3.2 Hydraulic part
3.2.3 Modeling the hydraulic parts and systems
Before building the test rig, a dynamic Matlab Simulink model has been made in order to predict the properties of the system. The transfer functions from the real spool position to the corresponding motor torque have to be calculated. The corresponding Bode plots show the torque amplitudes that can be reached.
Mathematical descriptions
For modeling the system, mathematical descriptions of all parts have to be known.
hydraulic pump unit
/
drive motor/
brake pump: Because the hydraulic pump and (depends on the valve geometry), the pressure difference over the ports of the valve A p [Bar] and the spool position u (-1 to + I ) .q,,, of the Bosch valve equals 4 [ L l m i n ] . Because all. ports are connected, the nominal flow is doubled.
Oil: Under dynamic conditions, the oil in the pipe (with length L and internal diameter D) acts like a spring (fluid capacity) and as an inertia (fluid inductance). Due to friction, there is also resistance. The corresponding formula's for these effects are:
Fluid capacity:
dp T D ~ L
gin - qout = C- w i t h C = -
d t 4P
The formula relates the incoming and outgoing flow rates with the time rate of change of the pressure in the pipe. C is the capacity of the oil volume. second low of motion to the hydraulic system.
Fluid resistance:
128pL
pa - pb = R q w i t h R = -
7rD4
R is the resistance of the pipe. Assuming the flow to be laminar this linear formula may be used.
A model of the system can be made now the mathematical descriptions of all parts are known. The pressure and flow are variables in all formulas. These variables will be used to link the individual parts. A library that contains all occurring parts has been made in Matlab Simulink. Besides the hydraulic parts described in the previous section, also the mechanical parts like inertia and stiffness are modeled. The used formulas can be found in figure A.9. Sometimes, two or more library blocks have to be made from the same part. For exampie, in some situations the pressure is the input of the capacity block. In other situations the fiow is the input. in this case formula 3.5 has to be rewritten from a differential to an integral form with an initial pressure. Because a pipe may be modeled as a combination of capacity, inductance and resistance, a special library block is made that contains all these effects. Figure 3.7 shows the contents of the pipe block.
Figure 3.7: Contents of the Simulink pipe block.
Modeling the rig
Figure 3.8 shows the simplified model. The complete Simulink model can be found in appendix E. Some remarks concerning the modeled parts:
Part 2 represents the filter, modeled as a capacity.
0 Part 3, 4 and 6 represent the pipes, modeled as a combination of inductance, capacity and resistance part.
Part 5: represents the pressure pulsation damper. The pulsation damper is modeled as a pipe. The special dynamic behaviour (dampifig out pressure pulses) is not taken into account.
0 Part 7: represents the resistance caused by the needle valve.
Part 8: represents the capacity of the oil in the motor and in the short pipe between the needle valve and motor.
Part 10: represents the inertia of the motor, axle and torque transducer.
Part 11: represents the stiffness of the torque transducer.
8 Part 12: represents flywheel inertia.
Figure 3.8: Simplified hydraulic model. assumed not to have any influence on the performance of the rig. That's the reason why the brake system is modeled as a constant torque on the flywheel. Resistance due to pipe bends is not modeled. The input parameter of the transfer function is the real spool position u. The motor torque
Tout
is the output parameter of the function. w andTin
are constant during each simulation.As can be seen in figure 3.6, the oil properties depend on the oil temperature and pressure.
The temperature is assumed constant during the simulation because the temperature of the oil in the reservoir is kept constant by a heater/cooler at 35 [OC]
.
In this case the oil properties only depend on the nominal load (pressure).E x p e c t e d properties Pump
1
The Simulink model has been used to predict the performance of the rig. The transfer functions of the mechanical and hydraulic system Hmh have been calculated. Input is the actual valve spool, output is the motor torque. From this analysis it was found that the motor speed doesn't influence the transfer functions. Several simulations have been performed to determine the influence of the load torque. The transfer has been calculated at 25, 50, 75, 100 and 125 [ N m ] . The needle valve was opened completely. Figure 3.9 shows the corresponding Bode plots.
In the figure, are peaks are visible at four frequencies. Increasing the load results in higher magnitudes of the transfer function. This is due to the higher pressure resulting in higher flow rates through the proportional valve. Higher flow through the valve causes higher pressure differences and thus higher torque amplitudes.
Resistace
Ap~ariable
Figure 3.10 shows the influence of the pressure difference over the needle valve on the transfer function. The nominal load was set to 50 [ N m ] during the simulations. The needle valve was set corresponding to the following pressure differences over the valve: Ap = 0, 5, 10, 15, 35, 55, 75 and 95 [Bar]. Larger pressure differences causes higher magnitudes in the Bode piot. Small pressure differences effect the increase of the magnitude significantly. The effect at high pressure differences is smaller.
10" 10 l o i 10' 10"
Frequency [rads]
Figure 3.9: Bode plots of the calculated transfer functions Hmh at different loads.
- -
l o 0 lo1 lo2 l o 3
Frequency [rads]
Figure 3.10: Influence of the pressure difference over the needle valve on the Bode plot.
Unfortunately, the magnitude of the transfer seems to be too low. In combination with Bode plot of the proportional valve (appendix D), the desired torque amplitudes can not be generated. Causing a pressure drop by the needle valve improves the magnitude, but the effect will not be enough. Nevertheless, the rig is realized for investigating dynamic hydraulic systems. The simulations have to be validated (section 4.2.2). In a later stadium the rig can be improved. The hydraulic system has to be optimized and better chosen parts have to be applied (chapter 5).