Dynamic, Kinematic and Static Analysis of a Shaper …ijaegt.com/wp-content/uploads/2015/04/asy-last-copy.pdf · Dynamic, Kinematic and Static Analysis of a ... Computer-Aided Design

Dynamic, Kinematic and Static Analysis of a Shaper

Machine

Prof. Dr. M. A. Nasser Dr. M. A. Asy [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 sub-

assemblies. 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 taken-

up 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

715 www.ijaegt.com

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 [26-

30]. 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

716 www.ijaegt.com

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 .

By the standard eigenvalues , when A is n order

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 DiscussionsA 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),

717 www.ijaegt.com

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).

-80 -60 -40 -20 0 20 40 60-60

-40

-20

0

20

40

60

Motion of the Shaper Mechanism Links

Stroke Length (cm)

Machin

e H

ight

(0 c

m is t

he C

rank C

entr

Poin

t)

(a)

-80 -60 -40 -20 0 20 40 60-60

-40

-20

0

20

40

60

Stroke (cm).

Machin

e H

igh (

0 c

m is t

he C

rank C

ente

r P

oin

t)

Motion of the Ram, End of the Rocker and Crank

Crank

End of of the Rocker

Ram

(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

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.

Figure 3 The Ram or Cutting Tool Displacement with Crank Angle for Crank

Length 3, 6, 9 & 12 cm.

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

718 www.ijaegt.com

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.

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

static deformation and dynamic performance have direct effect

on the tool/workpiece dimensional accuracy and vibration.

(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.

719 www.ijaegt.com

(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.

Figure 6 The Kinematic of

the Shaper Gear Box.

Figure 7 The Speed Chart of the Shaper

Gear Box.

Table 1

Gears Number of Teeth

Table 2

The Gears Dimensions

Gear

No

Gear

Module

(mm)

Gear

Addendum

Diameter Da

(mm)

Gear Pitch

Diameter

Dp (mm)

Gear

Dedendum

Diameter

Dd (mm)

Z1 3.5 115.50 122.50 106.75

Z2 3.5 98.00 105.00 89.25

Z3 3.5 98.00 105.00 89.25

Z4 3.5 115.50 122.50 106.75

Z5 3.5 80.50 87.50 71.75

Z6 3.5 133.00 140.00 124.25

Z7 3.5 63.00 70.00 54.25

Z8 3.5 150.50 157.50 141.75

Z9 4 65.86 72.86 55.86

Z10 4 210.75 217.75 200.75

Z11 4 210.75 217.75 200.75

Z12 4 351.25 358.25 341.25

Z13 4.5 73.11 80.11 63.11

Z14 4.5 488.90 495.90 478.90

Table 3

The Maximum Deformation (µm) at Different Shaping Machine Speeds

(stroke/min)

Speed No Speed

(Stroke/min)

Mode Maximum

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

+

First shaft assembled

components

Second shaft assembled

components

+ +

+

Third shaft assembled

components

Forth shaft assembled

components

=

720 www.ijaegt.com

Figure 8 The Assembled Shaper Machine Gear Box.

Table 4

The Mode Frequencies at Different Shaping Machine Speeds (stroke/min)

Speed

No

Speed

(Stroke

per min)

Mode Frequency (Hz)

Mode

#1

Mode

#2

Mode

#3

Mode

#4

Mode

#5

Mode

#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.

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 (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 semi-

cylindrical 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 Mode # Frequency (Hz)

1 432.31

2 450.35

3 568.73

4 629.97

5 747.29

6 923.24

721 www.ijaegt.com

Table 7

The Maximum Static Deformation in the Cutting Tool

When Fixed at Different Tool Overhang Distance ( ).

Tool Overhang

Distance (mm)

Max Deformation in the Tool ( )

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)




Figure 1 The Static Deformation of the Gear Box

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)




Figure 91 The Gear Box Mode Frequencies.

722 www.ijaegt.com

Cutting Tool Mode # 1 Cutting Tool Mode # 4



Figure 12 The Cutting Tool Mode Shapes.

Figure 13 The Tool Holder Equipped with Tool Shank Mode Frequencies

Figure 14 Ram and Tool Holder Assembly.

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

Figure 15 The Maximum Static Deformation in the Cutting Tool

when Fixed on Tool Head at Different Tool Overhang Distance ( ).

(a) (b) Figure 16 The Carriage Tool Deformation (a) and

The Carriage Rigid Body Modes (b).

723 www.ijaegt.com

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 andreturn stroke both change with the change in length ofslotted 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.

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 [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 quick-

return 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 I-

Kinematics; 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 Finite-

Difference Grids”, Journal of Sound and Vibration,; 297(1), PP 365-

381, 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.

[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 2-

Stage 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

on Innovations in Engineering and Technology (ICIET'2013) Dec. 25-

26, 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.

725 www.ijaegt.com

http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5996364

http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5996364

http://www.scientific.net/AMM

Dynamic, Kinematic and Static Analysis of a Shaper …ijaegt.com/wp-content/uploads/2015/04/asy-last-copy.pdf · Dynamic, Kinematic and Static Analysis of a ... Computer-Aided Design

Documents