Dynamic Simulation of a Novel Free-Piston Linear Generator

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linear generator (FPLG) which consists of double two-strokes combustion chambers with inner and outer piston-couples and a linear electric generator with ...
2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM) July 7-11, 2015. Busan, Korea

Dynamic Simulation of a Novel Free-Piston Linear Generator * Peng Sun1, Fei Zhao1,2**, Chi Zhang1,2, Member, IEEE , Jie Zhang1,2 , Jinhua Chen1,2 

Abstract—This paper proposes a new structure of free-piston linear generator (FPLG) which consists of double two-strokes combustion chambers with inner and outer piston-couples and a linear electric generator with multi-movers in order to improve the system efficiency. The one-dimensional thermodynamics model of the combustion chambers and the model of the linear electric generator have been respectively derived mathematically. And the hybrid simulation model of the whole FPLG has also been established using MATLAB/SIMULINK. The features and operation process with basic igniting and scavenging strategy have been analyzed. It indicates that the novel FPLG has comparative potential and capacity for producing higher electric power and reaching higher power density.

I. INTRODUCTION FPLG is a novel energy converter which has outstanding advantages of higher combustion efficiency, higher power density and law emissions compared with conventional internal combustion generator. Specially, the piston of FPLG is not restrained by the crankshaft, so the compression ratio can be adjusted through appropriate control to adapt various fuels, such as diesel, gasoline, ethanol, hydrogen, methane and natural gas[1]. Therefore, the FPLG is suitable for HEVs as a novel alternative hybrid power system which is promising for high efficiency and the potential to be environmental friendly. There are various integrate configurations of FPLG. One common structure is two-strokes with two opposite-cylinders at both ends and a linear generator in the middle, which has been studied a lot by Pawiz Famouri et al. [2], Jorgen Hansson et al. [3], Vysoký et al. [4] and Zuo et.al.[5]. The most advantage of this structure is its structural balance and continuous power output in every motion stroke. And how to optimize the linear electric generator to improve the power density and efficiency is still a crucial study focus. Siqin Chang et al. have proposed a four-strokes configuration with a * This research is supported by the International S&T Cooperation Projects of China (Grant No.2014DFA71010), the Science and Technology Innovation Group of Ningbo (Grant No.2012B82005) and One Hundred Talents Program of the Chinese Academy of Sciences. Peng Sun is with the Ningbo Institute of Materials Technology & Engineering, Chinese Academy of Sciences, Zhejiang 315201 China (PhD student, email: [email protected]). Fei Zhao** is with the 1Ningbo Institute of Materials Technology & Engineering, Chinese Academy of Sciences and 2Zhejiang Provincial Key Laboratory of Robot and Intelligent Manufacturing Equipment Technology, Zhejiang 315201 China (Research Assistant Professor, corresponding author, Tel:86-574-86324587,Fax:86-574-86382329, email: [email protected]). Chi Zhang is with the 1Ningbo Institute of Materials Technology & Engineering, Chinese Academy of Sciences and 2Zhejiang Provincial Key Laboratory of Robot and Intelligent Manufacturing Equipment Technology, Zhejiang 315201 China (Research Professor , email: [email protected]).

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coil-moving linear generator and a mechanical spring as the rebounder[6]. However, the mechanical spring is not reliable and the operation life is limited, and the rebound efficiency is law. Johnson and his colleagues have been devoting to developing a FPLG system with 30kW power output as the fuel cell for a hybrid electric vehicle for a long time. The prototype has two opposite pistons respectively combined with two linear generators sharing one common combustion chamber and two bounce chambers assembled on both sides, of which the electric output power is nearly 19.5KW[7]. Recently, Frank Rinderknecht et al. have also proposed a FPLG concept, expecting to be designed to output 50KW electrical power, with two pistons respectively connected to two linear generators sharing a middle combustion chamber, and two gas springs are designed besides the common combustion chamber[8]. Yoshihiro Hotta et al. have also published their FPLG achievement, in which with a linear generator mover assembled to a piston and a bounce chamber acting as gas spring[9, 10]. Particularly, this structure is highly praised as the most perspective integration approach[11]. However, to improve the power density and the electric power output performance is still the future work. In this paper, a new structure of FPLG is proposed. In order to study the dynamic character of the proposed structure, the one-dimensional thermodynamics model of the combustion chambers and the model of the linear electric generator are derived respectively. And the hybrid simulation model of the whole FPLG is established using MATLAB/SIMULINK. The features and operation process with basic igniting and scavenging strategy have been analyzed. II. PROCEDURE FOR PAPER SUBMISSION A. The novel structure of the proposed FPLG One effective approach to improve the power density is to reduce the mass of the piston-rod and to increase the electric power output capacity at each generating stroke as much as possible. Considering this, this paper proposes a novel two-stroke FPLG shown as Figure 1. Figure 2 shows the illustration of this FPLG. This is a very special configuration, of which the linear electric generator is equipped with one double-sided HALBACH permanent magnets-moving flat inner mover and two single-sided HALBACH permanent magnets-moving mover-couples. And it can adapt carbon fiber material to reduce the mass of the movers so as to improve power density and dynamical performance. There are two combustion chambers but two pistons in each cylinder, which has the potential to improve the effective power output.

