Modeling and improving of an Hydraulic Test Bench for car seats D.J.W. Belleter - 63931 CST 21.49 Bachelor End Project Project supervisor: dr. Ir. W.J.A.E.M. Post Eindhoven University of technology Department of Mechanical Engineering Control Systems Technology Group Eindhoven, July, 21
Table of contents 1. Introduction.1 2. The test bench 2 3. The model.3 3.1 The hydraulic power unit.3 3.2 The hydraulic control valves. 5 3.2.1 The physical model..5 3.2.2 The simulink controlled model 6 3.2.3 The orifice settings..7 3.3 The hydraulic cylinders and the load 9 3.4 Model expansions.. 11 3.4.1 Advanced stick-slip friction model.11 3.4.2 Pipeline dynamics. 13 4. Model validation and simulations. 14 4.1 Model validation and single cylinder simulations 14 4.2 Multiple cylinder simulations.16 5. The solution of the problem.. 2 6. Conclusions 22 References.23 Symbol list.24 Appendix A: Data sheets.25 Appendix B: Orifice calculations...35 Appendix C: Single cylinder model..36 Appendix D: Pipeline and Stick-slip simulations.37 Appendix E: Test results on actual actuators provided by B-style.41 Appendix F: Simulations with an identical input signal.42 Appendix G: Accumulator simulations....43
1. Introduction Assessment The firm B-style automotive located in Eindhoven has an RDW (Rijksdienst voor het wegverkeer) certified test bench to tests car seats and wheel chair fastening points. The tests on car seats and wheel chair fastening points are designed to simulate the conditions of a car crash. The seats and fastening points have to meet the criteria set by the RDW before collapsing. However this hydraulic test bench shows some problems: - The speed of the force build up in case of a maximum of six actuators is too low. - Under some circumstances a sagging effect is present in the force build up of several actuators. This effect slows down the test. The goal of this research is to find the cause of the problems and to come up with a solution. In order to do so the following steps have to be taken: - Investigate the behavior of one or more actuators with a Matlab/Simulink model. The emphasis should be on the hydraulic and load part of the system. - Investigate if the problems stated above can be reconstructed using the model. - Generate one or more solutions for these problems based on the insights gained from the model. Test the feasibility of these solutions. Report The report contains the following process steps. First the system and its problems are briefly described. After this the steps in the modeling of single components is described and their simulation model is presented. A few model expansions including an advanced friction model are introduced too. Then the complete simulation model was validated and some simulations with a single cylinder were done. Some multiple cylinder simulations were done to check for capacity or interference problems. The simulations showed that the model was valid and it had the same aberrations as the actual system. After these simulations a solution was developed and an adapted simulation model was made. Finally the adapted simulation model was tested to check if the solution is a success. This solution will be presented and then some conclusions and further recommendations to improve the system will be given. 1
2. The test bench In this chapter a description of the system that was modeled will be presented. First the purpose of the system will be described, followed by the description of the system components and finally the problems with this system. The systems purpose The system is a hydraulic test bench used to test if (modified) car seats comply with legislated safety demands. In these test the car seats have to be aggravated with defined force levels during defined time- intervals. The purpose of these tests is to see how the car seats perform in a crash. The seat has to withstand the defined load in order to comply with the safety demands. The car seats can be loaded on 6 possible locations on the seats. Hydraulic cylinders are applied to introduce these loads. After the test the damage at each connection point of the seat to the car structure is assessed to ensure safety legislation. The system components The system consists of a hydraulic power unit connected to a valve block consisting of 6 proportional pressure reducing/relieving valves. A hydraulic cylinder is connected to each of these valves. All of the valves are connected to a controller. The control electronics for the valves get their input from a computer. A calibrated force sensor is connected between the cylinder rod and the connection point of the seat. The problems of the system The problem arises when the following test procedure is executed. First the cylinders are pre-stressed. Then the force in all cylinders is increased to a defined force level and held at that level for a defined time-interval. After this the cylinders are made pressure-less again. The problems occur when the force of every cylinder is increased to the prescribed level. Some cylinders will respond to slow and the force build up will start to late. Another common problem is a sagging effect during the force build up. These effects make the system to slow and prevent the system from following the proper pre-described load cycle. The results of a test with the actual actuators are shown in Appendix E. 2
