MODELLING, SIMULATION AND VALIDATION OF COMPLEX FLUID AND MECHANICAL SYSTEMS J Larsson, P Krus and J-O Palmberg Mechanical Engineering Systems, Department of Mechanical Engineering Linköping University, SE-581 83 Linköping, Sweden
[email protected]
ABSTRACT Technical systems are becoming increasingly integrated, e.g. because of the intensive use of software due to demands on energy efficiency, performance and customisability. This means that there are a lot of interactions among the sub systems during operation. The dynamical behaviour of such a system is hard to predict since every sub system needs to be taken into account. Also, often the sub systems are from different engineering domains. Engineers therefore need to collaborate to make the prediction. To predict how a change to a system would affect its behaviour, a validated model of the original system is needed. It is investigated in the paper how the modelling, simulation and validation process could be organised in the mentioned case when several engineers from different domains are involved.
KEYWORDS Co-simulation, TLM, multi-domain, heterogeneous, hydraulics, MBS
INTRODUCTION In the beginning of 1998, Volvo Construction Equipment and Linköping University started collaborating round the subject of system design using simulation. The aim of the project has been to find out the most appropriate ways of modelling, simulating and validating functional behaviour of multi-domain systems. A wheel loader was chosen as a test system for the ideas developed since it is difficult to design but also contains most functions used by other heavy vehicles.
Figure 1. The test system.
The hydraulic pumps are load sensing, the steering is hydrostatic and the transmission is hydro-mechanical where all gears are constantly in contact. Between the six cylinders, four stroke direct injected turbo-charged diesel engine and the transmission is a one-stage hydraulic torque converter.
The load case in which the loader model is supposed to work is in the short work cycle where soil is transported from the soil pile to a nearby hauler or truck as in Figure 2.
Figure 2. The short work cycle.
The hydraulics and transmission share the power of the engine and can both consume all of the power. During a normal work cycle the two consumers are used concurrently at certain times, thus interacting. The chassis and tires respond both to the hydraulics and the transmission.
MODELLING ISSUES In [1] it was found that when several engineers are available for collaborative modelling, their ordinary used tools should be used at least for the modelling phase. The general tools will always lag behind when it comes to features within certain domains, such as the ability to handle 3D geometry. If a company was using only one model tool, then when some other tool becomes better, it is difficult to introduce that other tool at the same time over the whole company due to ongoing projects etc. and in practice several tools would be used in that overlap phase. In the project, Adams, Matlab/Simulink and Hopsan were chosen as modelling tools. In Simulink, the diesel engine and transmission was modelled, in Adams the tires, chassis, frames and loading unit were modelled and finally Hopsan was used for the working- and steering hydraulics. The models are shown below. Simulink was chosen due to its extendibility, Adams for its 3D capabilities and Hopsan for its high simulation performance on systems with small time constants and for its extensive hydraulic library.
the sub systems together with the subcontractors. The integrator therefore needs models that have physical parameters. Who should do the modelling; the integrator or the subcontractor? The subcontractor will in the future have an interest in providing sub models to integrators since they then will have an easier task in creating customspecific solutions and will therefore have time serving more integrators than earlier. Also, the subcontractor wants to keep knowledge on their products in-house because that’s what they are competing with. The supplied sub model should have few parameters to change since the subcontractor wants to keep some secrets and the integrator doesn’t want to get lost in the model. The top-level system description should remain constant in time, as shown below. This level describes how the main sub system models are connected, variables that are exchanged during simulation and the most important input variables to the system model, such as gas pedal position, gear level position and more. In each of the boxes shown, a pointer exists to the modelling tool containing the actual sub model.
Figure 4. The top-level description of the system.
Figure 3. The different models produced.
