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- Open Access
- Total Downloads : 186
- Authors : Vivek M. Ingawale, Ashok Hulagabali
- Paper ID : IJERTV4IS060780
- Volume & Issue : Volume 04, Issue 06 (June 2015)
- DOI : http://dx.doi.org/10.17577/IJERTV4IS060780
- Published (First Online): 27-06-2015
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Design and Analysis of Loaded Slat with Support in Both Side Clamped Boundry Condition
Vivek M. Ingawale and Ashok Hulagabali
Dept. of Mechanical Engineering, Maratha Mandal Engineering College, Belagavi, Karnataka, India.
Abstract The geometry approach is introduced for accurate stress, bending and FOS analysis of rectangular Slat with two edges fixed boundary conditions. Solid Edge V5 software and are in good agreement. Slats are used in slat conveyor system in automobile assembly line system.
KeywordsClamped Slat, Stress, Deflection, FOS
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INTRODUCTION
Conveyor system is a mechanical system used in moving materials from one place to another and finds application in most processing and manufacturing industries such as: chemical, mechanical, automotive, mineral, pharmaceutical, electronics etc. There are various types of conveyor systems available such as gravity roller conveyor, belt conveyor, slat conveyor , bucket conveyor ,flexible conveyor, belt driven live roller conveyor, chain conveyor, etc. It includes loading, moving and unloading of materials from one stage of manufacturing process to another. A slat conveyor has the open links of chain drag material along the bottom of hard faced MS (mild steel) or SS (stainless steel) trough. The trough is fixed and slats are movable. The slats are the mechanical components that fixed between two strands of chain which drags the material from feeding end to the discharge end. These slats are available in different widths and lengths as per the site requirements. A small gap is made purposely between slats and trough. The slat conveyors are designed for horizontal and inclined transport of sawdust, chips, bagasse and other bulk goods. Slat conveyors are the traditional and most common means for distributing bagasse to boilers.[1]
Slat is a rectangular plate, which is an important structural part of various engineering applications such as in assembly conveying system, houses and bridge decks, pavement of airports and highways. Slat bending with various boundary conditions have been investigated for many year, but most of past methods are not suitable for all boundary conditions[2]. Timoshenko and Woinowsky-Krienger.[3] the superposition method for bending solution. Chang[4] was investigated accurate solution for slat with two edges clamped and others edges are free, which superposed six solutions, yet used trial functions. Leissa and Niedenfuhr [5] employed the method of point matching to reveal the
solutions for four problems of a square plate with two adjacent edges free and the others fixed or simply supported. Some numerical methods are used for to determine the deflections of slat such as finite element method, finite difference method, integral equations, finite strip method etc.
The design of slat that deflect under edge loading and lateral loading, which neglect the shearing as well as stretching in middle surfaces of slates.
Bengston [6] to attack the problem of rectangular plates with simply supported or clamped edges, under combined axial and lateral loading.
The case of a clamped rectangular plate subjected to uniformly distributed lateral loading and. [7] forces in its plane was obtained by Chang and Conway by the so-called Marcus' method. Thus, in general, when plate deflection becomes larger the stretching of the middle plane and hence the effect of the membrane stresses should be considered.
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DESIGN OF SLAT
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Design of Loaded Slat under clamped boundry condition.
Figure 1. Solid model of slat
Problem statement
In many structural problems, the analysis of stresses, deflections in rectangular plates subjected to two end clamped boundary conditions. Axial loading- loading in the plane of the plate
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Units
TABLE 1 Symbols Description Units
Where, values of
b = 55 mm d = 240mm
t = s = 8 mm h = 224
Bending moment of beam,
Mb = M1 + M2 1
Symbols
Description
Unit
L
Length of Slat
mm
d
Width of Slat
mm
t
Thickness of Slate
mm
W
Load
N
b
Height of Slat
mm
I
Moment of Inertia
mm4
Mb
Bending Moment
Nmm
Deflection
mm
y
Distance From Natural axis to extreme
fiber
mm
a
Area of section
Mm2
Stress
Mpa
WL Wa
Mb = + 2
8 8
Mb = 2.45 x 106 N-mm
Moment of inertia for body 1, For C shape
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Theoretical Calculations
I1=
(2 x s x b3 ) + (h x t3 ) 3
– A (b – y)2 3
Calculations of slat deflection, stress & factor of safety.
Given data is,
Length of slat L= 1300mm, a = 1150mm Width of slat d= 240mm
Where, y = b-
(2 x s x b2 ) + (h x t2 )
4
2bd – 2h(b – t)
(2 x 8 x 552 ) + (224 x 82 )
Thickness of slat t= 8mm Height of Slat b
y = 55 –
(2 x 55 x 240) – 2 x 224(55 – 8)
Load W=8000N
Material= Mild Steel (Fe410)
We going to considering slat is beam which has both end is clamped or fixed and load is acting on a center of beam.
