Design and Analysis of an Automatic Shell Cracking Machine of Metohuayo (“Caryodendron Orinocense Karst”) with a Capacity of 50 Kg/H

agriculture

Article Design and Analysis of an Automatic Shell Cracking Machine of Metohuayo (“Caryodendron orinocense Karst”) with a Capacity of 50 kg/h

Carlos Gianpaul Rincón Ruiz , Marco Antonio Tejada Cardeña and Juan José Jiménez de Cisneros Fonfría *

Mechanical Engineering Department, Pontiﬁcia Universidad Católica del Perú, Lima 15088, Peru; [email protected] (C.G.R.R.); [email protected] (M.A.T.C.) * Correspondence: [email protected]; Tel.: +51-1-626-2000

Received: 9 October 2020; Accepted: 2 November 2020; Published: 9 November 2020

Abstract: This article presents the design and analysis of an automatic shell broken machine of seeds of Metohuayo (“Caryodendron orinocense Karst”) with a production capacity of 50 kg/h, considering manufacturing and maintenance of local facilities. Metohuayo is the fruit of a tree that grows in various jungle areas of Perú, and the Metohuayo oil is very requested because of its nutritional properties. Starting with these specifications, the design was developed according to the systematic approach established by the VDI-2221 standard, with seven basic steps to analyze the optimum design. Once the definitive project was reached and the commercial components were selected, finite element simulations were performed to analyze the strength of the shell broken system and to evaluate the strength and the dynamic response of the structural support of the machine components. Additionally, complementary experimental studies were performed, such as the analysis of the required force to break the shell or the measurement of their dimensions.

Keywords: Metohuayo; machine design; computer-aided design; computer-aided engineering; ﬁnite element simulation; agricultural engineering design

1. Introduction The Amazon rainforest is a jungle with a huge variety of vegetation and wildlife; to date, more than 40,000 plant species and 3500 animal species are considered over the nine countries on the 7 million km2 of covered area. In this diversity, a special fruit named Metohuayo “Caryodendron orinocense Karst” is native to northwestern South America, particularly the Orinoco and Amazon river basins of Colombia, Venezuela, Ecuador, Perú, and Brazil (Figure1a) [ 1]. The fruit, which has the same name as the tree, must be collected immediately after detaching because of its fast seed exposure and germination [2]. Metohuayo is characterized by a tough exterior shell that wraps and protects the seed inside (Figure1b). Its seed is edible and consumed either directly or by extracting oil. The oil extract from seeds has a higher nutritional value in quantity and quality than the oil extracted from others fruits such as peanut, soybean, and olive; there is about 75% linoleic acid contained in Metohuayo seed, which gives a high concentration of polyunsaturated fats [1–3]. It can also be considered in the production of cosmetic products. Traditionally, the cracking process for Metohuayo and similar species used to be done by a group of people using human force. Because of the continuous rise in demand, small farmers need to increase their production capacity. This forced the creation of machines to automatically crack the fruit shell. In this sense, diﬀerent shell cracking machines were developed specially for well-known nuts. The food processing industry proposed diﬀerent machines to process the Cacay, Sacha Inchi,

Agriculture 2020, 10, 537; doi:10.3390/agriculture10110537 www.mdpi.com/journal/agriculture Agriculture 2020, 10, 537 2 of 23 and macadamia fruits [6–8]. In South America, these machines are usually developed empirically for small farmers [9]. They improve their machines via trial and error, but they do not have a clear procedureAgriculture 2020 for, 10 fabricating, x FOR PEER a REVIEW machine which depends on the capacity requirements, local technology,2 of 25 and fruit mechanical characterization.

(a) (b)

Figure 1. ((a) Metohuayo’s growing regions [[4];4]; (b) composition of the Metohuayo fruitfruit [[5].5].

Moreover,Traditionally, it has the been cracking identified process that for there Metohu is noayo mechanical and similar characterization species used to available be done which by a quantifiesgroup of people the magnitude using human of force force. and Because strain required of the continuous to crack the Metohuayorise in demand, shell, small information farmers which need to is neededincrease in their order production to designa capacity. machine specializedThis forced forthe the creation processing of machines of Metohuayo to automatically fruits. Their crack complex the geometricalfruit shell. In characteristics this sense, different vary;furthermore, shell cracking an machines appropriate were study developed is required specially to design for well-known a machine capablenuts. The of food processing processing different industry Metohuayo proposed dimensions. different machines to process the Cacay, Sacha Inchi, and macadamiaIn this research, fruits a [6–8]. novel In shell South cracking America, machine these is machines proposed are by usually applying developed the design empirically methodology for establishedsmall farmers in VDI-2221[9]. They [10improve]. The proceduretheir machines proposed via trial considers and error, the problem but they through do not research have a aboutclear Metohuayo’sprocedure for characteristics fabricating a andmachine mechanical which characterization,depends on the presentingcapacity requirements, conceptual solutions local technology, evaluated onand the fruit basis mechanical of a list of characterization. requirements previously established. This led to the final project consisting of the developmentMoreover, it ofhas a functionalbeen identified machine that ready there for is fabrication.no mechanical Computer-aided characterization design available/engineering which (CADquantifies/CAE) the simulations magnitude were of performedforce and instrain order requ to evaluateired to thecrack functionality the Metohuayo of the machineshell, information proposed, extendwhich is the needed analysis in order previously to design done a bymachine hand, spec andialized improve for thethe mechanicalprocessing of behavior, Metohuayo as well fruits. as dynamicTheir complex response. geometrical characteristics vary; furthermore, an appropriate study is required to design a machine capable of processing different Metohuayo dimensions. 2. Materials and Methods In this research, a novel shell cracking machine is proposed by applying the design methodology 2.1.established Mechanical in VDI-2221 Characterization [10]. The of theprocedure Metohuayo propos Fruited considers the problem through research about Metohuayo’s characteristics and mechanical characterization, presenting conceptual solutions evaluatedMetohuayo on the fruits,basis of consisting a list of requirements of a shell and previously seed, are establish depositeded. into This the led machine to the final (Figure project2). Theyconsisting can be of found the indevelopment different dimensions of a functional in terms machine of their length, ready width, for fabrication. and thickness Computer-aided [3]. As part of thedesign/engineering problem clarification, (CAD/CAE) the Metohuayo simulations fruit were needed perfor tomed be mathematically in order to evaluate represented the functionality in order toof satisfythe machine the space proposed, requirements extend and the processing analysis previously capacity. Hence, done by a sample hand, and of 100 improve Metohuayo the mechanical fruits were measured,behavior, as and well the as results dynamic are response. listed in Table 1.

2. Materials and Methods

2.1. Mechanical Characterization of the Metohuayo Fruit Metohuayo fruits, consisting of a shell and seed, are deposited into the machine (Figure 2). They can be found in different dimensions in terms of their length, width, and thickness [3]. As part of the problem clarification, the Metohuayo fruit needed to be mathematically represented in order to satisfy the space requirements and processing capacity. Hence, a sample of 100 Metohuayo fruits were measured, and the results are listed in Table 1.

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Figure 2. Metohuayo fruit processed by the machine. Figure 2. Metohuayo fruit processed by the machine. Table 1. Average dimensions measured from a sample of Metohuayo fruits. Table 1. Average dimensions measured from a sample of Metohuayo fruits. Table 1. AverageDescription dimensions measured from a sample Dimensions of Metohuayo fruits. Description Dimensions FruitFruit length, length,Description width, width, and thicknessthickness 33.5 mm,mm, 35 Dimensions35 mm, mm, and and 25 25 mm mm Fruit weight 18.9 g Fruit length,Fruit width, weight and thickness 33.5 mm, 35 18.9 mm, g and 25 mm Seed length, width, and thickness 27.5 mm, 21.75 mm, and 16 mm Seed length,SeedFruit width, weight weight and thickness 27.5 mm, 21.75 12.6 18.9 mm, g g and 16 mm Seed length,Seed width, weight and thickness 27.5 mm, 21.75 12.6 mm, g and 16 mm Seed weight 12.6 g It was identified that there is no mechanical characterization of this fruit which establishes the It was identified that there is no mechanical characterization of this fruit which establishes the magnitude of force and strain required to crack its shell. In this sense, there are different types of magnitudeIt was of identified force and that strain there required is no mechanicalto crack its shecharacterizationll. In this sense, of therethis fruit are different which establishes types of test the test which can be used for this purpose, such as the well-known impact compression test, as well whichmagnitude can be of used force for and this strain purpose, required such to as crack the we itsll-known shell. In impactthis sense, compression there are differenttest, as well types as otherof test as other more difficult tests related to the production of shear stresses in the shell. According to the morewhich difficult can be usedtests relatedfor this topurpose, the production such as the of weshearll-known stresses impact in the compression shell. According test, asto wellthe fracture as other fracture mechanism proposed for the Metohuayo shell, compression tests were done at the material mechanismmore difficult proposed tests related for theto the Metohuayo production shell, of shear compression stresses in teststhe shell. were According done at tothe the material fracture characterization laboratories of Pontificia Universidad Católica del Perú (Figure3). characterizationmechanism proposed laboratories for theof Pontificia Metohuayo Universidad shell, compression Católica del testsPerú (Figurewere done 3). at the material characterization laboratories of Pontificia Universidad Católica del Perú (Figure 3).