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Figure 2 shows the illustration of this FPLG. To start the FPLG, the linear machine operates as a start motor to drive the piston rod to reach the ignition condition and the ignition position, e.g. the TDC1L (TDC2L) or TDC1R (TDC2R) positions. In order to describe the operation principle of this system, assume that the first ignition occurs in right cylinder. Before ignited, it's the scavenging process when the burnt gas produced in the previous cycle is exhausted through the exhaust port meanwhile the fresh air is introduced from the intake port. When the right cylinder ignited, the inner piston-couples and the outer piston-couples are pushed towards the opposite direction and driven the generator movers to produce electric power. When the right cylinder is at expansion stroke, the left cylinder is at compression stroke. When the pistons reach the left-ignition position, the fuel in the left cylinder is again ignited and begins to release energy to push the pistons back. The igniting and the scavenging process occur alternating-complementarily. Thus, every stroke is generating stroke. And the inner mover and the outer mover-couples can run at the same velocity in the opposite direction. Therefore, the voltage induced respectively by the inner mover and the outer mover-couples in the stator windings can be directly superimposed, which can extremely improve the electric power output capacity.

B. Modeling of thermodynamic The thermodynamic model involved in this paper is a one-dimensional model. To derive the model, there are several basic hypothesis as follows. 1) Ignoring the distribution variation of the pressure, temperature and density in the cylinder, the refrigerant is considered to be instantaneously homogeneous. 2) The refrigerant in the cylinder obeys the ideal gas law. 3) The thermodynamic parameters such as the specific heat capacity, the specific thermodynamic energy and the specific enthalpy are simply related to the gas temperature and gas composition. 4) The effects of vaporizing liquid droplets, fluid flow, combustion chamber geometry or spatial variations of the mixture’s composition are ignored. 5) The gas leakage loss through the piston ring pack or the valves is not taken into account. 6) The energy loss through intake and exhaust ports is neglected. 7) The energy loss of heat transferring through the cylinder wall is neglected. Based on the hypothesis above, using the Weiber combustion rate function, the changing rate of temperature and the pressure in the combustion chambers can be expressed as[5] dTL dV  1  dQBL   pL L  dt m1Cv  dt dt 

(1)

 dV  dpL 1  Rg dQBL  Rg     1  pL L  dt VL  Cv dt C dt  v   dTR dV  1  dQBR   pR R  dt m2Cv  dt dt 

where TL , the left and right cylinders, pL , pR represents the pressure in the left and right cylinders, mi is the total mass of the working medium in each cylinder, Rg is the gas constant, Cv is

Stators

v

v

the constant volume specific heat, QBL and QBR respectively represents the combustion heat released in left and right cylinders, VL and VR is respectively the instantaneous volume of the left and right cylinders. Using the Weiber function, the released combustion heat in each cylinder can be calculated as follows.

Permanent magnets

v

Coils Inner mover

Permanent magnets

Permanent magnets

Coils

(b) explosive view

dQB d B  H u g f c dt dt  t  t0 mc 1   B  1  exp  6.908( )  td  

Figure 1. 3D model of the novel FPLG with multi-movers Inner piston-couples BDC2L TDC2L

v2

TDC1L BDC1L

v1

FpL 2

FpL1

x2

Fe 21

Ff 1

x1

O

Outer mover-couples

Fe 22

stator BDC2R TDC2R

Ff 21

Fe1

(3)

 dV  dpR 1  Rg dQBR  Rg     1  pR R  (4) dt VL  Cv dt dt   Cv  TR respectively represents the temperature in

(a) assembly view

Outer mover-couples

(2)

v1

Ff 22

TDC1R BDC1R

FpR1

S

FpR 2

Sc

v2

S

x

Inner mover

Outer piston-couples

Figure 2. Illustration of the novel FPLG configuration

where

H u is

the law calorific value of fuel,

(5) (6) gf

is the injected

fuel mass of each operation cycle, c is the combustion efficiency,  B is the mass fraction percentage burned in combustion process, t0 is the ignition beginning time, td is the combustion duration, mc is the combustion quality factor. Based on Figure 2, the instantaneous volume of each cylinder can be expressed as follows.

