Dynamic express-analysis of hydraulic systems - Forming and solving of scheme math model
Forming of the scheme mathematical model and algorithm of the solution
The algorithm of forming of mathematical model of a hydraulic drive as a whole is based on its structural description as sets of making functional blocks. As already it was marked above, in a basis of the structural description of the hydraulic system the identification of functional blocks and concept that each of them has no more than four nodes (points) in which it incorporates to other blocks of the circuit (Fig. 1) lay. The binding of nodes and identification of functional blocks are realized, as is specified in tab. 1 «Classification of functional blocks of hydraulic systems» (see the section «Typical structures of hydraulic systems and their description»).
At inlet of input data their control is carried out. Following data are checked: correctness of the identifier (the name of type) of functional block; a continuity of numbering of blocks of one type; whether there is number of each block in admissible borders (proceeding from restrictions on quantity of blocks of the given type), etc. Here an input of entry conditions is made (thus all values, except for angular speed of a shaft of a diesel engine and position of a centrifugal regulator muff, are given equal to zero; angular speed a diesel engine shaft is given equal to speed of idling; position of a centrifugal regulator muff is given according to equal to the maximal value).
After that external influences and control signals given by user in the form of any functions are defined for the certain argument which can be current time or any phase variable in any node.
The external influences and control signals can be:
- regulation of geometric stroke volume of pump (volumetric regulation);
- regulation of geometric stroke volume of motor (volumetric regulation);
- spool movement of directional control valves (throttle regulation);
- control of fuel feed of diesel engine;
- resistance to machine movement;
- external forces and moments acting on working mechanism.
All these functions are simulated in the special program module either in the table form with interpolation of values during the solution, or in the form of final formula coefficients of which are given in input data or are calculated from input data.
The mathematical model of arbitrary hydraulic circuit consists as from differential, and algebraic equations. Solution of such mixed system of equations with admissible accuracy and comprehensible expenses of time of calculations is made as follows:
1) on a next time step differential equations are solved by method of numerical integration;
2) for the time moment corresponding end of a step of numerical integration, external influences, and control signals are defined;
3) proceeding from values of variables received by integration of differential equations, algebraic equations are solved.