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Summary This paper addresses a sustainable facility location‐allocation problem under uncertain environment with considering economic and sustainable dimensions simultaneously. We establish three types of belief degree constrained mathematical models to investigate the problem under the optimistic value criterion, the pessimistic value criterion, and the Hurwicz criterion. The corresponding crisp determinants of the models are derived, and several properties of the models are also discussed. The theoretical analysis demonstrates that the optimal objective values of the models crucially depend on the predetermined confidence level given by decision makers. What's more, the total cost of the problem in the belief degree constrained Hurwicz criterion model decreases as Hurwicz coefficient becomes larger. To evaluate the performance of our novel models, several numerical examples are conducted. The numerical results are obtained by using the standard optimization software LINGO.

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A planetary thread roller bearing (PTRB) is a state-of-the-art component in electromechanical actuators (EMA) due to its high load-bearing capacity and small volume. The study of the PTRB is a leading task in the domain of EMA application. In this study, we propose a mathematical model of PTRB friction torque on its working principle and causes. Specifically, the impact of basic properties of the PTRB on friction torque, i.e., rotating speed and external load, are modeled and analyzed. To verify the variation principle of friction torque, experiments are carried out on an actual PTRB. For the test PTRB, the rotating speed ranges from 200 to 2000 rpm with a reverse load from 2000 to 30,000 N at a constant temperature of 55 °C. Experimental results verify the effectiveness of the mathematical model under conditions of 200–2000 rpm rotating speed and 2000–30,000 N external load, which establish strong evidence for model accuracy and robustness.