 Open Access
 Total Downloads : 449
 Authors : S. M. Raj Kumar, R. Malayalamurthi, R. Marappan
 Paper ID : IJERTV1IS10236
 Volume & Issue : Volume 01, Issue 10 (December 2012)
 Published (First Online): 28122012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Analysis Of Locus Of Point On Rotating Disc In The Proposed Mechanism For Delivering Sago Granules
S. M. Raj Kumar
EBET Group of Institutions, Tirupur, Tamilnadu, India.
R. Malayalamurthi
Government college of Engineering, Salem, Tamilnadu, India
R. Marappan
K.S.R. College of Engineering, Namakkal, Tamilnadu, India
Abstract
In a novel mechanism for delivering sago granules in a disc rotating about an inclined axis plays the vital role. It is observed that the locus of a point on the rotating circular plate tends to move away from the centre, which confirms the delivery of sago granules from the plate when system of force applied in that point. This study is carried out through analytically as well as numerical simulation using ADAMS package. These results will provide some insight into the scaling transformation analysis and fabrication of the automatic simple granulation machine which enhances the granular production minimizes the granulation difficulty and labour requirement.
Keywords: Sago, Granulation, Point

Introduction
Granulation is one of the methods of processing powder materials into granulated products which are more suitable for storage, transport and further processing. The process consist the formation and growth of particles in a rotating drum or in a disc. This study will focus on the granulation of powder particle using a disc granulator as this equipment gives a product with high density and high sphericity. The efficiency of wet granulation process using disc granulator depends on many factors including binder content, rotational speed, surface roughness, size of plate, starch content of the raw material. This study provides analytical and numerical solutions for locus of particle in granulator mechanism. Several analytical as well as experimental studies have been performed for particle trajectories. Nakagawa [1] performed DEM simulation and checked against MRI result for granules flows in a rotating cylinder. From the Heim [2] observation the value of reduced torques are higher for
big diameter disk in the disk granulation process and also the angle of disk inclination on the reduced Torque was observed significantly. Heim [3] proposed the model for bed dynamics during the drum granulation by dimensionless equations and presenting the relation between power number Froude number and dimensionless parameters. Also he [4] showed a significant effect of bed wetting parameters on the kinetics of wet drum granulation and presents the effect of jet break up on the granule related to surface tension. Grift [5] analysis showed that the friction coefficient can be measured using a single radial velocity measurement of particle at a distance of 4m from the edge of the disc. The data showed that the larger particles attained slightly higher velocities than the smaller ones, and the friction coefficients showed a moderate inverse relationship with the particle diameter. Rioul [6] presented a dynamical transition between a rolling and sliding at the regime and also the purely sliding regime as function of the friction coefficient and elongation of the particle.
Vilketel [7] demonstrates that the every velocity component can be deduced from the horizontal outlet angle measurement and the rotational speed. Rioul [8] studies the trajectory of solid spherical particle bouncing at high velocity along the rotating plate with accurate statistical analysis of the trajectory for both radical and angular velocity. Montira [9] experiment results indicated that the growth of cassava pearl was very sensitive to binder content. At the initial stage to granulation stage (after 4 minute), cassava peal obtained from all treatments exhibited the maximum growth rate. Also showed that particle size enlargement decreased as the binder content increased. The result of drum filling degree indicated that growth behaviour of cassava pearl is dependent on drum filling degree. Alexadru [10] studied that the functional optimization of wiper mechanism was made by using virtual model
which was realized with ADAMS software. The optimization will be described as parametrizing the model, defining the design variables, performing studies to identify the main design variables and constraints. SitiMazlina [11] replacing the method of extracting sago starch by integration of both blending and mechanized squeezing into one unit operation aided by controlled amount of water. Labour and energy requirements could also be reduced reasonably owing to the fact that a few separate steps are combined into a single unit operation.

Present process & Innovative concepts
Traditionally wet starch is agglomerated in a cloth cradle which is used as a generator until larger granules are formed. Use of cloth cradle as a granulator can cause many problems because quality and productivity of granules produced from cloth cradle depend entirely on human skill. Additionally it makes it difficult to follow Good Manufacturing Practice (GMP) guidelines and regulations. In order to overcome these problems and achieve higher productivity, a new type of granulator need to be developed for powder granulation. In this new mechanism, delivery of various dimensions of granules can be obtained by varying rotational speed of circular plate. When sago powder is spilt on the rotating circular plate, the spherical shaped sago balls are formed by the addition of sprinkling water. The formed sago granules are in globules size and are roll over the edge of the circular plate and finally pushed out of the circular plate due to the centrifugal force.

