Detailed design process and assembly considerations for snap-fit joints using additive manufacturing

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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 84 (2019) 680–687 www.elsevier.com/locate/procedia

29th CIRP Design 2019 (CIRP Design 2019) 29th CIRP Design 2019 (CIRP Design 2019)

Detailed process and assembly considerations for Detailed design design28th process and Conference, assemblyMay considerations for snap-fit snap-fit joints joints CIRP Design 2018, Nantes, France using additive manufacturing using additive manufacturing A new methodology a,to analyze the functional and physical architecture of Jorge Luis Amayaa,*, Emilio A. Ramírezaa, Maldonado Galarza F.aa, Jorge Hurelaa Jorge Luis Amaya A. Ramírez , Maldonado Galarza F. , Jorge Hurel existing products for*,anEmilio assembly oriented product family identification aAdvanced Machining and Prototyping Laboratory (CAMPRO), Faculty of Mechanical and Production Sciences Engineering (FIMCP), aAdvanced and Prototyping Laboratory (CAMPRO), Faculty of Mechanical Sciences Engineering (FIMCP), ESPOLMachining Polytechnic University, Campus Gustavo Galindo Km 30.5 Vía Perimetral, and P.O.Production Box 09-01-5863, Guayaquil, Ecuador ESPOL Polytechnic University, Campus Gustavo Galindo Km 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat

* Corresponding author. Tel.: +593-42-269-295. E-mail address: [email protected] Écoleauthor. Nationale d’Arts etE-mail Métiers, Arts [email protected] Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France * Corresponding Tel.:Supérieure +593-42-269-295. address:

* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Abstract Abstract

The use of additive manufacturing (AM) technology has been widely adopted due to the facility to produce highly complex elements compared The use of additive manufacturing (AM) technology AM has been widelyisadopted to the facility to producesystems highly complex to conventional fabrication processes. Additionally, technology rapidlydue developing straightforward enablingelements designerscompared to make Abstract to conventional fabrication processes. Additionally, AM technology is rapidly developing straightforward systems enabling designers to make products faster, despite current technology limitations (i.e. processing defects, materials properties, etc.). However, not only AM technology or products faster, despite current technology limitations (i.e. processing defects, materials properties, etc.). However, not only AM technology or be analyzed to have solutions all existing limitations. This means, it is necessary to this takedevelopment, into account the AMneed design Inproducts today’s must business environment, the concrete trend towards moretoproduct variety and customization is unbroken. Due to of products must be analyzed to have systems concrete solutions all existing limitations. This it is necessary into account AM design process propose simpler solutions. Elements manufactured by AM technology have dimension limitations ontake build size regarding printers agile andtoreconfigurable production emerged totocope with various products andmeans, product families. To to design and optimize production process tocapabilities, propose solutions. Elements manufactured by AM technology have limitations onofbuild size regarding buildingas especially the product elements are moreproduct volumetric thanmethods the building chamber.Indeed, In those cases, AMknown design process printers takes systems well as tosimpler choose thewhen optimal matches, analysis aredimension needed. most the methods aim toa building capabilities, especially when the elements are more volumetric than the building chamber. In those cases, AM design process takes significant role and potential divide big elements in sections, which are later 3D-printed joined using as the cheapest analyze a product or aone productsolution family is ontothe physical level. Different product families, however, mayand differ largely in snap-fits, terms of the number anda significant role and a potential solution is to divide big elements in sections, which are later 3D-printed and joined using snap-fits, as the cheapest and fastest connectors available. the present workcomparison explores the and detail designofstages of a proposed design methodology for elements´ coupling nature of components. This fact Thus, impedes an efficient choice appropriate product family combinations for the production and fastest connectors Thus, theThe present work explores theisdetail design stages of a proposed design for elements´ coupling by snap-fit joints usingavailable. AM is technology. design methodology assembly of parts from amethodology 1-gallon plastic container. finite system. A new methodology proposed to analyze existing products tested in viewonofthe their functional and physical architecture. The aim is toAcluster by snap-fit joints using AM technology. The design methodology is tested on the assembly of parts from a 1-gallon plastic container. A finite element simulation the partsoriented coupling scenarios is presented and the effects of part’sassembly deflection on and the detail designofstages analyzed. In these products in newfor assembly product families for the optimization of existing lines the creation futureare reconfigurable element for the parts coupling scenarios is ergonomics presented and effects forces of part’s deflection on the detail design stages are analyzed. In addition,simulation a final design assembly andthe retention discussed in order tosubassemblies avoid part decoupling problems assembly systems. Basedvalidation on Datumregarding Flow Chain, the physical structure of the products isareanalyzed. Functional are identified, and addition, a final design validation regarding assembly ergonomics and retention forces are discussed in order to avoid part decoupling problems material failure. aorfunctional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the or material failure. similarity between product families by providing design support to both, production system planners and product designers. An illustrative © Published Elsevier B.V. example of nail-clipper is used by to explain proposed methodology. An industrial case study on two product families of steering columns of © 2019 2019 The Thea Authors. Authors. Published by Elsevierthe B.V. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of Design Conference Conference 2019approach. thyssenkrupp Presta France is then carried out to a first industrial evaluation of the proposed Peer-review under under responsibility responsibility of of the the scientific scientificgive committee of the the CIRP CIRP Design 2019. ©Peer-review 2017 The Authors. Published by Elsevier B.V. committee of the CIRP Design Conference 2019 Keywords: Design Additiveofmanufacturing, Peer-review undermethod, responsibility the scientificSnap-fit. committee of the 28th CIRP Design Conference 2018. Keywords: Design method, Additive manufacturing, Snap-fit.

