Software for Fluid Power Technology

1. Introduction

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        Fluid power systems, in which working pressure (pressure in pump output) is kept proportional to load, are called hydraulic load-sensing systems. Such systems are mainly used in mechanisms containing numerous drives to run with the purpose to save energy. Hydraulic load-sensing systems are automatically regulating systems with a number of components and several feedbacks. It is difficult to find optimal solutions for their static, steady-state motion and dynamics. A very precise parameter setting, especially for resistances of hydraulic valve spools and for spring characteristics, is required to make the system function.
As a result of current research, a simulation system is proposed that enables one to perform computer experiments at the first stage of design.
Theoretical fundamentals of the approach have been described in (Grossschmidt et al., 2009).

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At the first stage of the research the initial scheme of the hydraulic load-sensing system of Bosch GmbH has been modelled and simulated. Examples of modelling and simulation of this load-sensing system were discussed in (Grossschmidt et al., 2006). In the initial scheme feeding pressure of the controller was taken from the output of a variable displacement hydraulic pump. But the pressure in the pump output depends on the load and resistance of the system. Therefore the behaviour of the load-sensing system depends on the output pressure of the hydraulic pump. To get better results, it was necessary to improve the model.
A modified scheme of load-sensing system is proposed (Fig. 1), in which the controller has an independent constant pressure feeding. Feedback pressures have been taken directly from the measuring valve with pressure compensator RIDVW.
The scheme of hydraulic-mechanical controller is shown in Fig. 2 and the section of the valve block in Fig. 3.


        In Fig. 1, the variable displacement axial piston pump is driven by an electric motor M. Hydraulic- mechanical control of the pump volumetric flow is performed by a control valve and positioning hydraulic cylinder of the swash plate. The feeding chain of the hydraulic motor RVerbr contains tube RL-zu, pressure compensator RIDW, measuring valve RVW, check valve, meter-in throttle edge RSK-zu and connection elements. The output chain of the hydraulic motor RVerb contains a meter-out throttle edge RSK-r, and tube RL-ab. The device contains load-sensing pressure feedback.
The scheme of a hydraulic-mechanical controller (Fig. 2) contains a control valve (effective area AV) with meter-in and meter-out throttle edges, local hydraulic resistor (volumetric flow QDr), positioning cylinder (effective area AZ), and swash plate with spring.
The main part of the valve block (Fig. 3) is a directional valve with measuring throttle edge RVW, meter-in throttle edge RVS-zu and meter-out throttle edge RSK-r of hydraulic motor. The valve block also contains pres- sure compensator with throttle edge RIDW and check valve causing pressure drop 0.5 bars.

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        To build up the multi-pole model it is necessary to decompose the load-sensing system into subsystems and components.
The hydraulic-mechanical controller subsystem includes control valve, meter-in throttle edge, meter-out throttle edge, local hydraulic resistor and positioning cylinder with swash plate.
The valve block subsystem includes a measuring valve with pressure compensator, check valve, meter-in throttle edge and meter-out throttle edge of the hydraulic motor.
The hydraulic pump subsystem includes a variable displacement axial piston pump together with electric motor and clutch. The hydraulic motor subsystem includes a hydraulic motor together with meter-in and meter-our throttle edges and clutch with drive mechanism.
The system includes tubes and tube connection elements as well.
        Multi-pole models of all the components must be composed. The multi-pole model of the load-sensing system is built up using the components models. First, necessary components must be connected through poles. Second, variables of connection poles must be defined as inputs or outputs for every component depending on required oriented causalities (Grossschmidt et al., 1998, 2000 and 2003).
        All the multi-pole models of the load-sensing system components have been described as CoCoViLa (Grigorenko et al., 2005 and 2006) classes together with their icons and images. Relations (formulae) between variables of multi-pole models are described as equations or as user-defined Java methods. In relations state variables, inner iterations, logical conditions and CoCoViLa subtasks are used for describing the behaviour of the component.
The multi-pole model (Fig. 4) represents the scheme of the load-sensing system (Fig. 1).
The next step after configuring the hydraulic load- sensing system is parameters specification.
Firstly, the hydraulic motor and hydraulic pump parameters must be chosen. An axial piston hydraulic motor with a working volume V = 40 x 10-06 m³/rev has been taken. An axial-piston variable displacement pump with a maximum working volume V_max = 63 x 10-06 m³/rev, a nominal rotation frequency n_nom = 1475 min-1 and a maximum displacement angle of the pump swash plate α_max = 0.3264 rad have been taken.
Secondly, the fluid and its properties must be chosen. The oil HLP46 was chosen.
        Third, initial approximate values of pressures and pressure drops for pump control must be set. Maximum working pressure p_max = 250 bar, pressure drop in measuring valve Δp_IDW = ~5...7 bar, pressure drop in measuring    valve    with    pressure    compensator Δp_IDVW =~14...19 bar, pump control system feeding pressure p₀ = 60 bar and pump control pressure p_CP = ~4...19 bar were used.

