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RESEARCH OF MODIFIED GEAR DRIVE FOR
MULTIOPERATIONAL MACHINE WITH INCREASED
LOAD CAPACITY
Keywords
3D model, load capacity, machine gear drive, axoid generatrix, cylindrical gear transmission
Abstract
The presented work is devoted to the improvement of spur gears of the reduction drive for metal-
cutting machines according to the criterion of load capacity. A feature of this article is the creation of
such a constructive solution, which is aimed at finding a compromise between reducing contact loads
in the engagement zone and increasing the complexity and labour intensity of the manufacturing
gears process. A procedure for accelerated creation of 3D models of a gear drive and its
components using the specialized software application “Shafts and Mechanical Transmissions-3D” in
the environment of integrated CAD system KOMPAS-3D is proposed. A study of a new cylindrical
gear transmission design with a longitudinal generatrix of axoids, confirmed by the corresponding
patent solution is realized. A calculation form for the practical design and manufacture of a new
design cylindrical gear is proposed.
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Article citation info:
Xxxxxx X, Yyyyyy Y. Title of the article. Diagnostyka. 20xx;xx(x):xx-xx
1
DIAGNOSTYKA, 20xx, Vol. xx, No. x
ISSN 1641-6414
e-ISSN 2449-5220
DOI:
RESEARCH OF MODIFIED GEAR DRIVE FOR MULTIOPERATIONAL
MACHINE WITH INCREASED LOAD CAPACITY
Oleg KROL, Volodymyr SOKOLOV
Volodymyr Dahl East Ukrainian National University, Department of Machinery Engineering and Applied
Mechanics, 59-a Central pr., Severodonetsk, 93400, Ukraine
e-mail: krolos.snu.edu@gmail.com
Abstract (9 pt font)
The presented work is devoted to the improvement of spur gears of the reduction drive for metal-cutting
machines according to the criterion of load capacity. A feature of this article is the creation of such a
constructive solution, which is aimed at finding a compromise between reducing contact loads in the
engagement zone and increasing the complexity and labour intensity of the manufacturing gears process. A
procedure for accelerated creation of 3D models of a gear drive and its components using the specialized
software application “Shafts and Mechanical Transmissions-3D” in the environment of integrated CAD
system KOMPAS-3D is proposed. A study of a new cylindrical gear transmission design with a longitudinal
generatrix of axoids, confirmed by the corresponding patent solution is realized. A calculation form for the
practical design and manufacture of a new design cylindrical gear is proposed.
Keywords: cylindrical gear transmission, machine gear drive, axoid generatrix, 3D model, load capacity
1. INTRODUCTION
Based on the aggregate-modular principle,
multioperational machine tools (MT) of various
layouts are created [1-3]. At the same time, a
limited group of normalized nodes is developed and
specialized multioperational machines are built
from them, which most fully correspond to
technological tasks. The layout of the machines is
distinguished by the location of the spindle, the
main motion drive in space, the relative position of
the main nodes.
The main motion drive occupies a special
position in the structure of MT. They should
provide a high-productivity performance of various
operations when changing the rotation frequency in
a wide range [4, 5]. In machine tools, a spindle with
a cone of 40 – 5000 ... 7000 min-1 and the engine
power of the main drive is associated with the
dimensions of the table. In medium-sized machines
with a table width of 500 ... 800 mm is 11 ... 15
kW. Moreover, the speed of the working feed
reaches 8000 ... 10000 mm/min, the speed of fast
movements 10 ... 12 m/min [6].
One of the most common options for the main
motion drive of machines is an option with an
alternating current motor equipped with a frequency
converter and gearbox based on 2-3 mechanical
gears (various types of gears), to increase the range
of rotational speeds and torque. This type of
reduction drive provides high torque during
roughing and retains the possibility of high-speed
processing at speeds of about 104 rpm. The standard
configuration for most machines with a 40th cone
involves the use of conventional two-stage and
planetary gears.
The competitiveness of multioperational
machines is primarily associated with factors:
productivity, reliability and accuracy. At the same
time, reliability is one of the main requirements
made by consumers and often serves as the main
criterion for assessing quality.
Productivity and reliability of machine drives
are often limited by the smooth operation of pinion
and gears. Therefore, the issues of improving the
reliability, load capacity of the gears of the
machine's main motion drive due to the
improvement of design and technological solutions
are relevant.