3. The model The basic model consists of four parts; the hydraulic power unit, the valves with their electronic controller, the hydraulic cylinders and a load part. In this chapter the four basic parts will be shown and the decisions in their modeling will be discussed. After this an advanced friction model and some pipeline dynamics will be discussed to expand the model. All the model parts are made in the Simscap toolbox of MatLab/Simulink. The settings in the Simscape blocks are standard unless suggested otherwise in the data tables. First the data for a vital system component is shown, namely the hydraulic fluid. The system uses Shell Donax TM oil, the data for the hydraulic fluid can be found in table 3.1. Viscosity at 4 C Density at 15 C Table 3.1 Hydraulic fluid data 4. 884 Bulk modulus 8 1 System Temprature 4 C 3.1 The hydraulic power unit The hydraulic power unit was manufactured by Bosch and the data sheet can be found in Appendix A. The hydraulic power unit consists of a reservoir of hydraulic fluid, a pressure relief valve and an electric motor that drives a fixed displacement pump and a return filter. In table 3.2 the most important data for the hydraulic power unit can be found. The pump of the power unit is modeled as a fixed displacement pump driven by a constant angular velocity source. The pressure safety valve is modeled as a pressure relief valve. The return filter and the reservoir of hydraulic fluid were left out of the model. Table 3.2 Hydraulic power unit data Effective capacity 5 L Maximum pressure 2 bar Electric motor speed 15 rev/min = 5π rad/s Pump displacement 21.5 L/min = 3.583 1-4 m 3 /s Relief valve orifice maximum area 2.41 1-6 m 2 Additional information about the power unit can be found in the data sheets in Appendix A. All the data in table 3.2 is from the data sheets in Appendix A, except for the maximum are of the orifice of the relief valve. The maximum area of the orifice of the relief valve was determined using the orifice equation: 2 pmax q qmax = CD Amax Amax = ρ C max D ρ 2 p max (3.1) 3
With this equation, the fluid density, maximum flow and maximum pressure for the hydraulic power unit given in the data sheets of appendix A and the standard value.7. The maximum area of the orifice can be calculated. Rearranging the equation then leads to the maximum area of the orifice of the relief valve. Results of these calculations can be found in Appendix B. The data from table 3.2 is incorporated in a simulation model, created with the Simscape toolbox of MatLab, the model can be seen in figure 3.1. figure 3.1. the model for the hydraulic power unit The electric motor is represented by an angular velocity source driving the fixed-displacement pump. The pressure relief valve is the pressure safety valve and the hydraulic reference represents the hydraulic reservoir. 4
3.2 The hydraulic control valves The pressure reducing/pressure relief valves were also manufactured by Bosch and the data sheets can also be found in Appendix A. The valves are proportional pressure control valves; the pressure in the valve is controlled by force balance on the valve spool. Forces result from the pressures acting on the left- and right-end faces of the spool and the spring acting on the right side of the spool. A cross section of the valve can be seen in figure 3.2. Figure 3.2. cross section of the hydraulic valve The forces acting on the spool, determine the movement of the spool and thus the flow through the valve. The flow through the valve is either from pressure port P to user port A (pressure reducing) or from the user port A to tank port T (pressure relieving). The chamber at the right side of the spool is connected to user port A by means of a narrow channel through the spool, delaying pressure change of that chamber. The spring ensures that the spool is in a pre-defined position in case the valve is not actuated. The valve starts thus in pressure relief mode, i.e. user port A is connected to tank by means of the orifice in this flow passage. The chamber at the left side of the spool is pressurized by means of the pilot stage of the valve. The pilot stage is a direct acting pressure relief valve, controlled by means of the position controlled proportional magnet. Electronic position control is integrated in the valve. The pilot stage is connected to pressure port P by means of a flow control valve, setting the constant pilot flow. The spool defines two orifices: an orifice in the flow path from pressure port P to user port A; and an orifice in the flow path from user port A to tank port T. The first orifice represents the pressure reducing part, the second the pressure relief part of the valve. Initially the valve is in pressure reducing mode. When the orifice from port P to port A opens the pressure at port A will increase. In case the orifice from port A to port T opens the pressure at port A will decrease. For the modeling of this valve two options are considered. One is making a true and complete physical model of the valve using force balance for the valve control. The other option is to model the control signal for the valve opening in MatLab/Simulink signal builder. Both models will be analyzed here. 3.2.1 The physical model In order to create a physical model of the system, the components mentioned above have to be modeled. So the model will consist of two orifices, two cylinders to represent the chambers of the spool, the spring on the right side of the spool, the mass of the spool and the flow control valve on the left side 5
