Dynamic, Kinematic and Static Analysis of a Shaper
Machine
Dr. M. A. Asy
Prof. Dr. M. A. Nasser
[email protected]
[email protected]
Department of Production Engineering & Mechanical Design
University of Menoufia
Shebin El-Kom, Menoufia, Egypt
Abstract: Nowadays, machine tool builders can no longer have
enough money to consume time and money building and testing
real prototypes of the machine tool model, instead they use virtual
prototypes. Shaper machine has received limited attention
regarding their dynamic and static behaviour. Shaper machine
was remodelled for more static, kinematic and dynamic analyses.
This paper presents the current state of virtual prototyping of a
shaper machine tool; the work focuses on the design of the
machine tool structure, main gear box, tool shank and tool holder
systems. Shaper machine produced by the Egyptian Machine Tool
Factory is selected for this study. The structural behaviour under
static and dynamic loads is evaluated in order to obtain an
optimized design of the shaper machine elements. Several
software like Matlab, Excel, Ansys and Solidworks has been used
for remodelling and analysis. Kinematic analysis defined position
of shaper quick return mechanisms links, motion of ram, end of
the rocker and machine crank as well as the displacement,
velocity and acceleration of machine ram or cutting tool for
different values of crank length and number of strokes per
minutes. Finite element analyses of machine parts in static and
modal domains are carried out on machine parts and their subassemblies. Using Virtual Prototyping techniques, engineers are
able to shorten the design time and therefore shorten the time
needed for pushing to market new products.
Key Words: Dynamic, Deformation, Frequency, kinematic &
shaper.
1. Introduction
Shapers were very common in industrial production. The
shaping machine is used to machine flat metal surfaces
especially where a large amount of metal has to be removed.
Other machines such as milling machines are much more
expensive and are more suited to removing smaller amounts of
metal, very accurately. The shaping machine is a simple and
yet extremely effective machine. It is used to remove material,
usually metals such as steel or aluminum, to produce a flat
surface. However, it can also be used to manufacture gears
such as rack and pinion systems and other complex shapes.
The main parts include a gear box, rocker, floating link, ram
tool holder, casing, base and a table. The reciprocating motion
of the mechanism inside the shaping machine is obtained by
using quick return mechanism. The gear box last driven gears
is used as a rotating disk. As the disc rotates the top of the
machine, “ram” moves forwards and backwards, pushing a
cutting tool [1-4].
Quick-return mechanism design and kinematic analysis has
received a lot of attention [5-18]. The links displacement,
velocity and acceleration were found. Computer-Aided Design
and Analysis of the Whitworth Quick Return Mechanism was
studied in most references [5-22]. In the quick return
mechanism, the velocity of cutting stroke and return stroke
both change with the change in length of slotted link but the
total velocity ratio remains constant. The velocity ratio and
force output changes with the change in height of slider. The
ratio of length of slotted link to height of slider is 1.083 and at
this instant the velocity ratio and force are found to be with
their maximum value during the stroke [15]. Shaper
Mechanism is constructed by SolidWorks, and then it is
imported the multi-body dynamics simulation software
ADAMS in order to analyze the characteristic of the
kinematics and dynamics simulation. [18] To improve the
stability of the ram-movement and to make use of the power
consumed during the return stroke, the author built a model in
ADAMS to run its simulation to optimize the geometric
parameters of the shaper so that a bidirectional planer is likely
to be designed and applied in the industrial field, thus the
producing efficiency could be increased without inventing a
new kind of planer with a new mechanism, but only to change
some geometric parameters of the original slider-crank
mechanism [19]. Simulation of Whitworth quick-return
mechanism has been done by using MSC ADAMS software.
ADAMS software helps to study dynamic analysis and
animation of shaper machine parts. In this paper the velocity
and acceleration of cutting tool time in both cutting and return
strokes is discussed. Force and torque versus time for crank
pin are also discussed with the help of MSC ADAMS software
[20]. An attempt has been made to analyze both statically and
dynamically the three machine tool structures milling, shaping,
and lathe. It concluded that the deflection is increasing with an
increase in frequency. The frequency analysis has been takenup for the first 5 natural frequencies. Very limited results are
given without expansion [21]. A virtual machine tool is a
simulation tool of machine tools first given by [22]. In this
technique virtual modeling of machine tool kinematics,
machine tool structure and feed drive dynamics as well as tool
and workpiece behavior. The new design procedure with
virtual prototypes shorten design time. The developed methods
and software tools for improving the design and evaluation of
machine tool components and structures. The virtual machine
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concept allowed the study of the machine dynamic behavior
without building the practical prototype [22]. The finite
element was used to study the modal analysis of machine tool
structures [21-23], gear boxes [24 & 25] and cutting tools [2630]. References [31-33] were referred in studying theoretical
and experimental modal analysis. From the literature review it
is clear that the shaping machine has received very limited
attention in both static and dynamic condition. Trails made to
study quick return mechanism showed that there are no
integrated software platform for the virtual design and analysis
of the machine tools. Moreover, the direct experimental
approach to study shaper machine and shaping processes
dynamic analysis is expensive and time consuming, especially
when a wide range of parameters is included. The alternative
approaches are mathematical simulations where numerical
methods are applied. In this paper, Matlab is used in the
development of an accurate mathematical model and
subsequent simulations for the kinematic and dynamic analysis
of the mechanical shaper systems. From the present work it is
easy to compute position of links, displacement, velocity and
acceleration of quick return mechanism. Finite-element
analysis is used to derive a computational model predicting the
vibration behavior, deformations, stresses and strains in the
machine tool structure, rotating and reciprocating elements as
well as tool shank and tool holder.
