Stress & Deflection Analysis of Belleville Spring

IOSR Journal of Mechanical and Civil Engineering (IOSRJMCE)

ISSN : 2278-1684 Volume 2, Issue 5 (Sep-Oct 2012), PP 01-06 www.iosrjournals.org

www.iosrjournals.org 1 | Page

Stress and Deflection Analysis of Belleville Spring

1H.K.Dubey,

2Dr. D.V. Bhope

1Pg Student of Dept of Mechanical Engineering R.C.E.R.T, Chandrapur, India 2Professor, Dept of Mechanical Engineering R.C.E.R.T, Chandrapur, India

Abstrac: This paper reports stress and deflection analysis of a Belleville Spring using finite element method. The different combinations of ratios of its outer diameter and inner diameter i.e. (D/d) and its Height to

thickness i.e. (h/t) have been considered to investigate the principal stresses on inner (i) and outer (o) surfaces of the spring along with the deflections. Finite element method is used for analysis. The FE results are

compared with existing analytical results.

Keywords: Stress, Deflection, Finite element method, Belleville Spring

I. Introduction A Belleville spring, disc spring, Belleville washer, conical compression washers are all names for the

same type of spring. It has a frusto-conical shape which gives the washer a spring characteristic. Belleville washers are typically used as springs, or to apply a pre-load or flexible quality to a bolted joint or bearing. A

conical washer can be stacked to create a powerful compression spring. The Belleville washer is often used to

support applications that have high loads and insufficient space for a coil spring. Disc springs are conical shaped

washers designed to be loaded in the axial direction only. The spring geometry consists of four parameters

namely Internal Diameter (d), Outer Diameter (D), Thickness (t), and Height (h) which is shown in figure 1.

Figure 1: Front view& Top view of a Belleville Spring

A Belleville spring experiences a deflection and stress when a load is applied in the axial direction. It

has a very non-linear relation between the load applied and the axial deflection. The stress distribution is non-

uniform for this spring. The axial force is applied at the periphery of the inner diameter due to which the stresses

are induced at the inner surface & at the outer surface, which depends on geometric parameters. The deflections

and the stresses induced at the inner surface and at the outer surface depend on the ratios of its height to

thickness (h/t) and its outer diameter to inner diameter (D/d). This work deals with the deflection and the

stresses induced in Belleville spring due to constant axial force acting on the inner surface of the conical spring

for various ratios of (h/t) & (D/d).

II. Literature Review Many researchers have carried out stress and deflection analysis of a Belleville spring. Monica

Carfagni [1] carried out the stress and deflection analysis to prepare a CAD method for the checkout and design

of the Belleville springs. The method eliminates the need to resort to conventional trial-and-error techniques. In

a matter of seconds, it rapidly and accurately checks out and designs Belleville springs, outputting the load-

deflection characteristics in graphic and table formats and can generate a dimensioned drawing. G. Schrfmmer [2]

carried out the stress and deflection analysis of a slotted Belleville spring to develop a analytical relationship for

deflection and stress of a slotted conical spring.

III. Introduction To Problem, Scope & Methodology Though the geometry of the Belleville spring appears to be simple with conical shape but the stress

distribution is quiet complex due to the axial load. It is predicted that the axial load is responsible for axial

compressive stress and also for bending stress induced in the Belleville spring. The analytical equations are

Stress And Deflection Analysis Of Belleville Spring


derived largely on the basis of bending moments to simplify the derivations. In finite element analysis it is

possible to model the exact geometry of the spring and to investigate the effect of axial load on the stresses, and

deflections of the spring. Hence it is possible to determine the exact values of stresses in Belleville spring which

are induced on account of the combination of axial stress and bending stress.

Therefore, the present work deals with the determination of stresses and deflection in Belleville spring

using FEA. The results obtained from FE analysis are compared with existing analytical equations. This study will lead to justify the validity of existing analytical equations and to estimate the conditions where it may

become error prone. The scope & methodology is described as follows:

In the Present research work an approach for the analysis of a Belleville Spring has been carried out under axial compressive load (static axial load of 1000N has been considered for analysis).

The Various geometrical parameters of a Belleville Spring i.e. D, d, h & t have been varied to investigate the stresses and the deflections induced in the Belleville spring. Following ratios are considered for

analysis:-

D/d= 1.2, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5 & h/t= 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75,3

Lastly, the FE results have been compared with the existing analytical equations available for the Belleville Spring and an effort have been made to show the variations in the stresses and deflections with respect to

the geometrical parameters and an attempt have been made to establish certain relations which will help to evaluate the stresses & deflection for any geometry of a Belleville Spring with accuracy. The load

deflection characteristic is also investigated.

IV. Finite Element Analysis Of Belleville Spring In this work a simple Belleville Spring analysis has been done. For Each ratio of D/d, all h/t ratios have

been varied to calculate the Deflection, principal stresses on Inner and Outer surface which are induced in the

spring. Outer Diameter of Belleville Spring is considered as 125 mm and Height of the spring is considered as 5

mm. A constant Force of 1000N has been applied on the inner surface of the spring in Y- direction. The analysis

is done by imposing boundary conditions such that the spring could deflect only along X&Z-direction. The analytical equations for deflection & stresses are given in equations (1) to (6):

])2

)([(1

4 322

tththDME

F

(1)

2

/

1)/(

)/(log14.3

6

dD

dD

dDeM (2)

tChC

DM

Ei 2122

)2

(1

4

(3)

tChC

Eo 212

)2

(1

4

(4)

1

)/(log

1)/(

log14.3

61

dDe

dD

d

De

C

(5)

2

1)/(

log14.3

62

dD

d

De

C

(6) Where M, C1, C2 are Constants, E= modulus of Elasticity (2*10

5 Mpa) and = poisons ratio (0.3). The

representative stress and deformation contours for principal stresses on inner & outer surface along with the

deflection are shown in figures 2, 3,& 4 as an illustration for D/d= 1.5 & h/t= 1.5.The load- deflection

characteristic of the spring is also studied for the ratio of D/d=2;h/t=1.5 and D/d=4;h/t=1.5. The force is varied

from 100N to 1000N for load deflection characteristics. The results are presented in forthcoming sections.



Figure 2: Deformation (Deflection) of a Belleville spring (mm)

Figure 3: Minimum Principle Stress Contour at the Inner Surface (MPa)

Figure 4: Maximum Principle Stress Contour at the outer Surface (MPa)

V. Results The FE analysis revealed the principal stresses of outer and inner surface along with the deflections for

various ratios of D/d and h/t. The variation of deflection and principal stresses are shown in from figure 5 to

figure 19.The principal stresses and deflections are also determined using analytical equations and its

comparison are also shown in figure 5 to figure 19.

Figure 5: Deflection for D/d=1.2 Figure 6: Deflection for D/d=2



Figure 7: Deflection for D/d=3 Figure 8: Deflection for D/d=4

Figure 9: Deflection for D/d=5 Figure 10: Principal Stress on Inner

Surface for D/d=1.2

Figure 11: Principal Stress on Inner Figure 12: Principal Stress on Inner

Surface for D/d=2 Surface for D/d=3

Figure 13: Principal Stress on Inner Figure 14: Principal Stress on Inner




Figure 15: Principal Stress on Outer Figure 16: Principal Stress on Outer Surface for D/d=1.2 Surface for D/d=2

Figure 17: Principal Stress on Outer Figure 18: Principal Stress on Outer


Figure 19: Principal Stress on Outer Surface for D/d=5

The load deflection characteristics for D/d=2;h/t=1.5 and D/d=4;h/t=1.5 are shown in figure20 & 21

respectively.

Figure 20: Load Deflection Characteristic for D/d=2 & h/t= 1.



Figure 21: Load Deflection Characteristic for D/d=4 & h/t= 1.5

VI. Discussion And Conclusion 1. It is observed from the figs.5, 6, 7, 8, and 9 that the nature of variation is similar between analytical and FE

values for deflection. It is also observed that as the ratio of D/d varies from 1.2 to 5 the deviation between

analytical and FE values increases. It is also observed that for each ratio of D/d as h/t is increasing, the

deviation between analytical and FE values is also increasing. This trend observed for deflection may be

due to the following facts:

As D/d ratio goes on increasing, the Conicality of the spring also increases. Due to this Bending stress predominates the axial compressive stress and this deviation may have occured.

As h/t increases the spring behavior approaches to that of a plate due to reduction in its thickness. 2. From the figs 10, 11, 12, 13 and 14 it can be observed that the principal stresses at the inner side of the

spring is exactly same for the analytical calculations & FE results with a few exceptions for all values of D/d & h/t.

3. From the figs. 15, 16, 17, 18 and 19 it is seen that the analytical values of principal stresses for the Outer surface are more than FE values for all ratios of D/d & h/t. But as h/t increases the deviation between

analytical and FE values also increases. This trend is also observed for deflection.

4. From figs. 20 & 21 i.e. load-deflection characteristic it is seen that the Belleville spring with lower ratio of D/d has marginal deviation of deflection between analytical and FE values with the increase in magnitude

of the force. However for higher ratios of D/d the deviation of deflection between FE and analytical values

is quiet noticeable. This is due to the non-linear behavior of the conical spring. Thus the analytical

equations of deflection may become error prone for higher values of D/d and h/t for higher loads.