Figure 3. Fruit compression test set-up. Figure 3. Fruit compression test set-up. 2.2. Application of the VDI-2221 Design Methodology to Determine the Conceptual Design 2.2. Application of the VDI-2221 Design Methodology to Determine the Conceptual Design The VDI-2221 guideline [10] [10] proposes a systematic approach to the process design of technical systemsThe and and VDI-2221 products, products, guideline which which [10]is isvery proposes very useful useful a forsystematic forthe theparticular particularapproach case to case of the agriculture ofprocess agriculture design equipment. equipment.of technical The Themethodologysystems methodology and mainlyproducts, mainly consists which consists of is four of very four phases: useful phases: clarification for clariﬁcation the particular of ofthe the problem,case problem, of agriculture conceptual conceptual equipment. design, design, project The development,methodology andmainly detailed consists design. of four The phases: advantage clarification of this guideline of the problem, is the assessment conceptual ofdesign, alternatives project developeddevelopment, in each and phase detailed and design. the choice The of advantage the most optimalof this guideline alternative is the on theassessment basis of the of alternatives designer’s criteriadeveloped through in each their phase experience and the and choice knowledge.knowledge. of the most optimal alternative on the basis of the designer’s criteriaThe through first ﬁrst phase their is is experienceachieved achieved by by and making making knowledge. a arequiremen requirement t list list and and determining determining the the state state of ofthe the art. art. It Itinvolves involvesThe thefirst the characteristics characteristicsphase is achieved thatthat theby the making project project needs a requiremenneed tos achieve to achievet list and and characteristics and determining characteristics that the could state that be of could achieved.the art. be It Inachieved.involves order to Inthe meet order characteristics the to production meet the that demand,production the project the demand design need requirementss, theto achievedesign requirements wereand establishedcharacteristics were by established entrepreneursthat could bybe whoentrepreneursachieved. needed In to orderwho process needed to 50meet kg to perthe process hour.production 50 The kg machine per demand hour. function ,The the machinedesign covered requirements function fruit feeding covered were to the fruit established separation feeding oftoby shelltheentrepreneurs separation and fruit of seed.who shell needed Allowed and fruit to materialsprocess seed. Allowed 50 were kg per establishedmaterials hour. The were according machine established function to the according standards covered to fromfruit the standards feeding the Food to fromthe separation the Food ofand shell Agriculture and fruit seed. Organization Allowed materials of the United were established Nations (FAO) according and toWorld the standards Health from the Food and Agriculture Organization of the United Nations (FAO) and World Health

AgricultureAgriculture 20202020,,10 10,, 537x FOR PEER REVIEW 44 of 2325 Agriculture 2020, 10, x FOR PEER REVIEW 4 of 25 Organization (WHO). Local security standards were followed to assure operator safety and andergonomicOrganization Agriculture operation. (WHO). Organization Local ofsecurity the United standards Nations we (FAO)re followed and World to Healthassure Organizationoperator safety (WHO). and LocalergonomicThe security next operation. standardsstep was to were gather followed information to assure from operator research safety on technologies and ergonomic and operation. machines with the mainThe Thefunction nextnext step stepof separating waswas toto gathergather the informationshellinformation and seeds fromfrom of research redifferentsearch onon nutstechnologies technologies such as macadamia andand machinesmachines nuts withwith [11] the thein mainarticles,main function function patents, of of separatingvideos, separating and the other the shell shell information and and seeds seeds of sources. di ﬀoferent different nuts suchnutsas such macadamia as macadamia nuts [11 nuts] in articles, [11] in patents,articles,After videos,patents, the clarification and videos, other and information of other the informationproblem, sources. the sources. phase of conceptual design was implemented to determineAfterAfter thethe optimal clariﬁcationclarification concept ofof theorthe solution problem,problem, principle. thethe phaseph aseThe of ofmachine conceptualconceptual is described designdesign wasaswas an implemented implementedoverall function toto determinedepicteddetermine as thethe a black optimaloptimal box concept conceptin Figure oror 4. solutionsolution principle. principle. TheThe machinemachine isis describeddescribed asas anan overalloverall functionfunction depicteddepicted asas aa blackblack boxbox in in Figure Figure4 .4.

Figure 4. Black box of the machine. FigureFigure 4. 4.Black Black boxbox ofof thethe machine.machine. According to the aim, the strategy was to split the complex overall function into subfunctions. AccordingAccording toto thethe aim,aim, thethe strategystrategy waswas toto splitsplit thethe complexcomplex overalloverall functionfunction intointo subfunctions.subfunctions. AA sequencesequence ofof operationsoperations waswas establishedestablished toto orderorder thethe subfunctions.subfunctions. TheThe functionfunction structurestructure waswas representedA sequence inof connectedoperations blocks was established due to the establto orderished the sequence. subfunctions. Furthermore, The function some structuresubfunctions was representedrepresented inin connectedconnected blocksblocks duedue to to the the established established sequence. sequence.Furthermore, Furthermore, somesomesubfunctions subfunctions couldcould bebe groupedgrouped intointo one one block block which which resulted resulted in in a a number number of of alternative alternative function function structures. structures. Figure Figure5 5could shows be the grouped optimal into function one block structure which resultedcomposed in aof number both individual of alternative and groupfunction subfunction structures. blocks. Figure shows5 shows the the optimal optimal function function structure structure composed composed of of both both individual individual and andgroup group subfunctionsubfunction blocks.blocks. TheThe individualindividual subfunctionssubfunctions werewere feedfeed andand shellshell cracking.cracking. The groupgroup subfunctionssubfunctions werewere dosedose andand convey,The individual shell cracking, subfunctions and classify were andfeed collect.and shell cracking. The group subfunctions were dose and convey,convey, shell shell cracking, cracking, and and classify classify and and collect. collect.

Figure 5. Optimal structure of functions. Figure 5. Optimal structure of functions. Figure 5. Optimal structure of functions. Then, the functional elements performing the abovementioned blocks were determined through the Then, the functional elements performing the abovementioned blocks were determined through researchThen, of components the functional or systemselements satisfying performing the solutionthe abovementioned principles [12]. blocks Figure were6 shows determined a morphological through tablethe research in which of the components subfunctions or are systems listed in satisfying the first column the solution of the table principles and the [12]. functional Figure elements 6 shows are a morphologicalthe research of table components in which or the systems subfunctions satisfying are thelisted solution in the principlesfirst column [12]. of Figurethe table 6 showsand the a presentedmorphological in each table respective in which row. the The subfunctions elements are are linked listed by in arrows, the first resulting column in of alternative the table solutionand the concepts.functional In elements this sense, are the presented morphological in each table resp providesective row. a large The number elements of possible are linked solutions by arrows, which resultingfunctional in elements alternative are solution presented concepts. in each In respthisective sense, row. the morphologicalThe elements tableare linked provides by arrows,a large is both an advantage and a disadvantage of this method since the number of layouts must be reduced numberresulting of in possible alternative solutions solution which concepts. is both Inan this advantage sense, theand morphological a disadvantage table of this provides method a sincelarge according to the requirements previously established [13]. In the current design, the best three concepts thenumber number of possibleof layouts solutions must be whichreduced is accordingboth an ad tovantage the requirements and a disadvantage previously of established this method [13]. since In were chosen according to the requirements of farmers and the advantages of the functional elements thethe currentnumber design, of layouts the bestmust three be reduced concepts according were ch osento the according requirements to the previously requirements established of farmers [13]. and In presented as combinations. Three-dimensional (3D) freehand drawings were generated to visualize the thethe currentadvantages design, of thethe best functional three concepts elements were pres chentedosen according as combinations. to the requirements Three-dimensional of farmers (3D) and alternatives. The schematic concepts made with the program Autodesk Inventor are shown in Figure7. freehandthe advantages drawings of werethe functionalgenerated toelements visualize pres theented alternatives. as combinations. The schematic Three-dimensional concepts made with(3D) freehand drawings were generated to visualize the alternatives. The schematic concepts made with