2. Analysis
The slotted-lever quick return mechanism shown in figure (1)
is used in a shaper machine. For a constant rotation speed of
the driving crank, “from the machine gear box”, it produces
slow velocity in cutting stroke and fast velocity during return.
In quick return mechanism, stroke position, velocity and
acceleration of cutting stroke and return stroke both change
with the change in length links and crank rotation speed.
The ram displacement as a function of the crank angle can be
derived as the following:
Let OD=L, AB=R, OA= d
(1)
(2)
(3)
(4)
From above
(5)
For the given mechanism the stroke:
(6)
The ram or cutting tool speed:
(7)
(8)
(9)
(10)
(11)
The ram or cutting tool acceleration:
(12)
(13)
(14)
For the machine under study the length of rocking (L) and
floating links are 71 and 15 cm respectively.
The distance between fixed points is (d ) 35 cm while crank
shaft (R) is arbitrary from 0 to 15 cm.
Figure 1 The Crank and Slotted Lever Quick Return Shaper Mechanism.
Gearbox Kinematics
The number of speeds of the shaper can be written as:
8=2x1x4 as can be seen later in the machine speed chart.
Gear dimensions calculation cab be obtained from the
following equations:
The gear pitch diameter is:
(15)
Gear addendum diameter is:
(16)
Gear dedendum diameter is:
(17)
Finite Element Analysis
Generally in shaping operations there will be some level of
relative dynamic motion between the cutting tool and the work
piece. The repeated sudden impacts in the beginning of cutting
stroke and repeated sudden release when the cutting tool
leaves the cutting surface. Other excitation comes from the
rotating and reciprocated elements. Moreover, energy from the
chip formation process excites the mechanical modes of the
machine-tool system. Modes of the work piece may also
influence tool vibration. The dynamic properties of the
excitation, i.e. the chip formation process are correlated to the
material properties and the geometry of the work piece. The
vibrations may lead to unwanted noise, degraded surface finish
and reduced tool life. These complicated factors motivate the
Dynamic characteristics of the shaper elements, tool holder
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and tool shank as well as gear box and machine tool structure
by using the finite element method.
To carry out the static analysis by using finite element,
assemble the element equilibrium equations to obtain the
global equilibrium equations and introduce boundary
conditions.
(18)
Where F, K, D are the force, stiffness and deformation
respectively.
In matrix form the static behaviour of the system can be
estimated from the following form:
(91)
Where F, K, u are the force, stiffness matrix and deformation
respectively.
The equation (91) is solved for unknown nodal displacements
and then solving for element stresses and strains.
The shaper as a machine tool is an important machine in the
manufacturing processes, it is essential to know their static and
dynamic behaviour.
To carry out the shaper machine and/or its elements dynamic
analysis, their mass and the elastic parameters are continuously
distributed, it is discretized into a finite discrete system with
multiple degrees of freedom by means of the finite element
method. Then the system dynamics equations are established,
it is expressed as following:
(20)
where M is structural mass matrix, C is structural damping
matrix, K is structural stiffness matrix, δ(t) is generalized
coordinates vector, P(t) is structural load vector.
Calculation of natural frequency and vibration modes of the
structure is a basic problem in dynamic analysis. Calculation
of dynamic response by superposition will also use these mass
and stiffness parameters. Assuming that the damping and
external force is zero, the equation (20) can be expressed as
following:
(29)
System's inherent frequency and modal vibration mode is
obtained by the characteristic equation.
(22)
Where ω is the natural frequency, ϕ is eigenvector. We can see
that the natural frequency of the system increases
monotonically with the system stiffness meanwhile decreases
monotonically with the system quality.
Equation (22) can be obtained by generalized eigenvalues
or standard eigenvalues
.
, when A is n order
By the standard eigenvalues
real symmetric positive definite or positive semi definite
matrix, which has n real eigenvalues, it is expressed as
follows:
(23)
For the generalized eigenvalue problem
,
which can be solved by trigonometric process on K or M, and
the solution can be obtained separately.
Thus, n eigenvalues is obtained by solving the generalized
eigenvalues, the order is as follows:
(24)
(25)
Where,
are natural frequencies, and
are their corresponding vectors.