2. LITERATURE REVIEW
In [7-9], it is noted that, at the initial stages of
the research, it is necessary to implement a search
for the toolkit to describe the contour of the teeth
lateral surface of spur and bevel gears. Such a
description will be the basis for obtaining optimized
contact conditions in a wide range of gear
transmission. Important parameters include groove
profile parameters, which are largely determined by
the longitudinal generatrix shape of the pinion and
wheel axoid.
It is also important to equip the production of
gears with appropriate software for CAM systems.
Promising in this regard is the software Gleason 5-
axis Gear Studio (G5S) [7] company Gleason
Corporation. These specialized programs are
intended for profiling the tooth lateral surface,
evaluating the contact pattern and preparing the
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corresponding control programs for 5-axis CNC
machines and machining centres. To make this
technology truly practical, each operator, in just a
few simple steps and minimal knowledge about the
design of the gearbox, will be able to automatically
generate the optimal program for machining parts
and 3D models of gears, based on which a control
program for processing them is developed.
According to [8], one of the main goals is to
create a working 3D model for analyzing contact
geometry, visual identification, and evaluating the
relationships between the set of tooth geometric
parameters. The toolkit of the designer’s tools
should include a method for creating a three-
dimensional model of the gear in the corresponding
integrated CAD systems [8-10].
At the same time, the increase in reliability
achieved by constructive methods often conflicts
with technological improvements. Thus, within the
confines of the JSME RC-268 committee, a new
Invo-Planar [11] bevel gear was developed, the
tooth flank of which is flat, whose transverse tooth
profile is a straight line.
Processing the simplified contour of the tooth
lateral surface by grinding in one pass allows you to
reduce machine time for a standard gear contour by
more than 10 times. Moreover, the lateral surface of
the tooth is much smoother than the curved lateral
surface of the tooth formed by many trajectories of
the tool cutting blades. On the other hand, the
progress of machine equipment, 5 coordinate
centres makes it possible to accelerate the
production of complex contours of the tooth lateral
surface. So, on the 5-axis Gleason Heller machine,
with the help of the CAM “Heller uP-Gear [7],
gears are machined with the optimal geometry of
the tooth flank and the contact pattern. As a cutting
tool, insert disk knives are used for roughing, semi-
finishing and final gear cutting operations.
Another aspect, from the standpoint of the
criterion of contact stresses, and therefore
reliability, it is rational to increase the length of the
teeth working contact, which gives an increase in
the load capacity of the gear transmission. The
problem of the operational aspect associated with a
decrease in the process of working the contact
length of the teeth in the longitudinal direction
(especially at high cutting speeds) drew attention
[12]. This phenomenon leads to a decrease in the
length of the loaded tooth region and, as a result, to
the risk of excessive contact stress. The author
considers compensation methods for these
mechanical deviations so that the load on the gear
wheel surface is evenly distributed under normal
operating conditions. A generatrix of the single or
double helix type is proposed for describing the
side surface of a wheel tooth to increase the contact
length. Another constructive option for increasing
energy efficiency by the example of differential
mechanisms was proposed in [13].
Based on the analysis of the problem under
consideration, improving the efficiency of various
types of gears, we statement of the problem:
To develop a modernized gear design of the
machine reduction drive which implements a
compromise between increased reliability and
sophisticated manufacturing technology on modern
CNC machines.
To achieve this goal, the following tasks are
proposed:
1. To develop 3D models of the main motion drive
for multi-operational machines in the KOMPAS-3D
CAD environment using the specialized application
program “Shafts and Mechanical Transmiss ions -
3D”.
2. Explore and create a new design of the gear
transmission with a modified shape of the longitudinal
axoids generatrix of the pinion and wheel.
3. METHOD OF 3D MODELING
MULTIOPERATIONAL TOOLS GEARBOXES
DRIVE
As the object of research, a multi-operational
milling-drilling-boring machine with a six-spindle
turret was selected. Increasing the level of
complexity of projects in machine tool
manufacture, the creation of competitive designs
involves the widespread use of various computer-
aided design systems. In the technology of the
design process, the procedures for constructing 3D
models and parametric representations of parts and
assembly units are important.