Keywords: Assembly; Design method; Family identification

1. Introduction 1. Introduction

building chamber, studies have proposed voxelization-oriented building chamber, have proposed voxelization-oriented division methods studies and posterior part interlocking assembly division methods and posterior part interlocking assembly 1. Introduction of the product and they characteristics manufactured and/or procedures [2], range however, have been deemed inappropriate Additive manufacturing (AM) is a layer-by-layer fabrication procedures [2], however, they have been deemed inappropriate Additive manufacturing (AM) is a layer-by-layer fabrication assembled this system. In this context, mainstudies challenge in for hollowinparts and precision models.the Other have technology used to construct computer-aided designs (CAD) for hollow parts and precision models. Other have technology used construct computer-aided Due or to prototypes. the tofast development thedesigns domain of modelling and analysis is not only copestudies with single tested model division vianow Binary Spaceto Partitioning, and models The use of AM intechnology has(CAD) been tested model division viajoining Binary Space Partitioning, models or prototypes. The use ofto AM technology been communication and toanthe ongoing trend of digitization and products, aconnector-guided limited product range orwith existing product families, posterior bonding agents [3].and widely adopted due facility produce highly has complex posterior connector-guided joining with bonding agents [3]. widely adopted due to the facility to produce highly complex digitalization, manufacturing enterprises are facing important but In also to be to the analyze to compare productsastojoining define order toable avoid use ofand fasteners or adhesives elements compared to conventional fabrication processes, with In order to avoid the use of fasteners or adhesives as joining elements compared to conventional fabrication processes, with challenges market(e.g. environments: a continuing new product families.potential It can besolution observedisthat classical of existing methods, a proposed the addition snapa growing in listtoday’s of materials polymers, metal powder, methods, a proposed potential solution theclients addition of snapaceramics) growing list ofreduction materials polymers, metaltimes powder, tendency towards of (e.g. product development and product families areprinted regrouped in function of fit features to the parts, whichisconsists onora features. flexible depending of model’s functional requirements fit features to the printed parts, which consists on a flexible ceramics) depending of model’s functional requirements and shortened productcapabilities. lifecycles. In addition, there is an increasing However, assembly oriented families are element that deflects duringproduct the assembly andhardly fixes toinfind. the AM technology element that deflects during assembly andmainly fixes in in two the AMEven technology capabilities. demand ofthough customization, being at the in aprocess global On the product family level,the products differ mating component. recent advances on same AM time permit mating component. Even though recent advances on AM permit process competition competitors all over world. This trend, main characteristics: number of components and (ii) the Previous studies(i) the have developed general design stability on with industrial applications andthe economic feasibility, Previous studies developed design stability industrial andfrom economic which is on inducing the applications development macro to micro type of components (e.g. have mechanical, electrical, electronical). methodologies for models division, which aregeneral later 3D-printed elements manufactured by AM technology have feasibility, dimension methodologies for models division, are later 3D-printed elements manufactured by AMbuilding dimension markets, results in diminished lottechnology sizes capacities due have to augmenting considering mainly single products andClassical joined methodologies using snap-fits, taking which into account Design for limitations regarding printers and work and joined using snap-fits, taking into account Design for limitations regarding printers building capacities and work product varieties [1]. (high-volume low-volume production) [1]. or solitary, already existing (DFMA) product criteria’s families [4]. analyze the Manufacturing and Assembly piece volumes Thus, for toparts greater than the printer Manufacturing and Assembly (DFMA) criteria’s [4]. piece volumes [1]. Thus, for parts greater than the printer To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which identify in the existing causes difficulties regarding an efficient definition and 2212-8271 possible © 2019 The optimization Authors. Publishedpotentials by Elsevier B.V. 2212-8271 2019responsibility The Authors. of Published Elsevier B.V.of the CIRP Design Conference 2019 Peer-review©under the scientific committee production system, it is important tobyhave a precise knowledge comparison of different product families. Addressing this Peer-review under responsibility of the scientific committee of the CIRP Design Conference 2019

