Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.

Glossary of terms for fluid power.

Mode of access: Internet.

A glossary of terms for fluid power.

Mode of access: Internet.

Fluid handling equipment : a compilation /

At head of title: Technology utilization.

Hydraulisen kuristinmallin ja liikealustan ohjauksen kehittäminen reaaliaikasimulointiin

Diplomityön ensimmäisessä vaiheessa tutkittiin hydraulisen kuristimen ominaisuuksia ja esiteltiin numeerisesti tehokas kuristinmalli käyttäenpolynomifunktiota virtauksen laminaarisen ja transitioalueen kuvaukseen. Puoliempiirisen mallin paremmuus tulee esille siinä, että kuristimen geometriatietoja ei tarvita laskettaessa virtausta paine-eron perusteella. Reaaliaikasimuloinnissa esiintyy kompromisseja tarkkuuden ja laskentanopeuden välillä. Tätä asiaa tutkittiin kahden virtausalueen kuristinmallilla. Transition paine-eron ja integrointiaika-askelen valinnan vaikutus tarkkuuteen ja laskentanopeuteen tutkittiin. Toisessa vaiheessa tutkittiin mahdollisimman hyvän liiketuntuman tuottamista liikealustalla ohjaussignaalia kehittämällä. Liikealustan liikeradan rajallisuudesta johtuen ohjauksessa on perinteisesti käytetty washout-suodatusta, joka erottelee simuloitavan järjestelmän kiihtyvyyssignaalista vain nopeatkiihtyvyydet. Tässä työssä tutkittiin hitaiden kiihtyvyyksien ottamista mukaan liikealustan ohjaukseen liikealustan liikeradan puitteissa. Tämä toteutettiin kuvaamalla hitaat kiihtyvyydet kallistamalla liikealustaa, jolloin käyttäjään kohdistuva voima saatiin kuvattua gravitaatiota hyväksi käyttäen.

Simulation of wind powered hydraulic heating system

The objective of this master’s thesis was to design and simulate a wind powered hydraulic heating system that can operate independently in remote places where the use of electricity is not possible. Components for the system were to be selected in such a way that the conditions for manufacture, use and economic viability are the as good as possible. Savonius rotor was chosen for wind turbine, due to its low cut in speed and robust design. Savonius rotor produces kinetic energy in wide wind speed range and it can withstand high wind gusts. Radial piston pump was chosen for the flow source of the hydraulic heater. Pump type was selected due to its characteristics in low rotation speeds and high efficiency. Volume flow from the pump is passed through the throttle orifice. Pressure drop over the orifice causes the hydraulic oil to heat up and, thus, creating thermal energy. Thermal energy in the oil is led to radiator where it conducts heat to the environment. The hydraulic heating system was simulated. For this purpose a mathematical models of chosen components were created. In simulation wind data gathered by Finnish meteorological institute for 167 hours was used as input. The highest produced power was achieved by changing the orifice diameter so that the rotor tip speed ratio follows the power curve. This is not possible to achieve without using electricity. Thus, for the orifice diameter only one, the optimal value was defined. Results from the simulation were compared with investment calculations. Different parameters effecting the investment profitability were altered in sensitivity analyses in order to define the points of investment profitability. Investment was found to be profitable only with high average wind speeds.

Experimentation on Wind Powered Hydraulic Heating System

It is common knowledge of the world’s dependency on fossil fuel for energy, its unsustainability on the long run and the changing trend towards renewable energy as an alternative energy source. This aims to cut down greenhouse gas emission and its impact on the rate of ecological and climatic change. Quite remarkably, wind energy has been one of many focus areas of renewable energy sources and has attracted lots of investment and technological advancement. The objective of this research is to explore wind energy and its application in household heating. This research aims at applying experimental approach in real time to study and verify a virtually simulated wind powered hydraulic house heating system. The hardware components comprise of an integrated hydraulic pump, flow control valve, hydraulic fluid and other hydraulic components. The system design and control applies hardware in-the-loop (HIL) simulation setup. Output signal from the semi-empirical turbine modelling controls the integrated motor to generate flow. Throttling the volume flow creates pressure drop across the valve and subsequently thermal power in the system to be outputted using a heat exchanger. Maximum thermal power is achieved by regulating valve orifice to achieve optimum system parameter. Savonius rotor is preferred for its low inertia, high starting torque and ease of design and maintenance characteristics, but lags in power efficiency. A prototype turbine design is used; with power output in range of practical Savonius turbine. The physical mechanism of the prototype turbine’s augmentation design is not known and will not be a focus in this study.

Control of multi-actuator system by an electrically driven hydraulic pump-motor

The awareness and concern of our environment together with legislation have set more and more tightening demands for energy efficiency of non-road mobile machinery (NRMM). Integrated electro-hydraulic energy converter (IEHEC) has been developed in Lappeenranta University of Technology (LUT). The elimination of resistance flow, and the recuperation of energy makes it very efficient alternative. The difficulties of IEHEC machine to step to the market has been the requirement of one IEHEC machine per one actuator. The idea is to switch IEHEC between two actuators of log crane using fast on/off valves. The control system architecture is introduced. The system has been simulated in co-simulation using two different software. The simulated responses of pump-controlled system is compared to the responses of the conventional valve-controlled system.

An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Reducing auxiliary power of a fluid bed boiler island

The aim of this thesis is to find and analyze different methods which reduce fluid bed boilers’ auxiliary power consumption. The objective is to examine the effects and feasibility of these methods. The literature part explains how fluid bed boilers work and what are the main sources of auxiliary power consumption. Designs and operation of these equipment are presented. The literature part also discusses the basics of auxiliary power consumption reduction and introduces four low pressure drop constructions. The experimental part inspects six different methods. Effects of these methods on the auxiliary power consumption are calculated and their impacts on the operation of the boiler are modeled. Calculations show that reasonable changes can reduce fluid bed boiler’s auxiliary power consumption by 2,1-10,2 %. Biggest reductions come from lower air coefficients, smaller bed a-level pressures and lower primary/secondary air –ratios. Models showed no problems with the smaller bed a-level pressures. With the lower air coefficients and smaller primary/secondary air –ratios the models showed a significant increase in the carbon monoxide levels.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Single-fluid two-region aqueous homogeneous reactor power plant : conceptual design and feasibility study : final report /

"Other issues of this report may bear the number BAW-7."