Thus, it can be concluded that the analytical equation for Belleville springs though estimates the

maximum stresses and deflection for certain cases , but finite element analysis is recommended for accurate estimation of maximum stress and deflection in case of Belleville spring under given loading condition.

References

[1]. Almen. J. O., and Laszlo, A., "The Uniform Section Disk Spring," Trans. ASME, Vol. 58, 1936, pp. 305-314. [2]. Spotts, M. F., "Mechanical Design Analysis," Prentice Hall Inc., Englewood Cliffs, N. J., 1964, pp. 80-90. [3]. Shigley J.E. Mechanical engineerng design. McGraw-Hill International Edition (1986).

[4]. Wahl, A. M., "Mechanical Springs", McGraw Hill Book Co, New York, 1963, pp. 179-181. [5]. Schremmer, G., "Endurance Strength and Optimum Dimensions of Belleville Springs," ASME-paper 68-WA/DE-9, 1968. [6]. Belleville SpringsDesign Manual, E. C. Styberg Eng. Co., Racine, Wis.

[7]. Schnorr Disc Spring Handbook, Karl A. Neise Inc., Woodside New York.




Behavior of Lateral Resistance of Flexible Piles in Layered Soils

1B.S.Chawhan,

2S.S.Quadri,

3P.G.Rakaraddi,

1Asst. Prof, Govt. Engineering College, Haveri-581110, 2Prof.and Head, BVBCET, Hubli-580031,

3Associate Professor,BEC, Bagalkot,

Abstract: This paper presents an experimental investigation on the lateral load carrying capacity of model piles of different flexural stiffness embedded in loose sand between dense sand and dense sand between loose

sand layered soil strata. Attempts has been made to study the variation of lateral stiffness, eccentricity and soil

layer thickness ratio and the effect of various parameters on the magnitude of Nh. The result of a model tested

for the piles embedded in IS grade-II dry Ennore sand under monotonic lateral loadings. Experimental results

are used for the load-deflection curves (p-y curves) for laterally loaded piles. The proposed p-y curves were

compared to the existing curves with Nh and were evaluated with the experimental data. The ultimate lateral soil

resistance and subgrade modulus were investigated and discussed.

Key Words: Subgrade modulus, flexural stiffness, ground line deflection, model tests, piles, soil-pile interaction.

I. Introduction: Pile foundations are the most popular form of deep foundations used for both onshore and offshore

structures.They are often used to transfer large loads from the superstructures into deeper, competent soil layers

particularly when the structures is to be located on shallow, weak soil layers. Piles are frequently subjected to

lateral forces and moments; for example, in quay and harbor structures, where horizontal forces are caused by

the impact of ships during berthing and wave action; in offshore structures subjected to wind and wave action;

in pile-supported earth retaining structures; in lock structures, in transmission-tower foundations, where high

wind forces may act; and in structures constructed in earthquake areas such as Japan or the West Coast of the

United States.

The ultimate capacity of flexible piles and small pile groups in homogeneous and layered sand has been reported by Meyerhof and Ghosh 1989. But the state of art does not indicate a definite methodology by which

the values of Nh can be obtained. Most of the investigators agree that Nh depends on soil and pile properties and

value decreases with the increase in lateral load. Palmer et.al. (1954) indicated that width of pile has an effect on

deflection, pressure and moment along pile even when flexural stiffness (EI) of pile is kept constant. Murthy

(1992) has developed some relationship between Nh and other parameters like soil properties, flexural strength

and lateral load. Dewaikar and Patil (2006) studied the analysis of laterally loaded pile in cohesionless soil and

the Byung Tak Kim, Nak-Kyung Kim, Woo Jin Lee, and Young Su Kim studied the experimental Load Transfer

Curves of Laterally Loaded Piles (April 2004).

This paper presents the experimental investigation of lateral load carrying capacity of model piles of

various materials in homogeneous sand (both in loose and dense state), loose between dense and dense between

loose sand layers with horizontal loads acting at various eccentricities. In all the tests, the outer diameter (d) and depth of embedment (D) of piles are kept constant.

II. Experimental Set-Up And Model Tests The test were carried in IS grade-II dry Ennore sand having placement density of 13.35kN/m3 and =310 for loose soil condition and 15.89kN/m3, =390 for dense condition. The tests were conducted in two steps. a) The soil condition is loose sand layer between dense sand layer with H/D ratio of 0.25, 0.50, 0.75, and 0.90. b) The

soil condition is dense sand layer between loose sand layer with H/D ratio of 0.25, 0.50, 0.75,and 0.90, where

H is the thickness of middle layer and D is the total depth of embedment of the pile(=300mm). In both the cases

the eccentricities of 0, 50, 100, 150 and 200mm are conducted in homogeneous loose sand layer and dense sand layer. The outside diameters of the piles are 16mm for solid Steel and Wooden Piles. Hollow Aluminium pile

with 16mm outside and 0.3mm thickness. The embedment depths of all the piles are 300mm. The flexural

rigidity of steel, wooden and Aluminium piles were 642.106Nm2, 506.12Nm2 and 51.041Nm2 respectively. The

relative stiffness factors for steel, wooden and Aluminium were 0.1192, 0.939 and 0.0094 respectively for

Loose sand layer and 0.0263, 0.0207 and 0.0020 for Dense sand layer. The horizontal displacement and rotation

of pile cap are recorded by L.V.D.T. and two dial gauges. The stabilized Rainfall-Technique this standard technique is available in standard literature and this technique was used to pour the sand in the testing steel

tank. Figure.1 shows schematic sketch of experimental setup.

Behavior Of Lateral Resistance Of Flexible Piles In Layered Soils


Fig.1 Schematic sketch of experimental setup

The ultimate load bearing capacity of model piles are obtained from load deflection curves by the

following criteria.

(A). Single tangent method (B). Double tangent method

(C). Load corresponding to ground line deflection

equal to 10% pile diameter

(D).Load corresponding to ground line deflection equal to 20% pile diameter

(E). Log-Log method.

It is observed that different criteria yield different ultimate load (vide Table-1). For the present

analysis, the average of first three criteria is taken as ultimate pile capacity.

III. Method Of Analysis Reese and Matlock (1956) have developed a set of equations based on dimensional analysis for

computing deflection, slope, moment etc, along the pile. These equations are very useful for predicting the non-

linear behavior of laterally loaded piles provided the magnitude of Nh is known at each load level. For

deflection and slope of free head pile at ground level, the following equations are given by Reese and Matlock

(1956).

EI

MT

EI

PTYg

23 62.1435.2 (1)

EI

MT

EI

PTS g

75.162.1 2 (2)

where,Relative Stiffness factor4

1

n

hN

EIT (3)

P=Lateral load at pile head; M=Moment at pile head (=P*e); e=Eccentricity of horizontal load measured from ground level; and EI=Flexural stiffness of the model pile.

From the observed lateral resistance and corresponding ground line deflection and rotation, the value of

coefficient of soil modulus variation Nh is estimated for different types of model piles by using the above

equations (1) and (2).

Murthy .V.N.S (1976) has proposed the equations for determining Nh in cohesionless soil at each stage of

loading as

m

t

hP

AN (4)

where Pt= Lateral load at pile head, m is a constant equal to 0.8 and A is a factor which is a function of the

effective unit weight of the soil and flexural stiffness EI of the pile.

P

A

P

EIBCN s

t

f

h 2

15.1156 (5)

where, Pt=Lateral load; As=Constant for pile in sand; P=Pt(1+0.67e/T); and Cf =Correction factor for the angle

of friction = 3*10-5(1.315) , where is in degrees.

IV. Results and Discussions The experimental results were carried out and tabulated in following Table-1 and Table-2.



Table-1 presents ultimate loads of model Aluminium piles (embedded in Dense between loose sand layer)

estimated from observed load deflection curves using different criteria mentioned earlier. It can be noted that

ultimate load of a pile is not unique but depends on different methods or criteria. Table-2 presents ultimate loads

of different pile materials in Loose between Dense layers estimated from observed experimental values. It can

be noted that ultimate lateral resistance of pile decreases with the increase of H/D ratio in Loose between dense

sand layer where as it increases with the increase of H/D ratio in Dense between Loose sand layer. Fig.2 shows typical load deflection curves of steel, wooden and aluminium piles embedded in loose sand between dense sand

layer with e=50mm, H/D=0.25. In fig.3 the lateral load deflection curves of aluinium pile embedded in dense

sand between loose sand layer having H/D=0.9 with varying eccentricity. The figure reveals that ultimate lateral

resistance of pile decreases with increase in eccentricity. This phenomena is observed in all types of model piles

irrespective of all condition (i.e loose sand layer, dense sand layer, loose sand layer between dense sand layer

and dense sand layer between loose sand layer).

In fig.4 the variation of coefficient of soil modulus v/s flexural stiffness(EI) curve of three model piles

in dense between loose sand layer having h/D=0.90 with varying eccentricity. The figure reveals that flexural

stiffness of pile increases with increase in variation of coefficient of soil modulus. This phenomena is observed

in all conditions of soil layers.

In fig.5 indicates the variation ultimate load of model piles with flexural stiffness EI when they are

embedded in dense sand layer between loose sand layer having various H/D ratio and e=50mm. this reveals that ultimate load increases with increase in flexural stiffness of pile when all other conditions are kept constant.