of the spool and the pilot stage. The valve control electronics are left out of the model, because there is not enough data available. The Simscape model for this configuration can be seen in figure 3.3. figure 3.3. physical model of the hydraulic valve The hydraulic damping in the model, represented by the segmented pipeline, represents the narrow channel through the spool and introduces a small delay between the pressure in port A and the pressure of the right chamber, represented by the cylinder. The hydraulic damping has also a numerical advantage since it smoothens the signal which accelerates calculations. The advantage of creating a physical model is that this represents the actual system best. Because it allows to truly model the force balance on the spool. The conditions in the actual system determine whether or not an orifice opens or closes. The major drawback of the physical model is that a lot of data from the valve is needed that is not available. The only data available are the data sheets found in Appendix A. The data that was not made available thus needs to be estimated; which makes the model more inaccurate. Another drawback to this type of modeling is that the electronic part of the valve used for control hardly can be modeled, because there is no data available for the electronics. This means that the only way to control this valve is by pressure and since the pump delivers the pressure the only way to close the orifice from port P to port A and open the orifice from port A to port T is to turn the pump off. This may result in an inaccurate and unrealistic control of the valve. 3.2.2 The Simulink controlled model In this model the two orifices are controlled using a Simulink signal made in the signal builder. A positive signal will open the orifice form port P to port A while the orifice from port A to port T is closed and a negative signal will close the orifice form port P to port A while opening the orifice form port A to port T. 6
This makes the model much simpler; all what need to be modeled are the two orifices, a Simulink control signal and the pressure relieving action. The model for this configuration is shown in figure 3.4. Figure 3.4. the Simulink controlled model The model of figure 3.4 is much simpler than that of figure 3.3. There are far less parameters necessary; the only data that is needed is the data for the orifices. Another advantage over the physical model is that the valve can be easily opened and closed using the signal from the signal builder. A possible disadvantage of the Simulink controlled valve is generating an unrealistic signal. Another possible disadvantage of the Simulink controlled valve is that there is no feedback control loop in the system. It just follows the pattern set in the signal builder. For this specific case the Simulink controlled valve model is the best option, because of the limited available data for the physical valve model. In a situation where all data, including the control electronics, is available the physical model would probably be a better option, since this model can handle feedback control and is more realistic. 3.2.3 The orifice settings The most important settings for the valve model are the orifice settings. The data that is necessary to model the orifices are the initial opening, the maximum opening and the maximal passage area through the orifice. The initial opening and the maximum opening have to be estimated from the figures in the data sheets of Appendix A. The maximum passage area can be calculated using eqn. (3.1). Using figure 3.2 and the technical drawing with measurements from the data sheet it was estimated that the stroke of the spool is about five millimeters. The orifice from port P to port A seems to be a closed center valve judging from figure 3.2 with an initial opening of -.65 millimeters. The orifice from port A to port T appears to be more like a critically centered or open center valve. The orifice equation, equation (3.1), can be used to calculate the maximum passage area. To do this a pressure difference over the orifice is needed. The pressure difference over the orifice can be obtained by using the pressure-flow relations from the data sheets shown in figure 3.5. 7
figure 3.5. pressure-flow lines The 175 bar valve variant is present in the system. This means that the maximal pressure in port A is 175 bar and the maximum pressure in port P is the pressure of port A plus another 5 bar. The five bar pressure difference is a result from the pressure loss to the flow control valve. To calculate the maximum passage area the maximum flow and the minimal pressure difference have to be used. The minimal pressure in the orifice from port A to port T at the maximum flow of 4 L is 13% of 175 bar, min making 22.75 bar the minimal pressure difference. The minimal pressure difference between port P and port A is 5 bar according to the data sheet. Using equation (3.1) the maximum orifice area for the orifice from port A to port T is -5 2 1.328 1 m and the maximum orifice area for the orifice from port P to port 5 2 A is2.833 1 m. Calculations for the orifice areas can be found in Appendix B. 8
