Design and Analysis of Loaded Slat with Support in Both Side Clamped Boundry Condition

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

1. 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.

2. DESIGN OF SLAT

1. 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

2. 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

3. 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

4. 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

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

1. 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

2. Yuemei Liu, Rui Li, Applied Mathematical Modeling, Vol 34, 2010 pp. 856 – 65, ,

3. S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells,

   McGraw-Hill Book Company, New York, 1959

4. F.V. Chang, Rectangular plates with two adjacent edges clamped and other two adjacent edges free, Acta Mech. Solida Sin. 4 (1981) 491 502

5. 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

6. Bengston, H. W. SHIP PLATING UNDER COMPRESSION AND HYDROSTATIC PRESSURE, Trans. Society of Naval Architects and Marine Engineers, Vol. 47,pp. 80, 1939.

7. 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.