A servovalve is necessary for precise positioning in this hydraulic system. The PI (proportional integral) controller positions the actuator. It uses a table to program the position commands and model solenoid response. A stiff spring provides the load.
 
Each component has a data table that holds its operating characteristics. For instance, the table shows that pipe PI has a length of 600 cm (LEN_PI=600 cm) and diameter of 1 cm (DH_PI=1 cm). The table's other characteristics are not used in the example.
 
Subsystem models and components such as accumulators are represented by ISO1219-compliant icons. Each contains parametric data that defines system properties as well as equations that define the dynamics.
 
Picking on any component, a pipe in this case, reveals an information window for characterizing the component's behavior. The software establishes a bidirectional flow of several characteristics.
 
Several tables define heat-transfer dynamics for the heat exchanger's primary fluid. In this case, the table describes the heat transfer coefficient (W/m2/°C) as a function of airflow in kilograms/min. Users can add and change values.
 
The resulting plot tracks the command versus actual position of the actuator. The large gap between the graphs indicate response is sluggish and, hence, unacceptable.
 
Several plots with the optimized gain setting show the actuator's command and actual position versus time. The closer tracking indicates improved system performance. Plots of fluid temperature and pressure on both sides of the actuator piston are also generated, demonstrating the simulation's ability to calculate internal data for each component.

Joel Tollefson
MSC.Software Corp.
Santa Ana, Calif.

Hydraulic systems have been difficult to simulate because they include complex and diverse components with highly nonlinear and discontinuous dynamics. To get around these problems, engineers build low-fidelity models based on oversimplifications using linear approximations that frequently disregard a system's physics. But this often leads to costly engineering changes and multiple physical prototypes.

The latest ideas embodied in MSC.Easy5, a simulation and modeling program, provide a solution by letting engineers build accurate physics-based models of hydraulic systems, as well as multidisciplinary systems. These can include mechanical, electrical, thermal, pneumatic, powertrain components controlled by digital and analog systems.

Working though a simple example may be the best way to get a feel for how the new software works. The example has a hydraulic power supply, heat exchanger, hydraulic actuation, and a control system. This type of circuit is found on equipment that needs precise positioning and high power, such as aircraft control surfaces, machine tools, robotic assemblers, and heavy construction equipment. A more complex system could include digital controllers and electric motors on the hydraulic pump, but these were omitted for simplicity. The software includes libraries for modeling hydraulics, electric drives and motors, powertrain systems (gears, clutches, shafts), pneumatics, and control systems.

A drag-and-drop method lets users quickly assemble components into the hydraulic system. In fact, the task can be summarized in three steps:

  1. Build the model
  2. Trim and size the system
  3. Run transient simulations and optimize performance

Building the model

A thermal and hydraulic library in the software includes over 115 ready-to-use models of hydraulic subsystems for simulating compressible-fluid dynamics, mechanical dynamics, and heat transfer. What's also included, but not found in other hydraulic software, are the highly nonlinear and discontinuous dynamics of flow reversal, laminar and turbulent-flow transition, Coulomb friction with stiction, cavitation, water-hammer dynamics, and mechanical hard limits.

Working with the library's gas-charged accumulator shows how to select components and build systems. Simply dragging the icon for an Adiabatic Accumulator Gas Charged (model AB in the library) to the work area places the model onto the schematic. A pipe model connects the accumulator to the system.

Blue circles designate storage ports on components, and red circles designate resistive ports. The color coding prevents backward installations. Mouse clicking on a resistive port and then on a storage port makes connections between parts. The software makes the connection and correctly sets up the data flow. The single connection line to the accumulator is bidirectional, so data flows in both directions.

Components and connections are added as needed to finish the model. A Global Fluid Properties icon contains a database of 19 fluids, which can be expanded to include custom fluids. Users can also define a particular fluid and multiviscosity fluid properties (when present), an ambient temperature, and even a quantity of entrained air to see how the system might react to, for example, air in a brake line. The simulations also allow fluid aging factors to simulate old oil. Once fluid properties are defined, they're used throughout the model.

