- information on structure of the considered hydraulic circuit; - information about physical and design data of the hydraulic circuit elements.
The first part of the input information is formed according to the method of the
structure description of hydraulic circuits
stated above, based on
classification
of base hydraulic elements, introduction of the generalized three-node element with nodes
(output) and
j
(control, transformation of energy, supply or taking away of power). On a basis of the entered classification each hydraulic element has received the certain identifier
k
, designating type of element and unequivocally defining group of equations for mathematical description of the given type element. According to it special forms (tables) of input data have been developed.
е
Each element (except for directional control valves) is described by the line of table of input data having the following structure: (38)
where
– matrix-line of coefficients describing physical, geometrical and design data of the element that makes the maintenance of the second part of the input information.
А
At elements having only two nodes (for example, throttle, pipeline, diesel engine) the third node is designated by zero. Number of element
As already it was marked above, the unique element which is dropping out of the concept of a three-node element is a directional control valve as a number of nodes adjoining it can be more than three. Therefore its description differs from other hydraulic elements. After numbering nodes of directional control valve it is necessary to write down in pairs numbers of nodes of its channels in various positions of spool, and the order of following of nodes (input-output) for each channel of spool is defined by direction of flow of working liquid. Thus change of direction of flow at change of position of spool can occur not in whole circuit. For example, in pressure head and drain lines of the directional control valve the direction of flow does not vary. Therefore for account of the direction of flow in node for each connection alongside with number of node it is necessary to specify a sign on flow in this node which is defined by the accepted positive direction of flow in a pipeline adjoining the given node. Each connection of nodes of directional control valve represents local resistance with variable area of through passage section depending on position of spool (Fig. 4). In view of these features the tables for directional control valves with other structure have been developed: (39)
where
– number of the directional control valve;
– numbers of nodes of input (
n
) and output (
i
) of connections 1...,
j
N
;
– matrix-line of coefficients describing physical and design data of the directional control valve;
A
– a matrix of areas of through passage sections of connections 1...,
F
N
as function of the directional control valve spool movement
z
, and besides
z
is function of time, or function of some parameter (for example, pressure or movement of hydraulic cylinder piston, etc.).
Representation of input data in such kind allows to make the uniform description of the circuit as switching of a spool from one position in another will automatically define the scheme of connections of elements.
For forming of mathematical model of hydraulic system dynamics it is necessary to give also parameters of a working liquid entering into the equations (
(40)
where
generalized variables in nodes
;
For directional control valves the analysis of connections of its nodes is preceded with forming of the equations, as in intermediate position of a spool (at its switching from one position in another) in one node some connections can be crossed. Therefore flows in nodes belonging simultaneously various connections, turn out summation of flows in corresponding connections [see the equations (22), being analogue of the Kirchhoff’s first law for electric circuits].
The description of each hydraulic element is realized generally by two separate blocks:
On a basis of input information the following fields of input data are formed.
(41)
differing matrix
(42)
where
– arrays of parameters of pumps;
– arrays of parameters of hydraulic motors;
– arrays of parameters of hydraulic cylinders etc.;
– arrays of parameters of directional control valves;
Forming of mathematical model of hydraulic system is carried out on the following algorithm. The element
(
(43)
i.e. having taken values
on previous (
In view of small step of numerical integration, and also small all second addendum composed in the right part (43) an error received at such replacement, is negligible small. By virtue of the stated reasons the equation of losses of pressure on length of the pipelines, written down in the form of (43), yields quite satisfactory results and allows to solve other equations (for definition of flows) in a finite kind. |

Contents
>> Engineering Mathematics
>> Hydraulic Systems
>> Dynamic Analysis
>> Forming and solving algorithms of hydraulic circuit mathematical model