Static analysis is calculation of stationary mode at which position of control and regulation bodies of spools of directional control valves, variable displacement pumps, hydraulic motors, throttles is fixed; pressure, flows of liquid, speed of rotation of shafts of diesel engine, pumps and hydraulic motors, speeds of movement of pistons of hydraulic cylinders, shaft moments of diesel engine and hydraulic motors, forces acting to rods of hydraulic cylinders are constant; speeds of mobile parts of valves and hydraulic accumulators are equal to zero.
Static calculation is the basic stage at designing hydraulic drives and transmissions of various machines and mechanisms. On a basis of results of static calculation synthesis of the hydraulic circuit and selecting of elements of the certain standard size carry out.
For construction of equations of statics of hydraulic system the same method, as for dynamics is used. It is based on representation of hydraulic system in the form of finite element-node structure . The complex system always can be divided into separate functional elements which mathematical description is known and for which within the limits of considered system it is possible to define unequivocally conditions of communications of these elements with each other ( input –output ) conditionally. Then for description of the system as a whole it is enough to specify a name (the identifier of type) of element , to number its nodes in input and output, to give necessary physical, geometrical and design data (constants) and to write down the equations, transforming variables in input of element in variables in output.
As such base elements in hydraulic systems can be: pump, hydraulic motor, hydraulic cylinder, valve of direct action, valve of indirect action, local resistance (throttle), pipeline (including, deadlock site of pipeline or cavity ), tee ( divider or adder of flows ), power regulator , hydraulic accumulator , pilot operated check valve , diesel engine with centrifugal regulator , wheel carrier .
Then the structure of any arbitrary hydraulic circuit can be described by means of identification of elements, numbering of nodes (points of connection of elements in the circuit by principle input – output ) and forming on a basis of it matrices of communications describing structure (topology) of the circuit. Thus, for simulating of dynamic processes in hydraulic systems of arbitrary structure are necessary:
– algorithm of the structure description of arbitrary hydraulic circuits;
– library of base hydraulic elements and their mathematical models;
– ordering of input data, and way of their forming and preparation;
– algorithm of automatic forming of system of equations describing the hydraulic circuit of arbitrary structure as a whole;
– method of solving of generated system of equations;
– program realization of dynamic analysis of arbitrary hydraulic circuits;
– way of representation and analysis of received results.
The program analyzes the input information and depending on set of elements and structures of investigated hydraulic circuit chooses from library of base hydraulic elements and their mathematical models the necessary equations, forming the general mathematical model of hydraulic system and solving it at the given external influences.
Contents >> Engineering Mathematics >> Hydraulic Systems >> Static Analysis >> Introduction