3.3 The hydraulic cylinders and the load In this part of the model the hydraulic cylinders and the load are modeled. This part of the model contains the hose form the valve to the cylinder, an elastic load and a force sensor. The plastic part of the load is not modeled, because there is not enough information about the material behavior. There are two types of hydraulic cylinders applied in the system; one has a larger piston area and the other has larger stroke. Both types of hydraulic cylinders are modeled as single acting hydraulic cylinders that are used to pull the load. The parameters for both the types of cylinders can be found in table 3.3. Table 3.3 Hydraulic cylinder data Piston area DW-6-35-1 Piston stroke DW-6-35-1 Cylinder dead volume DW-6-35-1 Piston area DW-7-4-4 Piston stroke DW-7-4-4 Cylinder dead volume DW-7-4-4 2.83 1 3.671-5 3.85.7 4.221-5 The piston area was determined by calculating the circular area of the piston using its diameter, which is the first number in the cylinders identification number. The piston stroke can be found too in the cylinder identification number as the final number. Because data about the dead volume of the cylinders was not made available by the manufacturer, this data had to be estimated using cross sections of different makes of cylinders, see [2]. The data sheet for these cylinders can be found at the end of Appendix A. These cylinders are connected to a load which is modeled as a spring. The stiffness of this spring was determined by the test data made available by B-style in which they specify a force and an estimated displacement. The data for each load can be found in table 3.4. Table 3.4 Elastic load data Load name Force Deformation Stiffness shoulder seatbelt 135 N 3 mm 45 N/m hip seatbelt 1732 N 1 mm 1732 N/m chair leg 5298 N 5 mm 1596 N/m There is a pipeline in this model section as well. This is the hose between a valve and the hydraulic cylinder. It is modeled as a segmented pipeline to account for friction losses, fluid inertia and fluid compressibility. The pipes are 3 m long and have an internal diameter of a ½. The pipe wall type is set to flexible, because the hoses to the cylinder are made of rubber and will expand when internal pressure is applied. 9
The pipeline, cylinders and load combined result in a complete model for this part of the system. The Simscape model is shown in figure 3.6. figure 3.6. model of the cylinders and load 1
3.4 Model expansion To expand the overall system model an advanced friction model and some theory of pipeline dynamics will be presented here. 3.4.1 Advanced Stick-slip friction model In this subsection the phenomenon of stick-slip friction will be described and explained based on the theory of [1]. Furthermore a simulation model of stick-slip friction will be presented. This model is made with the Simscape toolbox of MatLab. The theory behind stick-slip friction: Stick-slip friction is a typical behavior for a system with friction and a certain amount of elasticity. It is caused by the fact that friction at rest is larger than in motion. A typical model for stick-slip friction is given in figure 3.7. When this system is actuated a typical stick-slip motion will occur. The mass in figure 3.7 is initially at rest and the spring force builds up. The static friction force counteracts the spring force, and there will be a small displacement only. When the spring force reaches the break-away force the mass starts to slide and the friction decreases rapidly due to the Stribeck effect. The spring will relax, and the spring force decreases. The mass slows down and the friction force increases because of the Stribeck effect and the motion stops. figure 3.7. model of the stick-slip system This phenomenon will repeat and causes the typical stick-slip motion that is shown in figure 3.8. This figure shows both a position-time diagram and a diagram with force and velocity plotted versus time. 11
figure 3.8. simulation of stick-slip motion Different friction forces contribute to the total friction force the main types of friction for the stick-slip phenomenon are static friction, Coulomb friction, Stribeck friction and viscous friction. Simulation model of the stick-slip friction: The simulation model was created in the MatLab Simscape toolbox, see figure 3..9. The model consists of the same basic components as the theoretical model of figure 3.7, a mass (Mass1 in figure 3.9), a translational spring and friction. The translational friction block requires input for the break-away friction, coulomb friction and the viscous friction. In addition to Mass1 this model also contains a second mass (Mass in figure 3.9) which is set to the minimal non-zero value of MatLab, to suppress numerical problems. The system also contains two sensors; one for velocity and position and one sensor for force. figure 3.9. The simulation model for stick-slip friction The model is integrated as a subsystem into the system model and gets input from the hydraulic cylinder while the output is connected to the load. The model results in the theoretical behavior as shown in figure 3.8. A validation of the model with arbitrary numbers for the friction is shown in figure 3.1. 12
