HOLLOW SHAFT MADE OF A MATERIAL HAVING A LOW MODULUS OF ELASTICITY, WITH DRIVE ELEMENTS SECURED THEREON BY EXPANDING THE SHAFT

ARBRE CREUX FAIT DE MATERIAU A FAIBLE MODULE D'ELASTICITE, GARNI D'ELEMENTS MOTEURS ADAPTES PAR ELARGISSEMENT DU DIAMETRE INTERIEUR DE L'ARBRE

English Abstract

Abstract of the Disclosure:
An assembly includes a hollow shaft formed of a material
having a modulus of elasticity of less than 150,000 N/mm2,
and drive elements secured on the shaft by expansion of the
shaft. The shaft and the drive elements have a relationship
such that:
?FA > 0.6 ?Fw EA/Ew [(rwa/rwi)2 - 1],
and rAi - rwa > ?Fw/Ew - rwa.
In this relationship, ?FA is the yield point and EA is the
modulus of elasticity of the material of the drive elements
in N/mm2. ?Fw is the yield point and Ew is the modulus of
elasticity of the material of the shaft in N/mm2. rwa is
the outside radius and rwi is the inside radius of the shaft
and rAi is the inside radius of the drive element, in mm.

Claims

Claim:
Assembly, comprising a hollow shaft formed of a material
having a modulus of elasticity of less than 150,000 N/mm2,
and drive elements secured on said shaft by expansion of
said shaft, wherein:
? FA > 0.6 ?Fw EA/Ew [(rwa/rwi)2 - 1],
and rAi - rwa > ?Fw/Ew - rwa,
?FA being the yield point and EA being the modulus of
elasticity of the material of said drive elements, ?Fw
being the yield point and Ew being the modulus of elasticity
of the material of the shaft in N/mm2, rwa being the outside
radius and rwi being the inside radius of said shaft, and
rAi being the inside radius of said drive element, in mm.
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Description

12~72'~6
28004-'
The invention relates to a hollow shaft formed of a material
havlng a modulus of elastlcity of ].ess than 150,000 N/mm2 and
havinq drive elements secured thereon by expansion of the shaft.
Published European Patent Application No. 0 213 52g, having two
inventors in common with the instant application, describes a
method for securing drive elements, such as cams, year wheels or
bearin~ bushings, on a hollow shaft, wherein hydraulic expansion
of certaln shaft sections is provided in order to attain a secure
fastening of the drive elements facing the shaft sections.
The inventors of the instant application have furthermore proposed
that in the course of the expansion process, the material forminy
the hollow shaft is to be plastically deformed, while the material
forming the drive element is only to be elastically deformed. The
springing back or resiliency of the material forming the drive
element after the disappearance of the
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exparlsion pressure then assures the necessary contact
pressure.
In this context, the materials of the hollow shaft and drive
elements along with the charact:eristic data thereof, were
each taken into account separately. Since proven materials
such as sintered metal, chill casting or high-strength
steels (hardened on their surface to the extent required)
were used for the drive elements, which in particular are
cams, while lower-grade standard engineering steels were
used for the hollow shaft, the method led to satisfactory
results.
In tests in which the hollow shaft forming the foundation
was manufactured from a lighter material in order to further
reduce the weight of the finished shafts, such as an alumi-
num alloy or titanium, that is materials that have a lower
modulus of elasticity, previously used values that had been
ascertained mostly by trial and error proved to be inade-
quate.
It is accordingly an object of the invention to provide a
hollow shaft made of a material having a low modulus of
elasticity, with drive elements secured thereon by expanding
the shaft, which overcomes the hereinafore-mentioned disad-
vantages of the heretofore-known devices of this general
type and which discloses a rule for dimensioning with which
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one skilled in the art can select a material having a lowmodulus of elasticity, that is one that is markedly below
that of steel, for use as the material for the hollow shaft,
and at the same time can determine a suitable material for
the drive elements, so ~hat the aforementioned fastening
method proceeds with satisfactory results.
With the foregoing and other objects in view there is
provided, in accordance with the invention, an assembly,
comprising a hollow shaft formed of a material having a
modulus of elasticity of less than 150,000 N/mm2, and drive
elements secured on said shaft by expansion of said shaft,
wherein:
~FA > 0.6 ~Fw EA/Ew [(rwa/rwi) ]'
and rAi ~ rwa > Fw/Ew rwa,
~FA being the yield point and EA being the modulus of
elasticity of the material of said drive elements, ~Fw
being the yield point and Ew b~ing the modulus of elasticity
of the matèrial of the shaft in N/mm2, rwa being the outside
radius and rwi being the inside radius of said shaft, and
rAi being the inside radius of said drive element, in mm.
If, as is intrinsically possible, this rule is applied to
other known methods for fastening drive elements on shafts,
such as shrinking them on, it results in values that are not
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practically attainable, such as results leading to an amount
of play between the elements that is too small to permit
slipping the elenlents onto one another.
Other features which are considered as characteristic for
the invention are set forth in the appended claims.
!
Although the invention is illustrated and described herein
as embodied in a hollow shaft made of a material having a
low modulus of elasticity, with drive elements secured
thereon by expanding the shaft, it is nevertheless not
intended to be limited to the details shown, since various
modifications and structural changes may be made therein
without departing from the spirit of the invention and
within the scope and range of equivalents of the claims.
The construction and method of operation of the invention,
however, together with additional objects and advantages
thereof will be best understood from the following descrip-
tion of specific embodiments when read in connection with
the drawing.
The drawing is a fragmentary, diagrammatic, axial
longitudinal-sectional view of an exemplary embodiment of
the invention.

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Referring now to the slnyle figure of the drawiny ln detail, there
are seen cams or drive elements 2 which are slipped over a hollow
shaft 1 formed of an aluminum alloy, and are secured b~ subsequent
expansion or en].argement of the hollow shaft in the regions
correspondi.ncJ to the cams. The dimension of the expansion shown
in the drawing has been enlarged to an exaggerated deyree, for the
sake of clarity.
In the drawing, 2rwa is the outside diameter and 2rwi is the
inside diameter of the hollow shaft 1. Furthermore, 2rAi is the
inside diameter of the drive element.
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Representative Drawing