Modelling of a working cycle of an electro-hydraulic

International Review on Modelling and Simulations (I.RE.MO.S.), Vol. 6, n. 6

Modelling of a working cycle of an electro-hydraulic forklift in Matlab Simulink Tatiana A. Minav1, Denis Filatov2, Juha Pyrhönen3 and Matti Pietola1 Abstract – Evaluation of an electro-hydraulic system of a working machine is carried out by a Matlab Simulink model. Modelling of the total forklift system is presented. Analysis and verification of the Simulink model with practical results are also performed for an axial piston hydraulic machine drive. Practical results are presented to demonstrate the cycle energy efficiency of the proposed electro-hydraulic forklift arrangement with potential energy recovery feature. Keywords: Drives, pumps, permanent magnet machines, energy efficiency, energy recovery, model

Nomenclature Be bulk modulus Cs Stribeck friction Fco Coulomb friction in cylinder Ff friction force Fload force created by load Fso static friction i current ia, ib, ic currents in the phases a, b, c isd direct-axis components of the stator current isq quadrature-axis components of the stator current Jeq combined inertia of the load Jm total equivalent inertia of the electric motor Jp total equivalent inertia of the hydraulic motor Ke motor voltage constant Lcyl length of cylinder piston Lsd direct-axis stator inductance Lsq quadrature-axis stator inductance m load mass mp mass of the cylinder piston mt total mass p number of pole pairs prtn tank pressure ps system pressure Qin input flow Rs stator resistance Sp cross sectional area of a hydraulic piston Tco Coulomb friction Te electromagnetic torque Tf,p frictional torque TL load torque Tmotor drive torque Tp,th theoretical torque required for compressing fluid Tso static friction Tv viscous friction ud direct-axis components of the stator voltage usd stator voltage for d-axis

Manuscript received October 2013, revised January 2013

usq V V0 Vth

stator voltage for q-axis cylinder volume dead volume of cylinder theoretical motor displacement per revolution down_tot system efficiency during lowering inverter efficiency during lifting inv efficiency of supercapacitor sc tot_cycle total cycle efficiency up_tot system efficiency during lifting volumetric efficiency of the motor vol viscous friction permanent magnet created flux linkage PM stator d-winding flux linkages sd stator q-winding flux linkages sq electrical angular velocity m rotation speed of the shaft xp , xp , x p piston position, velocity and acceleration

I.

Introduction

Non-road Mobile Machinery (NMM) is widely used, even though the energy efficiency of hydraulic systems is often poor. The key benefit of hydraulics is high power/weight ratio. Mobile machines are typically high power and many of them are used continuously during working day. These facts results in huge total waste of energy. As the prize of energy increases, the reduction of the losses and energy consumption becomes economically more and more important. Also as recently energy saving requirements in heavy machines and, especially, in battery-operated working machines has been highlighted from the CO2 reduction and energy efficiency points of view [1, 2]. Changes in machines are needed also from ecological point of view. New technologies and solutions are needed to further reduce fuel consumption and pollutant emissions. Ways to improve the energy efficiency of electrohydraulic systems are recently studied widely [3-8]. Most of the current researches suggest hybrid systems to Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved

T. A. Minav, D. Filatov, J.Pyrhönen and M. Pietola

replace the traditional mobile machine systems [9, 10]. Applying different modelling methods is common in research concentrating on the topic [11-14]. This article offers a comprehensive systems engineering modelling of an electro hydraulic system and concentrates on testing the proposed structure of an electro-hydraulic forklift. The target of the study was to create a simulation model for the electro-hydraulic forklift working cycle, enable investigations on its behaviour and compare the simulation results to prototype measurement results during the whole cycle.

II.

General Overview of Test Setup

Figure 1 illustrates the schematic of the test setup; where the conventional non-regenerative electric drive and hydraulic system of the forklift were replaced by industrial hydraulic and electric drive components. The test setup has the important feature of recovering the load potential energy instead of converting it into heat in a traditional valve. The speed-controlled electric motor servo drive (Fig.1, f) and a hydraulic machine are used to control the position of the hydraulic cylinder piston (Fig.1, a) instead of a proportional valve as in conventional forklifts. The electric motor rotates the hydraulic pump (Fig.1, d); the hydraulic pump takes oil from a tank (Fig.1, e) and delivers it to the hydraulic lifting circuit. The two-way normally closed poppet valve (Fig.1, b) is included in the system for safety reasons: to hold the load at standstill and direct oil to correct direction. The speed of the hydraulic pump is directly controlled by the rotating speed of the electric servomotor. The oil flow determines the piston speed, and the actuator load determines the oil pressure needed.

