Research On Mathematical Model On Non-uniformly Qualitative Suspension Cable

Suspension cable is pointed to be suspended on two points, under the force of gravity presenting a curve line. Force analysis and calculation theory for an ideal suspension cable is called suspension cable theory. Catenary theory is recognized as the most effective theory reflecting to the real suspension cable, and the catenary equation belongs to the transcendental function which is difficult to use and calculate. After lots of scholars’ research and exploration, parabola theory, cable curve theory and perturbation method gradually have become the theory basis for the suspension cable research. Based on the background of Five-hundred-meter Aperture Spherical radio Telescope, suspension cable with concentrated load modeling method have been analyzed, the mathematical models have been deduced.Parabolic equation that is composed of algebraic function can be thought as the first two series approximation of catenary equation that is composed of hyperbolic function. When there is a single concentrated load dividing the cable into two segments, they spearately obey suspension cable theory. Flexible feed support mechanism is supported by six parallel cables which have a large span, and their gravity can’t be neglected, so its precise mathematic modeling is important. Each support cable installs the curtain mechanism, which can be regarded as multiple concentrated load on the support calbe. Multiple concentrated load can be converted to uniformly distributed load and also can be separated into segments according to the load. In this paper, combining the above two kinds of modeling method, according to the structure characteristics of curtain mechanism, support cable is segmented. Each paragraph support line is approximated into uniformly qualitative suspension cable,piecewise model was deduced.The accuracy of piecewise model is analyzed through the simulation and experiment.Based on ADAMS virtual prototype platform, a wire rope with multiple concentrated load is simulated. There is no module for flexible body such as the wire rope, and we need to use anexisting module and approximate restriction condition. Bushing method is used beacuse of its advantage in efficiency and accuracy which can effectively simulate different wire ropes by seting stiffness coefficient and damping coefficient of bushing. Establishing the model automatically through macros, the parabolic model and the catenary model are derived, two theoretical models both can meet the accuracy requirement, and catenary model have smaller error than the parabola model integrally.Regarding the suspension cable load ratio and span as the single valued condition,system model is scaled down at the ratio. In the laboratory a non-uniformity qualitative wire rope with multiple concentrated load is builded and modeled according to segmentation model. In the same coordinate system, the paper compares the curve with two kinds of theoretical curve and analyzes the error and its cause. According to the 3rd segment suspension cable’s data, catenary model’s maximum value of relative error is 5.16%, the minimum value is 0.38%. Parabolic model’s maximum value of relative error is 7.80%, the minimum value is 1.38%. The results show that for non-homogeneous qualitative suspension cable, deducing its piecewise mathematical model is reasonable, and catenary model is more accurate than parabolic model on describing the overhang curve. The paper’s study have a certain reference value for the mathematical model of suspension cable in the engineering application.