, as the measurement with the LCR-meter, the core was pushed together to obtain the inductance of the core. By observing the voltage over the inductor, the inductance of the circuit was obtained using the phase diagram or the Pythagoras theorem. In addition, the reluctance of the core was obtained by using relation (9). The second step was to determine the reluctance of the air gap similarly as the first step but now with the airgap having the same dimension as the stainless steel. The third step was to determine the reluctance of the stainless steel by placing them in the air gap. The measurements here was identical as before, the inductance of the core and the stainless steel was calculated according to the phase diagram and (17). By using relation (9) the reluctance of the core and the stainless steel was obtained and by the eliminating the reluctance of the core from the first step, the steel reluctance was obtained. When the inductance was evaluated, the magnetic permeability of the stainless steels has been calculated in the same way as for the LCR-meter.
V. RESULTS A. Measurement 1
TABLE III
OBTAINED PERMEABILITY WITH LCR-METER Steel Type LCORE+STAIN (H) µr
Type 1 0,00012662 1,014186025
Type 2 0,00012784 1,028497846
Type 3 0,000127 1,018630238
Type 4 0,00012558 1,002085174
Type 5 0,0001273 1,022147481
Type 6 0,0001275 1,024496566
Type 7 0,000133 1,090460157
TABLE IV
OBTAINED PERMEABILITY WITH LCR-METER AFTER PLASTIC DEFORMATION
Steel Type LCORE+STAIN (H) µr
Type 1 0,000127 1,018630238
Type 2 0,0001276 1,025672387
Type 3 0,0001277 1,026849063
Type 4 0,00012833 1,034281823
Type 5 - -
Type 6 0,0001283 1,033927109
Type 7 - -
TABLE V
OBTAINED CHANGE OF PERMEABILITY AFTER PLASTIC DEFORMATION
Steel Type µr -straight µr -bent Change (%)
Type 1 1,014186025 1,018630238 0,4382049222
Type 2 1,028497846 1,025672387 −0,27471704
Type 3 1,018630238 1,026849063 0,8068506511
Type 4 1,002085174 1,034281823 3,212965289
Type 5 1,022147481 - -
Type 6 1,024496566 1,033927109 1,152439096
Type 7 1,090460157 - -
Fig. 10. Phase diagram for the electrical circuit in that is seen in Fig 9.
B. Measurement 2 C. Measurement 3
TABLE VI
OBTAINED PERMEABILITY WITH THE MAGNETIZATION CURRENT (50 Hz)
Steel Type UCORE+STAIN (V) IM (A) LCORE+STAIN (H) µr
Type 1 2,29 15 0,00022214 1,097060
Type 2 2,293 15,1 0,00021642 1,0305517
Type 3 2,298 15 0,00022583 1,142837
Type 4 2,28 15 0,00021745 1,042227
Type 5 2,289 15,09 0,00021524 1,017501
Type 6 2,34 15,13 0,00023571 1,276438
Type 7 2,28 15,01 0,00021673 1,034100
TABLE VII
OBTAINED PERMEABILITY WITH THE MAGNETIZATION CURRENT AFTER PLASTIC DEFORMATION (50 Hz)
Steel Type UCORE+STAIN (V) IM (A) LCORE+STAIN (H) µr
Type 1 2,29 15,11 0,00021428 1,006918087 Type 2 2,27 14,96 0,00021559 1,021305243 Type 3 2,28 15,04 0,00021457 1,010091896 Type 4 2,3 15,06 0,00022253 1,101756862
Type 5 - - - -
Type 6 2,29 15,03 0,00022001 1,07170459
Type 7 - - - -
TABLE VIII
OBTAINED CHANGE OF PERMEABILITY WITH THE MAGNETIZATION CURRENT AFTER PLASTIC DEFORMATION
(50 HZ)
Steel Type µr -straight µr -bent Change (%)
Type 1 1,097060748 1,006918087 −8,216742896 Type 2 1,030551788 1,021305243 −0,8972421118 Type 3 1,142683776 1,010091896 −11,60354975 Type 4 1,042227445 1,101756862 5,7117492
Type 5 1,017501231 - -
Type 6 1,276438469 1,07170459 −16,03946322 Type 7 1,034100913 -
TABLE IX
OBTAINED PERMEABILITY WITH THE MAGNETIZATION CURRENT (100 Hz)
Steel Type UCORE+STAIN (V) IM (A) LCORE+STAIN (H) µr
Type 1 2,63 15,03 0,0001757195626 1,035794521 Type 2 2,61 15,01 0,0001729304666 1,003373395 Type 3 2,66 15,03 0,0001807171142 1,096546233 Type 4 2,65 15,01 0,0001796464739 1,083232667 Type 5 2,63 15,02 0,0001760135749 1,039272463 Type 6 2,62 15,01 0,000174624017 1,022937243 Type 7 2,77 15,07 0,0001972470986 1,325653952
TABLE X
OBTAINED PERMEABILITY WITH THE MAGNETIZATION CURRENT AFTER PLASTIC DEFORMATION (100 Hz)
Steel type UCORE+STAIN (V) IM (A) LCORE+STAIN (H) µr
Type 1 2,66 15,02 0,0001810095632 1,100212066 Type 2 2,62 15 0,0001749188017 1,026381077 Type 3 2,63 15,05 0,0001751318217 1,028876883 Type 4 2,62 15,04 0,000173740208 1,012680824
Type 5 - - - -
Type 6 2,67 15,04 0,0001820729645 1,113648838
Type 7 - - - -
Table XI
OBTAINED CHANGE OF PERMEABILITY AFTER PLASTIC DEFORMATION (100 HZ)
Steel type µr -straight µr -bent Change (%)
Type 1 1,035794521 1,100212066 6,219143268 Type 2 1,003373395 1,026381077 2,293032884 Type 3 1,096546233 1,028876883 −6,171135081 Type 4 1,083232667 1,012680824 −6,51308304
Type 5 1,039272463 - -
Type 6 1,022937243 1,113648838 8,867757651
Type 7 1,325653952 - -
D. Sensitivity analysis
VI. DISCUSSIONANDANALYSIS