1.5 1.5 1 2 3 4 figure 3.1. force-time diagram created with the stick-slip model This figure clearly shows the sticking part until about 8 seconds and the slipping part from about 8 to 1 seconds into the test. This results in a modular stick-slip model that can be easily build into a larger model. 3.4.1 Pipeline dynamics Pipelines are an important part of the system, because their properties can seriously influence the systems behavior. Pipelines introduce a hydraulic resistance in the system and can have an accumulating effect. The magnitude of the resistance that results from the pipelines depends on the length and diameter of the pipes and for the hoses in this system on the amount of expansion with pressure variation. Longer pipes and pipes with a smaller diameter have a larger hydraulic resistance, because more friction is introduced. However in combination with accumulating effects making the pipes longer of smaller in diameter does not necessarily result in a negative effect on the reached force. When pressure is applied to the hose it expands. When the hose expands hydraulic fluid is accumulated, this takes energy away from the system. This does not necessarily have to be a bad thing, because when the system is used a second time the accumulated hydraulic fluid generates a larger force. 13
4. Model validation and simulations The model described in chapter 3 is used to perform simulations and hopefully finding the cause of the systems problems. First some simulations were done with a single cylinder for model validation and to check if some of the problems can already be identified. After this, simulations were done with multiple cylinders to find out if there are capacity problems or if there is interference between the cylinders. 4.1 Model validation and Single cylinder simulations The first simulations were done with a very basic model; without the hoses from the valve block to the hydraulic power unit and without an advanced friction model. The model that was used for these simulations can be seen in Appendix C. The input signal for the valve is shown in figure 4.1 and the resulting force verses time; and piston displacement versus time are shown in figure 4.2 and figure 4.3 respectively. spool position [m] 5 x 1-3 -5 5 1 15 2 25 3 Figure 4.1 the valve input signal 2.5 x 14 2 1.5 1.5 -.5 5 1 15 2 25 3 figure 4.2 time-force graph 14
.6.5.4 Position [m].3.2.1 -.1 5 1 15 2 25 3 figure 4.3 time-displacement graph As can be seen from figure 4.1 to 4.3 the model appears to be valid. When the valve opens the piston moves and force builds up. When the input signal of the valve is negative the piston moves back and the force reduces. When the input signal of the valve is set to zero the force is maintained. Problems cannot be identified from these simulations. There is no sagging effect in the force and the force increases linearly and without fluctuations. So in order to find the systems problems multiple cylinders, an advanced friction model and pipeline dynamics should be considered. Next some simulations were done to investigate the effects of stick-slip friction and pipeline dynamics. In advance some simulations were done to find out suitable settings for the stick-slip friction model and pipeline model. The models for and data from these simulations can be found in Appendix D. The pipeline model has an additional pipeline between the power unit and the valve. The results from stick-slip simulation 4 resemble the pattern seen in the tests performed on the actual actuators the best. The test on the actual actuators can be found in Appendix E. So the stick-slip friction in the model was set to the values in table 4.1. These settings result in the characteristic that is shown in figure 4.4. Table 4.1 Stick-slip friction settings Elasticity Static friction Coulomb friction Viscous friction 14 N/m 2 N 6 N 1 N 15
2 15 1 5-5 5 1 15 2 25 3 figure 4.4 The model including stick-slip From the pipeline simulations it can be concluded that it is better to have shorter and stiffer pipelines in the system. These characteristics seem to have the best effect on the first force peak in the simulation and this is the most important peak for this system. The additional signal cylinder simulations with the advanced stick-slip friction model and pipeline dynamics do not reveal any problems with the system. There is no sagging behavior in the force characteristic. So the problem probably involves interference between cylinders or capacity problems. This was investigated in the multiple cylinder simulations. 4.2 Multiple cylinder simulations To find out if there are capacity problems for the power unit or if there is interference between the cylinders some multiple cylinder simulations have to be done. For these simulations a model with 3 cylinders and valves was used. These three cylinders represent the cylinders pulling the shoulder seatbelt, the hip seatbelt and the chair leg. These cylinders are chosen because the simulations are compared to the data gathered by B-style from the actual set-up. This data can be found in Appendix E. The simulation with the standard model, with multiple cylinders does not show any capacity problems or interference between cylinders when each valve has an identical input signal. The results of this simulation can be seen in Appendix F. In the next simulation the objective is trying to replicate the first test of the tests done by B-style, which can be found in Appendix E. To do this the valve input signal for the chair leg valve is adapted, this valve now opens one second later than then the other two valves. The input signals are shown in figure 4.5. The input signals are chosen to be ideal; the opening and closing of the valves is controlled with a step signal. In reality this would be impossible because the system cannot react that fast. 16
