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JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
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Structure and Performance Analysis of Regenerative Electromagnetic Shock Absorber Zhen Longxin Yanshan University /Automotive Vibration and Noise Research Institute, Qinhuangdao, China [email protected]
Wei Xiaogang Yanshan University /School of Vehicle and Energy Engineering, Qinhuangdao, China [email protected]
Abstract—This paper analyzed the structure and principle of a regenerative electromagnetic shock absorber in detail. The innovative shock absorber resembles linear generator in principle and can generate electric power through the relative reciprocating motion between coil assembly and permanent magnet assembly. At the same time, the damping can remove discomfort caused by road roughness. The regenerated electric power can be recovered through battery. Analysis of magnetic flux density of the permanent magnet array of the innovative shock absorber was performed using ANSYS software based on the structure parameters given in the paper,then the performance parameters of the shock absorber was determined . Analysis and calculation results prove the viability of this shock absorber. Index Terms—electromagnetic shock absorber; energy recovery; magnetic field analysis ; principle
I.
INTRODUCTION
With the increasing quantity of possessed automobiles,it has received a great deal of attention from automobile manufacturers and government for the energy energy conservation and environmental protection both at home and abroad. To protect the environment and reduce vehicle emissions and fuel consumption of vehicles, it is necessary to recover the energy wasted by the car, such as the braking energy, engine exhaust emissions energy and vibration energy of suspension, etc. Usually the vibration energy caused by road roughness when car runs has not been paid attention to and it is wasted through conversion to thermal energy. If the vibration energy can be recovered and converted to other form of energy such as electric or hydraulic power so to suppy for other devices, then the aim of eco-friendly energy-saving is reached. In this paper the vibrational energy was converted to electric energy through the innovative electromagnetic absorber shock. Guidance plan of scientific & technological research and development of Hebei province (07213531)
© 2010 ACADEMY PUBLISHER doi:10.4304/jnw.5.12.1467-1474
Normally as we know active suspensions like pneumatic suspension with nolinear rigidity which is well known for its comfort and adaptability and its characteristics such as rigidity and damping ratio can be changed with road roughness.But this kind of suspension is rather complex and need much energy to change its characteristics, moreover it needs complex control algorithm and expensive hydraulic and electric element such as hydraulic pump, ECU, many sensors and control valves. Reference [1] introduces the control algorithm of a semi-active adaptive suspension based on LQG method. Reference [2] the vibratinal is recovered in hydraulic way and the tests results show that energy feedback suspension only costs 16% of that energy compared with common passive suspension. Reference [3] relates to the hydraulic way of reclaming vibrational energy by hydraulic accumulator to supply other components with hydraulic energy.But the structure is rather complx and the effciency is not idal actually. In Reference [4], the author mentions the electromagnetic way of recovering the vibrational energy generated by the suspension, its main operational principle is that when the coil cuts the magnetic line of force generated by the permanent magnet, then the electric power is generated and recovered by battery to supply other electric assemblies. But the effciency is low owing to its sturcture. Reference [5] introduces the design and control method of hybrid suspension system. Reference [6] introduces the selfpowered vibartion control using hydraulic energy input and its method and prrinciple is similar to the above paper refered. Reference [7] introduces the self-powered active vibration control using electric actutor which resembles linear generator in structure and principle,but the shortcoming is that the power effciency is low. Reference [8] introduces the design and principle of a autobile active suspensions with permanent magnets, but still needs improvement in effciency. I. Boldea, et aI. [9], J. Rizk, et aI [10] and J Wang, et al [11] introduce three different kinds of methods to design linear generators with high effciency.
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JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
This paper introduces the structure and principle of a regenerative electromagnetic shock absorber in detail and uses ANSYS software analyzed the magnetic flux density of the permanent magnet array of the electromagnetic shock absorber absorber, then caculated the performance parameters. For its special structure the max magnetic flux density in the place where coils come through reaches as high as 2.6T. It undoubtedly exceeds other previous energy-recovering shock absorber in perfomance. II. THE STRUCTURE OF REGENERATIVE ELECTROMAGNETIC SHOCK ABSORBER The regenerative electromagnetic shock absorber described in this paper mainly consists of four parts: a permanent magnet array, a coil windings array, 2 guide cylinders and a spiral spring. Its structure is shown in Fig. 1. A. PERMANENT MAGNET ARRAY As is ashown in fig. 2, the permanent magnet array includes 2 parts: internal magnet part and external part and both two parts comprise 14 layers of permanent magnet and 15 layers high permeability material and which was serparated by permanent magnet repectively. A axial guide rod axially penetrates these internal permanent magnets and high magnetic conductive material layers to enhance their strength. In this structure the axially and radially adjacent permanent magnets have opposite polarity shown as fig.3. So the magnetic induction line radiated from the adjacent permanent magnet as if it is distorted and forms magnetic vector superpositon.At this time the magnetic flux density is about twice that the single one radiates. Permanent magnets array is fixed to end plate which is fixed on inner side of the shock absorber shell. Permanent magnets are fixed with magnetic conductive layers by mighty bond or mechanical mean.
Figure 2. Diagram of permanent magnet array
Figure 3. Diagram of permanent magnet array
Hard magnetic materials can be chosen as permanent magnet material and in this paper Nd-Fe-B material is chosen. The Nd-Fe-B material has high magnetic energy product (10 times higher than ferrite magnet), high coercive force and high energy density. Soft magnetic materials which usually have high permeability can be chosen as high magnetic conductive material and in this paper 45CrNiMoVA material is chosen. B. COIL WINDINGS ARRAY 1) The coil windings array moves reciprocatingly along the air-gap between the internal part and external part of the permanent magnet array and cuts lines of magnetic force to generate electric power. Its structure is shown in fig. 4. • Both internal and external magnetic conductive guide sleeves are wound by certain number of coil windings groups. In order to enhance the permeability of coils, nickel-like coatings can be applied to outer surface of coils. • Figure 1. Diagram of structure of regenerative shock absorber.
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Various coil windings group can be connected in parallel or in series or in both ways.
JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
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→
→
→
Fl = q ⋅ V ⋅ B
(1)
→
Where Fl —Lorentz force (N)； q—queantity df electricity (C)； →
V —the velocity of electric charge (m/s)； →
B —magnetic flux density(T) The corresponding Lorentz electric field is defined as →
→
→
El = V × B
(2)
→
Where El —Lorentz electric field(V/m) We define the electrical conductivity of the coil as σ , mass as mcoil ,volume as Vcoil . When the coil array moves relatively to the magnet array at the speeed Vz, the induced electromotive force in the coil is defined L
Ve = Figure 4. Diagram of coil windings array
•
•
Internal coil windings groups wind around the outer surface of the internal magnetic conductive guide sleeve and external coil windings groups wind around the outer surface of the external magnetic conductive guide sleeve. Guide cylinder 1 which forms sliding pair together with guide cylinder 2 shown in figure 1 is attached to outside of the external magnetic conductive guide sleeve to stabilize the coil windings array and to maintain its absolute vertical direction and to avoid friction between it and the permanent magnet array. Thus the coil windings array can move smoothly relatively to the permanent magnet array. The internal and external magnetic conductive guide sleeves and guide cylinder 1 all have long axial slots along their outer surface. The purpose is to avoid heat generation and energy loss caused by eddy current. III.
THE PRINCIPLE OF OPERATION
The permanent magnet array of regenerative electromagnetic shock absorber is connected to wheel axles of the vehicle and the coil windings array is connected to the framework or body of the vehicle. When the vehicle travels on rough roads, the relative displacement between framework or body and wheel axles causes relative displacement between coil windings array and permanent magnet array. At this point coil groups will be cutting the magnetic induction lines in the air-gap, thus current occurs in the coil and in the mean time damping force occurs correspondingly. The direction of the damping force is relatively opposite to the movement of the coil group. When the conductor moves perpendicularly to the direction of magnetic induction line, the Lorentz force can be defined as © 2010 ACADEMY PUBLISHER
∫
→
E l dL = B r ⋅ V
z
⋅ L
(3)
0
Where Ve — induced electromotive force (V)； Br — radial magnetic flux density (T)； L— the total length of coil(m)； Vz — the relative velocity betweetn coil and magnet (m/s)。 The corresponding eddy current density J is given as J = σ ⋅ El
(4)
Where J — current density of the coil (A/m²)， σ — electric conductivity of the coil (S/m). The differential eddy current dI passing through a differential corss section area of the coil winding is
dI = JdAw
(5)
Where dI — differential eddy current dAw — differential corss section area of the coil winding By integraing the dI over the cross section comes the eddy current I I = σ
⋅ B
r
⋅ A
w
⋅V
z
(6)
Where Aw — area of the corss section of the coil (m²)， I — current of the coil (A)。 For each coil peak or maximum instanteneous regenerated electrical power Pmax is given as P max = V e ⋅ I / 4 = 0 . 25 ( V z ⋅ ⋅ B r ) 2 ⋅ V coil
(7)
Where Pmax — maximum instanteneous regenerated electrical power Vcoil —total volume of the coil winding Suppose the average diameter of the coil array as Dr， N as the total turns of the coil, then the inductive electromotive force is
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V
= π ⋅ N ⋅ D r ⋅V
e
z
⋅ B
(8)
r
The average current of the coil can be caculated through
The resistance of the coil is
Rc = N ⋅ π ⋅ Dr /(σ ⋅ Aw )
(9)
When the load resistance equals to Rc, peak power can be drawn from above equations P max = V e ⋅ I o / 4 = (V z ⋅ B r
)
⋅ N ⋅ π ⋅ Aw ⋅σ / 4
2
= (V z ⋅ Br ) ⋅ σ ⋅ Vcoil / 4 2
(10)
To simplify the caculation process we use the mean relative veloctiy between the car body and chassis to substitute for Vz T
Vz
2
∫V
=
2 z
dt
(11)
0
T
∫ dt
Where V z —the mean relative veloctiy between the car body and chassis(m/s) 2
=
(a t )
(12)
2
According to experience ,We suppose −
V
z
= V max / 3
(13)
Where Vmax — the maximum veloctiy between car body and the chassis. Then we can draw Pavg = (V z ⋅ B r
)2
⋅ N ⋅ π ⋅ A w ⋅ σ / 4 = (V max ⋅ B r
)2 ⋅ σ
V coil / 12 = Pmax/ 3
(14)
P max — the peak power of the coil Similarly, The average voltage of the coil can be caculated through avg
= V
e
/ 2
TABLE I.
(16)
Where Iavg— the average current of the coil（A） In order to get the results according with real circumstance, we using the typic road roughness data to estimate the relative power, current and inductive electromotive force. From the formula listed above we know that in order to generate more electrical power we need to reduce the resistance of the coil and magnify the radial magnetic flux density Br and volume of coil Vcoil in the air gap at the same time. The remanent magnetism is limited by the choosen permanent magnet and volume is limited by the space of car body. MAGNETIC FIELD ANALYSIS OF SHOCK ABSORBER
A. STRUCTURE PARAMETERS AND PERFORMANCE OF SHOCK ABSORBER The structure parameters of the shock absorber determined according to vehicle weighing 1.3 ton are shown in table 1. The vehicle has 2 wheel axles and 4 suspensions. Each suspension supports 270 kg. The relative magnetic permeability of the air is defined as 1 and the magnetic coercive force of the permanent magnet is defined as 900000 A/m. The relative magnetic permeability of the permanent magnets is defined as (17).
⋅
Where Pavg — the average power of the coil
V
I avg = I O / 2 3
IV.
0
Vz
Where Vavg — the average voltage of the coil (V)
µr = Br / (µ0Hc)
(17)
Where Br is residual magnetism of magnet, µ0 is Permeability of vacuum，Hc is magnetic coercive force of the permanent magnet. High magnetic conductive material chosen in this paper belongs to soft magnetic materials. Its data of B-H curve is shown in table 2.
(15)
3
STRUCTURAL PARAMETERS OF ELECTROMAGNETIC SHOCK ABSORBER
Thickness of radial air-gap
5 mm
Internal radius of internal coil windings group
35.5 mm
Thickness of single NdDy
22.5 mm
External radius of internal coil windings group
39.5 mm
Thickness of magnetic conductive layer
10 mm
External radius of external coil windings group
75.5 mm
Length of central guide rod
500 mm
External radius of external coil windings group
79.5 mm
Height of single coil windings group
10 mm
Internal radius of shell of shock absorber
96 mm
Height of end plate
5 mm
External radius of shell of shock absorber
106 mm
Height of whole magnet array
495 mm
Diameter of end plate
190 mm
Radius of internal cylindrical magnet
35 mm
Permeability of vacuum
4π×10-7
Diameter of central guide rod
10mm
Conductivity of coil
5×107 S/m
Internal radius of external cylindrical magnet
40mm
Mean diameter of internal coil windings group
75 mm
External radius of external cylindrical magnet Number of internal and external NdDy
75mm 14
Mean diameter of external coil windings group Number of internal and external coil windings group
15
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155 mm
JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
TABLE II.