Agriculture 2020, 10, x FOR PEER REVIEW 5 of 25 Agriculture 2020, 10, x FOR PEER REVIEW 5 of 25 Agriculturethe program2020, Autodesk10, 537 Inventor are shown in Figure 7. The determination of the optimal concept5 ofwas 23 basedthe program on economic Autodesk and Inventor technical are criteriashown insuch Figure as 7.minimum The determination components, of the fabrication optimal concept feasibility, was designbased onsafety, economic and requirement and technical accomplishment. criteria such as Figure minimum 7b shows components, the optimal fabrication solution feasibility, concept The determination of the optimal concept was based on economic and technical criteria such as minimum consistingdesign safety, mainly and of requirement a chute (Figure accomplishment. 6a), screw conveyor Figure (Figure7b shows 6d), the toothed optimal wheel solution with concepta tilted components, fabrication feasibility, design safety, and requirement accomplishment. Figure7b shows the toothedconsisting wall mainly (Figure of 6f),a chute and rotating (Figure screen6a), screw (Figure conveyor 6i). (Figure 6d), toothed wheel with a tilted optimaltoothed solutionwall (Figure concept 6f), consistingand rotating mainly screen of (Figure a chute (Figure6i). 6a), screw conveyor (Figure6d), toothed wheel with a tilted toothed wall (Figure6f), and rotating screen (Figure6i).

FigureFigure 6.6. Morphological table with functionalfunctional elements:elements: (a)) chute; ((b)) chute with channels;channels; ((cc)) circularcircular Figure 6. Morphological table with functional elements: (a) chute; (b) chute with channels; (c) circular dosingdosing unit;unit; ((dd)) screwscrew conveyor;conveyor; ((ee)) toothedtoothed wheelwheel withwith aa curvedcurved toothedtoothed wall;wall; ((ff)) toothedtoothed wheelwheel withwith dosing unit; (d) screw conveyor; (e) toothed wheel with a curved toothed wall; (f) toothed wheel with aa tiltedtilted toothedtoothed wall;wall; ((gg)) twotwo toothedtoothed wheels;wheels; ((hh)) vibratingvibrating screen;screen; ((ii)) rotatingrotating screen. screen. a tilted toothed wall; (g) two toothed wheels; (h) vibrating screen; (i) rotating screen.

(a) (b) (c) (a) (b) (c) FigureFigure 7.7. ThreeThree solution concepts according to the combination of functions presentedpresented inin thethe morphologicalmorphologicalFigure 7. Three matrix; solution ( (aa)) aconcepts a conceptual conceptual according design design basedto based the on combination on toothed toothed cylinder cylinderof functions and and wall wallpresented mechanism; mechanism; in (theb) (basedmorphologicalb) based on ontoothed toothed matrix; wheel wheel ( aand) a and curvconceptual curveded toothed toothed design wall wallbased mechanism; mechanism; on toothed (c) (based ccylinder) based on on twoand two toothed wall toothed mechanism; cylinders. cylinders. (b) based on toothed wheel and curved toothed wall mechanism; (c) based on two toothed cylinders.

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After the determination of the optimal solution concept, the phase of project development continued. The third phase was characterized by the development of preliminary layouts that differed from each other because of the power transmission and the arrangement of functional elements. Rough calculations according to the strength of materials were carried out in order to determine the dimensions of components, as well as the total power required by each component to determine the total power required by the electrical motor. This is discussed in Section 2.3. Three-dimensional freehand drawings and three preliminary layouts were generated. The selection of the optimal preliminary layout depended on the technical and economic criteria listed in Tables2 and3, respectively. This procedure allowed evaluating the solutions as a function of different criteria, where a better performance corresponded to a higher mark, and weighting factors were established for each criteria according to the project requirements [13]. In Tables2 and3, g is the weighing factor, p is the mark assigned from 0–4 depending on the performance achieved for each criterion, and gp is their product. The ideal solution represents the maximum grade possible assigned as 4 for each criterion, whereas the ratios between the sum of gp from the ideal solution column and the sum of gp from the other solutions correspond to the technical value xi or economic value yi. The best solution results from an equilibrium between both technical and economic criteria, which corresponds to the nearest solution to the 45◦ line (Figure8). Then, the layout was improved since the location of the components, materials, frame, and dimensions was defined. The assembly of the components and the final project were carried out using the program Autodesk Inventor (Figure9).

Table 2. Technical assessment of the preliminary layouts.

Technical Value (xi) Layouts 1 2 3 Ideal Number Assessment criteria g p gp p gp p gp p gp 1 Size 2 2 4 3 6 3 6 4 8 2 Design: stability, durability, wear 3 2 6 3 9 3 9 4 12 3 Safety 3 3 9 3 9 3 9 4 12 4 Fabrication 2 3 6 2 4 2 4 4 8 5 Assembly: feasibility 2 2 4 3 6 3 6 4 8 6 Maintenance 3 3 9 3 9 2 6 4 12 7 Ergonomic design 3 2 6 3 9 3 9 4 12 xi 0.61 0.72 0.68 1.00

Table 3. Economical assessment of the preliminary layouts.

Economical Value (yi) Layouts 1 2 3 Ideal Number Assessment criteria g p gp p gp p gp p gp 1 Power consumption 3 3 9 3 9 2 6 4 12 2 Increasing capacity 3 2 6 3 9 3 9 4 12 3 Operator training 1 3 3 3 3 3 3 4 4 4 Cost of spare parts 3 3 9 3 9 2 6 4 12 yi 0.675 0.75 0.6 1 Agriculture 2020, 10, 537 7 of 23 AgricultureAgriculture 20202020,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 77 ofof 2525

FigureFigure 8.8. AssessmentAssessment diagramdiagram inin accordanceaccordance withwith VDI-2221VDI-2221 [10].[10]. [10].

FigureFigure 9. 9. FinalFinal design:design: automaticautomatic automatic shellshell shell crackingcracking machine.machine. The final phase was the design consisting of the development of engineering drawings and the TheThe finalfinal phasephase waswas thethe designdesign consistingconsisting ofof ththee developmentdevelopment ofof engineeringengineering drawingsdrawings andand thethe 3D model with the use of computer-aided design (CAD) and computer-aided engineering (CAE) 3D3D modelmodel withwith thethe useuse ofof computer-aidedcomputer-aided desidesigngn (CAD)(CAD) andand computer-aidedcomputer-aided engineeringengineering (CAE)(CAE) software, as discussed in detail in Sections 2.5 and 2.6, respectively. software,software, asas discusseddiscussed inin detaildetail inin SectionsSections 2.52.5 andand 2.6,2.6, respectively.respectively. 2.3. Design and Component Sizing 2.3.2.3. DesignDesign andand ComponentComponent SizingSizing The procedure presented above allowed us to obtain different and creative solution concepts TheThe procedureprocedure presentedpresented aboveabove allowedallowed usus toto obtaobtainin differentdifferent andand creativecreative solutionsolution conceptsconcepts from the functional and physical principles. However, the machine’s morphology and aesthetics fromfrom thethe functionalfunctional andand physicalphysical principles.principles. However,However, thethe machine'smachine's morphologymorphology andand aestheticsaesthetics werewere were not sufficient to design a machine, and dimensions needed to be calculated in order to get a notnot sufficientsufficient toto designdesign aa machine,machine, andand dimensionsdimensions neededneeded toto bebe calculatedcalculated inin orderorder toto getget aa goodgood good performance. performance.performance. 2.3.1. Fracture Mechanism 2.3.1.2.3.1. FractureFracture MechanismMechanism Figure 10 schematically shows the proposed fracture mechanism. It consisted of a toothed cylinder Figure 10 schematically shows the proposed fracture mechanism. It consisted of a toothed whoseFigure profile 10 shape schematically was experimentally shows the determinedproposed frac forture cracking mechanism. macadamia It consisted nuts [11 ].of This a toothed fruit is cylinder whose profile shape was experimentally determined for cracking macadamia nuts [11]. This cylindersimilar to whose the Metohuayo profile shape in was terms experimentally of their dimensions determined and thefor cracking force required macadamia to crack nuts their [11]. shells. This fruit is similar to the Metohuayo in terms of their dimensions and the force required to crack their Thefruit torqueis similar on to the the shaft Metohuayo required in could terms be of calculated their dimensions by using and Equation the force (1), required where Ftois crack the forcetheir shells.shells. TheThe torquetorque onon thethe shaftshaft requiredrequired couldcould bebe calculatedcalculated byby usingusing EquationEquation (1),(1), wherewhere FF isis thethe force provided by the mechanical characterization in N, rgear is the radius from the center to the contact force provided by the mechanical characterization in N, rgear is the radius from the center to the contact point in meters, and nmetohuayos is the number of Metohuayos cracked at the same time. point in meters, and nmetohuayos is the number of Metohuayos cracked at the same time.