2212-8271©©2017 2019The The Authors. Published by Elsevier 2212-8271 Authors. Published by Elsevier B.V. B.V. Peer-review under responsibility of scientific the scientific committee theCIRP CIRP Design Conference 2019. Peer-review under responsibility of the committee of the of 28th Design Conference 2018. 10.1016/j.procir.2019.04.271

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Nomenclature 𝛼𝛼 𝛼𝛼 " 𝛽𝛽 𝛽𝛽" 𝛿𝛿% 𝛿𝛿& 𝛿𝛿'()*+, 𝛿𝛿-./ 𝜀𝜀)(1) 𝐸𝐸𝐹𝐹( 𝐹𝐹4 𝐹𝐹5 𝐹𝐹5" 𝐾𝐾 𝐿𝐿8 𝜇𝜇 𝑄𝑄 𝑅𝑅8 𝑇𝑇8 𝑇𝑇= 𝑊𝑊8 𝑦𝑦

Mounting angle Corrected mounting angle Dismounting angle Corrected dismounting angle Part A deflection Part B deflection Deflection correction factor Simulated joining deflection Calculated strain Secant Modulus Assembly force Disassembly force Deflection force Corrected deflection force Stress concentration factor Deflection beam length Material friction coefficient Feature location factor Base radius Feature thickness Wall thickness Deflection beam width Retention mechanism height

Most studies in snap-fit applications focus on a feature-level design methodology; this means them often consider the dimensioning of the deformable beam of the joint and the locking mechanisms for diverse snap-fit types and crosssectional areas [5]. Although traditional snap-fit design methodologies have been developed for polymer injection applications [6 – 8], recent studies have stated that the working principles of traditional snap-fit design prove to be independent of the manufacturing process and have proposed additive manufactured snap-fit design guidelines in which previous methodology needs to be adapted to the restrictions of the new manufacturing technology [9]. The available literature seems to suggest the need of further studies in developing design guidelines for integral snap-fit joint fabrication adapted to some of the current fabrication characteristics of AM technology. This present document further explores a previous study regarding design methodology for additive manufactured snapfit joints, which considered the interaction of conceptual and detail design, and a posterior design evaluation stages [4]. The objective of this article is to enhance the detail design stages, and introduce a finite element simulation procedure for design validation stages. 2. Snap-fit joints: Design process methodology for AM A systematic design procedure for additive-manufactured snap-fit systems can be developed accounting for general design guidelines. Common design methodologies are formed by four main stages: performance conditions or design specifications, conceptual design, detail design, and lastly a design validation stage.

Fig. 1. Proposed methodology for additive manufactured snap-fit joints design process.