3. Results and Discussions
A shaper is a type of machine tool that uses linear relative
motion between the work piece and a single point cutting tool
to machine a linear tool path. Kinematics is the study of
displacement, rotation, speed, velocity and acceleration of
each link at various positions during the one complete rotation
of cycle. Using this information one can compute various
results with the crank angles.
Quick returns motion mechanisms; drag link mechanism,
Whitworth mechanism and crank and slotted lever mechanism
are widely used in engineering applications. This mechanism is
used in shaping machines, slotting machines and in rotary
engines. When a mechanism like crank and slotted lever is
required to transmit power or to do some particular type of
work it then becomes a machine. Shaper machine is the
application of this mechanism. The static, kinematic and
dynamic analyses of any mechanism or machine is essential to
achieve good design. Kinematics is the study of motion
(position, velocity, acceleration). A major goal of
understanding kinematics is to develop the ability to design a
system that will satisfy specified motion requirements. This
will be the emphasis of this work. Kinetics is the study of
effect of forces on moving bodies. Good kinematic design
should produce good kinetics. The crank and slotted lever
mechanism shown in figure (1) is an application of second
inversion. The slider reciprocates in oscillating slotted lever
and crank rotates. Floating link connects slotted rocker to the
ram. The ram with the cutting tool reciprocates in the
horizontal direction. The ram with the tool reverses its
direction of motion when crank is perpendicular to the slotted
rocker. Thus the cutting stroke is executed during the rotation
of the crank through angle small and the return stroke is
executed when the crank rotates through angle 360 minus that
angle. Therefore, when the crank rotates uniformly, faster
return than cutting is obtained.
Kinematic analysis is important for find out position, velocity
and acceleration of each link in quick return mechanism. The
cutting speed, depth of cut and feed rate has direct effect on
machining variables. The cutting tool is fixed on the tool head,
which is fixed into the machine ram. The cutting tool is the
frontal part of the ram. In quick return mechanism, velocity of
cutting stroke and return stroke both change with the change in
length of slotter link while the total velocity ratio remains
constant. The velocity ratio and force output changes with the
change in height of slider. Matlab software is used to describe
the motion of the shaper mechanism links. This case study of
the shaper machine when the crank length is 12 cm., as shown
in figure (2-a). Moreover, the linear motion of the ram (red),
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the end of the floating link inverted pendulum like motion
(green) and crank circular motion (blue) are obtained as shown
in figure (2-b). This analysis of position of the rotating,
oscillating and reciprocating parts highlight the motion inside
the machine. The ram or cutting tool displacement with crank
angle for crank length 3, 6, 9 & 12 cm for one cycle of the
crank motion is given in figure (3). The displacement increases
with the increase of crank length. The ram or cutting tool
velocity with crank angle at different crank lengths and
strokes/min is shown in figure (4).
Motion of the Shaper Mechanism Links
Machine Hight (0 cm is the Crank Centr Point)
60
40
20
0
-20
-40
-60
-80
-60
-40
-20
0
20
Stroke Length (cm)
40
60
Figure 3 The Ram or Cutting Tool Displacement with Crank Angle for Crank
Length 3, 6, 9 & 12 cm.
(a)
Motion of the Ram, End of the Rocker and Crank
60
Machine High (0 cm is the Crank Center Point)
strokes/min is shown in figure (5). The selected values of the
virtual crank length in this study is 3, 6, 9, 12& 15 cm while
the speed of the machine is 12,18, 25, 35, 49, 71, 100& 140
stroke/min or crank rpm. The ram or cutting tool acceleration
increases as the crank length and/or ram strokes per minute
increase. As it can be seen in figures (4 & 5) the ram linear
velocity and acceleration along the stroke length are obtained
to study the kinematics of the cutting tool motion. A case study
those parameters for the given shaper machine at crank length
equals to 3 cm (10 cm stroke) 12 and 18 stroke/min is shown
in figure (6). A variable ram velocity and acceleration is exist
at each instant along the cutting and return strokes.
40
20
0
-20
Crank
End of of the Rocker
Ram
-40
-60
-80
-60
-40
-20
0
Stroke (cm).
20
40
60
(b)
Figure 2 The Position of Crank and Slotted Lever Quick Return Shaper
Mechanism (a) & Motion of Ram, End of the Rocker and Crank (b) (dim. in
cm).
The selected values of the virtual crank length in this study is
3, 6, 9, 12& 15 cm while the speed of the machine is 12,18,
25, 35, 49, 71,100& 140 stroke/min or crank rpm. The ram or
cutting tool velocity increases as the crank length and/or ram
strokes per minute increase. The ram or cutting tool
acceleration with crank angle at different crank lengths and
Figure (4) presents the ram velocity (cutting & return) with
crank angle and position along the stroke. The ram velocity is
a function of machine links dimensions and machine strokes
per minute. From the results it is clear that the maximum
cutting speed when working with 140 stroke/min are 40, 76.5,
108 and 136 m/min at stroke span 100, 200, 300 & 400 mm
respectively. While when working with 12 stroke/min, the
maximum cutting speed are 3.5, 6.55, 9.25 & 11.76 m/min.