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provided by the mechanical characterization in N, rgear is the radius from the center to the contact point inAgriculture meters, 2020 and, 10n,metohuayos x FOR PEERis REVIEW the number of Metohuayos cracked at the same time. 8 of 25

Figure 10. Fracture mechanism proposed.

ItIt cancan be be seen seen that that there there is anis anglean angle between between the force the andforce radius, and radius, but the but maximum the maximum torque possible torque waspossible considered was considered to occur whento occur this when angle this is 90angle◦; thus, is 90°; the thus, expression the expression was reduced was reduced to Equation to Equation (1). (1). T f .m = F rgear nmetohuayos (1) =⋅· ⋅· TFrnf. m gear metohuayos . (1) Power requirements for the shaft could be calculated using Equation (2), where Pf.m is the power requiredPower for therequirements fracture mechanism, for the shaftTf.m iscould the torque be calculated in N m, andusingω1 Equationis angular (2), velocity where of P thef,m shaftis the in power rad/s. · required for the fracture mechanism, Tf,m is the torque in N·m, and ω1 is angular velocity of the shaft P = T ω (2) in rad/s. f .m f .m· 1 =⋅ω 2.3.2. Screw Conveyor PTfm..1 fm . (2) According to the concept evaluation, a screw conveyor was selected to dose a quantity of Metohuayos2.3.2. Screw Conveyor from the chute to the fracture mechanism inside the machine. This dose corresponded to the capacity of 50 kg per hour previously established by small farmers’ requirements. Equation (3) According to the concept evaluation, a screw conveyor was selected to dose a quantity of allows determining the power required to achieve this capacity in a horizontal position [14], where Ps.c Metohuayos from the chute to the fracture mechanism inside the machine. This dose corresponded is the power required in kW, L is the screw length in m, c is the material factor in kW h/ton, Qme is the to the capacity of 50 kg per hour previously established by small farmers’ requirements.· Equation (3) mass per unit of time expressed in ton/h, and Dh is the screw external diameter in m. allows determining the power required to achieve this capacity in a horizontal position [14], where Ps,c is the power required in kW, L is the screw lengthc Qme in Dm,h c is the material factor in kW·h/ton, Qme Ps.c = L · + (3) is the mass per unit of time expressed in ton/h, and367 Dh is the20 screw external diameter in m.

Then, the torque required for screw conveyorcQ⋅ could beD calculated using Equation (4), where Ts.c is =+me h the torque on the shaft in N m, and ω isPLs.c the angular velocity of. its shaft in rad/s. (3) · 2 367 20 Ps.c Then, the torque required for screw conveyorTs.c = could be calculated using Equation (4), where T(4)s,c ω2 is the torque on the shaft in N·m, and ω2 is the angular velocity of its shaft in rad/s. 2.3.3. Rotating Screen Ps.c T = . (4) The dynamic behavior of the particles insides.c theω screen during operation is very complex to 2 determine analytically; hence, some suppositions were made in order to estimate the power required in a critical case corresponding to the start-up because of the inertial forces produced. 2.3.3. Rotating Screen The dynamic behavior of the particles inside the screen during operation is very complex to determine analytically; hence, some suppositions were made in order to estimate the power required in a critical case corresponding to the start-up because of the inertial forces produced.

Screen Rotational Inertia The screen could be modeled as a truncated cone surface whose rotational inertia could be calculated using Equation (5), where Iscreen is the screen rotational inertia in kg·m2, mscreen is the screen mass, rmax is the maximum cone radius in meters, and rmin is the minimum cone radius in meters.

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Screen Rotational Inertia The screen could be modeled as a truncated cone surface whose rotational inertia could be 2 calculated using Equation (5), where Iscreen is the screen rotational inertia in kg m , mscreen is the screen · mass, rmax is the maximum cone radius in meters, and rmin is the minimum cone radius in meters.

5 5 3 rmax rmin I = m − (5) screen screen 3 3 10 · · (rmax r ) − min Shaft Rotational Inertia

The rotational inertia of the solid shaft could be calculated using Equation (6), where Ishaft.3 is the shaft rotational inertia in kg m2, m is the shaft mass in kg, and d is the shaft diameter · shaft.3 shaft.3 in meters. 1 I = m d 2 (6) sha f t.3 4 · sha f t.3 · sha f t.3

Metohuayo Mass Rotational Inertia The critical case analyzed consisted of part of the mass deposited inside the screen which produced an inertial force. This inertia could be modeled as punctual mass inertia, Equation (7), where Ime is 2 the rotational inertia of the Metohuayos in kg m , mme is the Metohuayo mass in kg, and rcone is the · average radius in meters. In this calculation, the magnitude of mass corresponded to half the mass processed in an hour, due to the screen tilt.

2 Ime = mme rcone (7) · Total inertia could be calculated using Equation (8) as the sum of each component’s rotational inertia. Ir.s = Iscreen + Isha f t.3 + Ime (8) A constant angular acceleration was assumed to reach the operation angular velocity of 60 rpm in 2 s. Furthermore, the torque required to contrast these inertial forces was calculated using Equation (9), 2 where Tr.s is the torque required in N m, Ir.s is the rotating screen inertia in kg m , and αr.s is the angular · · acceleration of the shaft in rad/s2. Tr.s = Ir.s αr.s (9) · 2.3.4. Power Requirement Each component described needs a quantity of mechanical power in a determined angular velocity to operate. The drive system consisted of a main shaft mounted for the fracture mechanism with two pulleys. Each pulley was linked by a toothed belt transmission to the screw conveyor shaft and rotating screen shaft. Total power could be calculated using Equation (10) as the sum of each component’s required power considering the belt transmission eﬃciency, where Ps.c is the power for the screen conveyor, Pgear is the power for the fracture mechanism, Pr.s is the power for the rotating screen, and ηbelt is the transmission eﬃciency.

Ps.c Pr.s Ptotal = + Pgear + (10) ηbelt ηbelt

2.4. Dynamic Modeling of the Machine For each material’s mechanical properties, a system has its own dynamical characteristics depending on mass, stiffness, damping, and boundary conditions. These parameters together establish the natural frequencies of the system, in this case, the machine. If there is an excitation force near to one of these natural frequencies, high vibration amplitudes are produced and, when both coincide, Agriculture 2020, 10, 537 10 of 23 Agriculture 2020, 10, x FOR PEER REVIEW 10 of 25 excitationa phenomenon frequency known is sufficiently as resonance far occurs from the [15 natural]. In this frequency. sense, it must In the be same verified way, that the each forces excitation related tofrequency each excitation is suffi frequencyciently far must from not the occur natural in frequency.the plane of In their the samerespective way, modal the forces shape. related to each excitationIn order frequency to calculate must the not natural occur in frequency the plane of of the their machine respective designed, modal shape.an analytical model was proposed.In order In the to first calculate approach, the natural a one degree frequency of freedom of the machine (1DOF) model designed, was andeveloped analytical (Figure model 11a). was proposed. In the first approach, a one degree of freedom (1DOF) model was developed (Figure 11a). The equivalent mass meq corresponded to the sum of mass above the second level of the structure becauseThe equivalent of the mass mass distributionmeq corresponded along the to machine. the sum The of mass frame above for the the machine second was level modeled of the structure as four columnsbecause united of the massby eight distribution beams, with along four the on machine. each level. The Damping frame forwas the neglected machine in wasthis model, modeled and as smallfour columnsdisplacements unitedx bywere eight assumed beams, on with the four second on each level level. on top Damping of the structure. was neglected in this model, and small displacements x were assumed on the second level on top of the structure.

