The dynamic simulation of systems is only possible when the physics of each system component is accurately represented. MARS enables the modeling of individual components which we then integrate into a full system model for which performance is simulated and calculated.
The cable of the arresting system is modeled as a continuous string of beam finite elements. This type of finite element includes tensile and bending behaviors. The cable element employs a circular cross section. Diameter, linear density (mass per unit length), axial stiffness, and bending stiffness are specified via input. The cable formulation also incorporates a damping term to simulate the effect of internal friction due to the rubbing of the strands in the cable.
It is good modeling practice to discretize the cable with short beam elements whose length does not exceed 2 inches. This fine discretization makes it possible for the cable to wrap around sheaves and the tailhook in a realistic and geometrically accurate way.
Finite element discretizaton of the cable
Beam cross section and integration point locations
In our calculational simulations, the interaction of cables with sheaves and pulleys is controlled by point-face contact algorithms. In these algorithms, the cylindrical nodes, which define the cable, cannot penetrate the faces of the sheave external surface with the radius of the cylindrical nodes equal to the radius of the cable. Typically each node is in contact with the two faces of the sheave that form a groove as shown below. The contact algorithm provides normal contact forces and friction forces. A static/dynamic friction model is used. Static friction controls the contact tangential forces until sliding occurs. When sliding occurs, the contact tangential forces are limited by the dynamic friction coefficient, which is typically smaller (0.2) than the static friction coefficient (0.3). These friction forces are responsible for turning the sheaves. Note that it is only the contact conditions that keep the cable within the sheave groove. In these simulations as in real life it is possible for cables to disengage from the sheave, either for lack of tension or due to lateral cable motion.
Contact between cable and sheave groove.
A cable engaged inside the groove of a sheave with each two-inch cylindrical cable element shown in alternating colors of blue and red.
Hydraulic devices such as engines, snubbers, and shock absorbers are modeled using special elements defined by the connecting points. The axial force developed in the hydraulic devices is defined as a function of device elongation and elongation rate. For example, the snubbers used for the dead-load car simulation employs an equation of the type
where Dp is the pressure drop, r the hydraulic fluid density, Ap the piston cross section area, vf the fluid velocity (relative velocity between piston and cylinder), Cd the form factor (=0.65), and Ao the variable orifice area. The resulting force acting on the cylinder is
F = Dp Ap.
The geometric characteristics of the hydraulic devices are used for enabling realistic graphical rendering with visualization tools.
Graphical rendering of a hydraulic device.
A sheave damper provides a mechanism for reducing peak cable tension and cable vibration. A roller bearing sheave may spin around the sheave shaft. The shaft is connected to the sheave damper by beam elements that represent the side plate, base plate, and clevis of the crosshead assembly. This approach was used for modeling the snubber-sheave assembly in the dead load car simulation.
Movable crosshead assembly and damper cylinder assembly.
Cable is sometimes reeved around sheaves of larger assemblies. Such schemes are used in aircraft cable arresting systems. As the landing aircraft drags the cable on the deck, the crosshead assembly is pulled closer to the fixed sheave assembly, compressing the cylinder and ram components of the engine. Shown is a partial model of the crosshead assembly.
Partial model of the crosshead and fixed sheave assemblies of an aircraft arresting system.
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