The research of the main structural
characteristics of the machine drive is provided by
the corresponding 3D modeling toolkit in integrated
CAD/CAM/CAE KOMPAS-3D [14-18], in which a
three-dimensional model of the machine reduction
drive has been developed (Fig. 1).
In the process of creating this model, the latest
functionalities of CAD KOMPAS and specialized
applications were used. When developing such
complex parts as the bed housing with a gear drive
(speed gearbox) and the housing of a six-spindle
turret, specialized CAD application libraries were
used. It is significantly improved the process of
geometric modeling. Using the Artisan Rendering
photorealistic image module integrated into
KOMPAS forms the corresponding design and
understanding of the machine design [19].
The machine under consideration belongs to the
class of specialized machines of the 2nd standard
size, which are used in small-scale and series
production and are intended for multi-operation
machining of complex profile products from steel,
cast iron, light and non-ferrous metals. The
machine is equipped with an automatic tool
changer, which is carried out by turning the six-
spindle turret to the desired position according to
the program. In the upper part of the bed housing,
a gearbox is mounted with a gearshift mechanism
and a turret rotation mechanism (Fig. 2).
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The competitiveness of multioperational machines is
primarily associated with factors: productivity,
reliability and accuracy. At the same time, reliability
is one of the main requirements made by consumers
and often serves as the main criterion for assess ing
quality.
4. RESULTS AND DISCUSSION
Productivity and reliability of machine drives are
often limited by the smooth operation of pinion and
gear. Therefore, the issues of improving the
reliability, the load capacity of the gear wheels of
the main motion drive due to the improvement of
design and technological solutions are relevant [20,
21].
First of all, it should be noted that in the known
gear transmission on parallel axes, a pinion and a
wheel are used, the axoids of which are cylinders
with a rectilinear generatrix [11]. The disadvantage
of such a gear transmission on parallel axes is the
insufficient bending load capacity of the teeth
because the longitudinal direction of the teeth
coincides with the rectilinear axoid generatrix the
gears and wheels, and the length of the teeth is
limited by the width of the gearing.
The main idea of improvement is changing the
shape of the longitudinal pinion and wheel axoid
generatrixes [21]. The result of this modernization is
an increase, ceteris paribus, the length of the teeth,
which ultimately will increase the load capacity of
the gear teeth in bending. The problem is achieved
by receiving in a gear transmission on parallel axes,
the pinion and wheel longitudinal axoid generatrix in
the shape of a circular arc with radius
0
r
:
01
0.25 ( 1)
ba
r m k z i
where
m
– gearing module, mm;
k
– coefficient
that ensures the fulfillment of the obvious condition:
00.5 W
rb
what should be accepted
1k
;
/
ba W W
ba
– gear width ratio expressed in terms
of gear width
W
b
and center distance
W
a
;
1
z
– the
number of gear teeth;
i
– gear ratio.
In this case, the pinion axoid in the longitudinal
direction is concave, and the axoid of the wheel in
the same direction is convex.
The gear transmission on parallel axes (Fig. 3)
contains a pinion 1 and a wheel 2, the longitudinal
axoid generatrixes of which is a circular arc with
radius
0
r
, operates as follows. The teeth of the gear
1 in an amount
1
z
that rotates at an angular speed
1
are engaged with the teeth of the wheel 2 in an
amount
2
z
. In this case, the angular speed
1
of the
pinion 1 is converted into the angular speed
2
of
the wheel 2. As a result, the gear ratio of the gearing
12
/i
is needed.
The surfaces of the gear teeth are the envelope
surfaces of a disk milling cutter with straight cutting
edges in relative motion and are described by the
following system of equations (1):
11
11
11
11
1
11
( cos ) sin cos
[( cos ) cos (0,5 1.25) ] sin ;
( cos ) sin sin
[( cos ) cos (0,5 1.25) ] sin ;
0.33 sin ;
( ) 0.
t
tt
t
tt
XY
X r u v
r u v m z r
Y r u v
r u v m z r
Z m u
R Y n X n
(1)
Here:
1
[0,25 ( 1) 1,25]
t ba
r m k z i
–
nominal radius of a disk milling cutter;
0
20
–
the angle of inclination of the straight cutting edges
of the disk milling cutter;
, u
– independent variable parameters of pinion
teeth;
1 1 1
0.5 mz
– the angle of pinion
rotation relative to the axis
1
Z
; (
1
– pinion angular
speed);
11
( cos ) (cos sin sin cos ) sin
Xt
n r u v v
– the projection of the normal to the surface of the
pinion tooth on the axis X;
11
( cos ) (cos cos sin sin ) sin
Yt
n r u v v
– the projection of the normal to the surface of the
pinion tooth on the axis Y;
1
(0,5 1.25) t
R m z r
.