Table-1.Comparison of ultimate load (N) by various methods (Aluminium pile, H/D=0.5, Dense between loose

sand layer).

Eccentricity, e in mm Methods

(Different Criteria)

e (mm) A B C D E

50 20 14 16 32 33

100 19 19 15 26 33

150 12 09 12 24 26

200 10 08 08 22 24

Table-2. Ultimate load (N) of different pile (Steel, Wooden, and Aluminium pile, H/D=0.5, Dense between Loose sand layer).

Eccentricity

, e in mm H/D Steel

Woode

n

Alum

inum

50 0.50 16.96 29.66 14.98

100 0.50 13.04 22.82 11.52

150 0.50 11.74 20.54 10.37

200 0.50 10.43 18.25 9.22



0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

0.00 5.00 10.00 15.00 20.00

Loa

d (

N)

Deformation(mm)Fig.2 Load Deflection Curve of

model piles embedded in dense

between loose sand layer

steel Pile

Aluminium

Pile

Wooden Pile

S

0.00

20.00

40.00

60.00

80.00

100.00

0.00 10.00 20.00

Load

(N)

Deflection(mm)Fig.3 Load Deflection Curve of

Aluminium Pile embedded in

dense between loose sand layer

0mm ecc

50mm ecc

100mm ecc

150mm ecc

200mm ecc

Fig.4. Variation of soil modulus Nh with Flexural stiffness of piles embedded in dense between loose sand layer,

H/D=0.90, n=2/3.

Fig.5. Variation of ultimate load with Flexural stiffness of piles embedded in dense between loose sand layer.

Dense sand layer between loose sand layer, H/D=0.9

Dense sand layer between loose

sand layer, H/D=0.9



V. Conclusions The following conclusions are made based on the experimental investigations.

(i) The ultimate lateral resistance of single pile decreases with the increase in eccentricity of load, it is about 8 to 11%.

(ii) The ultimate resistance of single pile subjected to horizontal load decreases with increase in eccentricity

of load on the same pile provided the depth of embedment remains constant for homogeneous loose and

dense layers, also loose between dense and dense between loose layered soils, and it is about 10 to 12%.

(iii) The ultimate lateral resistance of pile increases with increased value of flexural stiffness of pile and it is

about 8 to 13% and the magnitude of Nh decreases with the increase in magnitude of horizontal load

irrespective of flexural stiffness of pile and soil condition.

(iv) In dense sand, the magnitude of Nh increases with the increase in value of flexural stiffness of pile where

as in case of loose sand the value decreases with the increase in EI value of piles and the ultimate lateral

load carried is more (10 to 12%) in dense between loose sand layer and vice versa.

The tests may be conducted in multiple layers of Loose sand layer and Dense sand layer with constant and

variable thickness of layers and also the Variation of Coefficient of soil modulus (Nh) in a different soil layers along the depth can be studied.

References [1]. Byung Tak Kim, nak-Kyung Kim, Woo Jin, Lee [2]. and Young Su Kim. (2004), Experimental Load- Transfer Curves of Laterally Loaded Piles In Nak-Dong River Sand, Journal of

Geotechnical and Geoenvironmental Engineering, 130(4),416-425.

[3]. Dewaikar D.M and Patil P.A. (2006), Analysis of a Laterally Loaded Pile in Cohesionless Soil, IGC 2006,14-16 December 2006, Chennai, INDIA, 467-4.

[4]. Dewaikar D.M and Patil, D.S.(2001), Behaviour of laterally loaded piles in cohesion-less soil under oneway cyclic loading, The New Millennium Conference, 14-16 December-2001.

[5]. Ghosh,D.P and Meyerhof,G.G.(1989), The ultimate bearing capacity of flexible piles in layered sand under eccentric and inclined

loads, Indian Geotech.J,(19)3, 187-201.

Murthy.V.N.S. (1992), Nonlinear Behaviour of Piles Subjected to Static Lateral Loading.

[6]. P.Bandopadhyay and. B.C.Chattopadhyay. (1989), Ultimate Lateral Resistance of Vertical Piles, (2)4, 165-168.

[7]. Rees.L.C and Metlock.H. (1956), Non-dimensional solutions proportional to depth, Prooceedings 8th Texas conference on Soil Mechanics and Foundation Engineering, Special publication no.29, Bureau of Engineering Research, University of Texas, Austin.

[8]. Terzaghi.K.(1955), Evaluation of coeeficient of subgrade reaction, Geotechnique, (5)4, 297-326.


ISSN: 2278-1684 Volume 2, Issue 5 (Sep-Oct 2012), PP 12-19 www.iosrjournals.org

www.iosrjournals.org 12 | P a g e

Measuring Transit Accessibility Potential: A Corridor Case Study

Rajesh J Pandya Town Planner, Town Planning Department, Surat Municipal Corporation, Gujarat, India

ABSTRACT: Buses are the most widely used and essential component of a public transit system and the selection of a bus route are very important as it affects the overall performance of the system and its efficiency.

Moreover the bus routes and bus stop locations are very important criteria for selection of this mode of

transport by commuters. Bus stops attain their importance to the transit service as they are the main points of contact between the passenger and the bus. Considering spatial attributes, both the location and the spacing of

bus routes and bus stops significantly affect transit service performance and passenger satisfaction, as they

influence travel time in addition to their role in ensuring reasonable accessibility. Knowing that every transit

trip begins and ends with pedestrian travel, access to a bus stop is considered a critical factor for assessing the

accessibility of the stop location. In this paper, on the basis of the actual population surrounding the stop, the

potential of a particular bus route / corridor is estimated for a particular corridor so as to assess a bus route /

corridor on a more spatial basis. This potential measures the efficiency of a bus route / corridor through the

surrounding road network, which can be used to compare the performance / efficiency of two or more routes /

corridors in a system and also o ways to improve the performance of a particular route by increasing number

of bus stops or changing their locations.

I. INTRODUCTION Public transportation is a key component of a sustainable transportation system that improves mobility

without placing economic and environmental burden of increased auto ownership on the travelling population.

Due to lack of public transport facilities, significant growth in personalized vehicle population and considerable

reduction in city bus transportation is observed.

Most of the metropolitan cities lack proper accessibility to public transport. Transport and land use

planning have a significant role in promoting accessibility, and at the same time accessibility is becoming

increasingly important in making sound and sustainable land use and transport decisions. Therefore, t is

important to develop models that are able to measure accessibility to public transport networks.

II. ACCESSIBILITY CONCEPT Accessibility is a commonly used concept in transport planning, urban planning and in geography.

Accessibility is often defined as the ease of travel between two locations. The Oxford Advanced learner's

Dictionary (2000) defines 'accessible' as "that can be reached, entered, used, seen, etc." Accessibility can be

defined as the effort or ease with which activities can be reached using the available transportation system.

Accessibility has been regarded a property of places showing how easily they can be accessed from other places,

as well as a property of people indicting how easily they can reach a set of potential destinations.

2.1 ACCESSIBILITY MEASURES: CERTAIN APPROACHES

Baradaran & Ramjerdi (2001) classified the approaches for measuring accessibility into:

Travel cost approach which reflects the "spatial separation" characteristics of a transportations net work, i.e.,

distance, time, generalize cost, etc. Constraints based approach which reflects the number of activities (or opportunities) that can be reached from

an origin point within a certain time limit.

Gravity approach derived from the gravity model formula, which reflects both the attractiveness of zones and

the quality of the transportation system that connects them.

Utility based approach developed on basis of disaggregate / behavioral approach originally proposed by Ben

akiva and Lerman(1978) and therefore they reflect, in addition to the characteristics of the transportation system,

the utility that different alternatives of services or facilities have to the users;

Composite approach developed by combining the space time and utility based models and it assumes uniform

travel speed;

2.2 TRANSIT ACCESSIBILITY Many factors contribute to transit accessibility, including reasonable proximity from the origin and the

destination to the service, safe, pleasant and comfortable walking pathways to transit facilities, and acceptable

parking facilities for cars or bicycles, etc. In public transit planning, access to the service and accessibility



provided by the service are two very important issues (Murray et al 1998). Access is the ease with which people

can reach the transit stop. Accessibility is the suitability of the transit system in helping people get to their

destinations in a reasonable amount of time as shown in Fig 1.

Fig 1 Public Transport System Access

(Source: Murray et al 1998)

Of the many factors, walking distance to transit facilities is recognized as an important determinant of

transit use. A quarter mile approximately 400 m. is the commonly accepted distance for people willing to walk

to use transit (Demetsky and Lin 1982) Cerero (1994) found that proximity to a rail station was a much stronger

determinant of transit use than land use mix or quality of the walking environment. Levinson and Brown West

(1984) indicated in their study that transit use sharply drop after the first 0.06 mile, and diminish beyond 0.36 mile. Zhao, Li, and Chow (2002) found that transit use deteriorates exponentially with walking distance to

transit stops. A decay function was developed to reflect the deteriorating trend in transit use with respect to walk

distance. So, increasing suitable access to transit systems is seen as a means of attracting more people to the

transit system.

