Load Sensing System

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Application of innovative analysis methods in the development of a Load Sensing System

 Authors: Dipl. –Ing Daniel Bürcky Dipl. –Ing Dennis Berghaeger  Dr. Elysé Botellé

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I Introduction The problem HAWE would like to know if AMESim was able to handle two situations in a system that is used normally in fork-lifters and similar applications as seen in Figure 1.

Figure 1 - Fork lifter

The system example that was sent to us can be seen in Figure 2 and represents a load sensing system. This kind of system has the particularity of allowing load variations (in the fork lifter for example) without a speed velocity change in the movement of the load.

This is obtained with a pressure balance valve (Druckwaage) which maintains the pressure drop over the orifice constant and allows a flow non dependant of the load.

In this kind of system, engineers faced vibrations found in the lowering movement of the mass. The vibrations were happening not always in the same situations but when it happened it produced a vibration that was around 2 to 3 Hz (visual observation). This vibration problem was solved along the years at HAWE and the company is now able to avoid this. The proposal of HAWE to IMAGINE was to give us a chance of analyzing these vibrations using our software AMESim.

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The questions of HAWE were the following ones: •

Is it possible with AMESim to calculate the ideal orifice diameters in the system in order to reduce the vibrations of the Load? 

•

When the load is vibrating the whole system is affected by this oscillation. This means that all the valves are oscillating as well, implying a  geometrical change. Is it possible to simulate this geometry variation during the simulation? 

The answer to both questions is yes. AMESim is able of doing this two operations in a very rapid and efficient way.

Figure 2 – Scheme

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II AMESim Model II.1 The system In Figure 3 we have access to the geometry of the relevant details for a simulation. From this detail and some other additional details supplied by HAWE we were able to built a model that can reproduce the normal behavior as well as the unwanted behavior of the valve.

Figure 3 - Load sensing detail With the information gathered from HAWE we managed to build a preliminary model and with it we managed to achieve some results. It was our concern to avoid to build a to complex model as what we were looking for was a typical behavior of  the system. We resumed the model to the most important parts of the system as shown in Figure 4 and even in this reduction we concentrated mainly on the modeling of the pressure balance valve ( 1). The pressure balance valve (PB valve) was modeled with relative accuracy due to the importance of it in the working of  the system. From HAWE came the information that the system was sometimes unstable (load oscillations) and the way this was avoided was by reducing the diameter of the orifice (2). Since the diameters involved were very small an alternative solution was encountered. This restriction is obtained by putting several blades together

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with small orifices that are opposed in 90º degrees which should mean (according to HAWE) an equivalent diameter of about 0,2mm.

Figure 4 - AMESim Model (see Load_Sensing_ame41_Lin_01.ame) In AMESim we do not have this kind of limitations. For the modeling of this particular geometry we choose to introduce only an orifice ( 2) with an approximated diameter (we started with 0,2mm). Concerning the flexible line, an equivalent bulk modulus corresponding to the hose plus the fluid have been fixed to 500bar. For this type of application the range of the equivalent bulk is inbetween 300 and 800 bar. The 500 bar match with the frequency oscillation that were observed by HAWE hydraulic on the real system. We will notice that this bulk modulus parameter is the only one that has been tuned. The other parameters come from the real dimensions, mass, overlaps, etc...

II.2 Verification of the model  With the information we had from HAWE we started to try to reproduce behaviors of the real system in order to see if the system was working accurately. In a first stage we concentrated in the PB valve and tried to be sure that it was correctly modeled. Only after introducing all the relevant geometrical details did our PB valve worked as expected and presented as result a constant speed value independent of the load as seen in Figure 5.

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Figure 5 – Load velocity for different loads After having a working PB valve we connected it to the remaining system and it was then that we had some interesting results. As it is possible to see in Figure 5 the system was oscillating and with it the load.

II.3 Linear analysis II.3.1 Overview of linear analysis theory We think that it is not necessary to work to much in the time domain when we have an unstable system. Actually, the time domain leads to a lot of runs and a lot of  parameter changes. In order to better understand the dynamic behavior of this valve, we are going to use the linear analysis facilities of AMESim. This part of the work is presented in paragraph II.3.

