International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 7, July 2014)
Mathematical Analysis of Pneumatic Reciprocating Feeder
Isha Jain1, Nidhi Gahlot2, Pradeep Khanna3, Mukul Wadhwa4, Prachi Garg5
1,2,3
Department of Manufacturing Processes and Automation, Netaji Subhas Institute of Technology, University of Delhi, Azad
Hind Fauj Marg, Sector-3, Dwarka, New Delhi – 110078.
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Abstract— The project aimed in design, fabrication and
graphical analysis of a Pneumatic Reciprocating Block
Feeder. The project starts with an extensive study on feeders,
their different types, designs, characteristics, performance
and applications. It progresses with development of a
Pneumatic Reciprocating Block Feeder. Its individual
components were developed and assembled and dimensional
accuracy was ensured to maintain a feeding mechanism. The
preliminary knowledge and constraints on design of feeder
hence developed led to selection of three parameters of
interest which are stroke rate (number of strokes per minute)
of reciprocating part-lifter, part population and part size
(diameter). A series of experimentation was carried out on
feeder wherein each parameter of interest is changed and feed
rate is recorded. To study the interaction among these factors
a full 23 factorial method has been adopted. Minitab®
statistical package is used to examine the effect of these
factors. The outcome is represented graphically and in the
form of empirical model which defines the performance
characteristics of the pneumatic reciprocating block feeder.
Belt feeders
Rotary feeders
Belt feeders
C. Need for optimization
Part feeders are critical components of automated
assembly lines. Ad-hoc setting of system parameters results
in either starvation or saturation, where too less or too
many parts are delivered to the work cells respectively.
Hence, optimization of feeders is a cause of concern [3].
This project aims at design, fabrication and
mathematical analysis on behaviour of a Pneumatic
Reciprocating Block Feeder. Tests are designed by
carefully choosing different input parameters in an attempt
to explore the relationship between the system inputs and
outputs.
II. PRINCIPLE OF WORKING
The basic principle of working of a pneumatic
reciprocating block feeder is the relative motion between a
stationary block and a reciprocating part lifter. The parts
chosen are circular discs of specific dimensions. The
stationary block acts as a temporary reservoir for randomly
oriented parts. Its walls are tapered internally so as to
facilitate the parts to the storage area and hence avoid deadzone formation. A pneumatically driven part-lifter
reciprocates through the storage area past a tapered cut slot
in the block. It lifts parts during the upward strokes which
are subsequently directed towards the window at the end of
upward stroke. Top of the part-lifter is machined at an
angle to facilitate sliding of parts towards the window; the
window cut within the block has dimensions equal to that
of a part (with some added tolerances); the stroke length of
the pneumatic actuator is equal to the height of part-lifter,
where the window has been provided; all factors
contributing to delivering of parts to the chute through the
window in a specific orientation and position.
Keywords— ANOVA, design of experiments, full factorial
design, pneumatic reciprocating feeder, feed rate
I. INTRODUCTION
A. What are feeders?
Application of automation to assembly processes is
important to meet the requirements of any manufacturing
system. Feeders form a critical part of automated assembly
lines [1]. Assembly processes require the presence of parts
in adequate amounts and correct orientation. Feeders serve
this purpose by feeding discrete parts to assembly cells on
the production line from bulk supplies.
B. Types of feeders
Vibratory feeders are the most widely employed and
versatile part-feeding devices in industries [2]. While
vibratory feeders remain the part-feeders of choice for
general purpose requirements, many other designs of
feeders have been developed for feeding parts having
special features like headed parts or abrasive materials.
Such feeders can usually be classified under:
635
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 4, April 2013)
TABLE I
III. FABRICATION
COMPONENTS AND SPECIFICATIONS
A. Components and Specifications
S.NO.
1
COMPONENT
PART
2
STAND
3
STATIONARY
BLOCK
Figure 1: labeled view of feeder
636
4
PART-LIFTER
5
DRIVE
SPECIFICATIONS
Material- plastic (acrylic sheets)Shapecircular discs
Thickness- 5 mm
Diameter A- 40 mm
Diameter B- 30 mm
Material used- steel
Height (of legs)- 1000 mm
Length- 550 mm
Breadth- 380 mm
Height of supporting structure- 100
mm
Material used- wood
Thickness of plank- 20mm
Length- 550 mm
Breadth- 380 mm
Height- 300 mm
Slope of walls1. For 2 side walls- 30 from base
2. For 1 back wall- 60 from base
Dimensions of slotDepth- 25 mm
Breadth- 9 mm
Dimensions of windowLength- 400 mm
Breadth- 80 mm
Height from base- 160 mm
Material used- wood
Length of incline- 150 mm
Breadth of lifter- 20 mm
Height from base- 160 mm
1. Cylinder bore diameter- 16 mm
2. Stroke length- 200 mm
3. Solenoid actuated 5/2 way control
valve
4. Compressor- 4 to 6 bars
5. 555 timer
6. Connecting pipes
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 4, April 2013)
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Stroke rate
Part population (PP)
Diameter of parts
B. Range of parameters
TABLE II
RANGE OF PARAMETERS
S.NO.
1
2
3
PARAMETER
Stroke rate (number
strokes per minute)
Part population
Diameter of parts (mm)
of
MIN.
23
MAX.
67
50
30
400
40
Since we have three factors to consider, the experiment
design is known as 23 factorial designs which require eight
tests runs each with combinations of three factors across
two levels of each. According to the general statistical
approach for experimental design three replicates were
obtained to get a reliable and precise estimate of the effects.
Therefore, twenty four observations were taken in all to
employ full factorial design.