2.3 MEASURING TRANSIT ACCESS

GIS can be thought of as a system, digitally creates and "manipulates" spatial areas that may be

jurisdictional, purpose or application oriented for which a specific GIS is developed. For measurement of

accessibility GIS is very important tool. Traditionally, transit access is measured using the GIS buffer technique.

In this method access is defined as a walking distance to a public transit stop, and then all the areas within the

threshold distance of all stops are identified. People living in the areas identified as within the threshold distance

are said to have suitable access. Generally the specified distance is quarter mile from bus stops. There are problems with this method. One is that it assumes Euclidean walking distance to a transit stop. When in reality

the pathways are always longer, and must follow the actual street network. Another issue is that information on

the exact residence or location of individuals is not available. The most precise geographic information which

exists is census data reported at some aggregate scale.

III. STUDY CORRIDOR 3.1 Location and Linkages

Dumas road is one of the major roadway corridor for the city of Surat. It is located on the western part of the city. It starts from Athwa gate junction at the inner ring road and ends at the coastal villages of Dumas

and Bhimpore. The population density is very high at the eastern part of the corridor where, important

government establishment like Government Multi story Office Complex, Police Bhavan, Session and District

Courts generate a very high volume of traffic. Moreover educational and commercial campuses, hospitals and

commercial establishments also add to the heavy traffic flow.

A number of important traffic routes are linked with this corridor like inner ring road at Athwa junction; Ghod Dod road at Parle Point junction; City light road at Jani Farsan junction; Piplod / University

Road at Kargil Chowk; Vesu Road near Big Bazar, Udhana Magdalla Road at Y junction and the 90 mts. outer

ring road i.e. Sachin Magdalla National Highway. These major roads are very important linkages and increase

the importance of Athwa Dumas Corridor.

ORIGIN

DENSTINATION

ACCESSIBI

LITY

WITHIN

NETWORK

Access

Access



85

57

88

58

93

101

91

97

96

94

89

9060

6134

62

59

33

37

13

99

30

92

SW.Z.

1110

12

13

02

100

98

98

98

0201

0304

06

07

08

0910

11

14 13

12

15

17

16

18

20

19

21

22

24

23

05

31

29

30

28

26

25

27

32

339

491

379

276

33

395

95

491

548

647

589

389

271

501

293

501

618

316

766

337

892

399

194

193

176

1193

301

664

656

642

346

419

636

1613

Locations of Bus stops

RIVE

R TA

PI

Fig 2 Athwa Dumas Corridor and Location of Bus Stops

3.2 DEMOGRAPHIC PROFILE

This corridor of length 16.47 km is located the South West (Athwa) administrative zone of Surat City and in doing so it passes through nine different census ward out of which three wards are in the old city limits

and six census wards fall within the areas newly annexed into municipal limits after 2006. The population and

density of these words are shown in Table 1 and 2.At present there are 33 designated bus stops along the route.

Table 1 Census Wards of Old City Areas Through which Athwa Dumas Road passes

Ward Nos. 33

( TP 5 Athwa Umra) 61

(Umra)

62

(Piplod)

Population 30,585 54,046 17,588

Density 17,991 11,852 9,160

Table 2 Census Wards of New City Areas Through which Athwa Dumas Road passes

Ward Nos. 95

(Rundh)

96

(Magdalla)

97

(Gavier)

99

(Dumas)

100

(Sultanabad)

101

(Bhimpor)

Populations 4355 6104 2585 7225 3659 7861

Density 1192 2655 637 351 814 1230

IV. POTENTIAL OF CORRIDOR. 4.1 Public Transit Accessibility Index (PTAI)

It is required to bring the walking distance in certain modules for relative comparison so that one can consider the level of service status. In view of this Accessibility Index value with reference to walking distance

accessibility may be defined as the increase of walking distance (in Kilometers).

TABLE 3 PUBLIC TRANSIT ACCESSIBILITY INDEX

Walking Distance (Meters) < 250 350 * 450 550 > 950

PTAI (WD) 4 2.85 2.2 1.81 1.05

* 1x 1000 = 2.85

350

Here the PTAI (WD) value of 250, 350, 450, and 950 are converted into index values of 4, 2.85, 2.22,

1.81 and 1.05. Higher the index value better is the transit accessibility.



4.2 Potential of a Bus Stop

BUS STOP BUS STOP

1 2 3 n-2 n-1 n

d

L (Length of corridor)

FIGURE 3 SCHEMATIC DIAGRAM OF BUS ROUTE

Number of Bus Stop = i (1 to n)

Population of Zone = Pi Persons

Area of Zone = Zi Square kilometer

Density of Zone Di = Pi / Zi Person per square kilometer

Public Transit Accessibility Index

for a Walking Distance w = PTAI w

Area within walking distance Aw = w2 Population catered by Bus Stop (i)

Within Walking Distance w is Piw = Di x Aiw

Potential of Bus Stop for

walking distance w (i) = Piw x PTAI w

Gross Potential of Bus Stop for all three walking distance = Potential w Average Potential of Bus Stop = Gross Potential (i) + GrossP(i + i) 2 d

n Average Potential of Bus Stop Overall Potential Index of route = i=1

'L'

4.3 Calculating the Potential

(1)First of all the density of population for the census ward within which the bus-stop is located is

found.

Density (persons / km2) = (population of Zone) Di = Pi

Area of Zone Zi

(2) For different walking distance (250 m, 350m, 450 m) The Public Transit Accessibility Index (PTAI) is found.

Walking

Distance (w)

250 350 450

PTAI (w) 4.00 2.86 2.22

(3) Population within the command area (walking distance) of bus-stop which has direct walking accessibility to

bus stop is calculated and D (i) is found.

Population (iw) = Density Di x Aw

Potential of a bus stop (i) for a walking distance w is for = P iw x PTAI (w).

(4) Using different walking distances 250m,350m and 450 m different potentials for all bus stops is found and

the sum of all three potentials for a particular bus stop gives the gross potential of a bus stop (i) for all three

walking distances. Using 6TPAI (i) and using gross potential of adjacent bus stops the average Potential of a bus

stop is found. (5) Sum total of all the Average potentials divided by number of stops gives the overall Public Transport

Accessibility Index of the route per bus stop.

Overall Potential = Average Potential Total number of bus stops

If the sum is divided by the total length of the route (bus corridor 'L') we get the overall Potential per

running kilometer. n

Average Potential of Bus Stop Overall Potential = i=1

Length of the Route 'L'



In the present case study the potential of the corridor is calculated w.r.t. 33 present / designated stops

and also w.r.t length of the corridor (per km).the Potential w.r.t length can be utilized for comparison of

performance / potential of different corridors or for some corridor for different time.

The potential w.r.t bus stands ( per stop) can be used for analysis of improvement of the bus route by

increasing the number of bus stands and their locations.

V. CONCLUSION Using the powerful GIS network analysis functions, indices can be developed to assist in the

assessment of a bus stop locations, also the process can be used to find out the potential of the bus route as a

whole or for different parts of it. The results can be utilized for improvement of the performance of the public

transport system and can be used for further studies.

Accessibility and linkage with potential users of the bus stop and using information on population

densities for different urban districts and transforming it in terms of persons per km; hence, an extra important

attribute for the polyline layer can be added other than the travel distance or time. This can be viewed as a three dimensional coordinate where the third dimension represents the population. Moreover, the effect of time on the

demand variability also can be introduced through the use of appropriate data in morning / evening peak periods

or even on a seasonal basis.

Distribution of potential users within the circular buffer zone for example, by creating various circles

radiating from the location of the bus stop with 50m increments and locating the share of the total network

length in km within each.

Study of accessibility thirst areas and analysing ways to meet this requirement so as to satisfy a demand

and at the same time improve the potential of the transit system.

Analysis of important routes meeting, closing and making with the present Athwa Dumas corridor

under study and the effect of changes, variations, improvement of the new additional roads.

Accessing the effect of feeder services though para transit modes or feeder routes to strengthen the existing bus

route. Suggesting new bus stops after assessing the shortfall for present condition and additional requirement for projected population growth and development of the area.

REFERENCES

[1] AccessibilityGuidelineforBuildingandFacilitiescap:10TransportationFacilities,Availableashttp://www.accessboard.gov/adaag/html/a

daag2.htm;

[2] Ammons, D.N.2001, Municipal Benchmarks: Assessing Local Performance and Establishing Community Standards, Second

Edition. Sage,thousand Oaks,CA.

[3] Central Ohio Transit Authority, 1999, Planning and Development Guidelines for Public Transit.COTA,Columbus,OH. [4] Christchurch, Bus Stop Location Policy, Available as http://www.ccc.govt.nz/policy/bus-2,asp;

[5] Mohamed A. Foda, Using GIS for Measuring Transit Stop Accessibility Considering Actual Pedestrian Road Network.

APPENDIX I

PTAI ( i ) FOR WALKING DISTANCE 250 METRE

Bus

Stop

CensusWard

Area

(Sq.