Figure 6 - Damped oscillator Let us take as example a damped oscillator to take a brief overview of linear analysis theory. Often, the characteristic equation for this kind of system can be expressed as 2nd order equation like the one presented by eq.1.  s 2 + 2 ⋅ z ⋅ ω n ⋅ s + ω n2 = 0

eq.1

In this 2nd order equation the undamped natural frequency is given by ω n and the damping ratio given by  z  . The solutions for this characteristic equation are :

 s1 = − z ⋅ ω n +  j ⋅ ω n ⋅ 1 −  z 2 ,

 s2 = − z ⋅ ω n −  j ⋅ ω n ⋅ 1 − z 2 eq.2

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for the behavior of the system of relevance will be the value of   z  . Z<1

the system is said to be underdamped

Z>1

the system is said to be overdamped

Z=1

the system is said to be critically damped

Z<0

the system is unstable

Interpretation of the solutions of a 2nd order characteristic equation

•

 s1 = − z ⋅ ω n +  j ⋅ ω n ⋅ 1 − z 2 ,  s2 = − z ⋅ ω n −  j ⋅ ω n ⋅ 1 − z 2  R realpart = − z ⋅ ω n  I imaginary  part  = ±  j ⋅ ω n ⋅ 1 − z 2

Module of s1 or s2

( z ⋅ ω n )2 + (ω n ⋅

 M  s1 s 2 =

 M  s1 s 2 = ω n sin (θ ) = θ 

ω n

( z )2 + 1 −  z 2 ⋅ z 

ω n

1 −  z 2

)

2

= ω n

⇒ θ  =  ArcSin ( − z )

= 45º ⇒  z  = 7.07( 70% damping )

Figure 7 The characteristic equation eq.1 can be written using the dissipation parameter of  the system (R), the inertial value (M) and the stiffness (K).  s 2 +  s ⋅

 R  M 

+

 K   M 

=0

In that case the solutions of the characteristic equation are :

 s1 =

[

]

−  R  M  + ( R  M ) − 4 ⋅ K   M  2

2

1/ 2

;  s 2 =

[

]

−  R  M  − ( R  M ) − 4 ⋅ K  M  2

1/ 2

2

If  ( R  M ) − 4 ⋅ K  M  is less than zero then we have a complex solution where : 2

–0.5*R/M is the real part and +/- 0.5 ⋅

( R  M )2 − 4 ⋅ K  M  the imaginary part.

For the real part if its value is greater than zero this means that R or M are negative. We have in that case two solutions : if the system is not a controlled system we have a sign problem in the equation that leads it to act like a negative

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mass or negative dissipation. If this is the case it is possible that a mistake has been done in the value of M or R but AMESim will send an error message in simulation mode. If the system has a control loop like a pressure valve, the positive real part means that the system is not stable.

II.4 Analysis of the system II.4.1 Linear analysis 1- Root locus analysis

Knowing that the system was becoming unstable function of the mass and the orifice diameter (2) we searched in the nearby region of the operating point to see the evolution of the behavior. To better understand the dynamic behavior of the system we did a root locus analysis. We have linearized the system for different times during the simulation run. At the beginning of the simulation the valve number 3 see Figure 4 is closed, at t=1sec we open it to 100% of it’s opening in order to move the load from 2.4m to 0m. The linearization occurs at the following times: 1.1

1.15 1.2

1.25 1.3

1.35 1.4

1.45 1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Table 1 - system linearization times The evolution of the roots in these condition show us the influence of the cylinder position. If we look at the curves of Figure 8, the blue curve shows that the reduction of volume in the cylinder increases the natural frequency of the first mode from ~3.5Hz to 5Hz. By reducing the length of the cylinder we increase the hydraulic stiffness and the associated mode. We will notice that this behavior is the same for the six simulations. In order to see the influence of parameters on the system, the simulation described previously has been ran for different parameters configuration. Two parameters have been changed: the diameter of the orifice number 2 see Figure 4 and the mass of the load. The following table gives the different values that have been tested.

φ [mm] Mass [Kg]

Run 1 0.5 600

Run 2 0.1 600

Run 3 0.5 1500

Run 4 0.1 1500

Run 5 0.5 3000

Run6 0.1 3000

Table 2 - parameters used for each simulation run The comparison of the different root locus shows the influence of the orifice diameter. Obviously with 0.1 mm diameter we provide more damping in comparison to 0.5 mm. Also for important load (see black root locus) even with 0.1 mm diameter the system is not very well damped (14%). We can notice that the critical behavior will occur for high load and large orifice. The pink curve is very close to instability (real part close to zero). These results have been obtained with a viscous friction of 2000N.s/m which means that 1000N resistive force will be produce at 0.5m/s load velocity.