As mentioned earlier the permeability of stainless steel should in theory be one i.e. non-magnetic but because of impurities and plastic deformation they tend to become slightly magnetic. Our result show that the permeability is close to one in the samples of stainless steels although they vary. There are multiple reasons for why the samples of stainless steel types show different permeability’s depending on what method we used. In method 1 an LCR-meter was used, and it sends out a current much lower the intended magnetization current which means that the B-curve might not be linear when the electromagnet is weakly magnetized. If the B-curve is not linear the assumption of linearity in equation (2) is not valid. In Fig. 2 the hysteresis curve of soft and hard materials is shown. Around the origin where the B-curve is close to 0 T the line might not be so linear, iron is more sensitive to its earlier history of magnetization when exposed to a weak magnetization.
Equation (2) is an approximation, only valid when the material is under the saturation point but significantly over the origin.
The method using the magnetization current applied a circuit where Eddy-current losses occur. The construction of the magnetic core can also be wrong when it comes to dimensional errors as we assumed that the cross-sectional area of the iron and air gap was equal when they probably are different. The inductance was not measured directly as the case with the LCR- meter, L had to be found through the induced voltage on the inductor, the resistance of the copper wire and the magnetization current through the phase diagram shown earlier.
We have used a constant resistance on the copper wire in our calculations but in reality the resistance of the copper wire varies depending on the temperature of the copper wire[14].
The wires used in the circuit are dimensioned to handle currents up to 10 A while our magnetization current is 15 A. The longer we had a current of 15 A flowing in the circuit the higher the resistance of the wires became and the higher the induced voltage became. The calculation of the inductance might then be little inaccurate if the power source is on for a long time.
Two frequencies were also used to calculate the inductance.
The higher frequency leads to higher reactance of the circuit, making our calculation of the permeability less dependent on the resistance of the copper wire. The results show that the permeability was closer to 1 with a frequency of 100 Hz, making it more accurate.
As mentioned earlier the relative permeability of austenitic stainless steel is expected to increase when exposed to plastic deformation. The results show the change of permeability varied depending on the method used. In the first measurement with the LCR-meter almost all the steels showed an increase in permeability when they were bent with a curve radius of 3 cm except type 3. Method 2 with frequencies of 50 and 100 Hz showed very different results where some of the steel increased in permeability and others decreased. A reason for this might be the increased resistance which will change the results heavily. When the curved steels were measured it occurred right after the other measurements which means these measurements occurred under a higher resistance.
Theoretically the measurement with the magnetization current will show more accurate results because with a B of 0,3 T we know for sure that we are operating under the saturation point of iron and the linear condition in (2). In our measurements method 1 with the LCR-meter showed much better results as the relative permeability was very close to 1 in all the steels and almost all of them increased when exposed plastic deformation. The measurement with magnetization current was filled with error sources such as the cables capacity, voltage drop over the cables, and the wires temperature dependency when it comes to its resistance. The sensitivity analysis for method 1 showed that the permeability would have varied if the inductance of the measurement would’ve differed 20 µH, this can be seen in table XII. The sensitivity analysis for method 2 also showed different result when the second and third decimal in voltage and current valued changed, this can be seen in table XIII and XIV.
Table XII
MEASUREMENT 1: VALUES OF PERMEABILITY FOR DIFFERENT INDUCTANCES
L(H) µr
0,0001256 1,002317027
0,000126 1,006961118
0,000128 1,030384225
Table XIV
MEASUREMENT 3: VALUES OF PERMEABILITY FOR DIFFERENT VOLTAGES AND CURRENTS
U (V) I (A) Lstain+core (H) µr
2,289 15,09 0,000215249259 1,017501231
2,29 14,99 0,0002228520875 1,105648627
2,2889 15,3 0,0001998749841 0,86247155
2,28 15 0,0002174569308 1,042227445
Table XIII
MEASUREMENT 2: VALUESS OF PERMEABILITY FOR DIFFERENT VOLTAGES AND CURRENTS
U (V) I (A) Lstain+core (H) µr
2,62 15,03 0,0001740347212 1,016087197
2,64 15 0,0001782754077 1,066424505
2,64 14,7 0,0001871380763 1,180045865 2,6 15,07 0,0001694520448 0,9643365078
If our results are correct it would be ideal to have the steels with the least permeability as close to the air gap as possible to prevent undesired extra flux leakage through the stainless steel.