The maximum return speed for the above strokes spans are
46.8, 101.27, 165.28 & 241.75 m/min while they are 4.02,
8.68, 13.87& 20.72 m/min for 12 stroke/min. When moving
from 100 to 400 mm span at machine speed 12 stroke/min.
The ram velocity increases 3.36 times. For 100 mm stroke
when moving from 12 to 140 stroke/min the ram velocity
increases 11.42 times. The cutting speed plays an important
part in machining accuracy and cost. Unfortunately, the
repeated impacts between the cutting tool and workpiece could
result in tool and/or workpiece and hole machine problems.
To avoid the sudden impacts between the tool and workpiece
the stroke span should be as short as possible. Smaller distance
has to be used in the tool approach side. The positive side of
the higher cutting speed is the increase of ram and
consequently cutting tool kinetic energy. Kinetic energy is
proportional with the square velocity. Negative effects could
happen as a result of higher kinetic energy of associated higher
return speeds. Figure (5) presents the ram acceleration for
some selected strokes at machine different machine speeds
(12, 18, 25, 35, 49, 71, 100 & 140 stroke/min). When using
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140 stroke/min and stroke span 100, 200, 300 & 400 mm, the
acceleration is 10.54, 23.6, 39.18 and 56.55 m/sq s, while the
acceleration values are 0.077, 0.17, 0.28 & 0.4 m/sq s for 12
stroke/min and same stoke spans. When moving from 100 to
400 mm span at machine speed 12 stroke/min. the acceleration
increases 5.3 times, while it was 6.22 times when using 140
stroke/min. For 100 mm stroke when moving from 12 to 140
stroke/min, the acceleration increases 137.14 times. The ram
acceleration increases as the stroke span increase and
significantly increase as the machine speed increases. The
machine elements are subject to high repeated inertia forces as
a result of repeated acceleration and deceleration of the
massive ram (110 kg), this could result in complicated
vibration and fatigue problems in the shaper machine.
Shaper machine gearbox kinematics has been studied. The
kinematic diagram and speed chart of the shaper gear box are
shown in figures (6& 7) while table (1) gives the number of
teeth of each gear in the gearbox and table (2) gives those
gears dimensions. Low speeds (strokes/min) are required in
shaping machine to reduce the static and dynamic problems.
static deformation and dynamic performance have direct effect
on the tool/workpiece dimensional accuracy and vibration.
The static analysis calculates the effects of steady loading on a
structure, while ignoring inertia and damping effects, such as
those caused by time-varying loads. A static analysis can,
however, include steady inertia loads (such as gravity and
rotational velocity), and time varying loads that can be
approximated as static equivalent. Static analysis is used to
determine the displacements, stresses, strains, and forces in
structures or components caused by loads that do not induce
significant inertia and damping effects. Finite element is a
mathematical method for solving ordinary and partial
differential equations that has the ability to solve complex
problems that can be represented in differential equation form,
as these types of equations occur naturally The sudden impact
in the beginning of cutting stroke and sudden release when the
cutting tool has gone out the cutting surface. Moreover, the
inertia of massive ram represents an additional problem.
Figure (8) shows the assembled gears and shafts as well as the
assembly of the shaper machine gear box. Static deformation
of the gear box at each speed is given in figure (1) and table
(3). High deformation appears at lower speed meshing.
The dynamic analysis is used to determine the vibration
characteristics (natural frequencies and mode shapes) of a
machine and/or machine component while it is being designed.
It also can be starting point for another, more detailed,
dynamic analysis, such as a transient analysis, a harmonic
analysis, or a spectrum analysis. Dynamic analysis is the study
of the dynamic properties of structures under vibrational
excitation. Figures (90& 11) and table (4) show the gear box
mode frequencies at each machine stroke/min. Mode
frequency increases with the increase of machine speed gear
box meshing. Fortunately, the gear box natural frequencies
increase as the meshing of speed increases.
The tool head of a shaper holds the tool rigidly, provides
vertical and angular feeds movement of the tool and allows the
tool to have an automatic relief during its return stroke. The
(a) Ram velocity-crank angle
(b) Ram velocity-stroke position
Figure 4 The Ram or Cutting Tool Velocity with Position Along the
Stroke Span at Different Crank Lengths and Strokes/min.