Analytical Models
In analyzing motion the first and most basic problem encountered is that of defining and dealing with the concept of position and displacement. So the position of the point must be defined in terms of some reference coordinate system.

Origin provides a location from which to measure the location of point.

Coordinate axes provide the direction along the measurement are to be made and also provides the lines and planes for measurement of angle.

Unit distance along the axes provides a scale for quantifying distances.
The coordinate of a point P (x, y, z) in the XYZ coordinate reference frame which is rotated radians around the ZZ axis. The coordinates and new position of the point P*(x, y, z) can be expressed as in the equation (1) are only considering the rotational transformation and its position can be investigated by numerical iterative approach and initially substituting
the values as follows, Initial coordinate conditions:
X=Y=Z=1, transformation angle: 300
x' x.cos y.sin .
y' x.sin y.cos. (1)
z' z.
From the positional results obtained from the equation (1) is shown in figure 1 it can be concluded that the rotational motion of the point is deviated from its circular path as the displacement range of 7.17958 x109 units for one complete rotation in the X coordinates.
Figure 1 Graphical plot for moving point deviation in XY plane


Software Models and Simulation
The virtual model of the sago sizing mechanism has been made using ADAMS package and the simulation of this model consists of modelling the prototype, defining variables, solving the model, running simulation, post processing and determining the position of point. The mechanism modelling consists of creating settings, creating points, creating parts, creating variables, creating constrains and adding motion using the ADAMS software. The major
comonents are ground, cylindrical rod, circular plate and revolute joints and after performing all the modeling procedure using the required specification, the three dimensional model was developed in ADAMS/View 12.0.0 shown in figure 2. The motion added to the model with ground is shown in figure 3. The important dimensions are,

Length of the Cylindrical Rod 1500.0 mm,

Radius of the Cylindrical Rod 25.0 mm,

Diameter of the circular Plate 500 mm,

Thickness of the circular Plate 15 mm.
Figure 2 Views of the model
Figure 3 Motion of 3D model with ground
The analysis of the mechanism can be done by the sequence operations are, setting up the simulations, running and animating a simulation and solving the model for displacement analysis of point. The running time for complete rotation is 6.283 s and steps are 100. The figure 4 shows the recorded results of simulation view in ADAMS 12.0.0. Analyzing of point on the circular plate with respect to origin, the translational displacement of the point with respect to the global XY axes in the X, Y and Z directions are shown in figure 5.
Figure 4 Recorded simulation results
Figure 5 Translational displacement


Results and Discussion
The position analysis results of the point on the model are plotted graphically. All the plots are obtained by the last run simulation during the time of 12.566 s and corresponding value of displacement. The following figure and table show the translational displacement of the point at the speed of 1 rad/s in the X Y Z direction.
The figure 6 shows the maximum translational displacement length of the point is at the every half rotation of the model and minimum translational displacement length of the point is at the every quarter rotation of the model in the X axis direction and the maximum translational displacement length of the point is at the every quarter rotation of the model and minimum translational displacement length of the point is at the every half rotation of the model in the Y axis direction. From the table 1 it is clear that the point will move outward from its centre as it displaced away by 0.0331mm in one complete rotation of the model in time period of 6.4087 seconds in the X axis direction and the point is deviate as the displacement range of –
0.0025 mm. in one complete rotation of the model in time period of 6.4087 seconds in the X axis direction.
The force on the point at the speed of 1 rad/sec in the X Y Z direction is Zero. No force is acting on the point in the mechanism as shown in Table 1.
Figure 6 Translational displacement of the point in the X and Y component
S.
No
Time
Displacement
X
Displacement
Y
Force
1
0.0
400.0
1515.0
0.0
2
0.1257
388.7231
1515.8403
0.0
3
6.283
400.0
1515.0
0.0
4
6.4087
388.7562
1515.8378
0.0
Table 1 Translational displacement of the point in the X and Y component

Conclusion
Results from the analytical solution, the rotational motion of the point is deviated from its circular path as the displacement range of 7.18×109 units for one complete rotation and from the software solution also the point will move outward from its centre as the displacement range of 0.0331 units in one complete rotation. This is clear that these deviations are
accumulation of numerical error since the particle on that specified point in the plate will not deviate without action of force, but the system of force is added to particle in that particular point it will deviate from its path when rolling and automatically delivered from the plate. It is used to conclude that the rotational motion of the particle will move outward from the centre of the plate due to centrifugal force, mr2 with respect to the angular velocities of the circular plate.