It’s important to find out what parameters rule the behaviour the most, what ones that make little difference and which ones that are the most difficult to estimate. This determines the type of models that need to be done. In the case of the hydraulics, the flow forces determine the speed of certain functions. They cannot be determined analytically and it is still difficult to use CFD due to complex valve geometry. So, here the system integrator needs grey-box models from their subcontractors. This means that the models are adapted to measurements of in this case the flow forces. The black-box models are not an option here since the system integrator is seldom a pure integrator, but tunes
One way of modelling is to make a custom system model for each purpose. If the static behaviour is interesting a low-fidelity model is done and if only the driveline is to be studied the rest of the system is done simplified. This yields a number of models presenting the same system from different viewpoints. This way the complexity is reduced for each case and a shorter simulation time is gained. However, in total the complexity is increased since it is difficult to determine how design changes to a low-fidelity model should be introduced into a high-fidelity model and vice versa. The problem is in short how to keep all those models up to date with each other. Instead, in order to keep down the number of models, only one system model (consisting of the most recent sub models) is used and the input signals are used to constraint certain sub models to gain a more predictive behaviour.
SIMULATION ISSUES
qH (nTH ) = ...
It is not obvious how the simulation should be performed; if one or several solvers should to used. In our case it is necessary to be able to view the simulation results in each tool since e.g. the animation capability of Adams is difficult to mimic. This means that in the case of one solver, the sub models need to be exported to it and connected somehow in a neutral modelling language and then the results are to be distributed back among the modelling tools. It is a complicated procedure to write the necessary translators, two for each tool to handle both model and results. Also the simulation performance wouldn’t be as good as in the case of several solvers working together as shown below.
pH (nTH ) = cH (nTH ) + Zq H (nTH )
Co-simulation is when several simulation tools using individual numerical solvers, collaborate to find a common solution. The solvers will advance simulation time differently and synchronisation is needed. If only a straightforward exchange of state-variables is performed among the solvers, the couplings may generate numerical problems. There is however a number of ways of improving the coupling as has been shown in [4]-[6]. The method of characteristics (presented in [2] and [3]) is used in [4] and [5] and in [6] timeinterpolation/extrapolation of the state variables is utilised. In the project, the method of characteristics has been used to create a stronger bond between the models in Adams and Hopsan as shown in Figure 5. Simulink controls the simulation and communication occurs once every millisecond with the other tools. This way Hopsan can communicate with Adams through Simulink. Without the characteristics, a communication interval of 0.1 ms is needed. In the example below, Hopsan uses the constant time step TH, Adams has a variable time step and the communication between the tools occurs with a time interval of TA seconds. As can be seen Z acts as impedance. The variable c has in this case, with flow and pressure as exchanged variables, the unit Pa. The rectangle is a volume in Hopsan with constant size. The Z and c used by Adams need to be adjusted since the communication interval TA is different from TH. Z’A and c’A are calculated as described in [5].
Z , cH (nTH )
qH (nTH )
βe TH V cH (nTH ) = c A ((n − 1)TH ) + 2 Zq A ((n − k )TH ) Z=
c A (nTH ) = cH ((n − 1)TH ) + 2 Zq H ((n − 1)TH ) T Z 'A = Z A TH
T c' A (nTH ) = c A (nTH ) − A − 1 Zq A ((n − k )TH ) TH Z ' A , c' A (mTA )
Hopsan Adams
q A (mTA ) p A (t ) = c' A (mTA ) + Z ' A q A (t ) q A (t ) = ...
Figure 5. Communication between numerical solvers using the method of characteristics.
The simple model in Figure 6 is used to show the influence of characteristics on a co-simulation. The system is a mass that is positioned-controlled using a 3/3-direction valve. The reference position is a step with a sinusoid on top. The valve and piston is simulated in Hopsan with a constant time step and the mass is simulated in Simulink that makes use of a variable time step. The time step in Hopsan is tuned to be as large as possible with respect to accuracy. In Figure 7 and Figure 8, co-simulation results are shown with and without the use of characteristics. What can be seen is that the solution stays stable if characteristics are used even if the communication interval is very large.