(a) (b)

FigureFigure 11. 11. (a(a) )One One degree degree of of freedom freedom (1-DOF) (1-DOF) model model of of the the machine; machine; (b (b)) frame frame model model used used to to calculate calculate thethe stiffness stiﬀness to to the the horizontal horizontal displacement displacement from from the the equivalent mass.

InIn thethe operationaloperational conditions conditions of theof machine,the machine, dynamical dynamical forces areforces produced are produced through thethrough interaction the interactionbetween mass between equivalent mass andequivalent frame. Inand order frame. to analyze In order the to dynamicsanalyze the corresponding dynamics corresponding to the horizontal to thedirection, horizontal the sti direction,ffness in thisthe directionstiffness neededin this todire bection calculated. needed The to stibeff calculated.ness is the relationshipThe stiffness between is the relationshipa force applied between and the a force displacement applied and produced the displacement in that direction. produced In this in that sense, direction. a force F Ink produced this sense, a displacement x in the horizontal direction (Figure 11b). The displacement was calculated using the a force Fk produced a displacement xin the horizontal direction (Figure 11b). The displacement was calculatedbeam deflection using theory.the beam The deflection columns weretheory. analyzed The columns as fixed were beams, analyzed with the asupper fixed andbeams, lower with beams the upperproducing and alower force beams because producing of their interaction a force because with the of columns;their interaction thus, the with superposition the columns; principle thus, wasthe superpositionused, resulting principle in Equation was (11), used, where resultingE is the in YoungEquation modulus (11), where of the E material is the Young in MPa, modulusI is the inertialof the 4 l materialmoment in from MPa, the I sectionis the inertial of the column moment used from in the m , section1 is the of length the column from the used ground in m to4, thel1 is lower the length beam l fromin m, the and ground2 is the to length the lower from beam the ground in m, and to the l2 is upper the length beam infrom m. the ground to the upper beam in m. ! F l 3 l l 2 l 2l x = k 2 2 1 2 1 (11) EI 12322− 12 − 8 Fk lllll22121 x =−−. (11) Then, the stiffness keq in N/m correspondingEI 12 to the 12 horizontal 8 direction is the relationship between Fk and x (Equation (12)). Then, the stiffness keq in N/m corresponding EIto the horizontal direction is the relationship keq = (12) between Fk and x (Equation (12)). 3 2 2 l2 l2l1 l2 l1 12 12 8 − EI − k = . The differential equation representingeq the movement322 of the machine along the horizontal direction lllll22121 (12) with no external forces had the form shown in Equation−− (13), where meq is the equivalent mass in kg, 12 12 8 The differential equation representing the movement of the machine along the horizontal direction with no external forces had the form shown in Equation (13), where meq is the equivalent mass in kg, and keq is the equivalent stiffness corresponding to the displacement x. The natural frequency of the machine ω modeled with 1-DOF was estimated using Equation (14).

Agriculture 2020, 10, 537 11 of 23 and k is the equivalent stiﬀness corresponding to the displacement x. The natural frequency of the Agricultureeq 2020, 10, x FOR PEER REVIEW 11 of 25 machine ω modeled with 1-DOF was estimated using Equation (14).

.. mxm x+=+ kxk x =00 (13) eqeq eqeq . (13) s keqkeq ωω == (14) (14) mmeq eq . 2.5. Computer-Aided Design (CAD) of the Machine 2.5. Computer-Aided Design (CAD) of the Machine According to the basic specifications and calculations developed and exposed in previous points, a detailedAccording three-dimensional to the basic specifications computer-aided and calculat modelions of thedeveloped complete and machine exposed andin previous the support points, was modeled.a detailed Autodeskthree-dimensional Inventor computer-aided software was considered model of the to createcomplete a digital machine prototype and the ofsupport a general was 3D mechanicalmodeled. Autodesk solid modeling Inventor application, software was commonly considered used to create in the a digital design prototype of machinery of a general for diff 3Derent sectors,mechanical such solid as the modeling construction, application, automotive, commonly or agriculture used in the sectors. design All of components machinery for of thedifferent machine (structuralsectors, such profiles, as the mechanicalconstruction, devices, automotive, and standard or agriculture and commercialsectors. All co components)mponents of were the machine assembled (structural profiles, mechanical devices, and standard and commercial components) were assembled and positioned in a unique model, where the geometric and manufacturing information was obtained, and positioned in a unique model, where the geometric and manufacturing information was such as part and assembly drawings, bill of materials, or models to generate toolpaths in manufacturing obtained, such as part and assembly drawings, bill of materials, or models to generate toolpaths in applications (CAM software). The software also allowed the export of geometry in standard formats manufacturing applications (CAM software). The software also allowed the export of geometry in recognized by CAE software. standard formats recognized by CAE software. Figure 12 shows the assembly plan of the shell cracking machine and its four main components. Figure 12 shows the assembly plan of the shell cracking machine and its four main components. Figure 13 shows main views of the machine. Each was developed by following the structure of Figure 13 shows main views of the machine. Each was developed by following the structure of functionsfunctionsin in thethe conceptualconceptual design phase. phase. As As can can be be seen, seen, a amodular modular design design was was favorable favorable in order in order to to facilitatefacilitate fabrication,fabrication, maintenance,maintenance, and and assembly. assembly.

FigureFigure 12. AssemblyAssembly plan plan of of the the shell shell crac crackingking machine machine and and its itselements. elements.

Agriculture 2020, 10, 537 12 of 23 Agriculture 2020, 10, x FOR PEER REVIEW 12 of 25

Figure 13. AssemblyAssembly plan plan of of the shell cracking machine and its elements: main main views. views.

Figure 1414 shows shows a sectiona section of theof machinethe machine describing describing the Metohuayo the Metohuayo fruit processing. fruit processing. The operation The operationstarted with started Metohuayo with Metohuayo fruits being fruits fed through being fed a chute through fed. Thea chute screw fed. conveyor The screw controlled conveyor the controlledquantity and the velocityquantity of and processing velocity of according processing to according the capacity to the 50 kgcapacity/h. Fruits 50 kg/h. were Fruits then sentwere to then the sentfracture to the mechanism fracture composedmechanism of acomposed toothed cylinder of a toothed and a toothercylinder wall and with a toother variable wall clearance with providedvariable clearanceby the wall provided tilt. This by allowed the wall processing tilt. This allowed diﬀerent processing dimensions different of Metohuayo dimensions fruits of Metohuayo according tofruits the accordingsample analyzed. to the sample analyzed.

AgricultureAgriculture 2020,2020 10, x, 10FOR, 537 PEER REVIEW 13 of 1325 of 23

(a) (b)

FigureFigure 14. ( 14.a) Section(a) Section of the of shell the shell cracking cracking machine machine corresponds corresponds to the to fruits the fruits flow; ﬂow; (b) Dosify (b) Dosify and and crackingcracking of fruits of fruits section. section.

WhenWhen the thefruits fruits were were cracked, cracked, they they were divideddivided into into shell shell and and seed, seed, which which needed needed to be separatedto be separatedin order in toorder get to only get the only seeds. the seeds. Under Under the fracture the fracture mechanism, mechanism, there there was awas duct a duct leading leading the cracked the crackedfruits fruits to the to rotatingthe rotating screen. screen This. This rotating rotating screen screen had had a truncated a truncated cone cone shape shape to generate to generate a tilt a tilt for the for theshells shells to dropto drop to the to the end. end.