controlled by a high-performance frequency converter ASCM1 by ABB (Fig.1, g). The converter rectifies the generated electric energy to the DC link, where a battery should be located. In this test arrangement, the brake resistor is used as “energy storage”, because of the lack of a suitable battery. The pressure relief valve (Fig.1, c) controls the safety limit of the pressure in the pipes. An upper-level program to control both the electrical and hydraulic parts of the forklift system through the electric drive, was realised in dSPACE DS1103 [15]. The test setup was equipped with pressure, height, current and voltage sensors. The measured data was used to calculate efficiencies of different parts of the system [16].

III. Simulink Model In this case, to obtain a simulation model for the control design of the electro-hydraulic forklift, the differential equations of the configuration have been implemented in Matlab. Detailed information about the Simulink model for lifting can be found in [14]. In this section we will concentrate on the Simulink model for load lowering motion. The electric part of the forklift can be divided into the electric machine and its control, the converter. The hydraulic part can be divided into hydraulic machine and cylinder. The valve model is simplified and just replaced by a control signal. III.1. Electrical servo machine model The model of generator is identical to model of electric machine. The following equations were used to describe PMSM in the simulation are presented [17, 14]. The current vector is written as (1) je0 je 2 je4 2 ia (t ) e 3 ib (t ) e 3 ic (t ) e 3 , 3 where ia, ib and ic are phase currents. The current vector is divided into its d- and q-axis components id and iq. The stator d- and q-winding flux linkage components can be expressed as follows:

i

a

b g

i

f Frequency converter

d

c

M/G e

Fig. 1. Electric and hydraulic circuits of the main lift function with PERS. The experimental system consists of: a) single-acting cylinder, b) two-way normally closed poppet valve, c) pressure relief valve, d) hydraulic machine (pump/motor), e) oil tank, f) permanent magnet synchronous motor/generator, g) frequency converter h) connection panel and i) computer and dSPACE [14].

During lowering a mass, the potential energy of the load produces a flow that rotates the hydraulic machine which now acts as a motor. The mechanically connected electric machine acts as a generator, whose speed is

Lmq

isd L

(2)

PM ,

isq ,

(3) where Lmq and Lmd are magnetic inductance in d- and qaxes, respectably, L is stator leakage inductance, PM is permanent magnet created flux linkage, isd and isq are stator current d- and q-axes components, respectably. The voltages for the d- and q-axes can be expressed as follows: sq

h

Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved

Lmd L

sd

m

usd

Rs isd

usq

Rs isq

d dt d dt

sd

m

sq

m

sq

sd

(4)

, .

(5)

is the electrical angular velocity and is equal to p

,

International Review of Electrical Engineering, Vol. xx, n. x


where is the actual rotor speed and p = 3 is the number of pole pairs. The electromagnetic torque Te of a non-salient pole PMSM can be expressed as [17]:

p 2

Te

PMisq .

Te

TL J eq

.

(7)

where TL is the load torque. In the practical case of the test system, the motor parameters for CFM112M at the rated operation point are stator resistance Rs = 0.193 and stator inductance Lsd = Lsq = 0.31·10-3 H. The total equivalent inertia of the CFM112M is Jm = 88.2·10-4 kgm2 [18]. The motor voltage constant is Ke = 0.22 Vs/rad. III.2. Cylinder model The theoretical modelling of a hydraulic single-acting cylinder was based on the equation of piston motion and dynamic pressure equation [19, 20]. The equation for an actuator chamber is derived from the continuity of mass equation:

ps

Be Qin V

Be V, V

(8)

where the bulk modulus Be = 1400·106 Pa, ps is the system pressure in Pa, V is the cylinder volume in m3 and Qin is the input flow in m3/s.