On a 600 MHz Pentium III single processor, Hopsan calculates its part of the loader model in 75 real sec/simulation sec. For Simulink that figure is 25 and in Adams 100-150. Hopsan uses a constant time step of 0.1µs, Simulink uses the variable time step solver Ode45 with auto settings on accuracy and Adams uses a maximum time step of 1 ms (seldom goes below). The communication time step between Simulink and the other tools is 1 ms. Here we can see the advantage of partitioning the problem. The hydraulic model needs a very small time step compared to the MBS model. If the hydraulic model had been executed in Adams, the simulation time would have increased significantly. This is also because a short work cycle is quite transient giving the Adams solver small chances to increase the time step. Figure 6. Simple characteristics.
test
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To get better simulation performance, the models could of course be simplified. This is, however, not much of an option in this case since then several system model constellations would be produced to work in different situations. The drawbacks are explained earlier in the paper. More processors can be used so that Adams and Hopsan execute in parallel. This has been tested on a 700 MHz Pentium III with two processors and that yielded a decrease in simulation time by 30%.
Communication every time step 6000 Comm. interval 10 4000
2000
0 0
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Figure 7. Co-simulation results from the test model in Figure 6 with the use of characteristics. Communication has been performed each, every third and every tenth time step. 5
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VALIDATION ISSUES
2.5 2 Comm. interval 3 1.5 1 0.5 0
Between every communication, calculation today takes about 0.1 s to finish. This means that with double precision and ten variables to exchange, a data transfer rate of 3.2 kbit/s between the tools is needed not to slow down the present performance. This is not much even if the tools were spread on the Internet, but what slows down when communicating over the Internet is the number of packages that need to be sent. This means that it would be difficult to simulate in real-time since 1000 packages/s need to be sent in that case. Also, it is not guaranteed that all packages arrive at all or in the correct order. Furthermore, the speed of light represents an upper bound of communication speed. Already a physical distance of 300 km represents a minimum delay of 1 ms in each direction.
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Figure 8. Co-simulation results from the test model in Figure 6 without using characteristics. Communication has been performed each, every third and every tenth time step.
To limit the size of models, an upper limit in frequency of the interesting system behaviour needs to be established. In our case, this limit is 10 Hz. Certain sub systems, models and measurements on some internal parts may need to be correct for higher frequencies for the system model to reach that goal. But actually, often just by being able to predict the static behaviour of a complex system, a lot of insight has been gained. In the case of validating the lift cylinder speed, a number of sub systems needed to be taken into account. As shown in Figure 9, the test case is such that the bucket is lifted slowly, with the engine running at idle
speed. Then the servo pressure to the manoeuvre valve is instantly increased to a maximum and the speed increases to a maximum. The bucket is lowered in the same manner. At the low speed, the load sensing pumps make sure that a constant pressure difference is maintained over the valve and the speed is totally determined by the flow forces. At the higher speed, the pumps can’t supply enough flow and the engine and the efficiency models of the pumps determine the speed. The flow forces determine the lowering speed both at high and low speeds since half the pump flow is needed.
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A problem for all systems that include humans as an important part of some control loop is that real-time simulations are needed if such systems are to be fully evaluated. This can be avoided if a model of the human is developed as well. In the case of the loader, this is actually quite difficult. Using recorded inputs from gas pedal and more, the driver model would ignore the strengths or weaknesses of a specific loader concept and that is not sensitive enough. The most difficult part is when the digging takes place (see [8] for models of granular material) since then the gas pedal is used concurrently with the tilt- and lift servo valves in a complex scheme, that not only results in a quick but also energy-saving loading of material. The system model can therefore mainly be used to match the different sub systems and individual components against some static characteristics as well as dynamical response.
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MEASUREMENT ISSUES
Simulation
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Lift cylinder speed [m/s]
the manoeuvre valves some. It takes about three seconds of the work cycle to reach the measured initial state.
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Figure 9. Comparison between simulation results (“slower curve”) and measurements on the lift cylinder speed.