2.6. Computer-Aided Engineering (CAE) of the Machine 2.6. Computer-Aided Engineering (CAE) of the Machine Conventionally,Conventionally, the theengineering engineering product product develo developmentpment process process employed employed a design–build–test a design–build–test philosophy,philosophy, where where the the“optimum” “optimum” solution solution was wasreached reached via a via trial-and-error a trial-and-error sequence, sequence, and andwhere where the experiencethe experience of the of designer the designer related related to the to prod the productuct was wasdecisive. decisive. Simulation-based Simulation-based design design methods, methods, as definedas defined in [16], in [ 16considerably], considerably reduced reduced this thisdesign design process, process, in terms in terms of time of time and andcost, cost, and andthe concept the concept of concurrentof concurrent engineering, engineering, for example, for example, is today is today considered considered in product in product design. design. In these In these techniques, techniques, the thetask task of ofcarrying carrying out out experimental teststests is is displaced displaced by theby simulationthe simulation through through numerical numerical techniques techniquesof the di offferent the different physicsinvolved physics ininvolved the problem in the which problem is the which object is of the study object bythe of designer.study by the designer.For the CAE simulation, the Altair Hyperworks simulation platform was considered, in which theFor preprocessing the CAE simulation, and postprocessing the Altair Hyperworks stages were simulation addressed. platform The CAD was three-dimensionalconsidered, in which model the waspreprocessing taken as a and starting postprocessing point (Figure stages 15a), we whosere addressed. components The wereCAD pre-dimensioned three-dimensional and model selected wasaccording taken as a to starting basic calculations. point (Figure In 15a), this model, whose some components simplifications were pre-dimensioned were implemented and in selected the bearing accordingsupports to basic (Figure calculations. 15b), since In these this subsetsmodel, so includedme simplifications all the elements were thatimplemented made them in upthe (balls, bearing cages, supportsraceways, (Figure seals, 15b), etc.), since which these complicated subsets included their al analysis.l the elements The di thatfference made in them results up at (balls, the level cages, of the raceways,overall seals, behavior etc.), of which the structure complicated was imperceptible. their analysis. The difference in results at the level of the overall behavior of the structure was imperceptible.

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(a) (b)

FigureFigure 15. ((aa)) Three-dimensionalThree-dimensional (3D) (3D) model model considered considered in computer-aided in computer-aided engineering engineering (CAE) analysis;(CAE) analysis;(b) bearing (b) supportbearing detail.support detail.

TheThe subdivision subdivision of ofthe the geometry geometry into into discre discretete approximations, approximations, known known as meshing, as meshing, was automaticallywas automatically done by done the bysoftware. the software. In calculations In calculations that consider that only consider stiffness, only as sti isff theness, case as of is the the analysiscase of theof buckling analysis ofmodes buckling and modesvibration and modes, vibration the modes, influence the influenceof the mesh of theon meshthe results on the is results very small;is very thus, small; two thus, different two di sizesfferent were sizes considered were considered and the values and the ob valuestained obtainedwere equal were or equalvery similar, or very guaranteeingsimilar, guaranteeing the mesh the independence mesh independence of the calculat of the calculations.ions. However, However, in stress in analysis, stress analysis, a coarse a coarsemesh canmesh yield can inaccurate yield inaccurate results; results; thus, it thus, was it necessary was necessary to carry to carry out a out mesh a mesh convergence convergence study study in order in order to achieveto achieve reliable reliable results. results. The The convergence convergence method method co considerednsidered in instatic static analysis analysis was was the the adaptative adaptative method,method, through thethe iterative iterative reduction reduction of theof meshthe me insh the in stress the concentrationstress concentration zone until zone the until difference the differencebetween twobetween consecutive two consecutive iterations wasiterations affordable. was Theaffordable. definitive The mesh definitive of the modelmesh of (Figure the model 16a,b) (Figurewas made 16a,b) up ofwas 281,128 made nodesup of and281,128 864,095 nodes elements. and 864 Solid,095 elements. second-order Solid tetrahedrons second-order were tetrahedrons considered werein the considered meshing calculation. in the meshing Finally, calculation. the interaction Finally, between the interaction elements makingbetween up elements different making parts of up the differentmachine parts was carriedof the machine out through was carried the kinematic out throug conditionsh the kinematic of the three conditions relative of degrees the three of freedomrelative degreesbetween of the freedom surfaces between in contact the (similar surfaces conditions in contact to (similar a welded conditions connection); to a thiswelded assumption connection); was validthis assumptionbecause the was loads valid were because relatively the smallloads andwere the relati focusvely was small on theand parts the focus to be was connected. on the parts Additional to be connected.conditions Additional such as bolt conditions prestress weresuch notas bolt considered, prestress further were not reinforcing considered, this further hypothesis. reinforcing this hypothesis.

Agriculture 2020, 10, 537x FOR PEER REVIEW 1515 of of 25 23

(a) (b)

Figure 16. ((aa)) Meshed Meshed shell shell craking craking machine machine model; model; ( (b)) Mesh Mesh of of the the machine. machine.

InIn the part in contact with the fruit, A304 stainless-steelstainless-steel components were considered, in order toto comply with the national hygiene and health regulations.regulations. For For the other components, A500 steel (yielding strength = 250250 MPa) MPa) for for hollow hollow structural structural sections sections was was considered, considered, and and A36 steel profiles proﬁles were considered for the sheet metal elements (yielding(yielding strength = 250 MPa), both easily found on the national market.market. TheThe Young Young modulus modulus of the of materialsthe materials considered considered was 200 was GPa. 200 The GPa. material The properties material propertiesused for modeling used for aremodeling listed inare Table listed4. in Loads Table and 4. Loads boundary and boundary conditions conditions correspond correspond to the machine to the machineworking, working, Figure 17 Figurea shows 17a the shows boundary the boundary condition co appliedndition to applied each support to each and support Figure and 17b Figure shows 17b the showsloads applied the loads to applied the structure to the by structure each component by each component support. support. In addition to the analytic calculations of the machine structure, a static analysis corresponding to the worst condition of the componentsTable and 4. structure Material properties. of the machine was simulated. This condition was the blocking produced if the mechanismSteel fractureValue could Units not crack the fruit or the stone inside. Figure 18a shows the fracture mechanism of the Metohuayo fruits analyzed, Figure 18b shows the Elastic modulus 200 GPa mesh used, and Figure 18c is a detailed form of the mesh. Poisson ratio 0.3 Density 7850 kg/m3 Table 4. Material properties.

Steel Value Units Elastic modulus 200 GPa Poisson ratio 0.3 Density 7850 kg/m3

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AgricultureAgriculture2020, 10 2020, 537, 10, x FOR PEER REVIEW 16 of 2516 of 23

(a) (b)

Figure 17. (a) Boundary conditions applied to each support; (b) loads applied to the structure.

Figure 18a shows the fracture mechanism of the Metohuayo fruits analyzed, Figure 18b shows the mesh used, and Figure 18c is (aa )detailed form of the mesh. (b) FigureFigure 17. (a 17.) Boundary (a) Boundary conditions conditions applied applied toto eacheach support; support; (b ()b loads) loads applied applied to the to structure. the structure.

In addition to the analytic calculations of the machine structure, a static analysis corresponding to the worst condition of the components and structure of the machine was simulated. This condition was the blocking produced if the mechanism fracture could not crack the fruit or the stone inside. Figure 18a shows the fracture mechanism of the Metohuayo fruits analyzed, Figure 18b shows the mesh used, and Figure 18c is a detailed form of the mesh.

Agriculture 2020, 10, x FOR PEER REVIEW 17 of 25 (a) (b)

(a) (b)

(c)

FigureFigure 18. (a 18.) Fracture (a) Fracture mechanism mechanism for for Metohuayo Metohuayo fruits; fruits; (b (b) mesh) mesh of offracture fracture mechanism; mechanism; (c) detailed (c) detailed meshmesh of the of toothed the toothed wheel wheel and and toothed toothed wall. wall. It was considered that this blocking would produce the maximum torque in the transmission, with a value of 2.4 corresponding to the nominal torque according to the electrical motor datasheet (144.8 Nm). Boundary conditions of the lateral supports corresponded to a sliding contact. All bolt connections were modeled as MPC (multipoint constraint) elements, which allowed connecting the nodes for which restrictions could be defined; hence, the behavior of these nodes was compatible with the boundary conditions established. Similarly, for the forced applied, a torque transmission proportional to the position of nodes in the outer surface was considered. The transmission from the toothed wheel to the Metohuayo cracking work plane was generated with RBE (rigid body elements).