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Table 1
Gears Number of Teeth
Gear
No
Gear
Module
(mm)
Z1
Z2
Z3
Z4
Z5
Z6
Z7
Z8
Z9
Z10
Z11
Z12
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
4
4
4
4
Z13
4.5
Z14
4.5
Table 2
The Gears Dimensions
Gear
Gear Pitch
Addendum
Diameter
Diameter Da Dp (mm)
(mm)
115.50
122.50
98.00
105.00
98.00
105.00
115.50
122.50
80.50
87.50
133.00
140.00
63.00
70.00
150.50
157.50
65.86
72.86
210.75
217.75
210.75
217.75
351.25
358.25
73.11
488.90
Gear
Dedendum
Diameter
Dd (mm)
106.75
89.25
89.25
106.75
71.75
124.25
54.25
141.75
55.86
200.75
200.75
341.25
80.11
495.90
63.11
478.90
Table 3
The Maximum Deformation (µm) at Different Shaping Machine Speeds
(stroke/min)
Speed No
Speed
Mode Maximum
(Stroke/min)
Deformation (µm)
n1
12.6
88.777
n2
17.5
88.785
n3
25.2
89.053
n4
35
18.693
n5
49.7
99.834
n6
70
11.451
n7
99.4
11.482
n8
140
31.725
+
(a) Ram acceleration-crank angle
(b) Ram acceleration-stroke position
Figure 5 The Ram or Cutting Tool Acceleration with Position Along the
Stroke Span at Different Crank Lengths and Strokes/min.
First shaft assembled
components
Second shaft assembled
components
+
+
+
Third shaft assembled
components
Forth shaft assembled
components
=
Figure 6 The Kinematic of
the Shaper Gear Box.
Figure 7 The Speed Chart of the Shaper
Gear Box.
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Table 5
The Cutting Tool Mode Frequency and Maximum Mode Deformation
Mode #
Mode Frequency (Hz)
Mode Deformation
(µm)
1
3948
4.321
2
4363.7
4.182
3
12564
4.399
4
17942
4.458
5
19381
4.501
6
20160
5.396
Figure 8 The Assembled Shaper Machine Gear Box.
Table 4
The Mode Frequencies at Different Shaping Machine Speeds (stroke/min)
Speed Speed
Mode Frequency (Hz)
No (Stroke Mode
Mode
Mode
Mode
Mode
Mode
per min)
#1
#2
#3
#4
#5
#5
n1
12
279.46 781.81 824.67 894.18 1080.2 1167.6
n2
18
279.36 621.42 781.66 892.57 941.03 1119.7
n3
25
278.98 781.02 892.14 902.69 1086.2 1162.7
n4
35
566.93 805.1 953.57 1031.9 1340.3 1380.5
n5
49
688.94 819.62 969.45 1085.1
1375
1411.7
n6
71
689
819.1
962.1 969.24 1353.1 1411.1
n7
100
689.17 819.42 969.13 1166.5 1409.6 1537.9
n8
140
688.84 819.14 969.35 1409.7 1654.2 1707.2
The vertical slide of the tool head has a swivel base which is
held on a circular seat on the ram. The swivel base is
graduated in degrees, so that the vertical slide may be set
perpendicular to the work surface or at any desired angle.
Apron consisting of clapper box, dapper block and tool post is
clamped up the vertical slide by a screw. The two vertical
walls on the apron called clapper box houses the clapper block
which is connected to it by means of a hinge pin. The tool is
mounted upon clapper block. In the cutting process, the tool
holder and machine structure is subjected to dynamic
excitation forces. The dynamic force excites the modes of the
structure, then the response of the structure may reach risky
proportions due to the excitation, depending on the rigidity
and inherent damping in the structure. The vibration of a
machine tool structure reduces the life of tool tips, the quality
of the surface finish and the tolerances obtained by the
machining process. The problem is related to the dynamic
stiffness of the machine tool structure. One of the objectives of
the research was set to study the dynamic stiffness of a shaper
machine structure, gear box, reciprocating parts, tool holder
and cutting tool. A finite element modal analysis was
conducted to determine the dynamic properties of the structure
to make sure that they are rigid enough to withstand the
dynamic loads applied on them. The level of vibration at the
tool tip, limits the tool life as well as tolerances and the surface
finish obtained by the machining process. The frequencies of
the cutting tool have high values. Higher frequencies can be
obtained when using shorter tool and/or larger tool cross
section. Figure (12) shows the cutting tool mode shapes. Table
(5) presents the cutting tool mode frequency and maximum
mode deformation. Higher tool cross section and shorter
overhang tool length give lower tool mode deformation.
Figure (13) and table (6) give the mode frequencies of the tool
holder equipped with the tool shank. Usually, the rate of
material removal is reduced to lower vibration levels during
machining obtain the required tolerances and surface finish.
The reduction in rate of material removal reduces the
efficiency of the machine. This because the component
manufacturing time is increased and lower production is
obtained from the machine over a period of time. The
objective of the vibration attenuation is to improve the
dynamic stiffness of the machine tool structure, to increase the
rate of material removal and thereby prolonging the life of the
tool tip. Moreover, acoustic noise emission in the machining
process results from the relative motion between the tool tip
and work piece. High levels of acoustic noise causes
discomfort in the working area. The problem is associated with
the dynamic stiffness of the machine tool structure. By
improving the dynamic stiffness of the structure, the level of
noise emission from the machining process can be reduced.
