Analysis of Nonlinear Mechanics of an Elevator Brake System
In this paper, the authors investigate the nonlinear mechanics of an elevator brake system that is subjected to uncertainties. They develop a deterministic model that relates the braking force with uncertain parameters based on mechanical equilibrium conditions. The goal is to account for parameter variabilities and analyze the influence of uncertainties on the system’s response.
The authors employ a parametric probabilistic approach to incorporate the random nature of the uncertain parameters. In this stochastic formalism, the uncertain parameters are modeled as random variables, with distributions specified by the maximum entropy principle. This approach ensures that the uncertainties are represented by the highest entropy probability distribution, which provides a reasonable representation of the unknown information about the parameters.
To characterize the response of the elevator brake system under the influence of uncertainties, the authors utilize the Monte Carlo method. This method involves generating a large number of samples for each uncertain parameter, each drawn from its specified probability distribution. These samples are then used to simulate the system’s behavior multiple times, resulting in a statistical characterization of the response.
The results obtained from the Monte Carlo analysis provide valuable insights into the system’s performance under uncertainties. By considering the optimum design of the brake system, the authors formulate and solve nonlinear optimization problems, both with and without the effects of uncertainties. This allows for a comprehensive evaluation of the system’s behavior and performance in different scenarios.
Overall, this paper contributes to the understanding of nonlinear mechanics in elevator brake systems and provides a framework for incorporating and analyzing uncertainties. The combination of the parametric probabilistic approach and the Monte Carlo method enables a detailed statistical characterization of the system’s response, facilitating better-informed decision-making in design and optimization processes.