Once design process has been validated, the final product can be manufactured. Previous studies for snap-fit systems design methodologies have separately considered conceptual and detail design frameworks [10], however there has been no formal integration between these design stages. Based on the previously proposed design methodology for snap-fit systems made by AM technology [4], new considerations regarding design validation stages and finite element evaluations are shown on Fig. 1. Posterior sections further details the procedure stages. The flowchart starts with the definition of design constraints and process limitations in

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the Design Specifications stage which ultimately defines the joint performance conditions and design parameters. The Conceptual Design stages starts with the calculation of printing material strain limits, followed by the partitioning mating design and the snap-fit systems type selection and location. In contrast with the previous methodology, the Detail Design stages now is formed by two procedures, i.e. the deflection mechanism dimensioning and the retention mechanism dimensioning. The first step of the Design Validation stages is a preliminary evaluation of the joint strain, followed by a finite element simulation of the joint in order to verify expected strains when applying a certain deflection force. Furthermore, the validation stages now considers a parallel evaluation of assembly and disassembly forces in order to assess joint ergonomics and retention forces, respectively. The final stage of the process corresponds to the 3D printing manufacturing of the pieces with the added designed and validated snap-fit joints. As stated in previous studies, the design process could be linear from an ideal standpoint but is iterative in most cases. Considering that the iterative condition could occur in the detail design or design validation stages, the initial design is subject to change [4]. 2.1. Performance conditions & parameters The present study is focused on previous defined design considerations or process limitations, which are AM technology, printing material, model geometry and snap-fit retention conditions. These restrictions are considered as input variables to the methodology and will not change during the design process. AM technology considerations refers to machinery specific constraints. Parameters such as printing layer thickness, limitations on small features printing, need of support structures, and building chamber dimensions affect directly to the model partitioning in the part mating design stage and posterior feature dimensioning. Regarding printing material, mechanical properties characterization is needed for the detail design stages such as in material deformation limits calculation and deflection and retention mechanisms dimensioning. Overall model geometry needs to be accounted as it can limit the partitioning approach and the location of the snap-fit features due to aesthetic or functional requirements. Model wall thickness and weight could also influence the final joining design. The last design specification considered in the proposed design process corresponds to the retention condition of the snap-fit system, which refers to operational restraints such as in the need of a permanent joint, or if the joint will be subject to frequent assembly and disassembly motions. These requirements can influence both conceptual and detail design stages. 2.2. Conceptual Design The conceptual design stages establishes a framework for the posterior joining features dimensioning, based on the

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corresponding design constraints and process limitations. The following subsections describes the three process considered in this preliminary design. 2.2.1. Material Strain Limits The initial step in the conceptual design stages corresponds to the calculation of the printing material strain limits. This deformation restriction is mainly influenced by the presence of a definite yield point in the printing material stress-strain curve and the number of cycles of frequent assemblies and dismounting motions for the mating parts. The need of material characterization data in this stage is crucial as it can affect the posterior joint deformation validation. 2.2.2. Part Mating Design A primary partitioning method can be selected based on the general model configuration, and the printing building chamber volume. As previous studies suggest, this model subdivision stage can be further optimized according to an efficient partitioning approach, which depends on support material utilization and printing times, and offers a quantitative validation. Both considerations of the efficient partitioning approach can be competing measures, as one orientation can use less support material but complete in a greater printing time. The anisotropy of the parts associated with the 3D-printer building directions could be a considerable restriction; therefore, the printing approach, as well as model wall thickness and model overhangs, can also affect the selected partitioning method and the posterior snap-fit features location. 2.2.3. Snap-fit System Type & Location The snap-fit system, as an assembly mechanism, consists on locking features, locating features and enhancement features [10]. The locking features, consisting of the deflection and retention mechanisms, are responsible for restricting the movement between mating parts in the assembly direction. The most common types of locking features are the cantilever, torsional and annular snap-fit joints. According to the snap-fit joint type, the location of the locking feature should be oriented in order to distribute the principal stresses along the most resistant building direction. 2.3. Detail Design Two simultaneous processes regarding the dimensioning of deflection mechanism and the retention mechanism of the locking features are mainly considered at the detail design stages. For the following subsections, general guidelines and calculations are shown based on the available literature regarding general snap-fit features design for cantilever snapfit joints [6 – 8]. The variables and geometry to be used in this subsections are shown on Fig. 2. 2.3.1. Deflection Mechanism Dimensioning The geometry of the deflection mechanism can be defined as a function of the snap-fit feature thickness 𝑇𝑇8 , which can be selected based on the positioning of the feature relatively to the part wall where it is mounted.