Figure 2: labeled view of feeding action
B. Driving Mechanism
The reciprocating motion to the part-lifter is provided by
a pneumatic system. It consists of a double acting
pneumatic actuator, a 5/2 way control solenoid valve, a 555
timer circuit, a pressure gauge, an air compressor and
connecting pipes. Refer figure 2. The pressure gauge
controls the pressure being provided to the actuator. The
flow control valve on the actuator can vary the flow of
compressed air in actuator and hence, intensity of strokes.
A 555 timer circuit automates the system, i.e. it controls
speed of forward stroke, hold time and speed of return
stroke.
Compressed air coming out of compressor, maintained
in the range of 4-6 bars, flows through pipes into the
control valve and is used to operate the actuator, which in
turn drives the part-lifter.
TABLE III
EXPERIMENTAL DATA
S.NO.
FACTORS
1
2
3
4
5
6
7
8
Diameter of
Parts(mm)
-1
1
-1
1
-1
1
-1
1
FEED
RATE
Part
Population
-1
-1
1
1
-1
-1
1
1
Stroke
Rate
-1
-1
-1
-1
1
1
1
1
5
8
16
13.3
15.6
16.3
51
29.3
V. ANALYSIS
The aim of the experiment is to establish a statistical
model to predict the output feed rate. The three factors
chosen for experiment are the controllable variables. To
study the effect of the process parameters 23 full factorial
method is used.
The Minitab® is an excellent statistical analysis package
that assists in data analysis. To examine the effects of
factors on output, various plots like cube plot; interaction
plot and main effect plots are obtained. Pareto plot and
Normal plot of the standardized effects are obtained to
compare the significance of each effect. Analysis of
Variance (ANOVA) table is constructed for the significant
factors affecting the output response.
A. Selection of process parameters
The feed rate can be varied by changing various factors
like part population, stroke rate, size of parts, shape of
parts, slope of walls of block, dimensions of slot,
dimensions of window, etc. However, the present analysis
has been carried out by varying following parameters:
A. Effects of factors on feed rate
The cube plot for feed rate is useful for representing the
effects of three factors at a time. The cube plot figure 3 for
feed rate shows the average feed rates at critical points. The
critical points are those points where all the parameters
have limiting values.
IV. EXPERIMENTAL WORK
637
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 4, April 2013)
Figure 3: Cube Plot
Figure 5: Interaction Plot
Figure 4 shows one factor plots. One factor plot shows
how the system behaviour when only one factor is varied
and all the other factors are kept constant.
Figure 5 shows interaction plot. Interaction plots are
used to interpret significant interactions between the
process parameters. It occurs when effect of one factor on a
response depends on level of other factors.
Two non-parallel lines indicate that the effect of one
factor depends on the level of the other and they also
exhibit significant interactions.
Figure 4: Main Effect plot
Figure 6: Pareto chart
638
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 4, April 2013)
VI. ANOVA
TABLE IV
ANOVA
Source
Model
DF
6
Adj SS
4415.36
Adj MS
735.89
A
1
160.68
160.68
B
1
1569.78
F-value
119.65
P-value
0.000
0.000
26.12
0.000
1569.78
255.17
C
1
1832.25
0.000
1832.25
297.83
Figure 7: Half-Normal Plot
The Pareto Chart of the Effects figure 6 and the Half
Normal Plot of Standardized Effects figure 7 also assist to
determine the magnitude and the importance of an effect.
Pareto chart displays the absolute value of the effects and
draws a reference line on the chart. Any effect that extends
within this reference line is statistically insignificant [4].
The effect of C has the highest standardized effect on the
feed rate followed by B, BC, AB, AC and A. However all
effects extend above the limit, hence significant.
The significance of all factors can be reasserted from the
half normal plot figure 7, in which the points that do not
fall near the fitted line are significant.
AB
1
296.10
296.10
BC
1
170.13
170.13
27.66
AC
1
386.40
386.40
62.81
Lack of
Fit
Pure
error
Total
1
104.58
104.58
16
0.00
0.000
23
4519.95
48.13
0.000
0.000
The F Value for a term is the test for comparing the
variance associated with that term with the residual
variance. It is the Mean Square for the term divided by the
Mean Square for the Residual. P value is the probability
value that is associated with the F Value for this term. It is
the probability of getting an F Value of this size if the term
did not have an effect on the response. [5]
639
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 4, April 2013)
The model is significant to explain 96% of variability in
new data. Such a model not only assists to estimate the
magnitude and direction of the effects of change in factors
but also predicts the effects of their mutual interactions. It
is expected that the present study would prove to be
beneficial in future research work on the related field.
VII. EMPIRICAL RELATION
Feed rate = -50.03
+ 1.475 *Diameter of Parts
+ 0.1398* Part population
+ 1.010 *Stroke rate
- 0.004014 Diameter of Parts*Part population
- 0.02420 Diameter of Parts*Stroke rate
+ 0.001042 Part population*Stroke rate
REFERENCES
[1]
TABLE V
S
R-sq
R-sq(adj)
R-sq(pred)
2.48032
97.69%
96.87%
95.39%
[2]
[3]
Table V indicates that the model is expected to explain
about 96% of the variability in new data and is in
reasonable agreement with the value of R-sq (adjusted). [4]
[4]
VIII. CONCLUSION
In the present setup, an attempt has been made to
generate a general procedure of mathematical analysis on
performance of feeders by taking into consideration a
Pneumatic Reciprocating Block Feeder. A reliable
statistical model based on full factorial experiment design
has been established which can be used for the optimization
of feed rate of feeder developed.
[5]
640
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“Statistical Modeling Approach for Optimization of a Stationary
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Two-level
factorial
design,
"Filtrate",
http://statease.com/dex8files/manual/dx/DX8-03A-TwoLevel-P1.pdf