The torque load spectrum is an important basis for the strength design and durability test verification of tractor power take-off (PTO), and the performance and reliability of tractor PTO directly affect the quality and efficiency of agricultural operations. In this paper, taking the PTO torque load as the object, a PTO loading method based on the dynamic load spectrum acquired in the actual field work was proposed in this paper. Based on the Peak Over Threshold model, the extrapolation of the PTO load spectrum was realized, and the load spectrum throughout the whole life cycle was obtained. On the basis of this, the mobile tractor PTO loading test bench and Fuzzy-Proportional-Integral-Derivative (Fuzzy-PID) controller were developed to achieve the dynamic loading of the PTO load spectrum, and the dynamic characteristics were analyzed and verified by the simulation and laboratory test. The results showed that with the time domain extrapolation method, the load extreme value was expanded from (63.24, 469.50) to (60.88, 475.18), and the coverage was expanded by 1.98%. By comparing with the fitting results, statistical characteristics and rain flow counting results, the load spectrum extrapolation method was effective. In addition, the response time of simulation and laboratory test were 0.05s and 0.75s, respectively; the maximum error was 1.77% and 4.03%, respectively; and the goodness of fit was 16.78 N·m, which indicated that the PTO loading test bench, can accurately restore the dynamic loading of the tractor and the Fuzzy-PID controller had better accuracy and stability. It would provide a reference for the practical application of PTO load spectrum of the tractors.

A detailed understanding of the mechanistic role of solid surface microstructures in modulating capillary forces and liquid transport in liquid bridge systems is crucial, for liquid bridges between rough surfaces are omnipresent in nature and various industries. In this work, Gibbs free energy expression was derived for a liquid bridge system confined between a smooth surface and a microstructured surface, based on the principle of minimum thermodynamic potential. Furthermore, by analyzing the energy conversion during spacing variation between the two solid surfaces, an analytical expression for the capillary force of the liquid bridge was derived that incorporates the geometric parameters of the microstructures and the contact angle. Finally, numerical simulations were performed using the Fluent UDFs (User-Defined Functions) to validate the proposed capillary force model. The simulation results validated the analytical expression and revealed the influence of the microstructures on the force distribution on the upper and lower surfaces of the liquid bridge, and on the droplet transport performance.