V

V0

xp S p ,

(9)

where the piston cross-sectional area is Sp=0.0028 m2. The initial end position equals zero, and it gives the initial position of the end of the cylinder tube and the piston. The length of cylinder piston is Lcyl = 1.82 m. The additional volume describes the dead volume V0 of the cylinder. The equation of piston motion is derived from Newton’s second law,

mt xp

ps S p

Ff x p

mt = mp+m,

Fload

The following equations were used to simulate the behaviour of the hydraulic motor [21,22]:

Q

(6)

The acceleration is determined by the difference between the electromagnetic torque and the load torque acting on Jeq, the combined inertia of the load Jp and the motor Jm.

d dt

III.3. Hydraulic motor model

Vth 2

,

(12)

vol

where Q is the motor output flow in m3/s, is the rotating angular velocity, Vth is the theoretical volumetric displacement of the motor in m3/rev, and vol is its volumetric efficiency, which is a function of the angular speed and pressure vol = f( , p). The second-order differential equation for the motor shaft rotation is given by [21]:

Jp

d dt

Tf, p

Tmotor

T

vol p, th

,

(13)

where the total equivalent inertia of the pump is Jp= 1.1·10-3 kgm2, Tmotor is the drive torque, Tp,th is the theoretical (ideal) torque required to compress the fluid, and Tf,p is the frictional torque. The volumetric efficiency of the motor is equal to vol = 0.95. The theoretical torque to compress the fluid can be modelled as [22]:

Tp, th

V th p s

p rtn ,

(14)

where the theoretical volumetric displacement for an internal gear pump is equal to Vth = 19·10-6 m3/rev, ps is the system pressure, and prtn is the tank pressure in Pa.

IV.

Model of test setup

Separate measurements for lifting and lowering were performed. Also the modelling of the forklift system was done separately. Sections IV.1 and IV.2 contain models for lifting and lowering movement, respectively. Section IV.3 combines the model for lifting and lowering. IV.1. Model for lifting movement Based on the modelling of each component, a system was established for lifting [15], as shown in Figure 2.

(10) (11)

where mt is the total mass, m is the payload mass equal to 920 kg in practical tests, mp is the mass of the cylinder piston equal to 50 kg, Ff is friction force and Fload force created by load; x p , x p , x p are piston position, velocity and acceleration, respectively. Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved

Fig. 2. Matlab/Simulink model of the test setup for lifting [15].

The speed reference has an acceleration period, constant speed and deceleration period. The PMSM block behaves according to the reference signal. The torque is transferred between the hydraulic pump and electric International Review of Electrical Engineering, Vol. xx, n. x


motor with mechanical coupling. Pressure is transferred between the cylinder and the pump. The pump delivers an amount of oil to the cylinder to move the tare and the payload with the motor reference speed wmech-0. The cylinder block Cylinder simulates the moving of the load during lifting [15].

Start

Input speed

IV.2. Model for lowering movement

Input payload

Figure 3 shows the Matlab/Simulink model of the test setup during lowering. The cylinder block simulates the motion of the load and cylinder during lowering.

Creation Control signal

Lifting motion Output cylinder position

Fig. 3. Matlab/Simulink model of the test setup for lowering [15].

The oil flows from the cylinder to the hydraulic machine which now acts as a motor. Torque is transferred between the hydraulic motor and the electric motor with mechanical coupling. The PMSM and converter with the implemented DTC control ensure that the speed of the load going down follows the reference speed.

Input data

Lowering motion

IV.3. Combined model for a lifting and lowering The two models discussed above can be combined to construct a full model of a cycle movement: up and down. For this reason, a logic block should be provided to couple the initial values in the direction changing point. Figure 4 shows the Matlab/Simulink model of the test setup for the cycle.

Output cylinder position

Stop Fig. 5. Flowchart of the logic block. The logic block helps to combine the models for lifting and lowering [15].

Fig. 4. Matlab/Simulink model of the test setup for the cycle [15].

Figure 5 shows an flowchart of the algorithm that was used to implement the logic block (see Figure 4). The user inserts the speed of the motor and payload. These are the required input data to produce a control signal for a lifting motion. The output information from the “Up” model is the end position of the cylinder (fork position). This information and also the required speed and payload become inputs for the “Down” model.

Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved

The output information from the “Down” model is the position of the cylinder. Also torque, pressure and speed can be checked. The program was implemented in Matlab 2012a.

V.

Analysis and verification of the Matlab Simulink model by measurements

Figure 6 illustrates the dynamic simulation results: speed, torque, pressure and position of forks for a payload of 920 kg with an axial piston motor and 10 kW PMSM for lifting-lowering cycle.



When comparing Figs. 6 and 7, it can be concluded that the dynamic simulation gives results that are well comparable with the measurement results. The total cycle efficiencies of the system for setup were calculated as shown below: tot_cycle=

up_tot

sc

inv down_tot,

(15)

where tot_cycle is total cycle efficiency, up_tot is system efficiency during lifting, is efficiency of sc supercapacitor, inv is inverter efficiency during lifting and down_tot is system efficiency during lowering.