When searching for errors in the model, it would be good to have a support tool that told the engineer what components that are currently influencing a certain variable such as lifting speed. Since there are quite a few parameters in a model of this size and the simulation takes time to perform, sensitivity analysis is difficult to achieve. Restrictions on component variables play a large role here. If e.g. the pump displacement is on its maximum, this means that the pump is not affecting the flow actively but rather passively follows the speed of the engine. For every test case, the system model needs to be in a certain initial state so that comparisons can be made. It could e.g. be that the lift and tilt cylinders should be in certain positions. The model should also be in static equilibrium. For MBS tools it is possible to do an initial static analysis to achieve initial equilibrium, but the results are a bit unpredictable. Also, since Hopsan is not part of that initial analysis, the cylinder forces in Adams are set to zero if nothing else is stated. The natural way is instead to have position controllers in Simulink that uses the normal servo pressures to get the bucket to the correct position when compared to corresponding measurements. The speed of the loader is handled in the same way using the gas pedal. When the loader is in the correct state, the measured input signals take control over the simulation. The hydraulic model is used to dampen initial transients in the MBS model by opening
In Figure 10 a scheme is shown on how the measurement devices were set up. All signals were measured in every load case since it was important to see how the loader behaved as a whole. It would also have been difficult to measure every component separately due to limits in time in particular. The disadvantage of using this large number of measurement devices is that it is hard to detect sensor failures. Of course, a measurement of this complexity is only done once for a product family to serve as a base material that can be studied for long time. Due to all the load cases that each component goes through, material exists that is maybe not interesting today, but could be tomorrow since the machinery isn’t changed in the same rapid manner as the control units. So it is a fast way of getting started with system validation, but future measurements should be ordinary component setups.
Figure 10. The measurement set-up used for the loader.
CONCLUSIONS A consistent engineering approach to modeling, simulation and measurement has been shown where only one system model exists, where the ordinary tools are used both for modeling and simulation and where the whole system is measured in one piece. The approach is especially suitable for companies that don’t have much resource for technology development in the system dynamics area. The method of characteristics is necessary to achieve a stable and fast co-simulation, but takes little effort to implement. Since the work has resulted in a validated system model, the ideas in the project have been applied to a complex application and engineers and students have done most of the work, we’re confident in saying that the industry can adopt the ideas already today with moderate difficulty
REFERENCES [1]
LARSSON J., KRUS P & PALMBERG J-O, “Techniques for Simulation of Multi-Domain Systems”, in Proc. of The Sixth Scandinavian International Conference on Fluid Power, SICFP'99, Tampere, Finland, 26th-29th May, 1999
[2]
AUSLANDER D.M., “Distributed System Simulation with Bilateral Delay-Line Models”, Journal of Basic Engineering, Trans. ASME, pp. 195-200, June 1968
[3]
JOHNS P.B. AND O’BRIEN M., “Use of transmission line modelling (t.l.m) method to solve nonlinear lumped networks”, The Radio Electron and Engineer, Vol. 50, pp. 59-70, 1980
[4]
POLLMEIER K., “Parallel simulation of complex fluid power systems – A new method to reduce the communication between processors”, Proceedings Part I, Journal of Systems and Control Engineering, ImechE, Vol. 210, No 14, pp. 221-230, 1996
[5]
JANSSON A., KRUS P & PALMBERG J-O, “RealTime Simulation Using Parallel Processing”, in Proceedings of 2nd Tampere Int. Conference on Fluid Power, pp. 27-39, 1991
[6]
ELLIOT A S, “A Highly Efficient , GeneralPurpose Approach for Co-Simulation with ADAMS”, 15th European ADAMS User’s Conference, 2000
[7]
JANSSON A., YAHIAOUI M & RICHARDS C, “Running Combined Multibody Hydraulic System Simulations within ADAMS”, 1998 International ADAMS User Conference, 1998
[8]
SLÄTTENGREN J. & ERICSSON A,”A model for predicting digging forces when working in gravel or other granulated material”, 2000 International ADAMS User Conference, Rome, Italy, 15th-17th November, 2000
ACKNOWLEDGEMENTS The work presented in the paper is a joint effort between Linköping University and Volvo Construction Equipment. Viking Engineering performed all measurements. The authors would like to thank Allan Ericsson and Conny Carlqvist at Volvo Construction Equipment for providing MBS- and driveline models. Also, students from Linköping University; Andreas Renberg, Johan Lillemets and Masood Akar, have modeled most of the working hydraulics. The work could not have been done without all these varying competencies.