Km)

Pop.

at 2011

Density

(Persons

per Km2)

For Walking Distance 250 Meter

PTAI=

1/0.250

Pop. 250 =

D x 0.1964

P(i) x

PTAI

1 33 1.7 30585 17991 4.00 3533.47 14133.87

2 33 1.7 30585 17991 4.00 3533.47 14133.87

3 33 1.7 30585 17991 4.00 3533.47 14133.87

4 33 1.7 30585 17991 4.00 3533.47 14133.87

5 33 1.7 30585 17991 4.00 3533.47 14133.87

6 33 1.7 30585 17991 4.00 3533.47 14133.87

7 61 4.56 54046 11852 4.00 2327.77 9311.08

8 61 4.56 54046 11852 4.00 2327.77 9311.08

9 62 1.92 17588 9160 4.00 1799.11 7196.42

10 62 1.92 17588 9160 4.00 1799.11 7196.42

11 62 1.92 17588 9160 4.00 1799.11 7196.42



12 62 1.92 17588 9160 4.00 1799.11 7196.42

13 62 1.92 17588 9160 4.00 1799.11 7196.42

14 95 3.652 4355 1192 4.00 234.21 936.83

15 95 3.652 4355 1192 4.00 234.21 936.83

16 95 3.652 4355 1192 4.00 234.21 936.83

17 95 3.652 4355 1192 4.00 234.21 936.83

18 96 2.299 6104 2655 4.00 521.46 2085.82

19 96 2.299 6104 2655 4.00 521.46 2085.82

20 97 4.061 2585 637 4.00 125.02 500.07

21 97 4.061 2585 637 4.00 125.02 500.07

22 97 4.061 2585 637 4.00 125.02 500.07

23 97 4.061 2585 637 4.00 125.02 500.07

24 97 4.061 2585 637 4.00 125.02 500.07

25 99 20.577 7225 351 4.00 68.96 275.84

26 99 20.577 7225 351 4.00 68.96 275.84

27 99 20.577 7225 351 4.00 68.96 275.84

28 99 20.577 7225 351 4.00 68.96 275.84

29 100 4.491 3659 815 4.00 160.02 640.06

30 100 4.491 3659 815 4.00 160.02 640.06

31 100 4.491 3659 815 4.00 160.02 640.06

32 100 4.491 3659 815 4.00 160.02 640.06

33 101 6.389 7861 1230 4.00 241.65 966.60

APPENDIX II

PTAI ( ii ) FOR WALKING DISTANCE 350 METRE

Bus

Stop

CensusWa

rd

Area

(Sq.

Km)

Pop.

at 2011

Density

(Persons

per Km2)

For Walking Distance 350 Metre

PTAI =

1/0.350

Pop. 350 =

D(i) x 0.385

Pop. of

350-250

P(i) x

PTAI

1 33 1.7 30585 17991 2.86 6926.60 3393.14 9694.67

2 33 1.7 30585 17991 2.86 6926.60 3393.14 9694.67

3 33 1.7 30585 17991 2.86 6926.60 3393.14 9694.67

4 33 1.7 30585 17991 2.86 6926.60 3393.14 9694.67

5 33 1.7 30585 17991 2.86 6926.60 3393.14 9694.67

6 33 1.7 30585 17991 2.86 6926.60 3393.14 9694.67

7 61 4.56 54046 11852 2.86 4563.09 2235.32 6386.64

8 61 4.56 54046 11852 2.86 4563.09 2235.32 6386.64

9 62 1.92 17588 9160 2.86 3526.76 1727.65 4936.16

10 62 1.92 17588 9160 2.86 3526.76 1727.65 4936.16

11 62 1.92 17588 9160 2.86 3526.76 1727.65 4936.16

12 62 1.92 17588 9160 2.86 3526.76 1727.65 4936.16

13 62 1.92 17588 9160 2.86 3526.76 1727.65 4936.16

14 95 3.652 4355 1192 2.86 459.11 224.90 642.59

15 95 3.652 4355 1192 2.86 459.11 224.90 642.59

16 95 3.652 4355 1192 2.86 459.11 224.90 642.59

17 95 3.652 4355 1192 2.86 459.11 224.90 642.59

18 96 2.299 6104 2655 2.86 1022.20 500.75 1430.70

19 96 2.299 6104 2655 2.86 1022.20 500.75 1430.70

20 97 4.061 2585 637 2.86 245.07 120.05 343.01

21 97 4.061 2585 637 2.86 245.07 120.05 343.01

22 97 4.061 2585 637 2.86 245.07 120.05 343.01



23 97 4.061 2585 637 2.86 245.07 120.05 343.01

24 97 4.061 2585 637 2.86 245.07 120.05 343.01

25 99 20.577 7225 351 2.86 135.18 66.22 189.20

26 99 20.577 7225 351 2.86 135.18 66.22 189.20

27 99 20.577 7225 351 2.86 135.18 66.22 189.20

28 99 20.577 7225 351 2.86 135.18 66.22 189.20

29 100 4.491 3659 815 2.86 313.68 153.66 439.03

30 100 4.491 3659 815 2.86 313.68 153.66 439.03

31 100 4.491 3659 815 2.86 313.68 153.66 439.03

32 100 4.491 3659 815 2.86 313.68 153.66 439.03

33 101 6.389 7861 1230 2.86 473.70 232.05 663.01

APPENDIX III

PTAI ( ii ) FOR WALKING DISTANCE 450 METRE

Bus

Stop

Census

Ward

Area

(Sq.

Km)

Pop.

at 2011

Density

(Persons

per Km2)

For WalkingDistance 450 Metre

PTAI

=

1/0.450

Pop. 450 =

D(i) x 0.6364

Pop. of

450-350

D(i) x

PTAI

1 33 1.7 30585 17991 2.22 11449.58 4522.98 10051.07

2 33 1.7 30585 17991 2.22 17991.18 11064.57 24587.94

3 33 1.7 30585 17991 2.22 17991.18 11064.57 24587.94

4 33 1.7 30585 17991 2.22 17991.18 11064.57 24587.94

5 33 1.7 30585 17991 2.22 17991.18 11064.57 24587.94

6 33 1.7 30585 17991 2.22 17991.18 11064.57 24587.94

7 61 4.56 54046 11852 2.22 11852.19 7289.10 16198.00

8 61 4.56 54046 11852 2.22 11852.19 7289.10 16198.00

9 62 1.92 17588 9160 2.22 9160.42 5633.66 12519.24

10 62 1.92 17588 9160 2.22 9160.42 5633.66 12519.24

11 62 1.92 17588 9160 2.22 9160.42 5633.66 12519.24

12 62 1.92 17588 9160 2.22 9160.42 5633.66 12519.24

13 62 1.92 17588 9160 2.22 9160.42 5633.66 12519.24

14 95 3.652 4355 1192 2.22 1192.50 733.39 1629.75

15 95 3.652 4355 1192 2.22 1192.50 733.39 1629.75

16 95 3.652 4355 1192 2.22 1192.50 733.39 1629.75

17 95 3.652 4355 1192 2.22 1192.50 733.39 1629.75

18 96 2.299 6104 2655 2.22 2655.07 1632.87 3628.59

19 96 2.299 6104 2655 2.22 2655.07 1632.87 3628.59

20 97 4.061 2585 637 2.22 636.54 391.47 869.94

21 97 4.061 2585 637 2.22 636.54 391.47 869.94

22 97 4.061 2585 637 2.22 636.54 391.47 869.94

23 97 4.061 2585 637 2.22 636.54 391.47 869.94

24 97 4.061 2585 637 2.22 636.54 391.47 869.94

25 99 20.577 7225 351 2.22 351.12 215.94 479.86

26 99 20.577 7225 351 2.22 351.12 215.94 479.86

27 99 20.577 7225 351 2.22 351.12 215.94 479.86

28 99 20.577 7225 351 2.22 351.12 215.94 479.86

29 100 4.491 3659 815 2.22 814.74 501.07 1113.48

30 100 4.491 3659 815 2.22 814.74 501.07 1113.48

31 100 4.491 3659 815 2.22 814.74 501.07 1113.48

32 100 4.491 3659 815 2.22 814.74 501.07 1113.48

33 101 6.389 7861 1230 2.22 1230.40 756.69 1681.54



APPENDIX IV

POTENTIAL INDEX FOR OVERALL ATHWA DUMAS CORRIDOR

B

us

St

op

Ce

ns

-

us

W

ar

d

Area

(Sq.

