Unlike hydraulic systems in mechanical and hydro mechanical transfers connection of elements can be rigid when angular speeds of elements are connected with each other through constant transfer ratios. For such chains of elements it is necessary to carry out reducing of moments of inertia and transfer numbers, uniting rigidly connected elements in one
(2)
where
The moments and transfer ratios undertake in view of their signs.
Fig. 2. An example of breakdown of the hydro mechanical transmission scheme on elements, nodes and sites
On Fig. 2 as an example the scheme of the hydro mechanical transmission consisting of a diesel engine (nodes 1, 2), a gear (1, 3, 4), a friction clutch (4, 6), a flywheel (6, 8), an elastic shaft (8, 9), a flywheel (9, 10), a wheel (10, 11, 12), a hydro dynamic clutch (3, 5), a gear (5, 7), a wheel (13, 14, 12), a flywheel (7, 13) is shown.
As a result of the structural analysis the scheme is broken into the following sites (in brackets numbers of nodes of these sites are specified):
All the nodes of the site, are divided on
Nodes
initial
: a diesel engine, a friction clutch, the hydraulic torque converter, a hydro dynamic clutch, a shaft, a wheel, i.e. those elements which are boundary elements of sites. To the boundary elements breaking the scheme on sites, the differential at which nodes
and
i
belong
to differential axes, and node k – to driver
belongs also
. In case if there is a division of a power stream in differential, nodes
j
and
i
are initial nodes of sites; at summation of a power streams nodes
j
and
i
– final; the node
j
to any site does not belong. If the flywheel in node
k
is not adjoined with other elements the node
i
a flywheel is initial. If a gear summarizes streams of power, its node
i
is too initial.
k
and
j
. Besides nodes
k
at a flywheel,
j
at a wheel,
k
and
j
at a gear at a branching of a stream of power or only
k
at summation of streams of power also are final nodes of sites if there are no other elements behind these elements in the scheme.
j
As a site can contain one or several gears, clearly, that such site can have some initial or some final nodes. We’ll agree, that the equations of dynamics of each site of a kind (2) we’ll form in its initial node and if there is some initial nodes – then in its initial node specified first.
Presence of several initial nodes of a site complicates algorithm of reducing of moments of inertia and transfer numbers, therefore it is accepted, that if a site has some initial nodes then each of them, since the second, should be simultaneously node
For storage of the information on structure of the scheme the special structural matrix describing result of breakdown of the scheme on sites is formed: (3)
where 1, 2, …,
As the site can have branches (at presence of gears) and accordingly some initial and final nodes, it is expedient to have two additional matrixes:
(4) where numbers of initial nodes of sites (zero fill the remained elements of matrix);
(5) where numbers of final nodes of sites (zero fill the remained elements of matrix). Elements of matrixes also allow to index moments in the right part of the equations (2); the first column of a matrix serves for indexation of speeds relatively which the equations of dynamics (2) are integrated. After the structural analysis of the scheme ending a number of additional actions is made. In particular, the site "wheel – road", in which some initial nodes (these are points of contact of tires with road) and one final node (the machine progressive moving) is under construction. This site differs from other that the equation of the machine progressive moving is written in final node of a site (the machine speed). Therefore its construction is spent separately, after forming of other sites. Thus, as a result of the structural analysis of the scheme the following matrices are formed: a matrix of sites, a matrix of initial nodes, a matrix of final nodes. |

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>> Hydro Mechanical Drives and Transmissions
>> Dynamic Analysis
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