5 x 1-3 shoulder and hip seatbelt Position [m] -5 1 2 3 4 5 6 5 x 1-3 chair leg Position [m] -5 1 2 3 4 5 6 figure 4.5 valve input signals above: shoulder and hip seatbelt, below: chair leg This simulation seems to reveal the problem with the system. As can be seen from figure 4.6, which is a graph of the force on the load versus time. A sagging effect can clearly be seen in the graph for the shoulder and hip seatbelt at the moment the valve for the chair leg opens. This means that there is clearly interference between the cylinders. 1 8 shoulder seatbelt hip seatbelt chair leg 6 force [N] 4 2-2 2 4 6 8 1 time [s] figure 4.6 force-time diagram 17
To identify the cause of the problem it is necessary to look at the flow and pressure characteristics for the flow to all the valves and the flow to the pump. The characteristics for flow and pressure are shown in figure 4.7 and 4.8 respectively. flow [m 3 /s] 8 x 1-4 6 4 2 shoulder seatbelt hip seatbelt chair leg pump flow -2-4 2 4 6 8 1 time [s] figure 4.7 the flow to the valves and from the pump pressure [Pa] 2 x 17 1.5 1.5 shoulder seatbelt hip seatbelt chair leg pump pressure 2 4 6 8 1 time [s] figure 4.8 the pressure in the system From figure 4.7 it becomes clear that, when the valve for the chair leg opens an outflow of hydraulic fluid from the shoulder and hip seatbelt valves arises. From figure 4.8 it can be seen that this is a flow problem because the pressure in the system is virtually unaffected by the opening of the chair leg valve. 18
As can be seen from the figures 4.6, 4.7 and 4.8 the first second of the simulation all appears to be as expected. The force build up in the cylinders develops linearly as expected, but after one second when the chair leg valve opens the force delivered by the shoulder and hip seatbelt starts to sag. This is caused by a large outflow of hydraulic fluid from these cylinders. That is caused by the pressure difference between the cylinders. The chair leg cylinder is still pressure less at the moment its valve opens while the other two cylinders are already under pressure. The three cylinders now act as communicating barrels. The pressure in the chair leg cylinder is raised with pressure from the other two cylinders. To do this flow is directed back from the other two cylinders into the chair leg cylinder. This is possible because the orifice from port P to port A in the shoulder and hip seatbelt valves is open at the moment the orifice from port P to port A opens in the chair leg valve. The outflow of hydraulic fluid in the shoulder and hip seatbelt cylinders causes a pressure drop in these cylinders. This causes the force delivered by these cylinders to drop as well. 19
5. The solution of the problem In this chapter a solution will be presented for the problem of the hydraulic test bench. This solution has been tested with a simulation model. The problem is that there is not enough pressurized fluid in the system to satisfy the sudden demand of the chair leg cylinder. So to solve the systems problems a pressurized buffer of hydraulic fluids needs to be introduced into the system. This can be done by adding an accumulator to the system. A gas charged accumulator seems to be suited best for the job because this way the pre load pressure for the accumulator can be adapted the easiest. To size an accumulator three parameters need to be considered: the capacity, the pre load pressure and the initial volume. Some simulations have been done with different settings for these parameters to investigate their effect on the system. Graphic representations of these test results can be found in Appendix G. The capacity influences the speed of the system, more specifically the response of the force build up. A relatively lower capacity speeds the force build up more than a relatively larger accumulator capacity. However the accumulator capacity should be large enough to provide the necessary flow to the system. So for this system a relatively small accumulator should be chosen that still can meet the demanded flow. The pre load pressure is the pressure at which the system starts to interact with the accumulator. If this pressure is higher the system is faster, because it can deliver fluid faster because of the higher pressure. However the pressure should not be raised too high, because there needs to be enough fluid in the accumulator when the chair leg valve opens otherwise the accumulator cannot satisfy the demand long enough and the sagging effect will still take place. The initial volume is important for this system as well. There need to be a volume of hydraulic fluid present when the simulation starts in order to raise the force delivered by the shoulder and hip seatbelt cylinder quickly. Enlarging the initial volume makes the system faster, however this should be traded off by the time to fill the accumulator. If the accumulator can be filled while the system is in steady state before a test this will not add up to extra time for a test. An impression of the systems behavior with an accumulator can be seen in figures 5.1 to 5.3. The system reacts faster and there is no sagging effect. The accumulator used in the simulation of figure 5.1 to 5.3 has a capacity of 8 L, a pre load pressure of 35 bar and an initial capacity of 1 L. So a small accumulator whit a modest pressure can be enough to fix the systems problems. 2