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2

D VL      x1  x2  2 2

D VR      2S  2Sc  x1 +x2  2

(8)

where   Sc Sc   x1   2 , 2  S       S S   x   c ,  c  S    2  2  2  cylinder bore, S is the

C. Modeling of linear electric generator The model of the linear electric generator can be derived through coordinate transforming. Because the inner rotor and outer rotor-couples are controlled to move at the same velocity in the opposite direction, the back EMF induced in the stator windings is series in the same direction. Figure 3 shows the vector diagram of the novel FPLG in d-q reference frame, in which d1-q1 and d2-q2 reference frames respectively corresponds the inner mover and the outer mover-couples[12]. 1

 1 q1

U

E1

d1

1

d2

2



Figure 3. The vector diagram of the novel FPLG in d-q reference frame.

The voltage and current relationship in d-q coordinate can be described as

Uq

,

(16)

I. SIMULATION AND DISCUSSION

cs

,

Referring Figure 2, the dynamics relationship of inner piston-couples and outer piston-couples can be respectively described as

as

I

Ud

(15)

(17) Fe 2  Fe 21  Fe 22 (18) where Fe1, Fe2 is the generating load forces at stable operation, and the direction is always opposite to the velocity of corresponding piston.

1

d

2

U2

where

3    ( Ld 1  Lq1 )id 1  iq1 F    e1 2  f   F  F  F  3   ( L  L )i  i e2 e 21 e 22 f d2 q2 d 2  q2  2  

Ff 2  Ff 21  Ff 22

E

U1

(14)

d1-q1 and d2-q2 coordinates. The electromagnetic force applied to inner mover and outer mover-couples can be calculated as follows.

q2

E2

(13)

where  is the pole pitch, v1 and v2 are respectively the motion velocity of inner piston-couples and outer piston-couples, idi and iqi are the components of id and iq at

 M1 x1  FpL1  FpR1  Ff 1  Fe1   M 2 x2    FpL 2  FpR 2  Ff 2  Fe 2 

 bs

 v  v   1 2 idi  cos i -sini  id        i  1, 2  iqi   sini cos i  iq 



2

q

(12)

where Ld , Ld 1 , Ld 2 are respectively the inductances components at d-q, d1-q1, d2-q2 coordinates,  f is the total flux linkage produced by the permanent magnets, and

(9)

where D is the stroke length, Sc is the combustion clearance space, x1 and x2 are respectively the displacement of inner piston-couples and outer piston-couples.

2

  Ld  Ld 1  Ld 2    Lq  Lq1  Lq 2 and Lq , Lq1 , Lq 2

(7)

d d  U d  dt   q  Rs id  U  d q    R i d s q  q dt id , iq are the components

As introduced above, the one-dimensional thermodynamics model and the model of linear electric generator have been derived theoretically. Combing the dynamics relationship of inner and outer piston-couples, the hybrid thermodynamics model of the FPLG has been established using MATLAB/SIMULINK. Figure 4 shows the thermodynamics simulation models of the left and right combustion chambers. Figure 5 shows the hybrid simulation model of the FPLG.

(10) of voltage U and

current I at d-axis and q-axis respectively,  d and  q are the components of flux linkage ,  is the angular velocity of q-axis, or the angular velocity of vector U , Rs is the windings resistance. The linear electric generator proposed in this paper is a surface-mounted PMSLM without saliency, therefore   d  Ld id   f    q  Lq iq

(11)

Figure 4. Thermodynamics simulation models of cylinders

The major simulation parameters are listed in TABLE I. The main structural parameters of the combustion chambers are almost the same with that of Toyota prototype published in[9, 10] , in which the cylinder bore is 68mm, the stroke length is 100mm, and the scavenging port height is 33mm.

