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A design criteria is developed for the axial length effect of pressurized multiple layered spiral wound hose with clamped end couplings. Upon application of hydraulic pressure, the hose section in the vicinity of the clamped end is assumed to deform from a right circular cylinder to a truncated cone with constant wire helix angle. The solution obtained from solving equations of equilibrium for a single naturally curved thin rod experiencing small axial deformation is used to piece-together a layer solution which in turn is plied-up to form a complete hose. Continuity of solutions at the interface of the conical and cylindrical regions is enforced. This enabled transition zone length (axial length of cone) to be expressed as function of hose geometry. Both four and six-layered hose with inside diameters 1.0, 1.25, and 2.0 inches (25.4, 31.8, and 50.8 mm) are considered.

A simple one dimensional radial displacement plane stress analysis is used to establish new equilibrium states at each of eight significant thermal and mechanical manufacturing stages of spiral hose fabrication. Individual effects are assumed additive. Cumulative layer hoop stress is used to approximate off-angle helical wire tension in the cured mandrel-free composite. These locked-in fabrication tensions are then superimposed on previously obtained thin shell laminate finite element results for a representative pressurized hose type. On an average, the locked in pre-tensions amounted to almost twenty percent of finite element generated pressurized tensions. Consequently, effective hose design must include both fabrication and working pressurized consideration.

Thick wire reinforced braided hydraulic hose is modeled as an equivalent thin-shell laminate consisting of alternate unidirectional sublayers. Stacking sequence and helical orientation of the sublayers are described both by a symmetric and an overlapping laminate. A knock-down factor, wire misalignment, is also applied to each model. Gough-Tangorra micromechanics is used in conjunction with a linear finite element code to solve for stress-strain behavior of the symmetric laminate throughout the hydraulic pressure range from an unloaded state to minimum burst conditions. Classical laminate theory is developed and applied to the overlapping model since the finite element code is not directly applicable. Both models exhibit satisfactory agreement with experimental data and output from a set of theoretical nonlinear equations. In addition, computed hose axial stiffnesses agree with those measured from static dead-weight loaded hose sections.

Multiple layered high pressure helically wound wire reinforced elastomeric hose are experimentally tested over a wide range of application pressure, hose size, construction, and type (spiral, braided, and combinations of spiral-braided). A mathematical model and computer analysis is presented which adequately fits the data for both radial and axial deformation and hose rotation as a function of hydraulic pressure. Net coupling torque, interlamellar pressure, and wire tension are also computed. Initial unpressurized parameters braid diameter and angle, wire dimensions, mechanical strength, and number of wires per layer are input data into the theoretical equations and can be varied throughout their practical range in search of the optimum hose design.

In practical operation, serpentine belts are subjected to parametric excitation caused by tension and translation speed fluctuations from pulley rotations and crankshaft speed oscillations. Each of these excitation sources has spectral content at multiple frequencies and arbitrary phases. Stability boundaries for primary, secondary, and simultaneous primary/secondary parametric instabilities are determined analytically. The classical result that primary instability occurs when one of the excitation frequencies is close to twice a natural frequency changes as a result of multiple excitation frequencies. Unusual interactions occur for the practically important case of simultaneous primary and secondary instabilities.