Mathematical Modeling of the Braking System of Wheeled Mainline Aircraft

The braking system of the landing gear wheels of a mainline aircraft has to meet mandatory requirements laid out in the Aviation Regulations AP-25 (Para 25.735. «Brakes and brake systems"). These requirements are essential when creating the landing gear wheel brake control system (WBCS) and are used as main initial data in its mathematical modeling. The WBCS is one of the most important systems to ensure the safe completion of the flight. It is a complex of devices, i.e. units (hydraulic, electrical, and mechanical), connected through piping, wiring, mechanical constraints. This complex should allow optimizing the braking process when a large number of parameters change. The most important of them are the following: runway friction coefficient (RFC), lifting force, weight and of the aircraft, etc. The main structural elements involved in braking the aircraft are: aircraft wheels with pneumatics (air tires) and brake discs, WBCS, and cooling system of gear wheels when braking.

To consider the aircraft deceleration on the landing run is of essence at the stage of design, development, and improvement of brakes and braking systems. Based on analysis of equation of the aircraft motion and energy balance can be determined energy loading and its basic design parameters, braking distances and braking time.

As practice and analysis of energy loading show, they (brake + wheel) absorb the aircraftpossessed kinetic energy at the start of braking as much as 60-70%, 70-80%, and 80-90%, respectively, under normal increased, and emergency operating conditions. The paper presents a procedure for the rapid calculation of energy loading of the brake wheel.

Currently, the mainline aircrafts use mainly electrohydraulic brake systems in which there are the main, backup, and emergency-parking brake systems. All channels are equipped with automatic anti-skid systems. Their presence in the emergency (the third reserve) channel significantly improves the reliability and safety of the aircraft braking mode with a slight increase in weight and complexity of the system.

Mathematical modeling of the WBCS is intended to provide the possibility for studying the effect of various parameters on the braking process, choice of a rational law of the anti-skid automatics and minimization of the brake way on the runway in designing the WBCS, and its certification for compliance with AP25 under normal operation and in appearing of credible failures. The article presents differential equations of motion of the braking system of the aircraft landing gear wheel, which is an electro-hydraulic actuator to form the braking torque Мт, depending on the control signal Uу. The actuator comprises a remote control system of pressure and multi-disc friction brake. This mathematical model of the braking system of aircraft landing gear wheel allows us to study the braking process in a wide variation range of different parameters both of the braking system itself and its components, and of the aircraft parameters, runway conditions, and anti-skid system parameters, i.e. it provides an optimized braking process in conditions of changing a large number of different parameters the most important of which are: RFC, lifting force and aircraft weight; speed of the aircraft; parameters of the WBCS hydraulic units, etc.

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