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Literature suggest that for joints extending from a wall, the feature thickness can be equal to the wall thickness; while for joints protruding from a wall, feature thickness can be 0.5 or 0.6 times the wall thickness. These limitations are mainly considered for injection molding applications [6]. Having defined the feature thickness 𝑇𝑇8 , the deflection mechanism beam length 𝐿𝐿8 needs to be greater than five times the feature thickness, but less than ten times the thickness value. Current cantilever snap-fit modelling treats the deflection mechanism as a beam with a fixed support and a free end. Thus, beam width 𝑊𝑊8 should be less than half the value of the beam length, as higher values could present calculations errors due to plate-like behavior. Furthermore, in order to mitigate stress concentration factors on the feature base, a base radius 𝑅𝑅8 is considered to be equal or greater than half the feature thickness. The geometric relationships for the deflection mechanism dimensioning detailed on this subsection are summarized on Table 1, as a function of feature thickness 𝑇𝑇8 . Table 1. Geometric relationships for deflection mechanism dimensioning. Variable

Description Thickness for feature extending from a wall

𝑇𝑇8

𝐿𝐿8

𝑊𝑊8 𝑅𝑅8

Thickness for feature protruding from a wall Beam length Beam width Base radius

Relationship 𝑇𝑇8 = 𝑇𝑇= 𝑇𝑇8 = 0.5𝑇𝑇= 5𝑇𝑇8 < 𝐿𝐿8 < 10𝑇𝑇8 𝑊𝑊8 < 0.5𝐿𝐿8 𝑅𝑅8 ≤ 0.5𝑇𝑇8

2.3.2. Retention Mechanism Dimensioning The retention mechanism is comprised of a raised surface with a front or mounting angle 𝛼𝛼 that engages the part during mating procedures, and back or dismounting angle 𝛽𝛽 that permits or inhibits the removal of the part. The following retention mechanism dimensioning considerations are detailed on Table 2. Table 2. Geometric considerations for retention mechanism dimensioning. Variable

Description Retention mechanism

𝑦𝑦

𝛼𝛼 𝛽𝛽

height, for 𝐿𝐿8 /𝑇𝑇8 ≅ 5 Retention mechanism

height, for 𝐿𝐿8 /𝑇𝑇8 ≅ 10

Mounting angle

Dismounting angle, non-releasing joint Dismounting angle, releasing joint

Relationship 𝑦𝑦 < 𝑇𝑇8 𝑦𝑦 = 𝑇𝑇8 𝛼𝛼 = 25°~30° 𝛽𝛽 > 80° 𝛽𝛽 = 𝑓𝑓(𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟)

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Fig. 2. Proposed methodology for additive manufactured snap-fit joints design process.

The height 𝑦𝑦 of the retention mechanism can be selected based on the deflection mechanism length and thickness ratio. For a 𝐿𝐿8 /𝑇𝑇8 ratio of 5, 𝑦𝑦 values should be less than the feature thickness; while for ratios of near 10, this height is suggested to be equal to feature thickness. This height corresponds to the maximum deflection of the snap-fit joint during assembly or disassembly motions. Common mounting angle values are in the range of 25 to 30 degrees, in order to ease the assembly procedures. Angles greater than 45 degrees make the joining difficult to assembly. The dismounting angle selection depends on the feature retention condition. In general, for a non-releasing joint, common angle values are above 80 degrees. For a releasing joint, the dismounting angle will depend on the desired feature retention force. 2.4. Design Validation Stages The proposed design validation stages are of great importance as it compromises the evaluation of the snap-fit joint system performance conditions, prior to the model additive manufacturing production. 2.4.1. Strain Preliminary Evaluation Having defined the deflection and retention mechanism dimensions, the calculated joint strain can be found as a function of feature thickness and length, retention mechanism height, and a feature location factor 𝑄𝑄, as shown on Eq. 1 based on beam theory calculations. 𝜀𝜀)(1) = 1.5

