Modeling Fracture and Cracking Resistance of Palm Nuts (Dura Variety)
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1 Modeling Factue and Cacking Resistance of Palm Nuts (Dua Vaiety) S.I. Manuwa Depatment of Agicultual Engineeing, Fedeal Univesity of Technology Akue, Nigeia Abstact Compessive stength of palm nuts (dua vaiety) was measued in tems of its factue foce and cacking foce. The palm nuts unde study wee gaded into categoies of small size nuts (), medium size nuts (), and lage size nuts (). The means of pincipal dimensions wee 19.2, 21.6, and 25.7 mm fo mino diamete (MID), intemediate diamete (IND) and majo diamete (MAD) espectively. The popeties of size, moistue content, shell thickness wee investigated and measued at thee moistue levels namely: 6, 10 and 16 (% db). Shell thickness vaied fom 0.1 to 1.7 kn while cacking foce vaied fom 0.2 to 3.7 kn at 10 % moistue content. Regession equations wee established to fit the elationships between factue foce, cacking foce and shell thickness. The models wee also validated and thee was close ageement between the measued and pedicted foces. The elative eo of the pedicted values anged between 4.2.and 9.6 % Keywods: Palm nuts, factue, cacking, compessive, esistance, models. Intoduction The fuit of the oil palm (Elaeis guineensis) is well known fo its economic impotance and nutitive values. Within the pulp o mesocap lies a had-shelled nut containing the palm kenel which gives thee useful poducts afte pocessing, namely: the shell, the kenel oil and the esidue cake (Asiedu 1989). The kenel oil is used fo shotening in the manufactue of had wates (detegents). The nutshell is used as a souce of enegy, that is, as fuel fo buning. Howeve, in ode to povide these input mateials, the palm nuts must fist be cacked. The taditional o manual method of cacking, involving the use of stones is associated with dudgey, an aduous, time-consuming and labo intensive opeation, and theefoe, unpopula. The effot cannot be quantified. The optimum moistue content at which cacking should be done is not known but imagined. Theefoe, the cacking execise of the taditional method is affected by losses and / o cackage of kenels due to dy nuts o poo pefomance due to high moistue content. Mechanical methods of cacking palm nuts had always been desied in the fom of cacking machines o nutcackes. In ode that nutcackes and equipment shall be designed and developed, the compessive stength of the nuts is equied. Popeties of seeds and gains unde compession have been investigated (Mohsenin 1980; Bilanski and Lal 1965; Zeob and Hall 1960); howeve, thee is no known publication in tems of the factue and cacking foce of the nuts. It was theefoe, necessay to investigate the compessive stength of palm nuts in tems of its factue and cacking esistance unde quassi-static loading. The objectives of this study, theefoe wee: (i) to detemine the compessive stength of palm nuts in tems of its factue and cacking esistance. (ii) to investigate the effects of moistue content and shell thickness on compessive stength. 184
2 (iii) to apply egession analysis to fit the best elationships between these popeties and also fo the pupose of pediction. Mateials and Methods Fo this study, fesh vaiety of palm nuts (dua vaiety) was puchased fom local maket in Akue. The nuts wee manually cleaned to emove foeign mateials, boken and immatue nuts. Since the size of the nuts play significant ole in pocessing and handling, the nuts wee gaded into thee categoies accoding to size namely: lage size nuts (); medium size nuts () and small size nut (). The popotion of each categoy in the bulk sample was also detemined. Gading of the nuts was accomplished by using the Tyle sieves: 19 mm apetue etained the medium size nuts; 25.4 mm apetue etained the lage size nuts; while the small size nuts wee those that passed though the 19 mm apetue. To detemine the physical dimensions of the nuts, nuts wee selected andomly fom each goup. This sampling method was simila to that epoted by Dutta et al. (1988). The dimensions of the nuts wee measued along thee pincipal axes with the aid of a venie calipe (of least count 0.01 mm). The pincipal dimensions wee: majo diamete (MAD); intemediate diamete (IND) and mino diamete (MID). The moistue content of the nuts was detemined by the standad oven method. The factue and cacking esistance wee detemined by using a Univesal Testing machine (SM, Model No CPI-60) of 0.1 kn calibations. The eading fo the factue esistance was ead on a digital display when the nut unde compessive foce made a clicking sound. The cacking esistance was the value on the digital display when the shell shatteed. The investigation was caied out fo the thee goups of nuts. The thickness of the shell was also measued fo the diffeent categoies with the aid of venie calipes. The palm nuts wee loaded in the hilium hoizontal position (HHP). Data Analysis Statistical models namely linea and intinsically linea models wee developed to fit the data collected in the study. The models investigated wee: (i) Linea fit (LINFIT) y = mx + b (1) (ii) Logaithmic fit (LOGFIT) y = mlnx + ) (2) (iii) Exponential fit (EXPFIT) y =be mx (3a) lny = mx + lnb (3b) (iv) Powe fit (PWRFIT) y = bx m (4a) y = lny = mlnx + lnb (4b) Othe statistical paametes of data analysis include: coefficient of coelation () which gives the degee of association; coefficient of detemination, R which evaluated the degee of association between obseved data points and pedicted values; the absolute mean diffeence (AMD) between measued and pedicted values; which evaluated the degee of coincidence; and the elative eo (RE) between the measued and pedicted values. Accoding to Chen et al. (1998): AMD = N 1 Mi Pi (5) N i= 1 N Mi Pi RE = N i= 1 Mi Whee N = numbe of data points, Mi = the ith measuement and Pi = the ith pediction. Results and Discussion Nut Dimensions and Size Distibution Table 1 shows the size distibution and gades of the palm nuts unde study. About 10 % of the total bulk of the nuts wee in lage size () categoy of diamete anging between 26.4 to 41.0 mm; 55% of the bulk in the medium size () categoy with majo diamete anging between 19.0 to 34.0 mm, while the small size nuts () about 35% with majo diamete anging fom 14.7 to mm. It was obseved that the dimensions along (6) 185
3 the thee pincipal axes had geate coefficient of vaiation in the than in the othe two Table 1. Pincipal dimensions of palm nuts at 10 (% db) No Dimensions Mean (mm) MAD IND MID MAD IND MID categoies. This was pobably due to the vaiability in shape of nuts. Range (mm) V* (%) MAD IND MID * V = coefficient of vaiation Effect of Moistue Content and Size on Compessive Stength Table 2 shows the effect of moistue content and size on compessive stength of palm nuts. The stength was measued in tems of factue foce and cacking foce. The foces vaied with moistue content and size as they deceased with decease in moistue content. Table 2. Effect of moistue content on compessive stength of palm nuts* The foces wee also significantly affected by nut size as they inceased with incease in nut size. The categoy of exhibited the lagest factue and cacking foces. The moistue content of 10 (% db) appeaed to be optimum moistue content at which nuts can be cacked without suffeing significant damage to the kenels at 96% confidence level. Factue Foce, kn Cacking Foce, kn MC (% db) Mean Range Mean Range * Each value is a mean of 15 obsevations. 186
4 Shell Size Distibution Statistical paametes of shell thickness in the gades of palm nuts ae pesented in Table 3. The thickness of the shell was detemined at the moistue content of 10 (%db). The means of shell thickness wee 2.72, 3.63 and 4.14 mm fo, and espectively. The had the lagest coefficient of vaiation of 23.7 (% db). Table 3. Statistical paametes of shell thickness in the gades of palm nuts Gade Obsevations Mean σ Range V (mm) (mm) (mm2) (mm) (%) σ = standad deviation σ 2 = vaiance V = coefficient of vaiation σ 2 Regession of Factue Foce on Shell Thickness Obseved data of factue foce wee egessed on shell thickness fo all the thee categoies of the nuts. Fou egession models (measued unde data analysis) wee tested to fit the elationships. The models coefficients namely: coelation coefficient; intecept; slope and covaiance ae pesented in Table 4 (a). All the models gave high positive coelation coefficients anging fom to The -values wee not significantly diffeent at 95 % confidence level. Howeve, fo the, the best-fit model fo the elationship was powe function, while fo the and the best-fit model was logaithmic function. Table 4(a). Models coefficients of egession of factue foce (F f ) on shell thickness (t) Paametes LINFIT LOGFIT EXPFIT PWRFIT Covaiance a a a a Covaiance a a a Covaiance a a a a = Coelation coefficient of best fit. a = coelation coefficients with the same lette ae not significantly diffeent at 95% confidence level. 187