Figure 2. Both side Fixed Beam
y = 43.26mm
Area = A,
A = bd – h (b-t)
A = (55 x 240) 224(55-8) A = 2672mm
So therefore,
I1 = 557.29 x 103 mm4
Moment of inertia for body 2, For L shape
3
I2 = 1 ty3 + a a – y3 – a – ta – y – t3 5
Where,
area a = t (2a t) = 5 [(2×5) 5] = 325 mm2
y = a-
a2 + at – t2
6
2(2a – t)
Therefore,
I2 = 36.35 x 103 mm4
Figure 3. LS View of Slat
Total moment of inertia, I
I = I1 + I2
I = 557.29 x 103 + 36.35 x 103
I = 593.64 x 103 mm4
Deflection of slat,
WL3
TABLE 4 Constraints
Number of Constrained Faces
=
192 EI
= 0.77 7
8
TABLE 5 Study Properties
Mesh Type
Tetrahedral mesh
Number of elements
9,373
Number of nodes
19,191
Solver Type
Nastran
Stress in slat,
M E
Wkt,
= = 8
I y R
Therefore, ,
Type
Extent
Value
X mm
Y mm
Z mm
Von Mises Stress
Min.
6.397e-003
kpa
-70.39
32.93
-4.35
Max.
1.751e+005
kpa
5.29
70.00
-4.35
M
TABLE 6 Stress Results
= y
I
6
= 2.45 x 10 x 43.26
593.64 x 103
= 178.53 N/mm2
Analysis of Loaded Slat With Support Under Two Sided Clamped Boundary Condition
Solid edge is modeling tool, which is easy to use to develop the parts. Solid edge is a product development tool, give the flexibility and parametric design. In this project work the slat model is developed in solid edge modeling tool. The clamped slat simulation process is carried out in solid edge simulation express for separate parts, to Femap for defining and analyzing the whole system. In simulation process gives the values of stress, deflection and factory of
safety.
Figure 3 Stress Analysis
TABLE 1 Part Properties
Part Name
240x55x8thkx1300lx35x35x5angle.par
Mass
29.512 kg
Volume
3767634.481 mm^3
Weight
289.216 n
TABLE 2 Material Properties
Material Name
steel, structural
Mass Density
7833.000 kg/m3
Young's Modulus
199947953 Kpa
Poisson's Ratio
0.290
Thermal Expansion
Coefficient
0.0000 /c
Thermal Conductivity
0.032 kw/m-c
Yield Strength
262000.766 Kpa
Ultimate Strength
358527.364 Kpa
TABLE 3 Load and Constraint Information Load Set
TABLE 7 Displacement Results
Type
Extent
Value (mm)
X mm
Y
mm
Z
mm
Resultant Displacement
Min.
0.00e+000
-16.78
47.07
8.65
Max.
1.39e+000
12.37
651.61
0.65
Figure 4 Deflection Analysis
Load Set Name
load 1
Load Type
Force
Number of Load Elements
2
Load value
8000.0
1.496
TABLE 8 Factor of Safety
FOS Value
Figure 5 Factor of Safety Result
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Results and Discussions
To comparing both results which are finding out by theoretically and by analytically. The both result are given below. The percentage of results variation was observed and are in permissible range.
TABLE 9 Displacement Results
THEORETICAL RESULT |
ANALYTICAL RESULT |
|
Stress |
1819.95 kg/cm2 |
1783.89 kg/cm2 |
Deflection |
0.77 mm |
1.39 mm |
FOS |
2.29 |
1.496 |
ACKNOWLEDGMENT
The authors would like to thank the TAL Manufacturing Solution Pvt. Ltd. Pune and MM Engineering College, Belagavi for support given to this project work.
REFERENCES
-
Udgave A. S., Khot V. J. Design of Slat Conveyor for Bagasse Handling in Chemical Industry, IJIRD, Vol. 3, 2014, Issue 8 pp. 140- 145
-
Yuemei Liu, Rui Li, Applied Mathematical Modeling, Vol 34, 2010 pp. 856 – 65, ,
-
S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells,
McGraw-Hill Book Company, New York, 1959
-
F.V. Chang, Rectangular plates with two adjacent edges clamped and other two adjacent edges free, Acta Mech. Solida Sin. 4 (1981) 491 502
-
A.W. Leissa, F.W. Niedenfuhr, Bending of a square plate with two adjacent edges free and the others clamped or simply supported, AIAA J. 1 (1963) pp. 116120
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Bengston, H. W. SHIP PLATING UNDER COMPRESSION AND HYDROSTATIC PRESSURE, Trans. Society of Naval Architects and Marine Engineers, Vol. 47,pp. 80, 1939.
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Conway, H. D. BENDING OF RECTANGULAR PLATES SUBJECTED TO A UNIFORMLY DISTRIBUTED LATERAL LOAD AND TO TENSILE OR COMPRESSIVE FORCES IN THE PLANE OF THE PLATE" J. of Applied Mechanics, Vol. 16, p. 301, 1949
AUTHORS BIOGRAPHIES
Mr. Vivek M. Ingawale student at Maratha Mandal Engineering College, Belagavi, completing his M.Tech in Mechanical Machine Design of Visvesvaraya Technological University, Belagavi, Karnataka, India.
Mr. Ashok Hulagabali is a Professor, Dept. of Mechanical Engineering, Maratha Mandal Engineering College, Belagavi, and he is my project guide.