𝑇𝑇8 𝑦𝑦 𝐿𝐿X8 𝑄𝑄

(1)

According to the available literature, the location factor 𝑄𝑄 can be found as a function of the 𝐿𝐿8 /𝑇𝑇8 ratio and the location of the snap-fit relative to the part. Tabular and graphical data is available for cantilever snap-fit joints perpendicular to a solid wall, perpendicular in the interior area of a wall, perpendicular to a wall and to an edge, perpendicular to a wall and parallel to an edge, and for a joint in-plane with a wall at an edge [6]. The calculated strain value is compared to the maximum strain, which is defined as the division of the material strain limits by a stress concentration factor 𝐾𝐾 = 𝑓𝑓(𝑅𝑅8 /𝑇𝑇8 ).

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included as a reference to denote that the primary deflection effects should occur on Part A (i.e. the deflection features). The joint operational point 𝑃𝑃 shows the corrected deflection force 𝐹𝐹5" and the joining deflection 𝛿𝛿-./ , which can be calculated from the simulation results using Eq. 3 and Eq. 4, respectively. 𝐹𝐹5" = 𝐹𝐹5 Fig. 3. Graphical correction for part deflection using finite element simulation results. Part A: having deflection features, and Part B: with retention features.

If the strain on the features is greater than the permissible strain limits, corrections should be made on the conceptual design stages or in the snap-fit feature geometry values, depending on the amount of the difference. For small deviations, a simple feature dimension correction can be sufficient, but for greater values a more in-depth analysis of the feature location and/or part mating orientation is needed. In the flowchart, the unacceptable condition is connected to the part mating design as it corresponds to the worst-case scenario. 2.4.2. Finite Element Simulation In order to verify the deformation scenarios for the part joints, a stage of finite element simulation is considered to include the part-specific rigidity effects during the joint deflection. For the simulations, the needed deflection force 𝐹𝐹5 is calculated as a function of the previous defined geometry, the calculated strain 𝜀𝜀)(1) , and the material secant Modulus 𝐸𝐸Z , as shown on Eq. 2. 𝐹𝐹5 =

𝑊𝑊8 𝑇𝑇8X 𝐸𝐸Z 𝜀𝜀)(1) 6𝐿𝐿8

(2)

As stated before, snap-fit modeling is based on beam theory calculations considering a rigid support and the force acting in the free end. However, the rigidity of the joint base will depend on the parts configurations. The finite element simulation stage ultimately shows a more accurate feature deformation when applying a certain deflection force. With the simulation results, a feature deflection correction can be graphically determined, thus accounting for the lack of rigidity on the features support and refining the posterior assembly and disassembly forces. In order to estimate the deflection during joining procedures, both mating parts are considered to have a linear behavior and the individual deflections results are plotted, as show on Fig. 3. Part A is defined as the part with the deflection features, and Part B having the retention features. As shown in the graph, for a calculated 𝐹𝐹5 , the model considers a deflection 𝛿𝛿% greater than the retention feature height 𝑦𝑦 for Part A, to account for greater joint base flexibility effects. For the Part B curve, the intersection with the X axis is located at 𝑦𝑦, and the part deflection 𝛿𝛿& is subtracted, so that the operational point can be graphically determined. A dotted line, corresponding to a rigid behavior for Part B, has also been

𝛿𝛿-./ =

𝑦𝑦 𝛿𝛿% + 𝛿𝛿&

𝑦𝑦𝛿𝛿% 𝛿𝛿% + 𝛿𝛿&

(3) (4)

In addition, the simulation results are used to define a deformation corrector factor 𝛿𝛿'()*+, , which is employed to adjust the calculated strain values, and find the effective mounting and dismounting angles. This deflection correction factor is equal to the ratio of the joining deflection and the retention feature height 𝛿𝛿-./ /𝑦𝑦. 2.4.3. Assembly Forces calculation and Ergonomics validation Joint system assembly forces are a function of the corrected deflection force 𝐹𝐹5" , material friction coefficient and a corrected mounting angle 𝛼𝛼 " . Equations 5 and 6 shows the corresponding formulae for mounting angle correction and assembly forces calculation, respectively. 𝑦𝑦𝛿𝛿'()*+, 𝛼𝛼 " = 𝛼𝛼 + tanab c d 𝐿𝐿8 𝐹𝐹𝑎𝑎 =