1471
DATA OF B-H CURVE OF HIGH MAGNETIC CONDUCTIVE MATERIAL
B(T)
H(A/m)
B(T)
H(A/m)
0.70
355
1.75
7650
0.80
405
1.80
10100
0.90
470
1.85
13000
1.00
555
1.90
15900
1.10
673
1.95
21100
1.20
836
2.00
26300
1.30
1065
2.05
32900
1.35
1220
2.10
42700
1.40
1420
2.15
61700
1.45
1720
2.20
84300
1.50
2130
2.25
110000
1.55
2670
2.30
135000
1.60
3480
2.41
200000
1.65
4500
2.69
400000
1.70
5950
3.22
800000
B. RESULTS OF MAGNETIC FIELD ANALYSIS As is known according to Faraday induction law, the energy recovery efficiency of this shock absorber depends on the magnetic flux density in the air-gap. This paper establishes the model of the permanent magnet array and generates mesh of the model, then analyzes the magnetic flux density in the air-gap with ANSYS software. Due to the symmetry of the permanent magnet array, its model can be simplified to the partial threedimension model shown in fig. 4 and partial twodimension model shown in fig. 3. Fig. 6 and fig. 7 respectively show the distribution of magnetic induction lines and magnetic flux density. As is shown in fig. 6, most of the magnetic induction lines at the air-gap distribute radially and they go as if they were bent because both radially and vertically adjacent permanent magnets have opposite polarity. Thus magnetic induction lines of adjacent magnets superpose mutually in the air-gap to magnify magnetic flux density and increase energy production efficiency. As is shown in fig. 7, the maximal magnetic flux density reaches as high as 2.7T and the average value is about 2.3T. So result of magnetic field analysis is satisfactory. V.
PERFORMANCE PARAMETERS OF THIS SHOCK ABSORBER
According to the structure parameters and the analyzed results of the magnetic field we can draw the performance results. A. THE PRINCIPLE OF THE MAGNETIC DAMPING FORCE We know that when the coil arry reciprocates through the magnet array axisly, the inductive currrent is influenced by the magnetic field of the permanent magnet, then the magnetic damping force Fd is generated. Actually two forces are applied to the coil array, one is
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Figure 5. Diagram of partial three-dimension model
Figure 6. Diagram of distribution of magnetic induction lines
Figure 7. Diagram of magnetic flux density
the magnetic damping force and the other is inertial force if the gravity of the coil is ignored.
Fo = Fi + Fd = m coil (dV z / dt ) + γ V z = m coil ⋅ a (18) Where F o — the external force applied to the coil array F i — the inertial force F d — the magneitc damping force
α — the acceleraion of coil array γ — the damping coefficient
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JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
When the initial velocity of the coil is defined as 0m/s, τ , then the
γ / m coil is defined as damping time constan
relative veloctiy between the car body and chassis is t ⎛ ⎞ V z = a ⎜⎜ 1 − e τ ⎟⎟ ⎝ ⎠
V z = bV
(19)
Equation (19) resemble the derivative of the following formula of the one dof free damping oscillation in behavior and perfomance. 2 (20) Z = Ae − nt ⎛⎜ ω − n 2 t ⎞⎟ + ϕ ⎝
x
⎠
o
b=dz/dx
Where b—the bump slope of the road ,its range is0.010.05 The waveform in half period is
z ( x ) ≈ bx
(22)
Where z(x) —the vertical displacement of the tire .
(23)
x
Where Z ( x) —vertical speed of the tire V x —the running speed of the vehicle
)
sprung mass Preg = (Vmax ⋅ Br ) ⋅ σ ⋅ Vcoil /12 = Pmax/3 2
(25)
The conductivity is 5×107 s/m, the turns of the single coil array is 40, so the volume of single inner coil array is about
)
Vcoil (inner ) = π ⋅ R4 − R3 ⋅ h5 = 9.4 × 10e − 6m 3
(26)
And the volume of single outer coil array is about V coil (outer
)= π
(
⋅ R6 − R5 2
2
)⋅ h
5
= 19 . 4 × 10 e − 6 m 3
(27)
The maxium magnetic flux density at the inner air gap is about 2.5 T and is about 0.8 T at the outer air gap. © 2010 ACADEMY PUBLISHER
Ve (outer) = 3.14× 40× (150e − 3) × 0.5× 0.8 = 7.8V
(29) (30)
Io (inner) ≈ Br ⋅Vz ⋅σ ⋅ Aw = 2.4 × 0.5× (5×10e + 7) × 3.142 ×10e − 6 = 60A
(31)
I o (outer) ≈ Br ⋅ Vz ⋅ σ ⋅ Aw = 0.8 × 0.5 × (5 ×10e + 7) × 3.142 ×10e − 6
= 20A
(32)
Pmax = Ve ⋅ I o / 4
(33)
According to (33)
Pmax(inner) = 11.3 × 60/ 4 = 169.5W
Pmax (outer ) = 7.8 × 20 / 4 = 39W
(34)
Pavg = Pmax(inner) + Pmax(outer) / 3 = 69.33W
(35)
So the total regenerated power with 4 shock absorbers is Ptotal = Pavg × 14 (array
)× 4 =
4158 W
(36)
µ = Preg /( Pexhausted + Preg ) = 4158 /( 4158 + 7000 ) = 37.2%
(24)
Where Preg — the energy regenerated by the shock abosrber Pexhuast — the power exhausted by supporting
2
V e (inner ) = 3 . 14 × (75 × 10 e − 3 × 0 . 5 × 2 . 4 ) = 11 . 3V
Pavg = Pmax / 3
C. CALCULATION OF THE PERFORMANCE PARAMETERS Suppose that car is equiped with four electromagnetic shock absorbers like this kind and the speed of the car in c-level road is 20m/s. According to related data, the consumed power of suspensions for holding sprung mass is 7500 w. The recovery efficiency is
2
(28)
According to (34)
.
η = P reg / (P reg + P exhuast
= 0 .5 m / s
The inductivie electromotive force in single coil is
(21)
Z ( x ) ≈ bV
x
The current of the coil will be
B. ROAD DATA REFERENCE According to relative road data information we know that mean roughness value of c-level road is about 1-6 cm, and the single wavelength is about 10-100 cm. To simplify the calculation we suppose that the road waveform is triangular.