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5 corresponds to frequency in Hz

H=0m

0.42 corresponds to 42% damping

H=0m

H=2.4m H=2.4m

H=0m

H=0m

 Y axis = Imaginary part

H=2.4m

Real part

Figure 8 – Root locus results for the first mode [2 to 5Hz] 2- Modal shape

The root locus has been plotted only for the first mode of the system. This mode is between 2 and 5Hz according to the position of the cylinder and the set of  parameters (load and orifice diameter). Now we would like to see what are the other modes and which components they involve. We will look at the first and second modes (~2Hz and ~65Hz) as the other modes are to high to be of interest for this example. Figure 9 shows the modes calculated by AMESim. The configuration for the calculation is 0.5mm orifice, middle position of the cylinder and a mass load of 3000Kg.

Figure 9 – System Eigenvalues In order to track this modes, we have set up observers on each velocity: mass velocity or fluid velocity. These observers allow to verify if one mode influences the components were we have the observers. The two following figures show respectively the influence of the mode at 2.15Hz and the one at 68Hz. The first mode see Figure 10 concerns mainly the lines and a little bit the mass of the load. The valve is not involved in this mode. Concerning the second mode at 68 Hz, only

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the hydraulic inertia of the line between the cylinder and the valve are concerned (see Figure 11).

Figure 10 - modal shape of the 1 st mode

Figure 11 - modal shape of the 2 nd mode

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II.4.2 Time response

Knowing in which region the system was working on a more stable way, we passed to the time domain with the best parameter configuration and performed some tests. We are able to analyze the system without having instability problems. In Figure 12 you can see how the pressure in the cylinder changes for variations of the load but remains exactly the same for different openings of valve 3.

Figure 12 – Cylinder pressure (left 100% ; right 50% opening of 3)

In Figure 13 it is possible to see the dynamics of the PB valve and how it acts differently for different openings of valve 3. The pressure balance has to be achieved and when valve 3 is not fully opened the flow conditions are not the same thus you have a different behavior of this PB valve. The displacement of the PB valve is greater when the opening of 3 is smaller.

Figure 13 – PB valve displacement (left 100% ; right 50% opening of 3) As a result of the study done in the linear analysis domain an overall behavior is possible to be observed and in Figure 14 you can see how the system is reacting to the opening condition but also to the variation of the load. In the upper left plot you are able to see that the total displacement time of the load is slightly different for full load and no load. The same happens in the upper right plot were the opening of valve 3 is not total (50%). By analyzing both lower plots you can see that the difference existing in the displacement evolution (upper

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plots) is due to the transient period at the beginning and at the end of the run. This transient is bigger when the load is smaller and depends on the friction condition. It takes longer for the lower load to overcome the friction forces. No longer present in the system are the oscillations that we had in preliminary stages of our work.

Figure 14 – Comparison of behaviors for 100% and 50% opening of valve 3 It would be possible to analyze and interpret other behavior and influences of other parameters like the overlap and underlap conditions in the valve or the diameter of  the valve but we concentrated in the elements that were important in this case study.

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III Conclusion As conclusion we can say that the main goals of this work were achieved. The reproduction of the behavior that is present in the real system was achieved with a simple model. This model is not only able to reproduce the real system as it is as well capable of giving indications of the functioning and intrinsic properties of the system that are not always easy to obtain in a real test bench. The use of linear analysis was useful to get to know what were the most important elements and parameters and how they influenced the system evolution. With the root locus feature we managed to locate the main instability cause and how it is affected. Big loads together with big orifices produced the most undamped systems. Although this fact alone is not the answer to all the instability problems it helps to understand how the system is working. With the modal shapes we were able to track the modes and see which components are being affected by a particular mode. With this feature we are able to find the origin of a mode. In the time domain we concentrated mainly on the characteristics that were important for our study namely the load displacement and it’s velocity. We managed to reproduce the existing problems and also managed to present a solution for them. We could have done other kind of investigations but that was not the aim of this work. This work has to be seen as a demonstrator of dynamic simulation capabilities.