𝐹𝐹′𝑃𝑃

𝜇𝜇 + tan 𝛼𝛼′ 1 − 𝜇𝜇 tan 𝛼𝛼′

(5) (6)

The ergonomics validation is made with the results from the assembly forces calculation multiplied by the number of snapfit features. This validation consists on the comparison of the force needed to join the parts and acceptable forces for manual assembly. Lee and Gu [11] reported a mean value of roughly 81 N for acceptable insertion forces in manual assembly of small connectors, and a mean maximum force of 141 N. It is also noted that acceptable and maximum coupling forces depend on the posture and size of the mating parts. If the assembly forces surpass the acceptable insertion forces, the proposed methodology suggest the revision of deflection mechanism dimensions. A possible correction approach is to vary the feature width 𝑊𝑊8 , as it does not affect the feature deflection results, but lowers the required deflection forces. 2.4.4. Disassembly Forces calculation and Retention evaluation Having similar considerations as in the assembly forces calculations, the formulae for dismounting angle correction and disassembly forces calculation are shown on Eq. 7 and 8, respectively.

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𝑦𝑦𝛿𝛿'()*+, 𝛽𝛽" = 𝛽𝛽 − tanab c d 𝐿𝐿8 𝐹𝐹4 = 𝐹𝐹5"

𝜇𝜇 + tan 𝛽𝛽" 1 − 𝜇𝜇 tan 𝛽𝛽"

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(7) (8)

The final design evaluation corresponds to the comparison of the calculated disassembly forces to the expected joint feature resistance. If the disassembly forces are not greater enough to ensure a reliable joint, the retention angle should be increased thus increasing the retention capability. This correction does not interfere with the general feature dimensioning. An additional consideration in this phase is the resistance of the sloped area, as it can fail by shear forces during part releasing.

Fig. 4. Part mating design: model division.

2.5. Additive Manufacturing Once the detail design has been validated, the final stage of the proposed methodology is the 3D-printing of the model parts and physical assembly and testing procedures. 3. Case Study: Finite element revision for a 1-gallon plastic container division The present study focuses on the analysis of a 1-gallon plastic container 6-part partitioning for printing, and posterior joining by snap-fit features designed following the proposed methodology. The design specifications for the manufacturing of the model are based on MultiJet Printing technology, using ABS (Acrylonitrile Butadiene Styrene) plastic for model part construction, with the utilization of permanent joints that does not affect the overall outward appearance. Based on printing material properties, a material strain limit of 2.49% was considered as a limiting factor for the features dimensioning. According to the model division shown on Fig. 4, the part mating sequence for the 6-part division starts with the union of the lateral Parts 2A and 2B. Both parts then lock to the Part 4, followed by the Part 1. The remaining parts (3A and 3B) are first joined together, and the locked to the main body [4]. The considered snap-fit type corresponds to a special case of a hook and loop snap-fit extended from a wall. Instead of extending the features from the wall, they were designed to extend parallel to the wall, thus preserving the outside model appearance and locating all mating features inside the body [4]. The hook and loop geometry was selected for its behavior as a cantilever snap-fit, and due to the ease of printing the deflection features body perpendicular to printer building direction. Following the aforementioned geometric relationships and considerations (Table 1 and 2), the deflection mechanism dimensioning considers a feature thickness of 2mm (equal to wall thickness), length of 13mm, width of 6mm, and a base radius of 1mm. Accordingly, the retention mechanism dimensioning stages results in a retention height of 2mm, mounting angle of 25°, and a dismounting angle of 50°.

Fig. 5. Part 4 total deformation finite element simulation results.

Fig. 6. Part 2A total deformation finite element simulation results.

