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JECET; September-November, 2012; Vol.1, No.3, 372-380.

372


E-ISSN: 2278–179X

JECET; September-November, 2012; Vol.1.No.3, 372-380.
Journal of Environmental Science, Computer Science and
Engineering & Technology
Available online at www.jecet.org
Engineering & Technology
Research Article

Dynamic Analysis of a Shaper Machine Cutting Tool and
Crank Pin

R. K. Tyagi, M.Verma, and Sukanya Borah
Department of Mechanical Engineering, Amity School of Engineering and Technology,
Amity University, Uttar Pradesh, Noida, India
Received: 01 October 2012; Revised: 23 October 2012; Accepted: 00 October 20122012
Abstract: in this article 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 velocity and acceleration
of cutting tool w.r.t time is discussed. Force and torque versus time for crank pin are
also discussed with the help of MSC ADAMS software.
Keyword: Shaper machine, cutting tool, crank pin, dynamic analysis.

1. INTRODUCTION
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 [1]. Machining process by shaper is
conventional machining process but in unconventional machining process there is no direct contact between
tool and work piece [5]
A number of papers have been presented to address the issues of multi-body mechanisms. Examples of their
applications are found in gasoline and diesel engines, where the gas force acts on the slider and the motion is
transmitted through the links. Whether the connecting rod is assumed to be rigid or not, the steady state and
dynamic responses of the connecting rod of the mechanism with time-dependent boundary condition were
Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

373


obtained. In addition, a number of controllers, for example, repetitive control, adaptive control, computed
torque control, and fuzzy neural network control was designed for the multi-body mechanisms [2].
The automatic derivation of motion equations is an important problem of multibody system dynamics.
Firstly, an overview of the matrix calculus related to Kronecker product of two matrices is presented. A new
matrix form of Lagrangian equations with multipliers for constrained multibody systems is then developed to
demonstrate the usefulness of Kronecker product of two matrices in the study of dynamics of multibody
systems. Finally, the equations of motion of mechanisms are derived using the proposed matrix form of
Lagrangian equations as application examples [3].
Operating Mechanisms: Whitworth Quick Return Mechanism: It converts the rotary motion of the electric
motor and gearbox into the reciprocating motion of the ram.

Hydraulic mechanism: A lever operates a valve that varies the quantity of oil delivered to the rain cylinder
and thereby governs the ram speed.
Whitworth Quick Return Mechanism, most widely used mechanism in shaper machines [3]



Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

374


Approaches to Dynamic Analysis: Newtons Laws of motion and D Alemberts Principle:

A free body
diagram of each of the member links
 Equations of force equilibrium
 Inertial forces using kinematic analysis
Multibody Dynamics Equations (Nguyen Van Khangs Approach):
 Kronecker product and a new matrix form of Lagrangian equations
 Differential-algebraic equations of motion of the quick return mechanism
MSC Adams:
 Software for Multibody Dynamics Simulation
Newtons Laws of motion and D Alemberts Principle: Kinematic Analysis of the Whitworth Quick
Return Mechanism. Position Analysis: Loop-closer equations [4]
321
rrr =+
3
3
2
2
1
1



i
i
i
errer =+ (1)
76583
rrrrr +=++
7
7
6
6
8
8
5
5
3
3

iiiii
rrrrer +=++ (2)



From the figure, it can be seen that
843

==,
843
rrr += substituting and rearranging above values in
equations 1 and 2.
2
2
1
1
4
3

iii
rrer += (3)
Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

375


(4)

Velocity Analysis: Taking the time derivative of the loop closer equations 3 & 4,
2
22
2
.
2
1
11
1
.
1
4
43
4
3
.
)()()(


iiiiii
eirereirereire
r
+++=+ (5)
7
77
7
7
.
5
55
5
5
.
4
44
4
4
.
6
66
.
6
6
.
)()()()(


iiiiiiii
eirereirereirereirer +++=+ (6)
These equations can be simplified and reduced using,
0
.
5
.
4
.
21
.
==== rrrr as the links are assumed to be rigid members that may not elongate
0
1
=