Km)

Pop.

at

2011

Densi

ty

(Pers

ons

per

Km2)

Potential for Walking

Diastance

Sum Of

{D(i) x

PTAI(i)}

Average

of

adjacent

stops

Dist

ance

betw

een

Bus

Stop

s

Potenti

al

Index 250

Meter

350

Meter

450

Meter

1 2 3 4 5 6 7 8 9 10 11 12

1 33 1.7 30585 17991 14133.87 9694.67 10051.07 33879.61

2 33 1.7 30585 17991 14133.87 9694.67 24587.94 48416.48 41148.05 339 121.38

3 33 1.7 30585 17991 14133.87 9694.67 24587.94 48416.48 48416.48 491 98.61

4 33 1.7 30585 17991 14133.87 9694.67 24587.94 48416.48 48416.48 379 127.75

5 33 1.7 30585 17991 14133.87 9694.67 24587.94 48416.48 48416.48 276 175.42

6 33 1.7 30585 17991 14133.87 9694.67 24587.94 48416.48 48416.48 395 122.57

7 61 4.56 54046 11852 9311.08 6386.64 16198.00 31895.72 40156.10 491 81.78

8 61 4.56 54046 11852 9311.08 6386.64 16198.00 31895.72 31895.72 548 58.20

9 62 1.92 17588 9160 7196.42 4936.16 12519.24 24651.82 28273.77 647 43.70

10 62 1.92 17588 9160 7196.42 4936.16 12519.24 24651.82 24651.82 589 41.85

11 62 1.92 17588 9160 7196.42 4936.16 12519.24 24651.82 24651.82 389 63.37

12 62 1.92 17588 9160 7196.42 4936.16 12519.24 24651.82 24651.82 271 90.97

13 62 1.92 17588 9160 7196.42 4936.16 12519.24 24651.82 24651.82 501 49.21

14 95 3.652 4355 1192 936.83 642.59 1629.75 3209.16 13930.49 293 47.54

15 95 3.652 4355 1192 936.83 642.59 1629.75 3209.16 3209.16 501 6.41

16 95 3.652 4355 1192 936.83 642.59 1629.75 3209.16 3209.16 618 5.19

17 95 3.652 4355 1192 936.83 642.59 1629.75 3209.16 3209.16 316 10.16

18 96 2.299 6104 2655 2085.82 1430.70 3628.59 7145.12 5177.14 766 6.76

19 96 2.299 6104 2655 2085.82 1430.70 3628.59 7145.12 7145.12 337 21.20

20 97 4.061 2585 637 500.07 343.01 869.94 1713.02 4429.07 892 4.97

21 97 4.061 2585 637 500.07 343.01 869.94 1713.02 1713.02 399 4.29

22 97 4.061 2585 637 500.07 343.01 869.94 1713.02 1713.02 194 8.83

23 97 4.061 2585 637 500.07 343.01 869.94 1713.02 1713.02 193 8.88

24 97 4.061 2585 637 500.07 343.01 869.94 1713.02 1713.02 176 9.73

25 99 20.577 7225 351 275.84 189.20 479.86 944.91 1328.96 1193 1.11

26 99 20.577 7225 351 275.84 189.20 479.86 944.91 944.91 301 3.14

27 99 20.577 7225 351 275.84 189.20 479.86 944.91 944.91 664 1.42

28 99 20.577 7225 351 275.84 189.20 479.86 944.91 944.91 656 1.44

29 100 4.491 3659 815 640.06 439.03 1113.48 2192.57 1568.74 642 2.44

30 100 4.491 3659 815 640.06 439.03 1113.48 2192.57 2192.57 346 6.34

31 100 4.491 3659 815 640.06 439.03 1113.48 2192.57 2192.57 419 5.23

32 100 4.491 3659 815 640.06 439.03 1113.48 2192.57 2192.57 636 3.45

33 101 6.389 7861 1230 966.60 663.01 1681.54 3311.15 2751.86 1613 1.71

Overall Potential Index=37.43 per stop Total= 1235.06

Overall Potential Index=74.98 per km




The Performance Evaluation of a Cassava Pelletizer

1O. B. Oduntan,

2O. A. Koya,

3M. O. Faborode,

4 A. O. Oduntan

1Department of Agricultural and Environmental Engineering, University of Ibadan, Ibadan Nigeria. 2Department of Mechanical Engineering, Obafemi Awolowo University, Ile-Ife 22005, Nigeria. 3Department of Agricultural Engineering, Obafemi Awolowo University,Ile-Ife 22005.Nigeria.

4National Horticultural Research Institute, P.M.B.5432, Idi-Ishin Ibadan Nigeria

Abstract: This paper reports on the performance evaluation of a machine for cottage level production of pellets from cassava mash. Peeling, grating and drying freshly harvested cassava tubers, produced cassava flour. The

flour was mixed with water at different blend ratios to form cassava mash of different moisture contents. The

performance of the pelletizer was evaluated in terms of the density, durability, crushing strength and cyanide

content of the pellets, and the throughput of the machine, against the moisture content of the mash (18, 20 and

22 % w.b.), die size (4, 6 and 8 mm) and the auger speed (90, 100 and 120 rpm). Test results showed that the

bulk density and the durability of pellets decreased while the moisture content increased significantly (p

The Performance Evaluation Of A Cassava Pelletizer


hopper, heat exchanger barrel, reduction gear and the frame. Each component was designed following standard

engineering principle [8].

Fig 1: A picture of the experimental cassava pelletizer

2.2 Performance Evaluation 2.2.1 Sample preparation

Cassava tubers were obtained from a local farm in Ibadan, Nigeria. The tubers were washed, peeled

with knife, grated and dried into cassava flour. The moisture content of the cassava flour at the time of the

experiment was determined using the oven method [9]. Samples of the flour were conditioned by adding water

at different blend ratio (2.5, 3.0 and 3.5 kg of water to 10 kg of the flour) for 10 minute in a mixer (Fexod AS

170, Nigeria). The samples were dried gradually at 140 oC in a heat chamber and weighed occasionally until the

predetermined moisture content of 18, 20 and 22% (w.b) were obtained. Each experimental run was replicated

three times.

2.2.2 Quality assessments of the pellets

The performance of the pelletizer was evaluated on the basis of the throughput of the machine and the

quality of pellets recovered at the various shaft speeds and die sizes, for cassava mash of different initial moisture contents. Quality of the pellet was defined in terms of its durability, crushing strength, bulk density and

the cyanide content.

The durability (D u ) of the pellets was determined according to ASABE S269.4 [10]. A 100 g sample

of the pellet was tumbled at 50 rpm for 10 min in a dust tight enclose (Engineering Laboratory Equipment,

London). Sieves with 3, 5, and 7 mm apertures were used respectively for the pellets extruded from the 4, 6 and

8 mm dies. Durability was expressed as the percent ratio of the mass of pellets retained on the sieve after

tumbling (Mpa) to mass of pellet before tumbling (Mpb). Durability is said to be high when the measured value is

above 80%, medium when between 70 and 80% and low when below 70% [7]:

uD = %100pb

pa

M

M (1)

Bulk density of the pellet was determined as recommended by ASABE S269.4 [10]. A container was

filled using a funnel, without compacting the content. The material was levelled with the top surface of the

container and weighed. Pellet and flour bulk densities were obtained from the ratios of the measured masses of

samples in the container to the volume of the container. Five measurements of each experimental run were taken

to obtain the average values and standard deviations. Bulk density is an important parameter in the design of

systems for drying, ventilation and cooling of pellets during storage [12]; [13].

The strength at rupture of the specimens of the pellet was measured in diametral compression (Lloyd

instruments, model 1000R, Hampshire, UK). The compression test equipment was fitted with a 500 N load cell.

The length of each pellet was measured with a calliper and recorded before it was positioned for compression at a rate of 10 mm/min. Thus, the force applied on the pellet increased gradually and the load at breakage was

noted.

In the determination of the cyanide content, 0.1 g of pellet from each of the 4, 6 and 8 mm dies was

weighed into a flatbottom plastic bottle with a screw cap lid; 0.5 mL of 0.1M-phosphate buffer at pH 6 was added with a pipette [14]. A yellow picrate paper was attached to a plastic strip in the bottle containing sample

but not touching the liquid in the bottle. The bottle was immediately closed with the screw-capped lid. A blank



was also prepared, as above, into another screw capped bottle and the difference was used in calculating the

total cyanide content.

III. Results And Discussion 3.1 Quality Attributes of the Pellets

A summary of the quality attributes of the pellets extruded from the machine is shown in Table 1. A

typical trend of the moisture content of the pellets is shown in Fig. 2. The results show that pellets extruded

through the largest holes and at the highest speed are more moisture-laden than pellets from the narrow die at

the least speed. This is not unusual, because running the mash against a smaller die holes generate heat and

pressure in the barrel, which reduced the moisture content of the pellet. However, statistical analysis showed

that only the moisture content of the

Fig. 2: Effect of die size on the moisture content of the pellet from cassava mash at 18% moisture content

(w.b.) pelletized at various speeds.

mash and die size had significant effects on the moisture content of the pellets, but the effect of the speed of the

pelletizer was not significant (Table 2).



3.2 Effects of Machine Parameters on Product Quality Performance evaluation of the machine showed that bulk density of the pellets decreased with higher

diameter of the die through which the pellets were extruded, indicating that the bigger pellets are more loosely

packed, providing more voids to facilitate air flow for ventilation and drying, but requiring more space for

handling and transportation.

Similarly, the crushing strength and the durability of the pellets decreased with the die size, showing that the bigger pellets will crumble more readily during handling than the smaller ones. Maximum durability of

84 % was recorded at 20 % (w.b.) moisture content using 4 mm die, while the least was 62% using the 8 mm

die. It is likely that the binding forces in small size pellets have strengthened the bond between individual

particles in the pellet. Furthermore, the higher quantity of heat generated in the barrel due to the stricter

frictional resistance, due to the small hole size (4 mm) must have enhanced starch gelatinization in the pellet,

thus, binding the particles together more firmly. A typical curve of variation of pellets durability with die size at the different auger speeds is shown in Fig. 3. Statistical analysis showed that only the die size has significant

effect on pellet durability.

Fig. 3: Effect of die size on the durability of the pellets at 18% MC pelletized at various speeds and die sizes.