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For this novel FPLG, to control the inner pistons and outer pistons moving with the same speed in the opposite direction is extremely crucial for stable and continuous operation. In this paper, the pistons run tracking certain operation reference profiles shown as Figure 6. At the first cycle, it’s the motoring start process, and the pistons are driven by the electromagnetic force to corresponding ignition positions (5mm before reaching TDC positions). Then the system run stably after 40ms showing as Figure 6. Seeing Figure 2 again, the stroke length of inner and outer pistons is the same, or 100mm. The TDC and BDC positions of the inner piston are respectively 5mm and 105mm, and correspondingly -5mm and -105mm for the outer pistons, i.e. TDC1L=5mm, TDC2L=-5mm, BDC1L=105mm and BDC2L=-105mm. The absolute maximum velocity of the pistons is no more than 9.5m/s. The reference stable operation frequency is 25Hz. The actual operation frequency is 24.88Hz. Therefore, the actual cycle duration is about 40.2ms.

cylinder moving towards TDC1L and TDC1R. And the left scavenging starts at the point 33mm away from the BDC1L and BDC1R during the compression process of the left cylinder. Since the FPLG mechanical structure is symmetrical, the igniting and scavenging sequences of the left cylinder and the right cylinder are alternating-complementary as shown in Figure 7. Figure 8 shows the P-V diagrams of the left and right cylinders. The enclosed area of the P-V diagram represents the effect mechanical power provided by the internal combustion engine. During combustion, expansion and compression processes, the pressure in both cylinders is no more than 3Mpa. Figure 9 shows the released heat in left and right cylinders. From Figure 8 and Figure 9, then the cycle indicated work and combustion released heat can be obtained through integrating. The cycle combustion released heat in each cylinder is QB=1600J.

During the stable operation process, the mass of the injected fuel in each cycle is almost controlled to be changed a little. Therefore, the injected fuel mass of each cycle gf could be regarded as constant. The effective system generating efficiency can hence be approximately calculated as follows

sys  c

PE Tcyc

(19) 2QB where PE is the effective electric power output, Tcyc is the operation cycle duration and QB is the combustion released heat in each cylinder during one operation cycle duration.

Figure 6. Reference motion profiles

Figure 5. Hybrid simulation model of FPLG TABLE I. Major simulation parameters

Sc (m)

0.1 0.010

D (m)

0.068

M2 (kg) Hu (kJ/kg)

Ld1 (mH)

0.69

gf (mg/cycle)

37.5

Lq1 (mH)

0.69 90 0.69

c td (ms)

97% 4

0.69 90 1.38

mc

2

 (m)

0.04583

1.38 90 1.34

Rs (  )

0.32

RL (  )

6

S (m)

Ld2 (mH) Lq2 (mH) Ld (mH) Lq (mH) Ls (mH)

M1 (kg)

4.75 4.75 44000

Figure 7. Basic operation characteristics

A motion state processor is also involved in the hybrid simulation model, which can provide basic igniting and scavenging triggers according to the feedback motion state of pistons. The left igniting starts at the point 5mm away from the TDC1L and TDC1R positions when the pistons in left

The simulation indicates that the proposed novel FPLG has great potential on electric power output capacity, as shown in Figure 10. Here, the load is simply assumed to be a pure resistive load, and RL=6  . The simulation results show that the voltage magnitude can reach 625V, and the current

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magnitude is about 100Arms. More importantly, the electric power output capability is promising, of which the maximum power output is 95KW, and the mean electric power is about 46.35KW. The electric power output is actually highly depended on the load. There is an optimal electric power output point as the variation of the load. Therefore, it is extremely essential to design the load. From Figure 10, it is easy to find that the effective electric power output is PE=46.35KW. Then, from (19), the simulation results indicate that it can further obtain the effective system efficiency is sys  56%, which is much higher than the designed effective system efficiency 35.5%.

Figure 10. Three phase voltage, current and electric power output

II. CONCLUSION

Figure 8. P-V diagrams of left and right cylinders

The prominent superiority of FPLG in efficiency, power density and ultra-low emission makes it suitable as a new power system for hybrid vehicle. This paper proposed a new structure of FPLG. The innovation is the completely new structure with inner and outer pistons and special inner and outer movers. The corresponding simulation model of the hybrid system has been established. The simulation results indicate that this novel FPLG has excellent performance especially on electric power output capability, which can even as high as 95KW, and the mean value even can reach 46.35KW when the load resistance RL=6  and the operation frequency is 25Hz under the reference motion trajectory. The effective system efficiency is simulated to 56%, which is much higher than the design objective 35.5%. Though it is simply a simulation study, it verifies that this novel FPLG can run continuously and stably with appropriate igniting and scavenging strategy. However, the challenge is still the control issue. To control the inner piston-couples and the outer piston-couples running stably in the opposite direction with the same speed is a crucial issue. And this will be the future work on this novel FPLG. REFERENCES

Figure 9. Released heat of left and right cylinders

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