3. Results and Discussion

3.1. Mechanical Behavior of the Metohuayo Fruit According to the mechanical characterization of the Metohuayo fruit, a sample of 100 Metohuayo fruits were tested. Figure 19 shows the two main specimens from the sample, where each one represents the maximum and minimum strain measured along the test (6 and 13 mm, respectively). This also indicates the maximum force required to crack the Metohuayo shell, which is approximately 550 N. The strain information was used to establish the clearance needed in the fracture mechanism, while the maximum force allowed sizing the fracture mechanism components on the basis of materials theory, as well as calculating drive requirements such as torque and power.

Agriculture 2020, 10, 537 17 of 23

It was considered that this blocking would produce the maximum torque in the transmission, with a value of 2.4 corresponding to the nominal torque according to the electrical motor datasheet (144.8 Nm). Boundary conditions of the lateral supports corresponded to a sliding contact. All bolt connections were modeled as MPC (multipoint constraint) elements, which allowed connecting the nodes for which restrictions could be deﬁned; hence, the behavior of these nodes was compatible with the boundary conditions established. Similarly, for the forced applied, a torque transmission proportional to the position of nodes in the outer surface was considered. The transmission from the toothed wheel to the Metohuayo cracking work plane was generated with RBE (rigid body elements).

3. Results and Discussion

3.1. Mechanical Behavior of the Metohuayo Fruit According to the mechanical characterization of the Metohuayo fruit, a sample of 100 Metohuayo fruits were tested. Figure 19 shows the two main specimens from the sample, where each one represents the maximum and minimum strain measured along the test (6 and 13 mm, respectively). This also indicates the maximum force required to crack the Metohuayo shell, which is approximately 550 N. The strain information was used to establish the clearance needed in the fracture mechanism, while the maximum force allowed sizing the fracture mechanism components on the basis of materials theory, asAgriculture well as 2020 calculating, 10, x FOR drivePEER REVIEW requirements such as torque and power. 18 of 25

FigureFigure 19.19. Compression force appliedapplied onon thethe fruit’sfruit’s shellshell (N)(N) vs.vs. strain produced (mm).(mm).

3.2.3.2. Static Analysis AA staticstatic analysisanalysis ofof thethe wholewhole structurestructure andand componentscomponents waswas carriedcarried outout inin orderorder toto determinedetermine thethe magnitudemagnitude ofof stressesstresses alongalong themthem andand thethe criticalcritical zoneszones wherewhere thethe stressstress waswas maximum.maximum. AA ﬁrstfirst analysisanalysis was was carried carried out out with with the the machine machine in nomi in nominalnal operation operation conditions, conditions, and the and results the results are shown are shownin Figure in Figure20a. The 20a. maximum The maximum stress stresscalculated calculated was was41.84 41.84 MPa, MPa, far farfrom from the theyield yield strength strength of ofa conventional steel which is 250 MPa; hence, the minimum safety factor was 5.97. This value was high as expected due to the structural shapes dimensions used. It could be considered an oversizing; however, it corresponds to the fabrication requirements and material availability in local mechanic workshops in the rainforest from Perú. The structural shape selected is used as a standard there for different mechanical applications. Additionally, it must be assured that the displacements do not affect the machine performance during its operation. In this sense, the displacement of each point along the machine and its structure was calculated, and the results are shown in Figure 20b. The maximum displacement was 0.4 mm and corresponded to the top of the chute, while there was practically no stress in this zone. This was due to the force locations, which were near the fracture mechanism at the first and second levels of the structure. There was a relatively large vertical distance between this zone, where the forces act, and the chute; hence, the displacements were amplified at the top.

Agriculture 2020, 10, 537 18 of 23 a conventional steel which is 250 MPa; hence, the minimum safety factor was 5.97. This value was high as expected due to the structural shapes dimensions used. It could be considered an oversizing; however, it corresponds to the fabrication requirements and material availability in local mechanic workshops in the rainforest from Perú. The structural shape selected is used as a standard there for diAgricultureﬀerent mechanical2020, 10, x FOR applications. PEER REVIEW 19 of 25

Figure 20. ((aa)) Von Von Misses stresses contour (MPa) in static load load case; case; ( (b)) resultant resultant displacements displacements (mm) (mm) in static load case, scaled 500500×.. × Additionally,A second static it analysis must be was assured carried that out the accordin displacementsg to the doworst not possible affect the situation machine in performance the machine during itsits operation.operation. In This this sense,situation the corresponded displacement ofto each the pointblocking along of the the machine fracture and mechanism its structure if wasMetohuayo calculated, fruits and could the results not be arecracked. shown When in Figure this 20situationb. The maximumoccurred, the displacement electric motor was transmitted 0.4 mm and correspondedits maximum possible to the top torque of the to chute, the shaft while and there toothed was practically wheel to nocrack stress the in fruits. this zone. Obviously, This was in duethis tosituation, the force electronic locations, components which were open near the the electrical fracture mechanismcircuit of the at motor the first in andorder second to avoid levels the of very the structure.high current There magnitude was a relatively produced. large The vertical stress distancemagnitudes between produced this zone, during where this the condition forces act, are andshown the chute;in Figure hence, 21, thewhere displacements the maximum were stress amplified was 86. at67 the MPa top. and corresponded to the minor diameter sectionA secondof the shaft, static where analysis torque was and carried flection out accordingwere superposed. to the worst This possible value was situation still farin from the the machine yield duringstrength; its hence, operation. the machine This situationwould resist corresponded the blocking to condition. the blocking of the fracture mechanism if Metohuayo fruits could not be cracked. When this situation occurred, the electric motor transmitted its maximum possible torque to the shaft and toothed wheel to crack the fruits. Obviously, in this situation, electronic components open the electrical circuit of the motor in order to avoid the very high current magnitude produced. The stress magnitudes produced during this condition are shown in Figure 21, where the maximum stress was 86.67 MPa and corresponded to the minor diameter section of the shaft, where torque and flection were superposed. This value was still far from the yield strength; hence, the machine would resist the blocking condition.

Agriculture 2020, 10, x FOR PEER REVIEW 19 of 25

Figure 20. (a) Von Misses stresses contour (MPa) in static load case; (b) resultant displacements (mm) in static load case, scaled 500×.

A second static analysis was carried out according to the worst possible situation in the machine during its operation. This situation corresponded to the blocking of the fracture mechanism if Metohuayo fruits could not be cracked. When this situation occurred, the electric motor transmitted its maximum possible torque to the shaft and toothed wheel to crack the fruits. Obviously, in this situation, electronic components open the electrical circuit of the motor in order to avoid the very high current magnitude produced. The stress magnitudes produced during this condition are shown in Figure 21, where the maximum stress was 86.67 MPa and corresponded to the minor diameter Agriculturesection2020, 10 of, the 537 shaft, where torque and flection were superposed. This value was still far from the yield 19 of 23 strength; hence, the machine would resist the blocking condition.

Agriculture 2020, 10, x FOR PEER REVIEW 20 of 25

Figure 21. Stress magnitudes (MPa) produced on the mechanism during a blocking condition. Figure 21. Stress magnitudes (MPa) produced on the mechanism during a blocking condition. 3.3. Buckling Analysis

3.3. Buckling AnalysisIn order to evaluate the reduction of the resistant capacity against compression stresses, a linear buckling analysis was performed. The results obtained in the buckling analysis correspond to the In orderfactor to of evaluate the critical the buckling reduction load that of the destabilized resistant the capacity system. Therefore, against compression a value greater stresses, than 1 refers a linear buckling analysisto a security was condition. performed. Table The5 summarizes results obtained the safety in factors the buckling associated analysis with the correspondmain buckling to the factor of themodes critical defined buckling in Figure load 22. that Due destabilized to the low load the to system. which the Therefore, system was a valuesubjected, greater the buckling than 1 refers to a securityfactors condition. were very Table high5 whensummarizes not assuming the safety a conditio factorsning associatedfor its design with and a the risk main for the buckling integrity modesof deﬁned inthe Figure equipment. 22. Due to the low load to which the system was subjected, the buckling factors were very high when not assuming a conditioningTable for 5. its Critical design load and factors. a risk for the integrity of the equipment.

TableMode 5. Critical load factors.Factor 1 669.74 Mode Factor 2 775.92 13 669.74896.89 24 775.921158.04 3 896.89 4 1158.04

(a) Mode 1 (b) Mode 2

Figure 22. Cont.