(
Here b=0.025, when the speed of the car is 20m/s, then
(37) For the generated current is alternative current, and the current in the adjacent coil has opposite plolarity, here the coils are connecetd in series and the alternative current need to be converted to direct current with current rectifier.To avoid short out, insulating substance needs to be applied on the coil. D. CONTROL OF THE DAMPING FORCE The length of the single coil array is L (inner ) = 15 × 10 × π × D r 1 = 15 × 10 × 3 . 14 × 0 .075 = 35.325m
(38)
L(outer ) = 15 × 10 × π ×D r 2 = 15 × 10 × 3.14 × 0.155 = 73.005m
(39)
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When it generates maximum power, the damping force is
F d = F d (inner ) + F d (outer )
(40)
Fd = (2 .4 × 35 . 3 + 0 .8 × 73 ) × 4 .77 = 572 .5 N The maximum magnetic damping force of single shock absorber is Fmax = BIo L = (2.4 × 35.3 + 0.8× 73) × 9.54 = 1145N
(41)
Where I o —no-load current in the circuit And normally the increase of the damiping is at the cost of the reduction of the Preg
Fd → Icoil →(Rcoil + Rload)
−1
(42)
Fmax occurs when the current is at maxmum. At this time, Rload=0，so
Fmax → R coil
−1
(43)
when Rcoil equals to Rload Fd=Fmax/2
F d / F max = R coil / (R coil + R load
(44)
)
The maximum power appears when R load
(45) equals
to Rcoil ，so
ξ = γ /2
m 1 k 1 = 0 . 35
(48)
Where ξ ——damping ratio of the suspension γ ——damping coefficient (N·s/m) From above two formulas it can be calculated that m1 =185kg， k1 =14300N/m. Along with the weight of the shock absorber and unsprung mass, the mass of the car will be about 1.3 ton. Furthermore, car equiped with this kind of shock abosrber need a car height adjustment assembly to make the coil working at proper position. Overall, after calculating according to above structural parameters and magnetic field analysis results, the current of the external and internal coil windings groups can reach above 60 A and supply electric power of 4158 W when a automobile assembled with 4 such regenerative shock absorbers travels on B-class road at the speed of 20 m/s (car body’s velocity will at 0.17 m/s). The maximal damping force generated by singular shock absorber can be as high as 1145N and average damping force can reach 517 N when generating maximal power. Based on the above calculation, shock absorbers with such parameters apply to a car of 1.3 ton if the damping ratio is defined as 0.3. VI. CONCLUSIONS
Pmax → V coil / 4 R coil .
(46)
From the formulas above we can infer it is necessay to design a circuti to change the resistance of the circuit to increase the damping force when the car runs on rough road and reduce the damping force when runs on even road. E. THE CAR THAT THE ELECTROMAGNETIC SHOCK ABSORBER SUITS According to following formula
F d ≈ σ ⋅ V z ⋅ B r ⋅ V coil = γ V z 2
(47)
The damping force of the single shock abosrber at the condition of maximum power is 572.5 N, Vz is 0.5 m/s, so the damping coefficient γ is 1145N·s/m. The mass that single suspension supporting is m1 . According to the natural frequency requirements of the suspension
n1 = Where
The damping ratio of the shock abosrber should be between 0.2-0.4, here we choose ξ equals to 0.35
k 1 m 1 / 2 π = 1 . 4 Hz
(48)
n1 — the natural frequency of the suspension(Hz)； k1 —suspension stiffness (N/m)；
m1 — the mass supported by single supension (kg)。
© 2010 ACADEMY PUBLISHER
This paper analyzes the structure and operation principle of a regenerative electromagnetic shock absorber and discusses the choice of magnetic materials. According to the structure parameters of the shock absorber and performance parameters of shock absorber material caculated we know that the shock absorber with such parameters is suitalbe for a car about 1.3 ton. The analyzed value of the magnetic flux density at the air gap with ANSYS software is satisfactory.When the car runs at 20m/s on the c-level road, the recovery efficiency reaches 39% and it still has margin to be increased by improvement of the structure. For example to substitute permeability material with high permeability alloy. The results of calculation and magnetic field analysis prove that the scheme of this shock absorber is feasible. ACKNOWLEDGMENT The author would like to thank Department of Science & Technology of Hebei Province for approving the guidance plan of scientific & technological research and development. REFERENCES [1] H C.HONG K T An adaptive LQG control for semi-active suspension systems[J],Inernationla Jornal of Vehicl Design,2004,34(4):309-326 [2] Yu Fan, Cao Min, Zheng Xuechun. “Research on the Feasibility of Vehicle Active Suspension with Energy
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[3]
[4] [5]
[6]
[7]
JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
Regeneration,” Journal of Vibration and Shock, 2005, vol. 24(4), pp. 27~30. Chen Shian, He Ren, Lu Senlin. “New Reclaiming Energy Suspension and ITS Working Principle,” Chinese Journal of Mechanical Engineering, 2007, vol. 43(11), pp. 177~182. Wendel G R , Stecklein GL. “A regenerative active suspension system,” SAE Paper 910659. Suda Y, Shiiba T. “New hybrid suspension system with active control and energy regeneration,” Vehicle System Dynamics, 1996, vol. 25, pp. 641 ~ 654. Nakano K, Suda Y, Nakadai S. “Self-powered active vibration control using continuous control input,” JSME International Journal , Series C, 2000, vol. 43(3), pp. 726731. Nakano K, Suda Y, Nakadai S. “Self-powered active vibration control using a single electric actuator,” Journal of Sound and Vibration, 2003, 260, pp. 213~235.
© 2010 ACADEMY PUBLISHER
[8] Martins I , Esteves J , Marques GD , et al . “Permanent magnets linear actuator applicability in automobile active suspensions,” IEEE Transactions on Vehicular Technology, 2006, vol. 55(1), pp. 86~95 [9] I. Boldea, et aI., "Linear Electric Actuators and Generators"1997 IEEE International Electronic Machines and Drives Conference Record, Milwaukee, WI (May 1821, 1997) [10] J. Rizk, et aI., "Design and Performance of Permanent Magnet Generators," Symposium on Power Electronics,Electrical Drives, Advanced Electrical Machines(SPEEDAM), Proceedings, Sorrento, Italy (Jun. 3-5, 1998) [11] J Wang, et al. "Design and Experimental Characterisatio of a Linear Reciprocating Generator," lEE Proc.-Electr. Power Appl., vol. 145, No.6 (Nov. 1998)
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Structure and Performance Analysis of Regenerative Electromagnetic Shock Absorber Zhen Longxin Yanshan University /Automotive Vibration and Noise Research Institute, Qinhuangdao, China [email protected]
Wei Xiaogang Yanshan University /School of Vehicle and Energy Engineering, Qinhuangdao, China [email protected]
Abstract—This paper analyzed the structure and principle of a regenerative electromagnetic shock absorber in detail. The innovative shock absorber resembles linear generator in principle and can generate electric power through the relative reciprocating motion between coil assembly and permanent magnet assembly. At the same time, the damping can remove discomfort caused by road roughness. The regenerated electric power can be recovered through battery. Analysis of magnetic flux density of the permanent magnet array of the innovative shock absorber was performed using ANSYS software based on the structure parameters given in the paper,then the performance parameters of the shock absorber was determined . Analysis and calculation results prove the viability of this shock absorber. Index Terms—electromagnetic shock absorber; energy recovery; magnetic field analysis ; principle
I.