Fig. 4: Multi-pole model of the hydraulic-mechanical load-sensing system

Fourth, maximum displacements of the valves must be set. Maximum displacement of the pump control valve y_V = 0.003 m, maximum displacement of the directional valve y_VW = 0.007 m and maximum displacement of the pressure compensator y_IDW = 0.007 m have been taken.

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        In this section mathematical models implemented as multi-pole models of the components of the load sensing system are presented. Values of parameters presented in the section were obtained from performed simulations. The initial values for iteration calculations, which have been found from stationary calculations, correspond to displacement of the direction valve 0.0045 m and load moment 65 Nm.

4.1    VP - Displacement of the Control Valve

Static displacement of the control valve                  
where     A = π D² /4;     F_f    = F_f0    + k_f    (p₁+ p₂) /2.

Difference of control valve velocity v


Difference of control valve displacement y
Parameters: D = 0.008 m, F_{f 0} = 0.3 N, k_f = 1E-7 m², c = 8377.5 N/m, y0    = 0.00846 m, m = 0.02 kg, h = 1200 Ns/m. Initial value: inity = 1.5819E-3 m.

4.2 RVP - Meter-in Throttle Edge of the Control Valve

Output pressure
where TR = 1 / (μ²A₁²) + 1 / (μ²A₂²)
A₁ - longitudinal area of two identical slots,
A₂ - sectional area of two identical slots.
Scheme of the meter-in throttle edge of the control valve is shown in Fig. 5.

Fig. 5: Scheme of the meter-in throttle edge of the control valve

Geometrical relations: y_S = y+l0,
h = y_S (if y_S <= h_max), h_max= R (1 – cos ((90 - β) π / 360)) l = R_α  l_max = R_αmax,

A₂ = 2 (5e-08 + dg)

Output volumetric flow Q^₁ = Q₂.    (5)
Parameters: D = 0.008 m, μ = 0.8, R = 1.1E-4 m, β = 0.30, l0 = 5.6E-4 m, g = 0.001 m.
Initial value: init p₂ = 1.1806E6 Pa.

4.3 RVT - Meter-out Throttle Edge of the Control Valve

4.4    ResG, ResH, ResY – Local Hydraulic Resistors Output pressure of local hydraulic resistor ResG

4.5    IEH1-3 - Hydraulic Interface Element

The hydraulic interface element expresses:

5. Computing Process Organization

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Using visual specifications of described multi-pole models of fluid power system components one can graphically compose models of various fluid power systems.
It is possible to solve a number of various computing tasks on each fluid power system model evaluating some components as inputs and computing some other components as outputs. When solving specific simulation problem, the model has to be adjusted by evaluating different parameters of the elements and adding sources to elements of the model that describe disturbances of necessary shape and value.
When simulating steady state conditions behaviour of some parameter of the fluid power system is calculated depending on the change of some other parameter of the system.
When simulating dynamic behaviour, transient responses caused by disturbances are calculated. Disturbances are considered as changes of input parameters in certain points of the hydraulic system (pressures, volumetric flows, load forces or moments, control signals, etc.). Disturbances of different shapes are considered, such as constant, step, impulse, sine, linear, etc. Calculations of dynamic responses are performed in time. Time step length and number of steps are to be specified. In all dynamic calculations the fourth-order classical Runge–Kutta method has been used.
Steady state and dynamic computing processes are organized by corresponding process classes. To follow the system behaviour in time, the concept of state is invoked. State variables are introduced for each functional element to characterize the element at the current simulation time step. The simulation process starts from the initial state and includes calculation of following state (nextstate) from previous states (usually from oldstate and state). Final state (finalstate) is computed as a result of simulation.
For solving a specific simulation task on the fluid power system model the CoCoViLa program synthesizer is used for automatic construction of the problem solving program.
We use a special technique for calculating variables in loop dependences. We split the variable, assign it an initial approximate value and try iteratively recompute the variable. Recomputing algorithm can be synthesized by the CoCoViLa program synthesizer. Splitting the variable, assigning an approximate value and asking CoCoViLa to find algorithm for recomputing must be described in the multi-pole model of the fluid power system component.
Variables with index “e” are obtained as results of iterations.

6. Modelling and Simulation Stages

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        The following steps must be performed for simulation both steady state conditions and dynamic transient responses.
First, all the models of components must be tested separately. For every component the simulation task must be composed and input signals must be chosen. Behaviour of the component must be simulated. Initial approximate components parameters values (e.g. etc.) must be refined as a result of simulation. Stiffness of springs, geometry of valves working slots, etc. must be refined for steady state conditions. Dynamic resistances, time constants, damping constants, etc. must be refined for dynamics.
        Second, the separately tested components models must be connected into sub-systems, tested in behaviour and adjusted.
Third, the whole load-sensing system must be built up, simulation tasks must be solved and the parameters must be adjusted.

7. Simulating Steady State Conditions

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  Fig. 14: Simulated dependences on the displacement of the directional valve (load moment 65 Nm)

  Fig. 15: Simulated dependences on the load moment of the hydraulic motor (displacement of the directional valve 0.0045 m)

8.    Simulating Dynamics of the Load-Sensing System

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