
In most of demanding torque transmission systems, the key
components are premium well designed and properly fabricated
gears. The gear hobbing process is widely applied for the
construction of any external tooth form developed uniformly about
a rotation center. As presented at the Figures above, the kinematics
principle of the process is based on three relative motions
between the workpiece and the hob tool. To produce spur or helical
gears, the workpiece rotates about its symmetry axis with certain
constant angular velocity, synchronized with the relative gear hob
rotation. Depending on the hobbing machine used, the worktable or
the hob may travels along the work axis with the selected feed
rate.
Despite the
fact that a big variety of simulating methods have been proposed,
their main characteristic is the reduction of the actual
3Dimensional process to planar models, primarily for
simplification reasons. The application of these former
approximations is leading to planar results, without to represent
the exact solid geometry of a real chip, with accuracy straightly
dependent from various input parameters such as the number of the
calculation planes. Furthermore, any post processing of the
extracted chip and gear planar geometries requires additional data
processing which leads to supplementary interpolations of the
2Dimensional results. Targeting to the
realistic and accurate simulation of the gear hobbing process,
without inevitable modeling insufficiencies, a new research
modeling approach, based on 3Dimensional Computer Aided Design,
is proposed. This effective and factual simulation, in contrast to
former modeling efforts, is primitively realistic, since the
produced gear and chips geometry are normal results of successive
penetrations and material removal of cutting teeth into a solid
cutting piece. A software program called HOB3D is developed for
the guidance of an existent commercial CAD system, exploiting its
powerful modeling and graphic capabilities. HOB3D is built in
terms of a computer program in Visual Basic, providing the extend
ability to other cutting processes based on the same cutting
principle. The resulting solid models output formats offer
realistic parts, chips and work gears, easily managed for further
individual research or as an input to any other CAD, CAM or FEA
commercial software packages.
The essential input data
of HOB3D concern the determination of
the hob and work gear geometries and the cutting parameters that
take place for the completion of the simulation process. When the
values of the input parameters are set, the work gear solid
geometry is created in the CAD environment and one hob tooth rake
face profile is mathematically and visually formed. At the same
moment the assembly of the effective cutting hob teeth (N) is
determined. The kinematics of gear hobbing process is directly
applied in one three dimensional tooth gap of the gear,
considering the axisymetric configuration. Moreover, a 3D surface
is formed for every generating position, combining the allocation
of the two involved parts, following a calculated spatial spline
as a track.
These surface paths are used to identify the
undeformed chip solid geometry, to split the subjected volume and
to create finally the chip and the remaining work gear continuous
solid geometries.
After the completion of one work cycle, i.e. the termination of
every spatial surface paths and the subtraction of the chip solid
geometries, the produced gear gap is finally generated. The
following Figure illustrates a cross section (Detail A) of the
generated gear gap, formed by the collective work of every
generating position. As it is shown, the remaining gear solid geometry holds
complete geometrical information, both for the removed and the
remaining material.
The flowchart of the simulation process is
presented at the figure
below.
The
output chip solid geometries at fifteen characteristic generating
positions of two different test cases for the production of a spur
gear, UC and CL, produced by the
activation of the HOB3D code, are presented in the left and right
parts of the next Figure. Except of the direction of the
axial feed, every other input data are identical, for both
examined cases. Examining each of the resulting chips, is obvious
that so much as the extreme geometrical changes of the chip shapes
are sufficiently determined, even if the generated chip solid is
parted from more than one domains.
The 3D solid
geometrical development of the UC case is presented at the
animated figure below:
while the 3D
geometrical characteristics of the generating position G.P.: 4
are presented below:
The
output chip solid geometries for the production of a helical gear
are presented in the following Figure. Examining each of the
resulting chips, is obvious that so much as the extreme
geometrical changes of the chip shapes are sufficiently
determined, even if the generated chip solid is parted from more
than one domains.