The heat exchanger in the schematic appears as two units in the model because it uses hydraulic fluid on the primary side and air on the secondary.

Building executable code

Users must create executable code before running a simulation. It's only done once. The software sorts code for each component, creates and compiles source code for the entire model, and links to necessary object files. This method has advantages over those that use interpretive code. For example:

  1. It runs faster because it is compiled and optimized. Advanced users can enter Fortran and C as inline code directly into the model. They could, for example, add code to control a variable-orifice opening.
  2. It makes debugging source code easier.
  3. It can directly link user-built object code with MSC.Easy5, so previous development efforts are not lost. This feature would also allow building complex systems as a series of smaller subsystems that could be stored and reused.

Users must define other system properties, such as dimensions, fluid type, and operating conditions such as pressures and temperatures. A data table associated with each component holds operating data such as input parameters, output states, variables, and connection data.

Before running a simulation, the system must calculate a steady-state operating condition. The steady-state operating point is the condition in which all system pressures and forces are balanced, and dynamic rates are zero -- there is no motion. Ordinarily, running simulations to obtain steady-state points is inefficient and time consuming. For example, the lowest frequency of this system is slow, about 0.001 Hz, so finding the steady-state point could take the better part of an hour. A Steady-State Toolkit in the software, however, calculates steady-state initial operating conditions in seconds. Steady-state-data values are calculated and easily loaded into models.

The heat exchanger's cooling airflow must also be sized so the hydraulic fluid does not exceed its recommended maximum operating temperature (55°C). Other simulation methods might require hundreds of simulations to size the blower. The Steady-State Toolkit instead allows varying a model parameter to calculate the steady-state condition for several operating conditions.

In addition, systems should be stable before running simulations. System stability is determined by running the Linear Model Generator program, which calculates system eigenvalues (dynamic modes of the system). In this case, the software calculates 25 eigenvalues to show the system is stable (no positive real values), with the highest mode frequency at -232,231 rps. This large figure indicates high stiffness, a type of system that was previously difficult to solve. Large frequencies, typical of hydraulic systems, are a result of the compressible fluid dynamics in small volumes, such as in valves.

Ready to roll

The Simulation Data Form defines parameters and formats the output data. Users select a simulation start and stop time and a type of integrator. The example uses the default BCS Gear method. Selecting Execute runs the simulations in the background. When finished, the software plots the data.

The output plots show the actuator not following the command position. One way to improve controller response is to increase the gain on the PI (proportional integral) controller. In systems past, PI-controller gain would be increased and the simulation repeated -- sometimes hundreds of times -- until performance improved. A better way to find the optimal gain is with the software's optimization tools. Results of the optimized gain appear in accompanying plots.

Simulation performance and accuracy is affected by the type of integrator and integration step size. Because hydraulic systems are nonlinear and discontinuous, variable-step-size integrators tend to work poorly. As a result, fixed-step integration methods, such as the fourth order Runga-Kutta method, are generally used. However, fixed step methods are also inefficient for stiff (high-frequency) hydraulic systems. For example, this model's highest mode frequency, 232,231 rps, requires a fixed-step integrator step size of about 1 X 10-5 sec. Such a system would take several hours to simulate by traditional methods.

Despite nonlinear and discontinuous events, special integration techniques resolve the problem by using a variable integration method. The proprietary BCS Gear integration method works best because it is a variable-step method that has been optimized for fluid-power systems. The sample model ran for 8 sec, using BCS Gear. It needs only 0.5% of the time used by the fixed-step method. Even when run on relatively slow Pentium III 700-MHz processors, the hydraulic simulation finished in 33% of the time needed for a physical test to collect the same information.

Make contact:
MSC.Software, (714) 540-8900, www.mscsoftware.com