2004
年
3
月
第
19
卷第
2
期
西安石油大学学报(自然科学版〉
Journal
of
Xi'an
Shiyou
University(Natural
Science
Edition)
文章编号
:1001-5361(2004)02-0058-05
沁
1ar.
2004
Vo
l.
19
No.
2
Meshing theory of beveloid gears with crossed axes
and calculation of induced normal curvature
LI
Gui-xian ,
WEN
Jian-min,
LI
Xiao ,
ZHANG
Xin ,
LIU
Fu-li
(Electromechanical College. Harerbin Institute
of
Technology. Harerbin
150001
Heilongjiang.China)
Abstract:
Based
on
the
space
meshing
theory
, it is
proven
that
non-involute
beveloid
gears
meshing
with
crossed
axes
can
achieve
to
line
contac
t.
The
meshing
equation
and
tooth
profile
equation
are
presented
by
using
meshing
theory.
A
theoretical
way
is
put
forward
to
calculate
the
induced
normal
curvature
along
the
normal
direction
of
the
contact
line.
Keywords :
crossed
axes;
noninvolute
beveloid
gear;
line
contact;
induced
normal
curvature
CLC
Number:
TH132.
429
Literature
Identification
Code:
A
The
parallel
axis
beveloid
gear
drive is
widely
applied
to
some
ultra-precision
transmissions
which
need
slight
backlash.
The
study
of
meshing
theory
on
parallel
axis
beveloid
gear
has
made
great
progress
recently['-3].
But
crossed
axis
beveloid
gear
drive
with
line
contact
has
not
been
reported
so
far.
Dueto
the
point
contact
of
this
type
of
gear
transmission
,
the
crossed
axis
beveloid
gear
drive
has
greater
contact
stress
and
lower
load
capacity.
This
greatly
limits
their
applications.
Crossed
axis
beveloid
gears
can
approximately
achieve
to
line
contact
by
adjusting
their
tooth
profile
parameters.
Because
modification
coefficients
are
different
in
different
sections
and
the
parameters
of
left
tooth
profile
are
different
from
those
of
right
tooth
profile ,
it
is difficult
to
adjust
all
these
parameters.
This
paper
will
study
crossed
axis
beveloid
gèars
with
line
contact
,
present
the
mathematical
model
and
analyze
the
meshing
theory.
Meanwhile
the
relative
normal
curvature
is
calculated.
All
the
work
will
be
helpful
to
other
fields
such
as
the
studies
of
stiffness
,
backlash
, efficiency
of
transmission
,
and
generation
methods
of
beveloid
gears
in
the
future.
1
Transformation
of
coordinate systems
The
motion
coordinate
systems
σ[0
仇
，
j
，
,k,J
and
σ
[0;i
20
j2
，
k
2
J
，
shown
as
Figure
1,
are
attached
to
the
involute
beveloid
gear
1
and
to
the
tooth
profile
(gear
2 )
which
is
conjugated
with
gear
1,
P.
P.
e
respectively. 0 ,
and
O
2
are
the
geometry
centers
of
the
two
gears.σ10=
[010;t
10
.J
,0,k
lO
Jand
σ20
=
[0
20
仇。，
)20
.k
20J
are
the
original
coordinates
systems
of
gear
1
and
gear
2,
respectively.
The
position
relationships
Date
of
receiving the paper: 2003-06-20
Fund
projects:the work
is
supported
by
Natural
Science
Fund
of
Heilongjiang Province (EOl-18)
and
Doctor Fund
(Z0010213022)
Introduction of the first author:
Li
Gui-xian (1941-) ,
woman
, born
in
Fangzheng , Heilongjiang, a professor, majors
in
robot transmission. mechanism
CAD
,
and
fuzzy
mechanics
of
gear system.
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