Figure (14) shows the ram and the tool holder assembly. The
ram is a reciprocating member of the shaper. This is semicylindrical in form and heavily ribbed inside to make it more
rigid. It slides on the accurately machined dovetail guide ways
on the top of the column and is connected to the reciprocating
mechanism contained within the column. It is massive
reciprocating part of the machine. Its kinetic energy and inertia
could result in ease metal cutting. In the quick return of the
ram it may causes a problem because it has high kinetic energy
and higher inertia. Figure (15) and table (7) shows cutting tool
and tool holder static deformation at different tool overhang
length. The tool deformation increases as the overhang
cantilever like length increase. The shorter cantilever part of
the cutting tool the rigid tool. This means that at shaping
process the overhanged part of the cutting tool should be as
short as possible.
Table 6
Tool Holder Equipped with Tool Shank Mode Frequencies
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Mode #
Frequency (Hz)
1
2
3
4
5
6
432.31
450.35
568.73
629.97
747.29
923.24
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Table 7
The Maximum Static Deformation in the Cutting Tool
When Fixed at Different Tool Overhang Distance (
).
Tool Overhang
Max Deformation in the Tool (
)
Distance (mm)
20
8.6055
25
8.8056
30
11.399
35
14.623
40
18.897
45
23.405
50
28.508
Figure (16-a) shows the carriage total deformation which is
very small due to higher rigidity and massive of its block,
which leads to the appearance of the first six modes as rigid
body modes, figure (16-b). The dynamic analysis is one of the
important phase in design the systems. A computer base
modelling and simulation gives better understanding regarding
rigid system parameters. There is much scope in development
of an accurate mathematical model and subsequent simulations
for the kinematic and dynamic analysis of the mechanical
systems for the precise application in the industry. From the
present work it is easy to compute velocity and force at each
joint for any real application of quick return mechanism, this
work can be extend in the direction of optimization of weight
of each link for the same dynamic behaviour. Figure (17) gives
the assembly of the shaper machine (structure, base, table and
rocker). The obtained results by using finite element show that
that the selected shaper machine is rigid enough to withstand
static loads and mitigate vibrations.
Total Deformation in Machine Gear Box Meshing # 1 (12 rpm)
Total Deformation in Machine Gear Box Meshing # 5 (49 rpm)
Total Deformation in Machine Gear Box Meshing # 2 (18 rpm)
Total Deformation in Machine Gear Box Meshing # 6 (71 rpm)
Total Deformation in Machine Gear Box Meshing # 3 (25 rpm)
Total Deformation in Machine Gear Box Meshing # 4 (35 rpm)
Figure 10 Mode Frequencies at Different Shaping Machine Speeds
(stroke/min).
Modes @ Machine Gear Box Meshing # 1 (12 rpm)
Modes @ Machine Gear Box Meshing # 5 (49 rpm)
Modes @ Machine Gear Box Meshing # 2 (18 rpm)
Modes @ Machine Gear Box Meshing # 6 (71 rpm)
Modes @ Machine Gear Box Meshing # 3 (25 rpm)
Modes @ Machine Gear Box Meshing # 7 (100 rpm)
Modes @ Machine Gear Box Meshing # 4 (35 rpm)
Modes @ Machine Gear Box Meshing # 8 (141 rpm)
Total Deformation in Machine Gear Box Meshing # 7 (100 rpm)
Total Deformation in Machine Gear Box Meshing # 8 (140 rpm)
Figure 91 The Gear Box Mode Frequencies.
Figure 1 The Static Deformation of the Gear Box
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Cutting Tool Mode # 1
Cutting Tool Mode # 2
Cutting Tool Mode # 3
Cutting Tool Mode # 4
Total Deformation of Cutting Tool @ Overhang length= 20 mm
Total Deformation of Cutting Tool @ Overhang length = 35 mm
Total Deformation of Cutting Tool @ Overhang length = 25 mm
Total Deformation of Cutting Tool @ Overhang length = 40 mm
Total Deformation of Cutting Tool @ Overhang length = 30 mm
Total Deformation of Cutting Tool @ Overhang length = 45 mm
Cutting Tool Mode # 5
Cutting Tool Mode # 6
Figure 12 The Cutting Tool Mode Shapes.
Figure 15 The Maximum Static Deformation in the Cutting Tool
when Fixed on Tool Head at Different Tool Overhang Distance (
).
Figure 13 The Tool Holder Equipped with Tool Shank Mode Frequencies
(a)
(b)
Figure 16 The Carriage Tool Deformation (a) and
The Carriage Rigid Body Modes (b).
Figure 14 Ram and Tool Holder Assembly.
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5. By using Solidworks, Matlab and Ansys it is possible to
optimize the design process by changing one or more of the
initial parameters; those parameters can be updated by
using CAD models.
6. There are no integrated software platform for the virtual
design and analysis of the machine tools.
7. By analyzing the calculation result in the post-processing
program the designers can evaluate the machine properties
during the design stage.
8. Today the main problem in checking structures consists in
importing and preprocessing the CAD model.