INTRODUCTION
With the increasing quantity of possessed automobiles,it has received a great deal of attention from automobile manufacturers and government for the energy energy conservation and environmental protection both at home and abroad. To protect the environment and reduce vehicle emissions and fuel consumption of vehicles, it is necessary to recover the energy wasted by the car, such as the braking energy, engine exhaust emissions energy and vibration energy of suspension, etc. Usually the vibration energy caused by road roughness when car runs has not been paid attention to and it is wasted through conversion to thermal energy. If the vibration energy can be recovered and converted to other form of energy such as electric or hydraulic power so to suppy for other devices, then the aim of eco-friendly energy-saving is reached. In this paper the vibrational energy was converted to electric energy through the innovative electromagnetic absorber shock. Guidance plan of scientific & technological research and development of Hebei province (07213531)
© 2010 ACADEMY PUBLISHER doi:10.4304/jnw.5.12.1467-1474
Normally as we know active suspensions like pneumatic suspension with nolinear rigidity which is well known for its comfort and adaptability and its characteristics such as rigidity and damping ratio can be changed with road roughness.But this kind of suspension is rather complex and need much energy to change its characteristics, moreover it needs complex control algorithm and expensive hydraulic and electric element such as hydraulic pump, ECU, many sensors and control valves. Reference [1] introduces the control algorithm of a semi-active adaptive suspension based on LQG method. Reference [2] the vibratinal is recovered in hydraulic way and the tests results show that energy feedback suspension only costs 16% of that energy compared with common passive suspension. Reference [3] relates to the hydraulic way of reclaming vibrational energy by hydraulic accumulator to supply other components with hydraulic energy.But the structure is rather complx and the effciency is not idal actually. In Reference [4], the author mentions the electromagnetic way of recovering the vibrational energy generated by the suspension, its main operational principle is that when the coil cuts the magnetic line of force generated by the permanent magnet, then the electric power is generated and recovered by battery to supply other electric assemblies. But the effciency is low owing to its sturcture. Reference [5] introduces the design and control method of hybrid suspension system. Reference [6] introduces the selfpowered vibartion control using hydraulic energy input and its method and prrinciple is similar to the above paper refered. Reference [7] introduces the self-powered active vibration control using electric actutor which resembles linear generator in structure and principle,but the shortcoming is that the power effciency is low. Reference [8] introduces the design and principle of a autobile active suspensions with permanent magnets, but still needs improvement in effciency. I. Boldea, et aI. [9], J. Rizk, et aI [10] and J Wang, et al [11] introduce three different kinds of methods to design linear generators with high effciency.
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This paper introduces the structure and principle of a regenerative electromagnetic shock absorber in detail and uses ANSYS software analyzed the magnetic flux density of the permanent magnet array of the electromagnetic shock absorber absorber, then caculated the performance parameters. For its special structure the max magnetic flux density in the place where coils come through reaches as high as 2.6T. It undoubtedly exceeds other previous energy-recovering shock absorber in perfomance. II. THE STRUCTURE OF REGENERATIVE ELECTROMAGNETIC SHOCK ABSORBER The regenerative electromagnetic shock absorber described in this paper mainly consists of four parts: a permanent magnet array, a coil windings array, 2 guide cylinders and a spiral spring. Its structure is shown in Fig. 1. A. PERMANENT MAGNET ARRAY As is ashown in fig. 2, the permanent magnet array includes 2 parts: internal magnet part and external part and both two parts comprise 14 layers of permanent magnet and 15 layers high permeability material and which was serparated by permanent magnet repectively. A axial guide rod axially penetrates these internal permanent magnets and high magnetic conductive material layers to enhance their strength. In this structure the axially and radially adjacent permanent magnets have opposite polarity shown as fig.3. So the magnetic induction line radiated from the adjacent permanent magnet as if it is distorted and forms magnetic vector superpositon.At this time the magnetic flux density is about twice that the single one radiates. Permanent magnets array is fixed to end plate which is fixed on inner side of the shock absorber shell. Permanent magnets are fixed with magnetic conductive layers by mighty bond or mechanical mean.
Figure 2. Diagram of permanent magnet array
Figure 3. Diagram of permanent magnet array
Hard magnetic materials can be chosen as permanent magnet material and in this paper Nd-Fe-B material is chosen. The Nd-Fe-B material has high magnetic energy product (10 times higher than ferrite magnet), high coercive force and high energy density. Soft magnetic materials which usually have high permeability can be chosen as high magnetic conductive material and in this paper 45CrNiMoVA material is chosen. B. COIL WINDINGS ARRAY 1) The coil windings array moves reciprocatingly along the air-gap between the internal part and external part of the permanent magnet array and cuts lines of magnetic force to generate electric power. Its structure is shown in fig. 4. • Both internal and external magnetic conductive guide sleeves are wound by certain number of coil windings groups. In order to enhance the permeability of coils, nickel-like coatings can be applied to outer surface of coils. • Figure 1. Diagram of structure of regenerative shock absorber.
© 2010 ACADEMY PUBLISHER
Various coil windings group can be connected in parallel or in series or in both ways.
JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
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→
→
→
Fl = q ⋅ V ⋅ B
(1)
→
Where Fl —Lorentz force (N)； q—queantity df electricity (C)； →
V —the velocity of electric charge (m/s)； →
B —magnetic flux density(T) The corresponding Lorentz electric field is defined as →
→
→
El = V × B
(2)
→
Where El —Lorentz electric field(V/m) We define the electrical conductivity of the coil as σ , mass as mcoil ,volume as Vcoil . When the coil array moves relatively to the magnet array at the speeed Vz, the induced electromotive force in the coil is defined L
Ve = Figure 4. Diagram of coil windings array
•
•
Internal coil windings groups wind around the outer surface of the internal magnetic conductive guide sleeve and external coil windings groups wind around the outer surface of the external magnetic conductive guide sleeve. Guide cylinder 1 which forms sliding pair together with guide cylinder 2 shown in figure 1 is attached to outside of the external magnetic conductive guide sleeve to stabilize the coil windings array and to maintain its absolute vertical direction and to avoid friction between it and the permanent magnet array. Thus the coil windings array can move smoothly relatively to the permanent magnet array. The internal and external magnetic conductive guide sleeves and guide cylinder 1 all have long axial slots along their outer surface. The purpose is to avoid heat generation and energy loss caused by eddy current. III.
THE PRINCIPLE OF OPERATION
The permanent magnet array of regenerative electromagnetic shock absorber is connected to wheel axles of the vehicle and the coil windings array is connected to the framework or body of the vehicle. When the vehicle travels on rough roads, the relative displacement between framework or body and wheel axles causes relative displacement between coil windings array and permanent magnet array. At this point coil groups will be cutting the magnetic induction lines in the air-gap, thus current occurs in the coil and in the mean time damping force occurs correspondingly. The direction of the damping force is relatively opposite to the movement of the coil group. When the conductor moves perpendicularly to the direction of magnetic induction line, the Lorentz force can be defined as © 2010 ACADEMY PUBLISHER
∫
→
E l dL = B r ⋅ V
z
⋅ L
(3)
0
Where Ve — induced electromotive force (V)； Br — radial magnetic flux density (T)； L— the total length of coil(m)； Vz — the relative velocity betweetn coil and magnet (m/s)。 The corresponding eddy current density J is given as J = σ ⋅ El
(4)
Where J — current density of the coil (A/m²)， σ — electric conductivity of the coil (S/m). The differential eddy current dI passing through a differential corss section area of the coil winding is
dI = JdAw
(5)
Where dI — differential eddy current dAw — differential corss section area of the coil winding By integraing the dI over the cross section comes the eddy current I I = σ
⋅ B
r
⋅ A
w
⋅V
z
(6)
Where Aw — area of the corss section of the coil (m²)， I — current of the coil (A)。 For each coil peak or maximum instanteneous regenerated electrical power Pmax is given as P max = V e ⋅ I / 4 = 0 . 25 ( V z ⋅ ⋅ B r ) 2 ⋅ V coil
(7)
Where Pmax — maximum instanteneous regenerated electrical power Vcoil —total volume of the coil winding Suppose the average diameter of the coil array as Dr， N as the total turns of the coil, then the inductive electromotive force is
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JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
V
= π ⋅ N ⋅ D r ⋅V
e
z
⋅ B
(8)
r
The average current of the coil can be caculated through
The resistance of the coil is
Rc = N ⋅ π ⋅ Dr /(σ ⋅ Aw )
(9)
When the load resistance equals to Rc, peak power can be drawn from above equations P max = V e ⋅ I o / 4 = (V z ⋅ B r
)
⋅ N ⋅ π ⋅ Aw ⋅σ / 4
2
= (V z ⋅ Br ) ⋅ σ ⋅ Vcoil / 4 2
(10)
To simplify the caculation process we use the mean relative veloctiy between the car body and chassis to substitute for Vz T
Vz
2
∫V
=
2 z
dt
(11)
0
T
∫ dt
Where V z —the mean relative veloctiy between the car body and chassis(m/s) 2
=
(a t )
(12)
2
According to experience ,We suppose −
V
z
= V max / 3
(13)
Where Vmax — the maximum veloctiy between car body and the chassis. Then we can draw Pavg = (V z ⋅ B r
)2
⋅ N ⋅ π ⋅ A w ⋅ σ / 4 = (V max ⋅ B r
)2 ⋅ σ
V coil / 12 = Pmax/ 3
(14)
P max — the peak power of the coil Similarly, The average voltage of the coil can be caculated through avg
= V
e
/ 2
TABLE I.
(16)
Where Iavg— the average current of the coil（A） In order to get the results according with real circumstance, we using the typic road roughness data to estimate the relative power, current and inductive electromotive force. From the formula listed above we know that in order to generate more electrical power we need to reduce the resistance of the coil and magnify the radial magnetic flux density Br and volume of coil Vcoil in the air gap at the same time. The remanent magnetism is limited by the choosen permanent magnet and volume is limited by the space of car body. MAGNETIC FIELD ANALYSIS OF SHOCK ABSORBER
A. STRUCTURE PARAMETERS AND PERFORMANCE OF SHOCK ABSORBER The structure parameters of the shock absorber determined according to vehicle weighing 1.3 ton are shown in table 1. The vehicle has 2 wheel axles and 4 suspensions. Each suspension supports 270 kg. The relative magnetic permeability of the air is defined as 1 and the magnetic coercive force of the permanent magnet is defined as 900000 A/m. The relative magnetic permeability of the permanent magnets is defined as (17).
⋅
Where Pavg — the average power of the coil
V
I avg = I O / 2 3
IV.
0
Vz
Where Vavg — the average voltage of the coil (V)
µr = Br / (µ0Hc)
(17)
Where Br is residual magnetism of magnet, µ0 is Permeability of vacuum，Hc is magnetic coercive force of the permanent magnet. High magnetic conductive material chosen in this paper belongs to soft magnetic materials. Its data of B-H curve is shown in table 2.
(15)
3
STRUCTURAL PARAMETERS OF ELECTROMAGNETIC SHOCK ABSORBER
Thickness of radial air-gap
5 mm
Internal radius of internal coil windings group
35.5 mm
Thickness of single NdDy
22.5 mm
External radius of internal coil windings group
39.5 mm
Thickness of magnetic conductive layer
10 mm
External radius of external coil windings group
75.5 mm
Length of central guide rod
500 mm
External radius of external coil windings group
79.5 mm
Height of single coil windings group
10 mm
Internal radius of shell of shock absorber
96 mm
Height of end plate
5 mm
External radius of shell of shock absorber
106 mm
Height of whole magnet array
495 mm
Diameter of end plate
190 mm
Radius of internal cylindrical magnet
35 mm
Permeability of vacuum
4π×10-7
Diameter of central guide rod
10mm
Conductivity of coil
5×107 S/m
Internal radius of external cylindrical magnet
40mm
Mean diameter of internal coil windings group
75 mm
External radius of external cylindrical magnet Number of internal and external NdDy
75mm 14
Mean diameter of external coil windings group Number of internal and external coil windings group
15
© 2010 ACADEMY PUBLISHER
155 mm
JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
TABLE II.