link 1 is a rigid link that is unable to rotate.
0
76
==

and 0
6
=

as the links 6 and 7 are assumed to be non-rotating imaginary members
0
7
.
=r Because the output slider 6 is assumed to remain on the ground at all times. The simplified equations
are
2
22
4
43
4
3
.
)()(


iii
eireire
r
=+ (7)
5
55
4
446
.
)()(


ii
eireirr += (8)
Acceleration Analysis: By differentiating equations 7, and 8
22
22
2
.
22
2
22
.
4
43
42
43
4
43
.
4
3
..
)()()()()()(2


iiiiiii
ereireireirereirer +=++ (9)
52
55
5
55
5
55
.
42
44
4
44
.
4
446
..
)()()()()()(


iiiiii
ereireirereireirr +++= (10)
These equations can be simplified by considering 0
.
5
.
4
.
3
=== rrr, simplified equations solved by breaking
the equations into imaginary and real components. Force and moment in a Whitworth quick return
mechanism [4]:
or link 2:


7
7
6
6
5
5
4
4


iii
i
rrrer =+
Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

376


0
23212
=++
xgxx
FFF (11)
0
232122
=+++
ygyy
FFFgm (12)
0)()(
232221228
=+++
ggg
TFrrFrT (13)
For link 3:


0cos
34323
=++
xgx
FFF

(14)
0sin
343233
=+++
ygy
FFFgm

(15)
For link 4:


0cos
4543414
=+++
xgxx
FFFF

(16)
0sin
45434144
=++++
ygyy
FFFFgm

(17)
Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

377


0)()()(
254443443144
=+++
gggg
TFrrFrrFr (18)
For link 5:

0
56554
=++
xgxx
FFF (19)
0
665455
=+++
ygyy
FFFgm (20)
0)()(
56555455
=++
ggg
TFrrFr (21)
For link 6:


0
65616
=+++
lxgxx
FFFF (22)
0
656166
=+++
ygyy
FFFgm (23)
Manually one can find solution of above equations by using matrix. MSC Adam is most likely used method
for dynamic and motion analysis. Adam help the designer how load and stress distributed and dimensions of
machine optimize.
Result and Discussion: Dynamic analysis of shaper machine mechanism by software is one of the prominent
techniques for force, torque, velocity, acceleration with a variety of time vital for industrial applications i.e
failure and life analysis. In this article, stab has been made to assess dynamic analysis for shaper machine
components and cutting tool which would work on the principle of quick return mechanism, and suitable for
Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

378


a wide range of materials for metal cutting. Statistical exploration with the help of MSC ADAM software on
machine components is systemically investigated by means of time variation.

Velocity v/s time plot for the cutting tool:



Acceleration v/s time plot for the cutting tool:



Force v/s time plot for the crank pin:
Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

379





Torque v/s time plot for the crank pin:


REFERENCES
1. R.A.Lekurwale, S.D.Moghe, P.B. Ingle, K.N. Kalaspurkar, Kinematic analysis of six bar quick
return mechanism using comlex algebra modeling, International Journal of Advanced Engineering
Sciences and Technologies, 2011, 6, 1, 070  076.
2. R.F.Fung, C.F. Chang, Force/motion sliding mode control of three typical mechanisms. Asian
Journal of Control, 2009, l.11, .2, 196-210.
3. N.V.Khang, Kronecker product and a new matrix form of Lagrangian equations with multipliers for
constrained multibody systems. Mechanics Research Communication. 2011, 38, 4, 294-299.
Dynamic... R. K. Tyagi et al.
JECET; September-November, 2012; Vol.1, No.3, 372-380.

380


4. M.Campbcll S.S. Nestingcr, Computer Aided Mechanism Design Project, Department of Mechanical
and Aeronautical Engineering, University of California Davis CA, 2004, 2-74.
5. R.K.Tyagi, Abrasive jet machining by means of velocity shear instability in plasma, Journal of
Manufacturing Processes, 2012, 14, 323-327.


*Correspondence Author: R. K. Tyagi; Department of Mechanical Engineering, Amity
School of Engineering and Technology, Amity Univers ity, Uatter Pradesh, Noida, India