9. This approach will help the designer to synthesize the
quick return mechanism for desired stroke length.
10. Dynamic analysis is one of the important phase in design
the systems. A computer base modeling and simulation
gives better understanding regarding rigid system
parameters.
11. There is much scope in development of an accurate
mathematical model and subsequent simulations for the
kinematic and dynamic analysis of the mechanical systems
for the precise application in the industry.
12. In conclusion, this paper has resulted in the creation of a
dynamic simulation model of the machine structure.
Although there is scope for the accuracy of the model to be
improved, in its current form it provides a firm basis for
predicting the behavior of the machine. In addition, much
can be learned from the simulation model in terms of how
the structure is likely to react to different types of
excitations.
References
Figure (17) Shaper Machine Assembly (Structure, Base, Table and Rocker).
Conclusions
1. In this paper complete kinematic analysis of quick-return
mechanism is done by using programming language
Matlab. Positions, angular velocities, angular accelerations
of members, of specific points of the given mechanism are
determined. The given methodology on kinematic analysis,
with a slight modification can be applied to any type of
planar mechanisms.
2. From the present work it is easy to compute position,
velocity, acceleration and force at each joint for any real
application of quick return mechanism, this work can be
extended in the direction of optimization of weight of each
link for the same dynamic behavior.
3. In quick return mechanism, velocity of cutting stroke and
return stroke both change with the change in length of
slotted link and crank length.
4. Using a set of committed software, engineers are able to
analyze and optimize many aspects of real life usage of
machine tool elements without spending money on real
prototypes and this could result in time and money savings.
[1] P.L. Ballaney, “Theory of Machine”, Khama Plublishers, 2-B, Nath
Market, Nai Sarak, Delhi-110006, 1996.
[2] Passi M, “Theory of Machine-I”, Technova Publications, Bungalow
No.44, Jeevan Prakash Hsg. Soc. LIC Colony, Pune-411009, 1st Jan
2000.
[3] Dr. Jagdishlal, “Theory of mechanisms and Machines”, Netaji Subhash
Marg, New Delhi- 110002, ISBN 91-200-0272-5, 1997.
[4] Norton, R., "Design of Machinery: An Introduction to the Synthesis and
Analysis of Mechanisms and Machines", McGraw-Hill, 2010.
[5] Asok Kumar Mallik, Amitabha Ghosh, Gunter Dittrich, "Kinematic
Analysis and Synthesis of Mechanisms", Taylor & Francis, 1994.
[6] Ha, J.L., Chang J.R & Fung, R.F, “Dynamic analyses of a flexible quickreturn mechanism”, the fixed and variable finite-difference grids,
science direct, Journal of Sound and Vibration, Vol. no. 297, PP. 365–
381, 2006.
[7] Erdman A., Sandor G., and Kota S.. "Mechanism Design: Analysis and
Synthesis". Published by Prentice Hall, 2001.
[8] Campbell, M., Nestinger, S.S., “Computer-Aided Design and Analysis of
the Whitworth Quick Return Mechanism”, Computer-Aided
Mechanism Design, Mechanical and Aeronautical Engineering,
University of California Davis, CA 95616, March, 2004.
[9] Uicker, J.J., “Dynamic Force Analysis of Spatial Linkages”, Journal of
Applied Mechanics, ASME Transactions, Vol. 89, Series E, No. 2,
1967.
[10] Paul, B. et. al., “Computer Analysis of Machines with planar Motion IKinematics; II-Dynamics”, Theory Mechanism and Machine, Vol. 10,
PP. 481-507, 1975.
[11] Harry H Cheng, “Computer-Aided Mechanism Design”, Journal of
Mechanical Engineering Science, Vol. 220, March 14, 2004.
[12] R.A. Lekurwale, S.D.Moghe, P.B. Ingle, K.N. Kalaspurkar, “Kinematic
Analysis of Six Bar Quick Return Mechanism using Complex Algebra
724
www.ijaegt.com
Modeling”, International Journal of Advanced Engineering Sciences
and Technologies, 2011, 6, 1, 070 – 076.
[13] Wen-Hsiang Hsieh and Chia-Heng Tsai, “A Study on a Novel Quick
Return Mechanism”, CSME-13, E.I.C. Accession 3051, Vol. 08, 2009.
[14] Ron P Podhorodeski, Scott B Nokleby and Jonathan D Wittchen ,
“Quick-Return Mechanism Design and Analysis Projects”,
International Journal of Mechanical Engineering Education, Vol. 32,
No. 2, pp. 100-114, 2004.
[15] Shrikant R. Patel, D.S.Patel, “Dynamic Analysis of Quick Return
Mechanism Using MATLAB”, International Journal of Engineering
Science and Innovative Technology (IJESIT) Volume 2, Issue 3, May
2013.
[16] Jih-Lian Ha, Jer-Rong Chang, Rong-Fong Fung, “Dynamic Analyses of
a Flexible Quick-Return Mechanism by the Fixed and Variable FiniteDifference Grids”, Journal of Sound and Vibration,; 297(1), PP 365381, 10/2006.