1471
DATA OF B-H CURVE OF HIGH MAGNETIC CONDUCTIVE MATERIAL
B(T)
H(A/m)
B(T)
H(A/m)
0.70
355
1.75
7650
0.80
405
1.80
10100
0.90
470
1.85
13000
1.00
555
1.90
15900
1.10
673
1.95
21100
1.20
836
2.00
26300
1.30
1065
2.05
32900
1.35
1220
2.10
42700
1.40
1420
2.15
61700
1.45
1720
2.20
84300
1.50
2130
2.25
110000
1.55
2670
2.30
135000
1.60
3480
2.41
200000
1.65
4500
2.69
400000
1.70
5950
3.22
800000
B. RESULTS OF MAGNETIC FIELD ANALYSIS As is known according to Faraday induction law, the energy recovery efficiency of this shock absorber depends on the magnetic flux density in the air-gap. This paper establishes the model of the permanent magnet array and generates mesh of the model, then analyzes the magnetic flux density in the air-gap with ANSYS software. Due to the symmetry of the permanent magnet array, its model can be simplified to the partial threedimension model shown in fig. 4 and partial twodimension model shown in fig. 3. Fig. 6 and fig. 7 respectively show the distribution of magnetic induction lines and magnetic flux density. As is shown in fig. 6, most of the magnetic induction lines at the air-gap distribute radially and they go as if they were bent because both radially and vertically adjacent permanent magnets have opposite polarity. Thus magnetic induction lines of adjacent magnets superpose mutually in the air-gap to magnify magnetic flux density and increase energy production efficiency. As is shown in fig. 7, the maximal magnetic flux density reaches as high as 2.7T and the average value is about 2.3T. So result of magnetic field analysis is satisfactory. V.
PERFORMANCE PARAMETERS OF THIS SHOCK ABSORBER
According to the structure parameters and the analyzed results of the magnetic field we can draw the performance results. A. THE PRINCIPLE OF THE MAGNETIC DAMPING FORCE We know that when the coil arry reciprocates through the magnet array axisly, the inductive currrent is influenced by the magnetic field of the permanent magnet, then the magnetic damping force Fd is generated. Actually two forces are applied to the coil array, one is
© 2010 ACADEMY PUBLISHER
Figure 5. Diagram of partial three-dimension model
Figure 6. Diagram of distribution of magnetic induction lines
Figure 7. Diagram of magnetic flux density
the magnetic damping force and the other is inertial force if the gravity of the coil is ignored.
Fo = Fi + Fd = m coil (dV z / dt ) + γ V z = m coil ⋅ a (18) Where F o — the external force applied to the coil array F i — the inertial force F d — the magneitc damping force
α — the acceleraion of coil array γ — the damping coefficient
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JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
When the initial velocity of the coil is defined as 0m/s, τ , then the
γ / m coil is defined as damping time constan
relative veloctiy between the car body and chassis is t ⎛ ⎞ V z = a ⎜⎜ 1 − e τ ⎟⎟ ⎝ ⎠
V z = bV
(19)
Equation (19) resemble the derivative of the following formula of the one dof free damping oscillation in behavior and perfomance. 2 (20) Z = Ae − nt ⎛⎜ ω − n 2 t ⎞⎟ + ϕ ⎝
x
⎠
o
b=dz/dx
Where b—the bump slope of the road ,its range is0.010.05 The waveform in half period is
z ( x ) ≈ bx
(22)
Where z(x) —the vertical displacement of the tire .
(23)
x
Where Z ( x) —vertical speed of the tire V x —the running speed of the vehicle
)
sprung mass Preg = (Vmax ⋅ Br ) ⋅ σ ⋅ Vcoil /12 = Pmax/3 2
(25)
The conductivity is 5×107 s/m, the turns of the single coil array is 40, so the volume of single inner coil array is about
)
Vcoil (inner ) = π ⋅ R4 − R3 ⋅ h5 = 9.4 × 10e − 6m 3
(26)
And the volume of single outer coil array is about V coil (outer
)= π
(
⋅ R6 − R5 2
2
)⋅ h
5
= 19 . 4 × 10 e − 6 m 3
(27)
The maxium magnetic flux density at the inner air gap is about 2.5 T and is about 0.8 T at the outer air gap. © 2010 ACADEMY PUBLISHER
Ve (outer) = 3.14× 40× (150e − 3) × 0.5× 0.8 = 7.8V
(29) (30)
Io (inner) ≈ Br ⋅Vz ⋅σ ⋅ Aw = 2.4 × 0.5× (5×10e + 7) × 3.142 ×10e − 6 = 60A
(31)
I o (outer) ≈ Br ⋅ Vz ⋅ σ ⋅ Aw = 0.8 × 0.5 × (5 ×10e + 7) × 3.142 ×10e − 6
= 20A
(32)
Pmax = Ve ⋅ I o / 4
(33)
According to (33)
Pmax(inner) = 11.3 × 60/ 4 = 169.5W
Pmax (outer ) = 7.8 × 20 / 4 = 39W
(34)
Pavg = Pmax(inner) + Pmax(outer) / 3 = 69.33W
(35)
So the total regenerated power with 4 shock absorbers is Ptotal = Pavg × 14 (array
)× 4 =
4158 W
(36)
µ = Preg /( Pexhausted + Preg ) = 4158 /( 4158 + 7000 ) = 37.2%
(24)
Where Preg — the energy regenerated by the shock abosrber Pexhuast — the power exhausted by supporting
2
V e (inner ) = 3 . 14 × (75 × 10 e − 3 × 0 . 5 × 2 . 4 ) = 11 . 3V
Pavg = Pmax / 3
C. CALCULATION OF THE PERFORMANCE PARAMETERS Suppose that car is equiped with four electromagnetic shock absorbers like this kind and the speed of the car in c-level road is 20m/s. According to related data, the consumed power of suspensions for holding sprung mass is 7500 w. The recovery efficiency is
2
(28)
According to (34)
.
η = P reg / (P reg + P exhuast
= 0 .5 m / s
The inductivie electromotive force in single coil is
(21)
Z ( x ) ≈ bV
x
The current of the coil will be
B. ROAD DATA REFERENCE According to relative road data information we know that mean roughness value of c-level road is about 1-6 cm, and the single wavelength is about 10-100 cm. To simplify the calculation we suppose that the road waveform is triangular.