References

M.Nakagawa, K.Yamane, S.A.Altobelli, T.Tanaka and Y.Tsuji. Steady particulate flows in a horizontal rotating cylinder. Physics of fluids 1998; 10(6):14191427.

Anderzej Heim, Robert kazmierczak and Anderzej Obraniak. The effect of equipment and process parameters on torque during disk granulation of bentonite. Physicochemical problems of mineral processing 2004; 38: 157166.

Anderzej Heim, Tadeusz Gluba, Anderzej Obraniak. Bed dynamics during drum granulation. Physicochemical problems of mineral processing 2004; 38: 167176.

Anderzej Heim, Tadeusz Gluba, Anderzej Obraniak, Estera GawotMlynarczyk, Michal Blaszczyk. The effect of wetting on silica flour granulation. Physicochemical problems of mineral processing 2006; 40: 307315.

T.E.Grift, G.Kweon, J.W.Hofstee, E.Piron and S.Villete. Dynamic friction coefficient measurement of granular fertilizer particles. Biosystems Enineering 2006; 95(4): 507 515.

F.Rioual, E.Piron and E.Tisjkens. Rolling and sliding dynamics in centrifugal spreading. Applied Physics Letters 2007; 90: no 2,021918.

S.Vlllete, E.Piron, F.Cointault and B.Chopinet. Centrifugal spreading of fetiliser: Deducing three dimensional velocities from horizontal outlet angle using computer vision. Biosystems Enineering 2008; 99: 496507.

F.Rioual, A.Le Quiniou, P.Heritier and Y.Lapusta . Experimental study of the bouncing trajectory of a particle along a rotating wall. Physics of fluid 2009; 21(12):10p.

Wanassanan Chansataporn and Montira Nopharatana. Effects of binder content and drum filling degree on cassava pearl granulation using drum granulator. Asian journal of Food and AgroIndustry 2009; 2(04):739748.

C.Alexadru. Functional optimization of wind shield wiper mechanisms in MBS(Multi Body System) concept. Bulletin of the Transilvania University of Brasov 2009; 2(51): Series I.

Siti Mazlina Mustapa Kamal, Siti Norfadhillah Mahmud, Siti Aslina Hussain and Fakrul Razi Ahmadun. Improvement on sago flour processing. International Journal of Engineering and Technology, Vol.4, No. 1, 2007, pp.814.
Appendix A. Analytical solution:
Sl.No 
X – Unts 
Y – Units 
Z – Units 
Rotation (Radian) 
Difference 

1 
1.000000000000000 
1.000000000000000 
1.000000000000000 
0 
0 
After One rotation for XY plane 