[17] Ali Mohammadzadeh, Nael Barakat and Salim Haidar, “Synthesis and
Dynamic Analysis of a Quick-Return Mechanism Using MATLAB
and SIMULINK”, ASME International Mechanical Engineering
Congress and Exposition, Volume 7: Engineering Education and
Professional Development, Seattle, Washington, USA, November 11–
15, pp. 461-469, 2007.
[18] Jing Zhang, Qiang Gao, “The virtual prototype combination simulation
in design for the Shaper Mechanism based on ADAMS and
SolidWorks”, Electronic and Mechanical Engineering and Information
Technology (EMEIT), 2011 International Conference on --- (Volume
6 ), Harbin, Heilongjiang, China, 12-14 Aug. 2011, PP 2800, 2803.
[19] Ji-gang DONG, “Optimization Design on the Performance of the
Shaper”, 4th International Conference on Mechanical Science and
Engineering (ICMSE2014), PP 3-7 Sanya, China, Jan.2~4, 2013.
Periodical Applied Mechanics and Materials (Volume 472).
[20] Tyagi R. K., Verma M., and Sukanya Borah, “Dynamic Analysis of a
Shaper Machine Cutting Tool and Crank Pin”, Journal of
Environmental Science, Computer Science and Engineering &
Technology, Vol.1.No.3, pp 372-380, 2012.
[21] B.V. Subrahmanyam, A. Srinivasa Rao, S.V. Gopala Krishna, CH.
Rama Krishna, “Static and Dynamic Analysis of Machine Tool
Structures”, International Journal of Research in Mechanical
Engineering & Technology IJRMET Vol. 4, Issue 1, Nov 2013.
[22] Altintas, Y., Brecher, C., Weck, M., and Witt, S., "Virtual Machine
Tool", CIRP Annals - Manufacturing Technology, 54(2), pp. 115-138,
2005.
on Innovations in Engineering and Technology (ICIET'2013) Dec. 2526, 2013 Bangkok (Thailand), pp 131-133.
[29] Sam Paul P., Varadararajan A.S., “Effect of Impact Mass on Tool
Vibration and Cutting Performance During Turning of Hardened
AISI4340 Steel”, RJAV, Vol. XI issue 2/2014, PP 154-163. [30] Nabin
SARDAR, Amiya BHAUMIK, Nirmal Kumar MANDAL, “Modal
Analysis and Experimental Determination of Optimum Tool Shank
Overhang of a Lathe Machine”, Sensors & Transducers Journal, Vol.
99, Issue 12, December 2008, pp. 53-65.
[31] Ewins, D.J., “Modal Testing: Theory and Practice”, Research Studies
Press Ltd., 1984.
[32] Inman, D.J., “Engineering Vibration”, Prentice-Hall, Inc., 1996.
[33] Maia, Silva, He, Lieven, Lin, Skingle, To, Urgueira, “Theoretical and
Experimental Modal Analysis”, Research Studies Press Ltd, 1997.
[23] Syath Abuthakeer S., Mohanram P.V., Mohan Kumar G.,
“Structural Redesigning of a CNC Lathe Bed to Improve its
Static and Dynamic Characteristics”, Annuals of Faculty of
Engineering Hunedoara – International Journal of Engineering,
Copyright Faculty of Engineering ‐ Hundoara, Romania, PP
389 – 394, TOME IX (2011), Fascicule 3, ISSN 1584 –2673.
[24] JongBoon Ooi, Xin Wang, ChingSeong Tan, Jee-Hou Ho and Ying Pio
Lim, “Modal and Stress Analysis of Gear Train Design in Portal Axle
using Finite Element Modeling and Simulation”, Journal of
Mechanical Science and Technology 26 (2), (2012), PP 575-589.
[25] Puttapaka Nagaraju, Ch. Ashok Kumar, “Modeling and Analysis of 2Stage Reduction Gear Box”, International Journal & Magazine of
Engineering, Technology, Management and Research, Volume No:
1(2014), Issue No: 12 (December).
[26] Heiko Panzer, J¨org Hubele, Rudy Eid and Boris Lohmann,
“Generating a Parametric Finite Element Model of a 3D Cantilever
Timoshenko Beam Using Matlab”, Technical Reports on Automatic
Control, Vol. TRAC-4, Nov. 2009. Institute of Automatic Control,
Technical University of Munich, Boltzmannstr, 15, D-85748
Garching, Germany.
[27] Pramod Kumar N., Avinash N. V. ,Sudheer K. V. and Umashankar K.
S., “Modeling and Harmonic Analysis of Turning Operation”
International Journal of Research (IJR) Vol-1, Issue-8, September
2014, pp 77- 86.
[28] Vivek Varia, and Prof. Jegadeeshwaran, “Finite Element Analysis of
Deformation of Single Point Cutting Tool”, International Conference
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