The steel type with the least permeability was type 2 making it the best alternative to use in the generator from a mass production point of view.
When it comes to sustainable development there is a lot of problems with the stainless steel used in the experiments. The origin of the stainless steel types are from China, but their production process is unknown, therefore it is impossible to say if they are sustainable for the environment or not. The structure material used in this generator could have been bought in Sweden, but it would have been much more expensive. The conditions of the workers in the industries etc. is also unknown.
Several studies agree that wave power has potential in the energy sector as a sustainable power source. However, when discussing if renewable energy is sustainable the structure materials construction process is often dismissed. If the austenitic stainless steels construction process is unknown, it contradicts the statement that wave power is sustainable as the structure material is an essential part of the wave power generator. Arguments have been made for fossils fuels continuation solely on the uncertainty of renewable energy sources. The benefit of the doubt should be given to sustainable energy sources, the technique and efficiency will certainly become better with given time and economical support. The focus should be on making these energy resources commercial and hopefully they become generators used world-wide, not just a prototype.
VII. CONCLUSION
The results of both experiments show that the relative permeability of the steel is close to 1. As it is discussed previously, changing the geometry of the steel through plastic deformation will have an impact on increasing the permeability of the steels given them a slightly magnetic behavior. Both experiments showed that the permeability’s of the samples was close to 1 gave close values but the second experiment was more inaccurate. The sensitivity analysis showed that small changes of the measured values will give noticeable change of the result. Moreover, other upcoming error sources were the power losses in the core and the variation of temperature on the copper wire in the electromagnet which changed its resistance.
The experiments gave different permeability values but the steel type with the lowest permeability is most cost efficient to use. The steels which are going to be placed closest to the air gap need to be the most non-magnetic and the work procedure should not change their magnetic properties.
There is no doubt about wave power as a sustainable energy source but not knowing the production process of the structure material could lead to some misunderstandings. Despite that, the generator will have low maintenance costs and huge impact in the energy sector and the future of wave power technology if the prototype fulfils the expectations.
VIII. REFERENCES
[1] B. a. E. Technologies. "Electric Drives - Electrical Machine Fundamentals - Description and Applications," April, 2018;
[online]. Available: http://www.mpoweruk.com/machines.htm#.
[2] W. L. Soong, "The Art of Electric Machine Reasearch," pp. 8-14, Adelaide: University of Adelaide, 2016.
[3] S. User. "Permeability Meters," April, 2018; [online]. Available:
http://www.stefan-mayer.com/en/products/permeability- meters.html.
[4] A. Hagnestål, and E. Guldbrandzén, “A highly efficient and low- cost linear TFM generator for wave power,” in EWTEC 2017: the 12th European Wave and Tidal Energy Conference 27th aug - 1st Sept 2017, Cork, Ireland, 2017.
[5] Naturvårdsverket. "Parisavtalet - Naturvårdsverket," Feb, 2017;
[online]. Available: http://www.naturvardsverket.se/Miljoarbete-i- samhallet/EU-och-internationellt/Internationellt-
miljoarbete/miljokonventioner/Klimatkonventionen/Parisavtalet/.
[6] O. US EPA. "Sources of Greenhouse Gas Emissions," April, 2018;
[online]. Available: https://www.epa.gov/ghgemissions/sources- greenhouse-gas-emissions.
[7] Energimyndigheten. "Vågkraft," Feb, 2018; [online]. Available:
http://www.energikunskap.se/sv/FAKTABASEN/Vad-ar- energi/Energibarare/Fornybar-energi/Vatten/Vagkraft/.
[8] Carpenter. "Magnetic Properties of Stainless Steels | Carpenter,"
April, 2018; [online]. Available: https://www.cartech.com/en/alloy- techzone/technical-information/technical-articles/magnetic- properties-of-stainless-steels.
[9] J. Pyrhonen, T. Jokinen, and V. Hrabovcova, "Design of rotating electrical machines," p. 298, Finland: John Wiley & Sons, 2013.
[10] Britannica. "Stainless steel | Types & Facts," April, 2018; [online].
Available: https://www.britannica.com/technology/stainless-steel.
[11] S. S. World. "An overview of the different types of Stainless Steel - Stainless Steel World," May, 2018; [online]. Available:
http://www.stainless-steel-world.net/basicfacts/stainless-steel-and- its-families.html.
[12] D. K. Cheng, "Field and Wave Electromagnetics: Pearson New International Edition," pp. 249-251, Harlow, Essex, England:
Pearson Education Limited, 2014.
[13] H.-P. Nee, M. Leksell, S. Östlund, and L. Söder, "Eleffektsystem:
EJ1200," Stockholm: US-AB, 2008.
[14] J. Dellinger, “The temperature coefficient of resistance of copper,”
Journal of the Franklin Institute, vol. 170, no. 3, pp. 213-216, 1910.
www.kth.se