2 
0.366025404601730 
1.366025403565440 
1.000000000000000 
30 
0.52333 

3 
0.366025402149855 
1.366025404222420 
1.000000000000000 
60 
1.04667 

4 
0.999999998205103 
1.000000001794890 
1.000000000000000 
90 
1.57 

5 
1.366025402908460 
0.366025407053604 
1.000000000000000 
120 
2.09333 

6 
1.366025404879400 
0.366025399697980 
1.000000000000000 
150 
2.61667 

7 
1.000000003589790 
0.999999996410206 
1.000000000000000 
180 
3.14 

8 
0.366025409505479 /td> 
1.366025402251490 
1.000000000000000 
210 
3.66333 

9 
0.366025397246106 
1.366025405536370 
1.000000000000000 
240 
4.18667 

10 
0.999999994615309 
1.000000005384680 
1.000000000000000 
270 
4.71 

11 
1.366025401594510 
0.366025411957353 
1.000000000000000 
300 
5.23333 

12 
1.366025406193350 
0.366025394794231 
1.000000000000000 
330 
5.75667 

13 
1.000000007179580 
0.999999992820412 
1.000000000000000 
360 
6.28 
0.000000007179580 
7.17958E09 
14 
0.366025414409228 
1.366025400937530 
1.000000000000000 
30 
0.52333 
0.000000009807498 
9.8075E09 
15 
0.366025392342357 
1.366025406850330 
1.000000000000000 
60 
1.04667 
0.000000009807498 
9.8075E09 
16 
0.999999991025515 
1.000000008974480 
1.000000000000000 
90 
1.57 
0.000000007179588 
7.17959E09 
17 
1.366025400280550 
0.366025416861103 
1.000000000000000 
120 
2.09333 
0.000000002627910 
2.62791E09 
18 
1.366025407507310 
0.366025389890482 
1.000000000000000 
150 
2.61667 
0.000000002627910 
2.62791E09 
19 
1.000000010769380 
0.999999989230618 
1.000000000000000 
180 
3.14 
0.000000007179590 
7.17959E09 
20 
0.366025419312977 
1.366025399623570 
1.000000000000000 
210 
3.66333 
0.000000009807498 
9.8075E09 
21 
0.366025387438607 
1.366025408164290 
1.000000000000000 
240 
4.18667 
0.000000009807499 
9.8075E09 
22 
0.999999987435721 
1.000000012564270 
1.000000000000000 
270 
4.71 
0.000000007179588 
7.17959E09 
23 
1.366025398966600 
0.366025421764852 
1.000000000000000 
300 
5.23333 
0.000000002627910 
2.62791E09 
24 
1.366025408821260 
0.366025384986732 
1.000000000000000 
330 
5.75667 
0.000000002627910 
2.62791E09 
25 
1.000000014359170 
0.999999985640824 
1.000000000000000 
360 
6.28 
0.000000014359170 
1.43592E08 
26 
0.366025424216726 
1.366025398309620 
1.000000000000000 
30 
0.52333 
0.000000019614996 
1.9615E08 
27 
0.366025382534858 
1.366025409478240 
1.000000000000000 
60 
1.04667 
0.000000019614997 
1.9615E08 
Appendix B. Software Solution:
Translational Displacement Point in XYZ 

