Method for optimizing plates of a plate link chain, and plate for a plate link chain
View Patent ↗A method for optimizing the link plates of a plate-link chain drive chain for use in a variable speed unit of a belt-driven conical-pulley transmission. The chain includes plate links formed from pairs of plates that have openings through which pairs of rocker members extend. The plates include longitudinally-extending legs that extend in the chain movement direction and vertical legs that extend perpendicular to the chain movement direction. The method is directed to minimizing bending stresses in the longitudinal and vertical legs of the plates as the chain passes around a pulley, and as the rocker members and the chain tension impose forces on the plates. The stress minimization results in minimal material usage and minimal weight of the chain.
1. A method for optimizing plate geometry of a plate of a plate link chain for use in a variable speed drive unit of a belt-driven conical-pulley transmission, said method comprising the steps of:
defining for a chain a predetermined applied longitudinal force to be transmitted by the chain and a predetermined applied longitudinal force lever arm;
providing an initial plate geometry for a plate that includes an opening for receiving pairs of rocker members that bear against sides of the opening, wherein the opening is bounded by spaced longitudinal legs that extend in a chain movement direction and spaced vertical legs that extend in a direction perpendicular to the chain movement direction, wherein the initial plate geometry includes an initial longitudinal leg length and longitudinal leg width, an initial vertical leg length and vertical leg width, and an initial plate thickness;
determining a bending moment (MB) acting on the longitudinal legs of the plate when the plate is subjected to a predetermined applied longitudinal force that is applied at a predetermined lever arm distance relative to the longitudinal leg from the following bending moment relationship based upon the following plate geometry variables:
MB
=
F
*
He
k
+
1
·
[
1
-
He
L
2
]
with
k
=
I
2
*
L
1
I
1
*
L
2
,
wherein
F
=
applied
longitudinal
force
He
=
lever
arm
of
the
applied
force
F
I
1
=
planar
moment
of
inertia
of
the
longitudinal
leg
(
=
leg
height
3
*
leg
thickness
/
12
)
I
2
=
planar
moment
of
inertia
of
the
vertical
leg
(
=
leg
width
3
*
leg
thickness
/
12
)
L
1
=
overall
length
of
the
longitudinal
leg
L
2
=
overall
length
of
the
vertical
leg
.
modifying respective ones of the plate geometry variables; and
calculating longitudinal leg bending moments for different plate longitudinal leg lengths and different longitudinal leg planar moments of inertia at the predetermined applied longitudinal force and the predetermined applied longitudinal force lever arm until a minimum longitudinal leg bending moment is achieved to thereby provide a plate of minimum longitudinal leg material usage and minimum longitudinal leg weight for the predetermined longitudinal force that is applied to the plate opening at the predetermined lever arm distance relative to the longitudinal leg.
2. A method in accordance with claim 1 , wherein 1≦k≦3.5.
3. A method for optimizing plate geometry of a plate of a plate link chain for use in a variable speed drive unit of a belt-driven conical-pulley transmission, said method comprising the steps of:
defining for a chain a predetermined applied longitudinal force to be transmitted by the chain and a predetermined applied longitudinal force lever arm;
providing an initial plate geometry for a plate that includes an opening for receiving pairs of rocker members that bear against sides of the opening, wherein the opening is bounded by spaced longitudinal legs that extend in a chain movement direction and spaced vertical legs that extend in a direction perpendicular to the chain movement direction, wherein the initial plate geometry includes an initial longitudinal leg length and longitudinal leg width, an initial vertical leg length and vertical leg width, and an initial plate thickness;
determining a bending moment (MA) acting on the vertical legs of the plate when the plate is subjected to a predetermined applied longitudinal force that is applied at a predetermined lever arm distance relative to the longitudinal legs from the following bending moment relationship based upon the following plate geometry variables:
MB
=
F
*
He
k
+
1
·
[
1
-
He
L
2
]
with
k
=
I
2
*
L
1
I
1
*
L
2
,
wherein
F
=
applied
longitudinal
force
He
=
lever
arm
of
the
applied
force
F
I
1
=
planar
moment
of
inertia
of
the
longitudinal
leg
(
=
leg
height
3
*
leg
thickness
/
12
)
I
2
=
planar
moment
of
inertia
of
the
vertical
leg
(
=
leg
width
3
*
leg
thickness
/
12
)
L
1
=
overall
length
of
the
longitudinal
leg
L
2
=
overall
length
of
the
vertical
leg
;
modifying respective ones of the plate geometry variables; and
calculating vertical leg bending moments for different plate vertical leg lengths and different vertical leg planar moments of inertia at the predetermined applied force and the predetermined applied force lever arm until a minimum vertical leg bending moment is achieved to thereby provide a plate of minimum vertical leg material usage and minimum vertical leg weight for the predetermined longitudinal force that is applied to the plate opening at the predetermined lever arm distance relative to the longitudinal leg.
4. A method in accordance with claim 3 , wherein 1≦k≦3.5.