(
Here b=0.025, when the speed of the car is 20m/s, then
(37) For the generated current is alternative current, and the current in the adjacent coil has opposite plolarity, here the coils are connecetd in series and the alternative current need to be converted to direct current with current rectifier.To avoid short out, insulating substance needs to be applied on the coil. D. CONTROL OF THE DAMPING FORCE The length of the single coil array is L (inner ) = 15 × 10 × π × D r 1 = 15 × 10 × 3 . 14 × 0 .075 = 35.325m
(38)
L(outer ) = 15 × 10 × π ×D r 2 = 15 × 10 × 3.14 × 0.155 = 73.005m
(39)
JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
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When it generates maximum power, the damping force is
F d = F d (inner ) + F d (outer )
(40)
Fd = (2 .4 × 35 . 3 + 0 .8 × 73 ) × 4 .77 = 572 .5 N The maximum magnetic damping force of single shock absorber is Fmax = BIo L = (2.4 × 35.3 + 0.8× 73) × 9.54 = 1145N
(41)
Where I o —no-load current in the circuit And normally the increase of the damiping is at the cost of the reduction of the Preg
Fd → Icoil →(Rcoil + Rload)
−1
(42)
Fmax occurs when the current is at maxmum. At this time, Rload=0，so
Fmax → R coil
−1
(43)
when Rcoil equals to Rload Fd=Fmax/2
F d / F max = R coil / (R coil + R load
(44)
)
The maximum power appears when R load
(45) equals
to Rcoil ，so
ξ = γ /2
m 1 k 1 = 0 . 35
(48)
Where ξ ——damping ratio of the suspension γ ——damping coefficient (N·s/m) From above two formulas it can be calculated that m1 =185kg， k1 =14300N/m. Along with the weight of the shock absorber and unsprung mass, the mass of the car will be about 1.3 ton. Furthermore, car equiped with this kind of shock abosrber need a car height adjustment assembly to make the coil working at proper position. Overall, after calculating according to above structural parameters and magnetic field analysis results, the current of the external and internal coil windings groups can reach above 60 A and supply electric power of 4158 W when a automobile assembled with 4 such regenerative shock absorbers travels on B-class road at the speed of 20 m/s (car body’s velocity will at 0.17 m/s). The maximal damping force generated by singular shock absorber can be as high as 1145N and average damping force can reach 517 N when generating maximal power. Based on the above calculation, shock absorbers with such parameters apply to a car of 1.3 ton if the damping ratio is defined as 0.3. VI. CONCLUSIONS
Pmax → V coil / 4 R coil .
(46)
From the formulas above we can infer it is necessay to design a circuti to change the resistance of the circuit to increase the damping force when the car runs on rough road and reduce the damping force when runs on even road. E. THE CAR THAT THE ELECTROMAGNETIC SHOCK ABSORBER SUITS According to following formula
F d ≈ σ ⋅ V z ⋅ B r ⋅ V coil = γ V z 2
(47)
The damping force of the single shock abosrber at the condition of maximum power is 572.5 N, Vz is 0.5 m/s, so the damping coefficient γ is 1145N·s/m. The mass that single suspension supporting is m1 . According to the natural frequency requirements of the suspension
n1 = Where
The damping ratio of the shock abosrber should be between 0.2-0.4, here we choose ξ equals to 0.35
k 1 m 1 / 2 π = 1 . 4 Hz
(48)
n1 — the natural frequency of the suspension(Hz)； k1 —suspension stiffness (N/m)；
m1 — the mass supported by single supension (kg)。
© 2010 ACADEMY PUBLISHER
This paper analyzes the structure and operation principle of a regenerative electromagnetic shock absorber and discusses the choice of magnetic materials. According to the structure parameters of the shock absorber and performance parameters of shock absorber material caculated we know that the shock absorber with such parameters is suitalbe for a car about 1.3 ton. The analyzed value of the magnetic flux density at the air gap with ANSYS software is satisfactory.When the car runs at 20m/s on the c-level road, the recovery efficiency reaches 39% and it still has margin to be increased by improvement of the structure. For example to substitute permeability material with high permeability alloy. The results of calculation and magnetic field analysis prove that the scheme of this shock absorber is feasible. ACKNOWLEDGMENT The author would like to thank Department of Science & Technology of Hebei Province for approving the guidance plan of scientific & technological research and development. REFERENCES [1] H C.HONG K T An adaptive LQG control for semi-active suspension systems[J],Inernationla Jornal of Vehicl Design,2004,34(4):309-326 [2] Yu Fan, Cao Min, Zheng Xuechun. “Research on the Feasibility of Vehicle Active Suspension with Energy
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[3]
[4] [5]
[6]
[7]
JOURNAL OF NETWORKS, VOL. 5, NO. 12, DECEMBER 2010
Regeneration,” Journal of Vibration and Shock, 2005, vol. 24(4), pp. 27~30. Chen Shian, He Ren, Lu Senlin. “New Reclaiming Energy Suspension and ITS Working Principle,” Chinese Journal of Mechanical Engineering, 2007, vol. 43(11), pp. 177~182. Wendel G R , Stecklein GL. “A regenerative active suspension system,” SAE Paper 910659. Suda Y, Shiiba T. “New hybrid suspension system with active control and energy regeneration,” Vehicle System Dynamics, 1996, vol. 25, pp. 641 ~ 654. Nakano K, Suda Y, Nakadai S. “Self-powered active vibration control using continuous control input,” JSME International Journal , Series C, 2000, vol. 43(3), pp. 726731. Nakano K, Suda Y, Nakadai S. “Self-powered active vibration control using a single electric actuator,” Journal of Sound and Vibration, 2003, 260, pp. 213~235.
© 2010 ACADEMY PUBLISHER
[8] Martins I , Esteves J , Marques GD , et al . “Permanent magnets linear actuator applicability in automobile active suspensions,” IEEE Transactions on Vehicular Technology, 2006, vol. 55(1), pp. 86~95 [9] I. Boldea, et aI., "Linear Electric Actuators and Generators"1997 IEEE International Electronic Machines and Drives Conference Record, Milwaukee, WI (May 1821, 1997) [10] J. Rizk, et aI., "Design and Performance of Permanent Magnet Generators," Symposium on Power Electronics,Electrical Drives, Advanced Electrical Machines(SPEEDAM), Proceedings, Sorrento, Italy (Jun. 3-5, 1998) [11] J Wang, et al. "Design and Experimental Characterisatio of a Linear Reciprocating Generator," lEE Proc.-Electr. Power Appl., vol. 145, No.6 (Nov. 1998)