Agriculture 2020, 10, 537 20 of 23 Agriculture 2020, 10, x FOR PEER REVIEW 21 of 25

Figure 22.FigurePrincipal 22. Principal buckling buckling modes modes shapes; shapes; (a) First; (a) ( bFirst;) Second; (b) Second; (c) Third (c) andThird (d and) Fourth (d) Fourth buckling buckling mode shape. mode shape. 3.4. Modal Analysis 3.4. Modal Analysis NaturalNatural frequencies frequencies obtained obtained analytically analytically and and usingusing finite finite element element method method (FEM) (FEM) are listed are in listed in Table6. TheTable first 6. The natural first natural frequency frequency calculated calculated byby the FEM FEM model model was was very veryclose to close that tocalculated that calculated by by the 1-DOFthe 1-DOF model. model. It mustIt must be be known known thatthat an analytical model model only only focuses focuses on vibration on vibration modes modesin in which thewhich designer the designer is interested. is interested. Hence, Hence, only only a a 1-DOF1-DOF model model was was considered considered to analyze to analyze the more the more flexible mode,flexible correspondingmode, corresponding to mode to mode 1. FEM 1. FEM allowed allowed determining determining moremore natural natural frequencies, frequencies, and and the the analytical result allowed concluding that the FEM model was well developed. analytical result allowed concluding that the FEM model was well developed. Table 6. Natural frequencies of the system. FEM, finite element method. Table 6. Natural frequencies of the system. FEM, finite element method. Mode 1-DOF Model FEM Mode1 1-DOF19.8 Model Hz 21.22 FEM Hz 2 - 23.54 Hz 1 19.8 Hz 21.22 Hz 3 - 40.35 Hz 2 - 23.54 Hz 4 - 47.72 Hz 3 - 40.35 Hz 4 - 47.72 Hz As explained before, each natural frequency corresponds to a characteristic modal shape. Figure 23a,b shows the modal shape for the first and second natural frequencies. Their magnitudes were Asvery explained similar as before, expected, each explained natural by frequencythe similarity corresponds between the stiffness to a characteristic in these two horizontal modal shape. Figure 23directions.a,b shows These the modal modal shapes shape could for thebe modeled first and as secondcolumns naturalfixed to the frequencies. ground and Theirfree on magnitudes their ends according to the dynamic model presented in Figure 11. Equivalent mass was still the same for were very similar as expected, explained by the similarity between the stiffness in these two horizontal each horizontal direction, but the structure also practically maintained the same components, with directions.no difference These modal between shapes bracings could added be in modeled each direct asion. columns The deflection fixed to caused the ground by an external and free force on their ends accordingin each direction to the dynamic corresponded model mainly presented to the large in Figurecolumn 11of the. Equivalent structure which mass did was not stilldepend the on same for each horizontalthe direction direction, because but it involved the structure the same also square practically tubes. If maintained the tubes were the not same square, components, the section with no differenceinertia between would bracingschange and, added thus, inalso each the stiffness direction. depending The deflection on the direction, caused but by this an was external not the force in each directioncase. corresponded mainly to the large column of the structure which did not depend on the direction because it involved the same square tubes. If the tubes were not square, the section inertia would change and, thus, also the stiffness depending on the direction, but this was not the case. Agriculture 2020, 10, x FOR PEER REVIEW 22 of 25

Figure 23c shows the third vibration mode corresponding to the torsional vibration of the structure. Maximum displacement occurred on the chute and was higher than other displacements from the first and second mode. Figure 23d shows the fourth mode corresponding to the translation of each component mass; in contrast to the first and second mode, the fourth mode presents a more independent component mass vibration, where they did not move in the same direction. It must be noted that each modal shape corresponded to free vibration. However, if an excitation frequency was sufficiently close to the corresponding natural frequency and the excitation force acted on the characteristic modal shape plane, the dynamical behavior would correspond to the vibration mode of this natural frequency. This condition must be avoided, as explained before. In this sense, it wasAgriculture verified2020 ,that10, 537 there were no excitation forces from components which could excite a modal shape;21 of 23 the values are listed in Table 7.

(a) Mode 1 (b) Mode 2

Figure 23. Principal modal shapes of vibration; (a) First; (b) Second; (c) Third and (d) Fourth mode of vibration.

Figure 23c shows the third vibration mode corresponding to the torsional vibration of the structure. Maximum displacement occurred on the chute and was higher than other displacements from the first and second mode. Figure 23d shows the fourth mode corresponding to the translation of each component mass; in contrast to the first and second mode, the fourth mode presents a more independent component mass vibration, where they did not move in the same direction. It must be noted that each modal shape corresponded to free vibration. However, if an excitation frequency was sufficiently close to the corresponding natural frequency and the excitation force acted on the characteristic modal shape plane, the dynamical behavior would correspond to the vibration Agriculture 2020, 10, 537 22 of 23 mode of this natural frequency. This condition must be avoided, as explained before. In this sense, it was verified that there were no excitation forces from components which could excite a modal shape; the values are listed in Table7.

Table 7. Excitation frequencies produced by components.

Component Frequency Rotating Screen 0.25 Hz Screw Conveyor 0.25 Hz Fracture Mechanism 0.5 Hz Electric motor 29.3 Hz

Finally, technical data of the automatic shell cracking machine developed are listed in Table8, as a result of the analytical calculations and simulation.

Table 8. Technical data of the machine developed.

Parameter Value Capacity 50 kg/h Torque 59 N m · Rpm 30 Power 0.185 kW Dimensions 1080 mm 60 mm 1745 mm × ×

4. Conclusions A shell cracking machine of Metohuayo fruits was developed by applying VDI-2221 methodology. Conceptual solutions were proposed and evaluated in order to obtain an optimal design. Analytical analysis was carried out to determine dimensions, mechanical requirements from materials, and power consumption. In order to extend the analysis along the machine, CAD/CAE techniques and simulations were applied. The CAD and CAE tools used in this work demonstrate their applicability to this type of equipment. Static analysis indicated a high safety factor in the structure as expected and could indicate an oversizing; however, it corresponded to the local requirements. The rainforest from Peru presents some particularities such as a corrosive environment and material availability. Local mechanic workshops only work with a few dimensions of structural shapes, including that selected for this machine as a standard. The worst operation conditions analyzed corresponded to a situation of fracture mechanism blocking, when the torque produced on the shaft increased to a maximum of 2.4 times its rated value. During this condition, it was found that each component of the machine and structure was able to resist with an acceptable safety factor, where the highest stress was 86.67 MPa, far from the yield strength of 250 MPa. Modal analysis revealed that the excitation frequencies from the components were not able to excite one of the modes of vibration since the natural frequencies were far from the values. In the same way, displacements determined in static analysis were very small and, hence, there would be no amplitudes of vibration negatively aﬀecting the dynamic performance of the machine. The design methodology presented was customized to a special fruit processing, and the addition of a new mechanical characterization allowed assuring good performance of the machine for this particular application. This procedure and analysis could be applied for the development of multiple processing machines for particular fruits, especially from the rainforest, where various species continue being processed manually. Finally, the results obtained from the analysis (safety factor related to static load of 670 against buckling, considering a long column) indicate that the machine designed was sturdy in its operation, including in the worst situation; thus, it is functional for small farmers’ requirements, as well as simple for fabrication with local technology. Agriculture 2020, 10, 537 23 of 23

As future research, an analysis of the dynamic behavior of Metohuayo fruits from feeding to separation could be carried out using the discrete element method (DEM). The interaction between their particles at each stage is very complex and, hence, requires experimentation and an appropriate statistical analysis of the data obtained.

Author Contributions: Conceptualization, J.J.J.d.C.F.; methodology, C.G.R.R., M.A.T.C. and J.J.J.d.C.F.; software, C.G.R.R., M.A.T.C. and J.J.J.d.C.F.; validation, C.G.R.R., M.A.T.C. and J.J.J.d.C.F.; formal analysis, C.G.R.R., M.A.T.C. and J.J.J.d.C.F.; writing—original draft preparation, C.G.R.R., M.A.T.C. and J.J.J.d.C.F.; writing—review and editing, C.G.R.R., M.A.T.C. and J.J.J.d.C.F. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to acknowledge CITE-Materiales PUCP for laboratory support. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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