16 14 12 shoulder seatbelt hip seatbelt chairleg 1 8 6 4 2-2 1 2 3 4 5 6 figure 5.1 force-time diagram with accumulator 2 x 1-3 1 Flow [m 3 /s] -1-2 shoulder seatbelt hip seatbelt chairleg accumulator pump -3 1 2 3 4 5 6 figure 5.2 flow-time diagram with accumulator 5.5 x 16 5 Pressure [Pa] 4.5 4 3.5 1 2 3 4 5 6 figure 5.3 pressure-time diagram with accumulator 21
6. Conclusions The system was successfully modeled in Matlab/Simulink. It was used to do simulations of tests with the hydraulic test bench. These simulations showed that the main problem which is a sagging effect in the force of some cylinders is not caused by friction, pipeline dynamics or capacity problems. It was demonstrated that the problem was interference between cylinders. The interference occurs when one of the valves opens later than the others. This causes an outflow of hydraulic fluid from the pressurized cylinders, resulting in a drop in the force that the cylinder delivers. To solve this problem the system needs a pressurized buffer of hydraulic fluid, to have enough pressurized flow when a valve opens later. An accumulator was integrated into the model and it was shown that this solved the problem. Simulations showed that a relatively small accumulator with a modest pressure can satisfy the systems demands. Furthermore if the accumulator is filled before a test while the system is in steady state, filling of the accumulator will not extend the time for a test. 22
References [1] C. Canudas de Wit, H. Olsson, K. J. Astrom, and P. Lischinksy, A new model for control of systems with friction, IEEE Trans Automat. Contr., vol. 4, pp. 429-425, Mar. 1995 [2] www: FlexHydro, http://www.flexhydro.com/dubbelwerkendstandaardcilinders/ [3] dr. Ir. W.J.A.E.M. Post, slides lecture 4N63, Fluid Power Transmissions and Servo Systems 23
Symbol list Symbol Quantity Unit Unit abbreviation A Area Square meter 2 m q Flow Cubic meter per second 3 m s C Flow discharge - - D coefficient ρ Density Kilogram per cubic kg meter 3 m p Pressure difference Pascal Pa 24
Appendix A: data sheets 25
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Appendix B: Orifice calculations In this appendix the orifice area for the pressure relief valve of the hydraulic power unit and valve are calculated. The areas for the two orifices that make up the valve are calculated too. All parameter values are from the data sheets of Appendix A. Relief valve for the hydraulic power unit The calculations are done with the orifice equation: 2 pmax q qmax = CD Amax Amax = ρ C max D ρ 2 p max A q ρ = = = 2.41 1 4 max 3.583 1 884 max 5 CD 2 pmax.7 2 2 1 Relief valve for the valve A q ρ = = = 4.789 1 4 max 6.67 1 884 max 5 CD 2 pmax.7 2 175 1 The valve orifices The orifice from pump to cylinder: m 6 2 m 6 2 A q ρ = = = 2.833 1 4 max 6.67 1 884 max 5 CD 2 pmax.7 2 5 1 m 5 2 The orifice from cylinder to tank: A q ρ = = = 1.328 1 4 max 6.67 1 884 max 5 CD 2 pmax.7 2.13 175 1 m 5 2 35
Appendix C: Single cylinder model In this appendix the simulation model used in the single cylinder simulations is presented. Signal 2 S PS Signal Builder Simulink-PS Converter1 f(x)= Solver Configuration S PS Simulink-PS Converter S A B Variable Orifice P-A Pressure Relief Valve1 S A B Variable Orifice A-T Pressure Relief Valve Position6 schoudergordel C R A R C B A B A Position5 S PS Position4 Mechanical Rotational Reference PS S Position3 PS S PS S Position2 PS S Position1 R C F Ideal Force Sensor PS S S C R B Q A Ideal Angular Velocity Source Hydraulic Flow Rate Sensor2 Hydraulic Flow Rate Sensor3 Hydraulic Reference A Q B Hydraulic Flow Rate Sensor1 A Q B B Q A Custom Hydraulic Fluid Fixed-Displacement Pump P S T 145/6*2*pi Constant A B 1/2" pipe3 Hydraulic Flow Rate Sensor 36
Appendix D: Pipeline and stick-slip simulations This appendix shows the pipeline and stick-slip model for the single cylinder simulations and the simulation data. First the pipeline model and simulations will be presented followed by the stick-slip simulations. Position5 Signal 2 S PS Signal Builder Simulink-PS Converter1 S B A Variable Orifice P-A S PS Position4 Pressure Relief Valve1 S PS Simulink-PS Converter PS S Position3 Q A B A B S B A Variable Orifice A-T PS S Pressure Relief Valve Position6 PS S Position2 schoudergordel C R A PS S Position1 PS S R C B A B A Mechanical Rotational Reference R C F Ideal Force Sensor S C R Q B A Hydraulic Flow Rate Sensor3 Hydraulic Flow Rate Sensor2 A Q B Ideal Angular Velocity Source Hydraulic Reference Hydraulic Flow Rate Sensor1 1/2" pipe3 B Q A 1/2" pipe2 Custom Hydraulic f(x)= Fluid Solver Configuration Fixed-Displacement Pump P S T 145/6*2*pi Constant Hydraulic Flow Rate Sensor A B 37