A summary of the effects of the moisture content of the mash and the operational parameters of the

machine on the quality of the pellets is shown in Table 3. The corresponding throughput capacities of the

machine are also shown in the table.

TABLE 3: Summary of Duncans multiple range tests on main effects (speed, moisture content and die) on pellets moisture content, durability and machine throughput

Variable MC (%) Durability (%) Throughput (kg/hr)

Speed 90 18.11a 73.84a 51.7a

100 18.16a 73.36a 54.4b

120 18.25a 74.11a 50.4b

MC 18 16.32a 74.30a 53.5a

20 18.17b 73.81

a 59.2

b

22 20.02c 73.76a 52.4b Die 4 17.49a 81.87a 53.7b

6 18.28b 75.79b 53.6b

8 18.75c 63.66c 57.7a

Values with the same superscript in the same column are not significantly different at p



References [1]. Adeeko, K. A. and Ajibola, O. O, Processing factors affecting yield and quality of mechanically expressed groundnut oil, Journal of

Agricultural Engineering Research, 45, 1990, 31-43.

[2]. Ashaye O. A., Couple A. A., Fasoyiro S. B. and Adeniji A, Effect of Location and Storage Environment on the Quality Attributes of

Gari in South-Western Nigeria, World Journal of Agricultural Sciences 1(1) 2005, 52-55.

[3]. Hrishi, N. Problems and prospects of cassava production in India. Cassava Processing and Storage. In: Proceedings of an interdisciplinary workshop, Thailand, Int. Develop. Res. Centre IDRC-031e 1974 pp.59-62.

[4]. Prestlokken, E, Protein value of expander-treated barley and oats or ruminants, Agricultural University of Norway, Doctor Scientiarum Thesis 1999:5,142pp, 1999

[5]. Pabis, S., Jayas, D. S, Grain drying Theory and Practice (John Wiley, New York, 1998)

[6]. Odigboh, E. U, Mechanization of cassava production and processing: A decade of design and development, University of Nigeria Inaugural Lecture, Series No.8, 1985.

[7]. Kwatai, J. T, Rural Cassava Processing and Utilization Centre UNICEF/IITA Collaborative Program for Household Food Security (

Lidato Press, Ibadan, 1986)

[8]. Oduntan, O. B, Development of a cassava pelletizer. Unpublished M.Sc. Thesis. Obafemi Awolowo University, Ile-Ife, Nigeria, 2010.

[9]. American Society for Testing and Materials (ASTM), Standard practice for reporting uniaxial strength data and estimating Weibull distribution parameters for advanced ceramics.(ASTM, 1995) C 1239-95: 1-18.

[10]. American Society of Agriculture and Biological Engineering (ASABE), Standard S269.4 Cubes, pellets and crumbles-definitions

and methods for determining density, durability, and moisture content. (ASABE, 2003) St. Joseph, M1

[11]. Adapa. P. K., Schoenau, G. J., Tabi, L. G., Sokhansanj. S. and Crerar. B .J. (2003), Pelleting of fractionated alfalfa products. ASABE Paper No. 036069. ASABE Paper, Joseph, M1,

[12]. Fasina, O. O. and Sokhansanj, S, Modelling the bulk cooling of alfalfa pellets, Journal of Drying Tech. 13, 1995, 1881-1904. [13]. Pipa F. and Frank, G, High-pressure conditioning with annular gap expander. A new way of feed processing: Advances in Feed

Technology (2), (Verlag Moritz Schafer, Detmold, 1989).

[14]. Bradbury, M.G., Egan, S.V. and Bradbury, J.H. Determination of all forms of cyanogens in cassava roots and cassava products using picture paper kits, Journal of Science Food Agriculture, 79, 1999, 593 601.




Finite Element Analysis of Various Shapes of Flexures

Sunil Girde1, Prof. Y. L. Yanarkar

2

1,2Department of Mechanical Engineering Rajiv Gandhi College of Engineering, Research and Technology,

Chandrapur (M.S.) India

Abstract: The flexural bearing is used for micro-machining and precision applications where low displacement is involved. It offers the advantage of almost frictionless, vibration free and maintenance free

operation. The bearing element is deformed to provide desire relative motion between the surfaces. They are

made up of deformable bodies called flexure. These flexures are to be designed for required displacement.

However the analytical procedure for analysis of the flexure is not available. Hence, an alternative approach

of using FEA is applied for design of flexure analysis.

In this work flexure having different size and shape such as triangular, square, rectangular and

elliptical are analyzed. The analysis of all the above shapes with various thicknesses for least axial,

maximum radial stiffness and equivalent stresses is made. Later the results have been analyzed to choose

optimum design of flexure.

Key Words: Flexural Bearing, Stress Analysis, Deformation, Finite Element Analysis

I. Introduction For micro-machining and precision applications where low displacement are involved the

frictionless, vibration-free flexural bearing are advantageous to the conventional bearings that involves

friction. The nature of application demands that the least energy be wasted in the bearing function. Hence,

maintenance free flexural bearings are the most suitable options. These are made-up of deformable bodies

called flexure, which deform on application of load retrieved their position removal of it. The flexural

bearing is unconventional and use in specific applications. It does not have standardized conventional design

procedure. The relations for standard design are not available. Hence, FEM is the tool in designing flexural

bearings. Malpani [1], Gaunekar et.al [2]

have presented the FE analysis approach using the circular shape

flexure with spiral cuts. The present study is on different shapes of flexures and thicknesses. The most commonly available

shapes triangular, rectangular, elliptical and square are considered as different possible shapes. For

triangular three flexural cuts and for all other shapes four flexure cuts have been chosen for this analysis. The

thicknesses for all the flexure are varied from 0.15 to 0.6mm in the steps of 0.15 mm. The FE models of all

the combination of shapes and thickness were made with periphery fixed and load applied at the center hole

in the steps of 0.5N from 0.5N to 5N. Each of flexure for with and without fillet flexural cuts was analyzed.

Fig. 1.1 shows the discretization of elliptical shapes flexure. The table 1.1 shows the discretization details of

flexures of various shapes.

Fig. 1.1: Discritization of Elliptical Flexural Bearing

1.1: Detail of Discritization of Various Flexures

Sr. No.

Shape Thickness (mm)

With Fillet Without Fillet

No. of

Nodes

No.

of

Element

s

No. of

Nodes

No.

of

Element

s 1

Elliptical

0.15 4057

2

1800

5

NA NA 0.3 3349

5

1468

3

NA NA 0.45 16070

0

7672

4

NA NA 0.6 9042

3

4219

5

NA NA

Finite Element Analysis Of Various Shapes Of Flexures


2

Rectangu

lar

0.15 1610

8

200

5

13848

7

1885

7 0.3 1329

8

163

5

31383

0

5992

5 0.45 10717

4

1803

2

14159

5

6693

2 0.6 7479

2

1236

4

30099

5

5736

9

3

Triangular

0.15 3435

2

446

6

11630

8

2116

8 0.3 3444

2

1546

9

13820

1

2380

2 0.45 3885

0

609

6

16925

0

3328

5 0.6 2835

5

432

6

19606

1

3720

6

4

Square

0.15 7460

6

991

1

7016

4

928

5 0.3 1333

3

163

7

30521

1

5819

4 0.45 10966

1

1843

0

30567

3

5829

3 0.6 7421

2

1223

2

29836

7

5682

3

II. Analysis Results

Each of the FE model prepared above was analyzed using ANSYS()

workbench and

results of displacement in axial and lateral direction and Von Misses stresses were noted. It was found

that all the flexures have similar pattern as the thickness drops axial deformation increases.

The FE results for the triangular case with and without fillet are tabulated in table 1.2 and 1.3

respectively.

Fig. 1.2, 1.3 and 1.4, 1.5 shows schematic view of Von Misses stresses and axial deflection of triangular

flexure with and without fillet respectively.

1.2: Triangular Shape Flexure 0.6mm thickness without fillet

Sr.

No.

Force

(N)

Lateral Deformation (mm) Axial

Deformation

(mm)

Von

Misses

Stress (MPa)

Axial

Stiffness

(N/mm)

Radial/Lateral

Stiffness

(N/mm)

X Y Z 1 0.5 0.0002782 0.000138082 0.041543 0.006328 12.03563 1796.881

2 1 0.0004174 0.000276169 0.083086 0.126556 12.03572 2395.783

3 1.5 0.0004174 0.000414251 0.12463 0.189829 12.03563 3593.667

4 2 0.0005565 0.000552322 0.166177 0.253116 12.03536 3593.664

5 2.5 0.0004632 0.000690433 0.2077 0.316386 12.03659 5396.456

6 3 0.0008348 0.000828503 0.24926 0.379673 12.03563 3593.662

7 3.5 0.0009739 0.000966574 0.29081 0.442944 12.03535 3593.662

8 4 0.0011130 0.001104685 0.33235 0.506216 12.0355 3593.664

9 4.5 0.0012522 0.001243543 0.3738 0.569502 12.03852 3593.664

10 5 0.0013913 0.001380866 0.46139 0.6158 10.83682 3593.663

Fig. 1.3: Axial Deflection Developed in Triangular Type Flexural Bearing without fillet at 5N force



1.3: Triangular Shape Flexure 0.6mm thickness with fillet

Sr.

No.