Fig. 6. Simulated speed, torque, pressure and position for cycle a payload of 920 kg.

Figure 7 illustrates the measurement results: speed, torque, pressure and position of the forks for a payload of 920 kg with an axial piston motor and 10 kW PMSM for lifting-lowering cycle. Figure 7 was created by combining separate empirical results during lifting and lowering. 2000

50 45 40 35 30 25 20 15 10 5 0

0 kg 690 kg 920 kg 0

1500 1000

0,2

0,4

0,6

Fork velocity, [m/s]

500

Speed, [rpm]

Cycle efficiency, [%]

Figure 8 illustrates the total cycle efficiencies for the system with the 0, 690 and 920 kg payload.

0 -500

Fig. 8. Cycle efficiency with the 0, 690 and 920 kg payload.

-1000 -1500 -2000 0

2

4

6

8 Time, [s]

10

12

14

16

60

With the 0 kg payload, the minimum cycle efficiency is 16 %. With the 920 kg payload, the maximum cycle efficiency is 46 %.

50

Torque, [Nm]

40

VI.

30 20 10 0

0

2

4

6

8 Time, [s]

10

12

14

16

0

2

4

6

8 Time, [s]

10

12

14

16

0

2

4

6

8 Time, [s]

10

12

14

16

160 140

Pressure, [bar]

120 100 80 60 40 20 0

4 3.5

Fork height, [m]

3 2.5 2 1.5 1 0.5

Conclusion

The presented work is a systems engineering model of an electro-hydraulic forklift with potential energy recovery feature during lifting and lowering. The behaviours of electro-hydraulic system components of the forklift system were simulated in Matlab Simulink. The model created does not, however, include all the possible details e.g. about the fluid flow behaviour, type of the hydraulic machine and are limited by the accuracy of the model. The electric machine model has been created based on the machine parameters that do not fully accurately describe the machine behaviour allowing some mistakes in the efficiency. The model was verified by measurements, and energy efficiency studies of the system were carried out. The verification of model by measurements shows that the energy and efficiencies can be estimated fairly accurately for an electro-hydraulic forklift.

0 -0.5

Fig. 7. Measured speed, torque, pressure and position for cycle a payload of 920 kg. Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved



Acknowledgements The research was enabled by the financial support of Tekes, the Finnish Funding Agency for Technology and Innovation, European Union, the European Regional Development Fund and Regional council of South Karelia and FIMA (Forum for Intelligent machines) at the Institute of Energy Technology, Department of Electrical Engineering at Lappeenranta University of Technology.

[17]. [18].

[19]. [20].

[21].

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Authors’ information Tatiana A. Minav was born in 1984 in Cherkassy, Ukraine. She received the M.Sc degree in 2008 from Lappeenranta University of Technology (LUT) and M.Sc. degree in 2008 from Saint-Petersburg State Electrotechnical University LETI. She received the Doctor of Science (D.Sc.) degree from Lappeenranta University of Technology (LUT), Finland in 2011. She is currently working in Department of Engineering Design and Production, Aalto University. Her current interests include position motion control with help of drive, hydraulics simulation and energy recovery systems in mobile working machines. Denis M. Filatov born in 1985 in Leningrad, USSR, received the M.Sc. degree in 2008 from Saint-Petersburg State Electrotechnical University LETI. He is currently the working in the Department of Automatic Control Systems and Faculty of Electrical Engineering and Automatics at St. Petersburg State Electrotechnical University (LETI), where he is engaged in the research and development of control systems and electric drives. Juha J. Pyrhönen (IEEE member) born in 1957 in Kuusankoski, Finland, received the Doctor of Science (D.Sc.) degree from Lappeenranta University of Technology (LUT), Finland in 1991. He became an Associate Professor of Electrical Engineering at LUT in 1993 and a Professor of Electrical Machines and Drives in 1997. He is currently the Head of the Department of Electrical Engineering in the Institute of LUT Energy, where he is engaged in research and development of electric motors and electric drives. His current interests include different synchronous machines and drives, induction motors and drives and solid-rotor high-speed induction machines and drives. Matti Pietola, born in 1954, Finland, received the Doctor of Science (D.Sc.) degree from Helsinki University of Technology (currently Aalto), Finland in 1989. He is currently Professor of Mechatronics (Fluid Power) at the Department of Engineering Design and Production. His main research interests are today related to functional hydraulic fluids and control of hydraulic system. He has an extensive global contact network for both industry and education in the area of fluid power.