The pipeline properties that are varied during the simulations are the length, the diameter, the Static pressure-diameter coefficient and the number of pipeline segments. Table A.D.1 pipeline dynamics simulation Simulation 1 Simulation 2 Simulation 3 Simulation 4 Length [m] 3 3 6 6 Diameter [m] 1.27e-2 1.27e-2 1.27e-2 1.27e-2 Static pressurediameter 2e-1 2e-1 2e-1 6e-1 coefficient [Pa/m] Nr. of segments 2 5 2 2 Simulation 5 Simulation 6 Simulation 7 Simulation 8 Simulation 9 Length [m] 3 3 6 3 3 Diameter [m] 1.27e-2 1.27e-2 1.27e-2 2.54e-2 6.35e-3 Static pressurediameter 6e-1 7e-11 7e-11 2e-1 2e-1 coefficient [Pa/m] Nr. of segments 2 5 2 2 2.5 x 14 Test 1 2.5 x 14 Test 2 2 2 1.5 1.5 1.5 1.5 -.5 5 1 15 2 25 3 -.5 5 1 15 2 25 3 2.5 x 14 Test 2 2.5 x 14 Test 4 2 2 1.5 1.5 1.5 1.5 -.5 5 1 15 2 25 3 -.5 5 1 15 2 25 3 38
2.5 x 14 Test 5 2.5 x 14 Test 6 2 2 1.5 1.5 1.5 1.5 -.5 5 1 15 2 25 3 -.5 5 1 15 2 25 3 2.5 x 14 Test 7 2.5 x 14 Test 8 2 2 1.5 1.5 1.5 1.5 -.5 5 1 15 2 25 3 -.5 5 1 15 2 25 3 2.5 x 14 Test 9 2 1.5 1.5 5 1 15 2 25 3 From these simulations it can be concluded that if the accumulative properties of the hoses are increased (by making the hoses longer, bigger in diameter and weaker) the first force peak will be lowered and the second increased. When the hoses are pressurized for the first time, they will expand and this consumes energy. When the hoses are pressurized for the second time the accumulated hydraulic fluid will help to reach a higher force. For this case the first force peak is more important so hoses should be chosen short and stiff, rather than longer and weaker. 39
The stick-sip properties that are varied during the simulations are the spring rate (see figure 3.9), the static friction force, the coulomb friction force and the viscous friction force. Table A.D.2 Stick-slip friction settings Simulation 1 Simulation Simulation Simulation Simulation Simulation 2 3 4 5 6 Elasticity 14 N/m 14 N/m 25 N/m 14 N/m 14 N/m 14 N/m Static friction 7 N 2 N 2 N 2 N 2 N 2 N Coulomb friction 6 N 18 N 18 N 6 N 6 N 18 N Viscous friction 1 N 8 N 8 N 1 N 8 N 1 N 2 Test 1 2 Test 2 15 15 1 5 1 5-5 5 1 15 2 25 3 Test 3 2-5 5 1 15 2 25 3 Test 4 2 15 15 1 5 1 5-5 5 1 15 2 25 3 Test 5 2-5 5 1 15 2 25 3 Test 6 2 15 15 1 5 1 5-5 5 1 15 2 25 3-5 5 1 15 2 25 3 4
Appendix E: Test results on actual actuators provided by B-style 41
Appendix F: Simulations with an identical input signal In this appendix the data will be shown from a simulation where each valve has an identical input signal. This input signal is shown in figure A.F.1. The resulting simulation data for the force, flow and pressure is shown in figure A.F.2. 5 x 1-3 shoulder and hip seatbelt Position [m] -5 1 2 3 4 5 6 figure A.F.1 valves steering signal 1 4 x 1-4 5 Flow [m 3 /s] 2-5 2 4 6-2 2 4 6 2 x 17 Pressure [Pa] 1 shoulder seatbelt hip seatbelt chair leg pump -1 2 4 6 figure A.F.2 test results From the simulation data it becomes clear that when all the valves have identical input signals there is no problem. The force builds up linearly without sagging, as can be expected from the system. 42
Appendix G: Accumulator simulations In this appendix the data gathered in the accumulator simulations is presented. The flow and pressure in the graphs are measured at inlet port of each valve. Important is to watch the flow. If the flow gets negative a drop in the force will be present. capacity [L] pre load pressure [bar] initial volume [L] Simulation 1 8 2 1 Simulation 2 8 2.5 Simulation 3 8 25.5 Simulation 4 2 2 1 Simulation 5 8 35 1 Simulation 6 8 5 1 Simulation 1 1 8 6 4 2-2 1 2 3 4 5 6 Flow [m 3 /s] 2 x 1-3 1-1 -2 1 2 3 4 5 6 3.4 x 16 Pressure [Pa] 3.2 3 2.8 2.6 2.4 shoulder seatbelt hip seatbelt chair leg accumulator pump 2.2 1 2 3 4 5 6 43
Simulation 2 1 8 6 4 2-2 1 2 3 4 5 6 Flow [m 3 /s] 2 x 1-3 1-1 -2 1 2 3 4 5 6 3 x 16 2.8 Pressure [Pa] 2.6 2.4 2.2 2 1 2 3 4 5 6 shoulder seatbelt hip seatbelt chair leg accumulator pump Simulation 3 15 2 x 1-3 1 1 5 Flow [m 3 /s] -1-5 1 2 3 4 5 6-2 1 2 3 4 5 6 3.4 x 16 Pressure [Pa] 3.2 3 2.8 2.6 shoulder seatbelt hip seatbelt chair leg accumulator pump 2.4 1 2 3 4 5 6 44
Simulation 4 1 8 6 4 2-2 1 2 3 4 5 6 Flow [m 3 /s] 2 x 1-3 1-1 -2 1 2 3 4 5 6 2.5 x 16 Pressure [Pa] 2.4 2.3 2.2 shoulder seatbelt hip seatbelt chair leg accumulator pump 2.1 1 2 3 4 5 6 Simulation 5 15 2 x 1-3 1 1 5 Flow [m 3 /s] -1-2 -5 1 2 3 4 5 6-3 1 2 3 4 5 6 5.5 x 16 Pressure [Pa] 5 4.5 4 shoulder seatbelt hip seatbelt chair leg accumulator pump 3.5 1 2 3 4 5 6 45
Simulation 6 1.5 1.5 2 x 14 1 2 3 4 5 6 Flow [m 3 /s] 2 x 1-3 1-1 -2-3 -4 1 2 3 4 5 6 7 x 16 Pressure [Pa] 6 5 4 3 shoulder seatbelt hip seatbelt chair leg accumulator pump 2 1 2 3 4 5 6 Comparing Simulation 1 and Simulation 4 it can be seen that the system when enlarging only the capacity will react slower. Comparing simulation 2 to simulation 3 and simulation 1 to simulation 5, shows that raising the pre load pressure makes the system faster. Simulation 1 and simulation 2 show that in case of a larger capacity the system will also react faster. Finally simulation 6 shows that if the pressure is set too high for the initial capacity the accumulator will be empty before the other valve opens and the force will still sag. 46