Time 
Current X 
Current Y 
Current Z 
0.0 
400.0 
1515.0 
0.0 
0.1257 
388.7231 
1515.8403 
79.6712 
0.2513 
355.657 
1518.2873 
153.4172 
0.377 
303.0462 
1522.1241 
215.6997 
0.5026 
234.4705 
1527.0057 
261.7297 
0.6283 
154.6218 
1532.4817 
287.7795 
0.754 
68.9905 
1538.0279 
291.437 
0.8796 
16.4731 
1543.0811 
271.7615 
1.0053 
95.7502 
1547.0784 
229.3586 
1.1309 
163.1385 
1549.4961 
166.351 
1.2566 
213.6229 
1549.8873 
86.2535 
1.3823 
243.2026 
1547.9143 
6.2405 
1.5079 
249.1559 
1543.3748 
105.5487 
1.6336 
230.2243 
1536.2201 
205.5472 
1.7592 
186.7061 
1526.5628 
299.953 
1.8849 
120.4511 
1514.6757 
382.7192 
2.0106 
34.7587 
1500.9795 
448.4166 
2.1362 
65.8158 
1486.0215 
492.5782 
2.2619 
175.7344 
1470.4466 
511.9857 
2.3875 
288.8121 
1454.9607 
504.8782 
2.5132 
398.5941 
1440.2914 
471.0717 
2.6389 
498.7509 
1427.1458 
411.9803 
2.7645 
583.4674 
1416.169 
330.5391 
2.8902 
647.7999 
1407.9078 
231.0322 
3.0158 
687.9834 
1402.7767 
118.8331 
3.1415 
701.6588 
1401.0353 
0.0884 
3.2672 
688.0235 
1402.7716 
118.661 
3.3928 
647.8781 
1407.8978 
230.8738 
3.5185 
583.5782 
1416.1548 
330.4046 
3.6441 
498.8871 
1427.1279 
411.8767 
3.7698 
398.7504 
1440.2707 
471.0026 
3.8955 
288.9779 
1454.9383 
504.8479 
4.0211 
175.9005 
1470.4234 
511.995 
4.1468 
65.9725 
1485.9988 
492.6257 
4.2724 
34.62 
1500.9582 
448.4985 
4.3981 
120.338 
1514.6567 
382.8299 
4.5238 
186.6245 
1526.5468 
300.085 
4.6494 
230.178 
1536.2076 
205.692 
4.7751 
249.1464 
1543.3662 
105.6972 
4.9007 
243.2293 
1547.9095 
6.3834 
5.0264 
213.6827 
1549.8862 
86.1249 
5.1521 
163.2266 
1549.4983 
166.2444 
5.2777 
95.8597 
1547.0832 
229.2802 
5.4034 
16.5961 
1543.0878 
271.7154 
5.529 
68.863 
1538.0358 
291.4252 
5.6547 
154.4984 
1532.4899 
287.8019 
5.7804 
234.3612 
1527.0132 
261.7827 
5.906 
302.9559 
1522.1306 
215.7804 
6.0317 
355.5927 
1518.292 
153.5196 
6.1573 
388.69 
1515.8428 
79.7859 
6.283 
400.0 
1515.0 
0.119 
6.4087 
388.7562 
1515.8378 
79.5566 
6.5343 
355.7209 
1518.2826 
153.3156 
6.66 
303.1365 
1522.1175 
215.6187 
6.7856 
234.5812 
1526.9979 
261.6758 
6.9113 
154.7453 
1532.4734 
287.7572 
7.037 
69.1182 
1538.0199 
291.4487 
7.1626 
16.3502 
1543.0743 
271.8076 
7.2883 
95.6408 
1547.0735 
229.437 
7.4139 
163.0505 
1549.4939 
166.4575 
7.5396 
213.563 
1549.8884 
86.382 
7.6653 
243.1759 
1547.919 
6.0976 
7.7909 
249.1653 
1543.3834 
105.4002 
7.9166 
230.2706 
1536.2325 
205.4023 
8.0422 
186.7877 
1526.5788 
299.8209 
8.1679 
120.564 
1514.6947 
382.6085 
8.2936 
34.8972 
1501.0008 
448.3346 
8.4192 
65.6592 
1486.0442 
492.5307 
8.5449 
175.5684 
1470.4697 
511.9764 
8.6705 
288.6462 
1454.9831 
504.9085 
8.7962 
398.4378 
1440.3121 
471.1407 
8.9219 
498.6132 
1427.1637 
412.0848 
9.0475 
583.3564 
1416.1833 
330.6737 
9.1732 
647.7221 
1407.9178 
231.1897 
9.2988 
687.9432 
1402.7819 
119.0049 
9.4245 
701.6588 
1401.0353 
0.2651 
9.5502 
688.0635 
1402.7665 
118.4892 
9.6758 
647.9559 
1407.8878 
230.7162 
9.8015 
583.6891 
1416.1405 
330.2699 
9.9271 
499.0247 
1427.11 
411.7721 
10.0528 
398.9067 
1440.25 
470.9335 
10.1785 
289.1438 
1454.9159 
504.8175 
10.3041 
176.0665 
1470.4003 
512.0042 
10.4298 
66.1292 
1485.9762 
492.6731 
10.5554 
34.4814 
1500.9369 
448.5804 
10.6811 
120.2249 
1514.6378 
382.9405 
10.8068 
186.5428 
1526.5309 
300.217 
10.9324 
230.1316 
1536.1952 
205.8369 
11.0581 
249.1369 
1543.3575 
105.8457 
11.1837 
243.2559 
1547.9047 
6.5263 
11.3094 
213.7425 
1549.8851 
85.9964 
11.4351 
163.3145 
1549.5004 
166.1378 
11.5607 
95.9692 
1547.0881 
229.2017 
11.6864 
16.719 
1543.0946 
271.6692 
11.812 
68.7354 
1538.0438 
291.4134 
11.9377 
154.3749 
1532.4981 
287.8241 
12.0634 
234.2504 
1527.021 
261.8366 
12.189 
302.8655 
1522.1371 
215.8613 
12.3147 
355.5287 
1518.2967 
153.6211 
12.4403 
388.6569 
1515.8452 
79.9004 
12.566 
399.9999 
1515.0 
0.238 