A Mathematical Model of Energy Conversion and a Method for Calculating the Safety Factor of a Suspension-Crossing Frame Impacted by a Broken Line

There is a risk of wire breakage and falls when constructing high-voltage transmission lines. If this occurs, it seriously endangers the safety of crossing objects. As key structures commonly used in power construction to protect crossing facilities from wire breakage, the scientific design and accurate calculation of the safety margins for suspension-crossing frames are particularly important. However, the existing energy transfer mathematical model for impact-bearing cables after conductor fracture cannot accurately describe the physical process, and the value of the fixed break impact coefficient (e.g., 2.89 for the double circuit) adopted in the design specification is not sufficiently accurate. Thus, there is a large deviation in the bearing cable safety factor, which can cause the safety margin to be either too large or insufficient, in turn seriously affecting the safe and efficient completion of cross-line construction. To this end, in this study, we first constructed a mathematical model of impact energy conversion based on the law of conservation of energy; then, we proposed an accurate method for calculating the safety factor of the bearing cable. To verify the method’s accuracy, a full-scale true wire breakage impact test was conducted. The results show that the error between the impact coefficient calculated by this method and the test result is only 6.7%, significantly better than the 38.3% error, found when the traditional design specification is used to fix the value. This method is applied to a 220 kV crossing project case. The analysis shows that, to meet the same safety requirements, the model recommends the use of Φ12 Dyneema rope, while the traditional method requires Φ16 Dyneema rope; simultaneously, for the Φ18 Dyneema rope, the maximum allowable span calculated by this method is 450 m, which is greater than the 400 m calculated using the traditional method. Thus, this method can calculate a more accurate impact coefficient based on actual working conditions, thereby significantly optimizing the selection of load-bearing cables and increasing the upper limit of span design while ensuring construction safety. Overall, the research conclusions provide important theoretical and technical support for optimizing the design and safety check of the suspension-crossing frame.