Dynamic instability of the flight control connecting rod in technological tests

For technological control strength of the flight control connecting rod (further rod) selective destructive tests of ready details in static and pulsating axial loads are used. In order to decrease the time and to use non-destructive control methods rods are tested on the experimental installation, which has the two-mass oscillating system. The oscillating system consists of a rod with two identical tipweights and hanging on a thin steel string vertically. A rod under action a longitudinal force P ( t )= = P cos Ω t has the resonant longitudinal oscillations which occur in actual use. A rod is the resonant longitudinal oscillations for the second natural form. The first natural form corresponds to the movement of a rod with end loads as a rigid body and has no practical interest. Experiments showed that there is a dynamic instability in the form of parametric resonance of longitudinal oscillations. In this case, besides the longitudinal oscillations further transverse (bending) oscillations appear. It is interesting to determine the conditions for the emergence of parametric resonance of a rod in the process of technological tests. The analytical solution of the problem results in the Mathieu’s equation. The results of solving this equation for various combinations of the coefficients of the equation represented as Ince-Strutt diagram. The calculation of the Mathieu’s equation of the rod with dimensions D × d × l = 35 × 32 × 1200 (mm) shows that at operating stress of 10 MPa the rod works in the zone of dynamic instability. This fact is confirmed experimentally. Experiment with the short rod by dimensions D × d × l = 25×22×600 (mm) showed that the rod is experiencing longitudinal oscillations without transverse oscillations up to stress 68 MPa. Thus, the short rods have a bigger range of working stresses at the experimental installation. The Mathieu’s equation is valid for all rod sizes. The equation allows determining such parameters of the oscillating system, in which the rod would experience only the longitudinal oscillations, which takes place in real conditions.

simulation, dynamic stability, Mathieu’s equation, Ince-Strutt diagram, flight control connecting rod