# Mathematical model of a passenger aircraft's emergency turbo-pump system drive

### Аuthors

Ionov V. A.1*, Lobkova L. A.2**, Makovetsky M. B.3***

1. Company «KEH eKommerc», 7, Lesnaya str., Moscow, 125047, Russia
2. Company «Kronshtadt», 18, Andropov avenue, bld. 9, Moscow, 115432, Russia
3. Company "Teсhnodinamika", 35, Bolshaya Tatarskaya str., build. 5,Moscow, 115184, Russia

*e-mail: vawsan@mail.ru
***e-mail: MakovetskiyMB@tdhc.ru

### Abstract

The paper tackles the problem of energy delivering to the onboard hydro system of an emergency turbo-pump station. This hydraulic energy is being fed into airflow by the air actuator. The turbo-pump station provides feeding for aircraft driving actuators before auxiliary power set is activated and main engines are started.

Output actuator should function without strike loads on reinforce mechanism of turbine, and without damage of aircraft structure. The pump station nominal functioning start needs 1 or 2 seconds, while total time period for the total hydraulic system action starts functioning in nominal mode is 6 to10 seconds.

Air hydraulic system, which provides station starting, has essential advantages compared to the previous emergency sources of hydraulic feeding.

Air hydraulic system needs no energy system power, its weight and size are smaller, and it is autonomous.

The article proposes the actuator mathematical model. The model is based on the gas state equations.

The coefficient of gas rate, pre-critical and post-critical gas flow depend on the vent gas flow geometry. Moving liquid volumes, liquid density, moving structure elements mass, spring stiffness, loading actuator level are accounted for.

The liquid consumption balance equation is used to describe the hydraulic cylinder action. Constant and variable throttles regulate fluid consumption. The liquid pressure gradient for these throttles depends on spring stiffness.

The results of modeling are presented as curves for the hydraulic cylinder plunger movement process, and liquid pressure in the hydraulic cylinder. Plunger movement velocity surge and plunger pressure surge are characteristic for initial period of actuator operation.

### Keywords:

emergency power supplies, turbo-pump unit, power supply block, hydraulic system, power supply autonomy, transient

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