5 Regession of Cacking Foce on Shell Thickness In simila manne, measued data of cacking foce wee egessed on those of shell thickness fo all the thee categoies of the nuts. The same fou models wee tested to fit the data and all the models gave high positive coelation coefficients that anged fom to (Table 4(b)). These coefficients wee not significantly diffeent at the 95% confidence level. Howeve, the best-fit model was logaithmic function fo both and and powe function fo. Table 4(b). Models coefficients of egession of cacking foce (F c ) on shell thickness (t) Paametes LINFIT LOGFIT EXPFIT PWRFIT Covaiance a a a a Covaiance a a a Covaiance a a a a = Coelation coefficient of best fit. a = Coelation coefficients with the same lette ae not significantly diffeent at 95 % confidence level. Linea Regession Equations The simple linea egession models obtained when factue o cacking foce was egessed on shell thickness ae pesented in Table 5. It was obseved that within the same categoy of nuts, the slope of the gaph of the cacking foce vesus shell thickness was steepe than the coesponding factue foce. The slopes of the factue foce in the diffeent categoies wee not significantly diffeent fom one anothe at 5 % level of significance. This was not the same fo the slopes of the cacking foce in the categoies. Table 5. Linea egession equations of factue and cacking foce on shell thickness Regession equations F f = t F c = t F f = t F c = t F f = t F c = t R F = factue foce F c = cacking foce Gade 188
6 Regession Equations and Pediction The linea egession equations wee used to pedict factue and cacking foces in the thee categoies of the nuts. The statistical paametes of the obseved and pedicted values ae pesented in Table 6. Fo the factue foce, the AMDs wee 0.048, 0.074, and kn fo, and, espectively, while fo the cacking foce, they wee 0.382, and kn in that ode. While the distibutions wee positively skewed and significantly diffeent (at 5% level of significance) in the, howeve, the distibutions wee negatively skewed in the and and also significantly diffeent. Table 6. Statistical paametes fo measued and pedicted data of factue and cacking foces Paametes Factue foce Cacking foce Co. coeff () Mean foce, kn Mean shell thickness, mm SD (foce) SD (shell thickness) Skewness AMD, kn RE, % Co. coeff () Mean foce, kn Mean shell thickness, mm SD (foce) SD (shell thickness) Skewness AMD, kn RE, % Co. coeff () Mean foce, kn Mean shell thickness, mm SD (foce) SD (shell thickness) Skewness AMD, kn RE, %
7 Conclusion The following conclusions can be dawn fom the study: The physical dimensions of the palm nuts (dua) vay even within size categoies. The bulk of the palm nuts has the in the lagest popotion followed by the and lastly by the. Compessive stength of palm nuts was significantly affected by moistue content and shell thickness. Stength deceased with decease in moistue content but inceased with incease in shell thickness. Linea and intinsically linea models can be used to descibe the elationship between compessive stength and shell thickness of palm nuts. Refeences Asiedu, J.J Pocessing of Topical Cops. Macmillan Publ., London, England. Bilanski, W.K.; and Lal, R Behaviou of theshed mateials in vetical wind tunnel. Tans. ASAE 8: Chen, Y.; Tessie, S.; and Rouffigant, J Soil bulk density estimation fo tillage systems and soil textue. Tans. ASAE, 41: Dutta, S.K.; Nema, V.K.; and Bhadwaj, R.K Physical popeties of gain. J. Agic Eng. Res. 39: Mohsenin, N.N Physical popeties of plant and animal mateials. Godon and Beach: Zoeb, G.C.; and Hall, C.W Some mechanical and heological popeties of gains. J. Agic. Eng. Res. 5:
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