The teeth surface of the wheel is an envelope of
surfaces relative to the surfaces of the pinion teeth
(1) with the same radius of the axoid
0
r
, but convex
in the longitudinal direction.
In Fig. 3 shows a general view of the gear
transmission on parallel axes, contains a pinion 1
and a wheel 2. The 3D-model of a modernized
cylindrical gear transmission (Fig. 3) in the "Shafts
and mechanical gears-3D” module of CAD
KOMPAS-3D was developed
Fig. 3. Spur gear with axial longitudinal
generatrix in the form of a circular arc
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In Fig. 4 and Fig. 5 show fragments of cutting
the pinion teeth 1 by a disk cutter 3 during a
running-in process, in which the rotation of the
pinion 1 with an angular speed
1
is consistent with
the translational movement of the disk milling cutter
3 at a speed
3 1 1 1 1
0.5V r m z
, where
1
r
–
pitch radius of the pinion in the average frontal
cross-section. On the example of pinion 1, it is
shown how, due to the curved shape of the axoid,
the length of the tooth increases – from the size
W
b
in the known gear transmission to the length of the
arc
MN
in the modernized gear transmission. If
the parameter
t
r
is expressed through,
0
r
(Fig. 5):
01
1.25 [0.25 ( 1) 1.25],
t ba
r r m m k z i
that ratio of variables
MN
to
W
b
determine by
the dependence:
1
1
1
5( 1)
0.25 ( 1)
arcsin .
0.25 ( 1) 1.25
W ba
ba
ba
MN k
b z i
zi
k z i
Fig. 4. Cutting gear teeth with a modular disk
milling cutter when coordinating movements
Calculations show that in a gear transmission on
parallel axes with constant parameters, when the
coefficient varies within the boundary
1.2...1.5k
,
the ratio
/W
MN b
changes from 1.13 to 1.08. This
means that the bending stress in the teeth of the
modernized gear transmission will be 8 ... 13% less
than in the known gear transmission.
Fig. 5. Pinion with extended tooth length
Along with the design component, the contact
component is also influenced by the technological
component associated with the quality of the
formation of the pinion tooth back surface. When
machining the relieving tooth back surface by
grinding it is rather difficult to choose the cutting
conditions. In this regard, the ideas of choosing and
optimizing the grinding process presented in [22, 23]
are of interest.
The operation of the proposed gearbox option is
associated with wear processes and the likelihood of
breakdowns [24]. To analyze these operational
phenomena and prevent possible breakdowns, it is
rational to use the thermovision method with the
Termovision Processing Software, developed by the
Machinery Systems Division, Wroclaw University
of Technology and tested on the example of a two-
stage belt conveyor gearbox [25]. Another method is
the Stochastic Resonance method [26-28], which is
based on the calculation of residual signals during
the operation of a cylindrical gearbox, and under
conditions of normative functioning is used.
In case of continuous operation, it is necessary to
monitor the vibrations of the gear drive. In this
regard, a promising method is the control of
distributed wear (pitting corrosion) in planetary
gears, proposed in [29].
CONCLUSIONS
This research describes the new design of a
cylindrical gear transmission of a stepped reduction
drive for the machine tools. At the initial stages of
development, a three-dimensional model of the
reduction drive and its component in the integrated
CAD system KOMPAS-3D was formed. The article
suggests moving away from the standard cylindrical
spur engagement profile to the design version of the
longitudinal axoid generatrix in the form of a
circular arc with radius
0
r
satisfying the condition
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00.5 W
rb
. This allows you to implement a
compromise solution: with an extended tooth width
of the wheel and, as a result, increased load capacity
on the one hand (about 8-13%) and rather
complicated manufacturing technology. The latter is
achieved using disc milling cutters with straight
cutting edges.
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