Математическая модель связи "винт-гайка" для универсальных программ анализа динамических систем

The article deals with a mathematical model of the "screw-nut" connection adapted for using in universal software systems to analyse dynamic characteristics. This article is sequel to a number of earlier authors-written articles devoted to object simulation of 3D mechanics. Such a model available in the library of mathematical models of the modelling system will significantly extend the list of simulated mechanisms. The mathematical model of "screw-nut" connection suggests such a connection between absolutely rigid bodies. The "screw-nut" connection parameters are the following: thread pitch by the radian of the angle of pitch; coordinates of the point on the axis of the screw in the local coordinate system of the body 1; direction cosines of the screw axis in the local coordinate system of the body 1. Note that the connection parameters have constant values. Two drawbacks of this model should be noted. 1. Some expressions of the mathematical model involve dividing by direction cosine  of the screw axis thereby eliminating "division by zero" when the axis of the screw is perpendicular to the x -axis of the global coordinate system. The software-based way allows eliminating this shortcoming. 2. The model does not include coordinates of mass centres of bodies tied by connection. This can lead to a significant "mismatch" in the position of the bodies in modelling of multi- periodic transient processes. However, adding an elastic model to the mathematical model can eliminate this drawback. The article demonstrates the "screw-nut" connection model to simulate a jack using the PA8 system and comparing its results with those obtained with help of the NX10 complex. Gives, in addition, the results of influence in terms of dry friction in the "screw-nut" connection. Taking into consideration the dry friction allows us to reflect the effect of "self-stopping" in the jack.