Force

(N)

Lateral

Deformation (mm)

Axial

Deformation

(mm)

Von

Misses

Stress

(MPa)

Axial

Stiffness

(N/mm)

Radial/

Lateral

Stiffness

(N/mm) 1 0.5 0.0002 0.0002 0.0626 0.0337 7.98 2500 2 1 0.0004 0.0004 0.12531 0.0675 7.98 2500 3 1.5 0.00064 0.00065 0.1879 0.1012 7.98 2343.75

4 2 0.00085 0.00085 0.2506 0.135 7.98 2352.94 5 2.5 0.00107 0.00108 0.3132 0.1687 7.98 2329.92

6 3 0.00128 0.0013 0.3759 0.2025 7.98 2343.75

7 3.5 0.0015 0.00151 0.4386 0.2362 7.98 2333.33 8 4 0.00171 0.00173 0.5012 0.2699 7.98 2339.181 9 4.5 0.00193 0.00195 0.5639 0.3037 7.98 2331.606 10 5 0.00214 0.00216 0.6265 0.3374 7.98 2336.448

Fig. 1.4: Axial Deflection Developed in Triangular Type Flexural Bearing with fillet at 5N force

Fig. 1.5: Von misses Stresses Developed in Triangular Type Flexural Bearing with at 5N force fillet

The Fig. 1.6 to 1.8 shows the Von Misses stresses distribution within the flexure. It should be noted

that at the sharp corners of flexural cuts the Von Misses stresses are high due to stress concentration factor. This

phenomenon is found to be present in all the shapes of flexural without fillet.

Fig. 1.6: Von Misses Stress Vs Thickness for Square Flexure



Fig. 1.8: Von Misses Stresses Vs Thickness for Rectangular Flexure

Fig. 1.9: Axial deflection Vs Thickness for Flexures

Fig. 1.9 shows the variation of axial deflection verses thickness that for all flexures. Since too

thin flexures tend to have more stresses and more lateral deformation, the flexures with 0.15 mm

thickness were found to be not suitable. Among rest of the thicknesses, the elliptical flexures were found

to have more axial displacement for applied load applied load.

The table 1.4 shows the FE results for different shapes and thicknesses at 5N force and obtained axial and lateral deformation. From the table it is evident that the elliptical flexures were found to have

more axial deformation. The Fig. 1.9 shows the variation of axial deformation against thickness for various

shapes, Hence it may be stated that for higher axial deformation as required by design, elliptical flexures are

most suitable.

However it was also found that the elliptical flexures show higher radial/lateral deformation for the

applied load that the other shapes. Hence decision parameters of ratio radial stiffness to axial stiffness may

be chosen as higher the stiffness ratio more the desirable flexure. Fig. 1.10 depicts the relationship between

stiffness ration and thickness for various shapes. Further it should also be noted that the maximum Von

Misses stresses for elliptical flexures were found to be higher than stresses for other shapes. Therefore it

can be said that when the radial/ lateral deformation and stresses in the flexure are to be limited the

shapes other than elliptical shapes offer better choice. Fig. 1.11 shows the stress variation among different shapes for 5N applied load.

1.4 : Optimization Of Various Shapes Of Flexure Bearing With Fillet

Shape

Thickness

(mm)

Force

(N)

Von

Misses

Stress

(MPa)

Axial

Deflection

(mm)

Radial

Deflection

(mm)

Axial

Stiffness

(N/mm)

Radial

Stiffness

(N/mm)

Radial /Lateral

Stiffness/Axial

Stiffness(N/mm

)

Square

0.15

0.3

0.45

0.6

5 N

4.386

1.552

0.543

0.3164

44.423

5.3772

1.7212

1.0239

0.02621

0.00633

0.0030

0.00242

0.11255

0.9298

2.9049

6.707

190.8396

789.8894

1666.67

2840.9091

1695.5984

849.5261

573.7443

423.57374

Triangular

0.15

0.3

0.45

0.6

5 N

5.129

1.4131

0.6081

0.3374

36.287

2.9594

1.4452

0.6265

0.03147

0.0052

0.0037

0.00214

0.13779

1.6895

3.45972

7.9808

159.0482

963.5974

1351.3514

2336.4486

1154.2797

570.3447

390.59559

292.7586

Rectangula

r

0.15

0.3

0.45

0.6

5 N

4.6569

1.223

0.6091

0.3112

59.812

5.3913

1.7306

0.7495

0.03489

0.0062

0.00302

0.00175

0.1148

0.9274

2.8891

6.67111

196.07

806.4516

1655.6291

2857.1428

1707.9268

869.5816

573.0605

428.2859



Elliptical

0.15

0.3

0.45

0.6

5 N

8.1969

3.9785

1.5228

1.5052

53.875

35.917

8.0241

8.6327

0.0387

0.0258

0.00773

0.01117

0.09281

0.1392

0.6231

0.7955

129.198

193.7984

646.6101

614.7717

1713.6968

1392.2298

1037.73086

772.81169

Fig. 1.10 : Ratio of Lateral Stiffness to Axial Stiffness Vs Thickness

Fig. 1.11: Von Misses Stresses Vs Thickness for All Shape Flexures

III. Conclusion: From the analysis results it may be concluded that the flexures with fillet have better distribution of

stresses that flexures without fillet. Furthers the different shapes of flexures with fillet were investigated

using FEA and it was found that they offers almost the similar behavior with comparable stresses when

loaded. Though the elliptical flexures offer more axial deformation and hence could be a better choice.

This advantage is negated by the more lateral/ radial deflection and the higher stresses in the flexure. Hence it

may be concluded that the exact choice of flexure may be made depending on acceptable stresses levels,

shape and space requirement of the application for which the flexural is to be used.

Reference [1]. Saurabh Anand Malpani, Yogesh Yenarkar, Suhas Deshmukh, FE Analysis of flexural bearing for linear compressor, International

Journal of applied research in Mechanical Engg. Vol. I, issue-I, 2011. S. Gaunekar, T. Goddenhenrich, C. Heiden, Finite

element analysis & testing of flexure-bearing elements, Cryogenics-1996, Vol. 36, No. 5, pp. 359-364.

[2]. W. E. Kepple, Dave W. Read, Fouad Y. Zeidan, Christian Paraskevakos, Matthew P. Dawson, proceedings of the 15th International pump users symposium.

[3]. M. Mai, I. Ruchlich, C.Rosenhagen & Th. Wiedmann, Development of the miniature flexure bearing cryocoolers, SFO70, International Cryocoolers Conference, INC, Boulder Co, 2009.

[4]. C. Rosenhagen & Th. Wiedmann, Flexure Bearing Compressor in the One Watt Linear (OWL) Envelope,

Electrodynamic

oscillating compressor Part- 1, pp.656-663 and Part-2, pp.664-670.

[5]. Shorya Awtar, Alexander H., Slocum, Parasitic Error-free Symmetric Diaphragm Flexure, and a set of precision compliant

mechanisms based it: Three and Five DOF flexible torque couplings, Five DOF motion stage, single DOF linear/axial bearing,

Paper publish in precission in Engg. Research Group, Massachusetts Institute of Technology.

[6]. Willem Van de Groep, Tony Benschop, Wordragen, The development of a new generation of miniature long life linear

coolers, Conference ICC16, p.1 of 10 year 2010, Thals publication.

[7]. T.R. Chandrupatla. A.D. Belagundu, Finite elements in engineering (Pearsons Education) [8]. Practical finite element analysis finite to infinite publications, Pune By Nitin Gokhale, Sanjay Deshpande.

[9]. Timoshenko, Theory of plates and shells ( M c G r a w H i l l p u b l i c a t i o n ) , second edition, p p . 62, 63



www.iosrjournals.org 30 | P a g e

Torque Control System for Diesel Engine

Rajesh H, Arihant U Department of Mechanical Engineering, Sri Venkateswara College Of Engineering, Sriperumbudur, India.

Abstract: This paper presents an idea on torque control system for variable speed diesel engine. A dynamometer assembly is designed to measure the frictional torque on the disc and hence the engine torque.

The resistance or frictional torque offered by the dynamometer will vary with time in a desired manner. A

transducer is used to measure the torque or force which is the output from dynamometer and is of

electromechanical type. The load acting on the transducer creates bending in the sides and a strain gauge has

been used to sense the strain. The output of the strain bridge is proportional to the load applied and hence the

transducer will give an electrical output proportional to the force. Thus the output of the measuring system will

be an emf. The emf signal is proportional to the load torque. However a calibration graph would be necessary

to relate the emf output to the load torque.

Keywords - Diesel engine, Dynamometer assembly, Emf signal- load torque, Transducer, Strain gauge,

I. INTRODUCTION

The experimental work on these engines has been conducted from no load to full load at constant

speeds. On these engines, no facilities exist for a continuous variation of load torque and speed. In case of

automobile engines depending upon the road conditions and road speed, the engine speed and torque will vary.

The road speeds and tractive resistances faced by the vehicle are converted to engine speeds and engine brake

torque. Variation of road speed and tractive resistance over a period of time, thus become a variation of engine

speed and torque. This setup facilitates varying the load torque representing the variations of the driving cycles,

on the test bed.

II. COMPONENTS The components used in setup are disc type dynamometer, torque and speed transd

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