Considering a 𝑄𝑄 location factor of 1.8 [6] and the dimensions of the deflection mechanism, the calculated strain is equal to 1.97%, using Eq. 1. This calculated value is greater than the predefined material limits. However, this difference was considered as a small deviation, and further evaluated via finite element simulations. Due to the lack of material characterization data, the Secant Modulus of 783 MPa used for the deflection force calculation was found by dividing the available values for ultimate stress and elongation at break. By using Eq. 2, a deflection force of 4.75N is calculated, which theoretically corresponds to a deflection of 2mm (retention height). Finite element simulations were conducted using this deflection force for Part 2A (part with deflection features) and Part 4 (part with retention features), in order to graphically verify the joining deflection. This pair of elements were selected due to an expected rigid behavior for Part 4, having the primary deflection effects on Part 2A. Figures 5 and 6 show the results of total deformation for Part 4 and Part 2A respectively.

Jorge Luis Amaya et al. / Procedia CIRP 84 (2019) 680–687 Author name / Procedia CIRP 00 (2019) 000–000

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As shown on Fig. 5, the maximum value for Part 4 total deformation of 4.34e-3mm is considered as minimal, thus behaving as a rigid part (𝛿𝛿& = 0). For Part 2A (Fig. 6), simulation results for total deformation varies depending the location of the deflection mechanism with respect to the part. For the applied force of 4.75N, the total deflection for feature (a) is 3.20mm, 5.62mm for feature (b), and 4.69mm for feature (c). The deflection profiles for the features were as predicted, having that the feature (b) was expected to be the less rigid due to being located in the center of Part 2A. Accordingly, deflection effects on feature (a) were estimated to be more rigid due to the closeness to the part back plate radius. Even though the resultant total deformations greatly exceeds the expected 2mm deflection, simulation results show that feature-specific deflection are of 1.33mm, 1.83mm, and, 1.69mm for features (a), (b) and (c), respectively. The maximum strain at the base of the joints of 1.22% is below the previously calculated value of 1.66%, therefore validating the feature strain resistance. These first simulated results do not correspond to real deformation responses, as the parts will only deflect the 2mm corresponding to the retention feature height 𝑦𝑦. In order to estimate the deflection forces for each feature, Eq. 3 was used to determine a corrected deflection force 𝐹𝐹5" . However, this approximation considers a linear response, and does not account for feature deflection interactions. Several finite element simulations were carried on, in order to account for feature deflection interactions and their nonlinear behavior. The corrected deflection forces, as well as the base strain simulated results, are reported on Table 3. Last simulation iteration results are shown on Fig. 7. Table 3. Deflection forces finite element simulation results. First analysis

Feature (a)

𝛿𝛿% [mm]

𝐹𝐹5" [N]

𝛿𝛿% [mm]

4.75

4.69

2.28

2.02

4.75

(b)

3.20

4.75

(c)

Last iteration

𝐹𝐹5 [N]

5.62

4.18

2.05

1.00

2.11

For the last iteration results, the corresponding featurespecific deflection values are of 1.06mm, 0.55mm, and, 0.77mm for features (a), (b) and (c), respectively. The maximum strain at the base of the joints of 1.01%. These last results further reinforces the feature resistance validation. As stated before, Part 4 is considered as rigid, thus 𝛿𝛿-./ exclusively accounts for the effects on Part 2A deflections, and the deflection correction factor 𝛿𝛿'()*+, is approximately 1. With these considerations, the assembly and disassembly forces are calculated by using Eq. 5 through 8. Results are shown on Table 4. Table 4. Assembly and disassembly forces results. Deflection force [N] 𝐹𝐹5 𝐹𝐹5"

4.75 4.18 (a)

𝐹𝐹% [N] 7.07 6.22

𝐹𝐹h [N] 29.37 25.85

1.00 (b)

1.49

6.19

2.28 (c)

3.40

14.12

7

Fig. 7. Part 2A total deformation finite element simulation results for corrected feature deflection forces.

Since assembly and disassembly forces are directly proportional to the deflection force, results clearly indicate that the initially calculated 𝐹𝐹5 will act as a maximum control value. For assembly forces, final values when considering the corrected deflection forces 𝐹𝐹5" for each feature will tend to be less than the values found before the finite element simulation stages, thus easing the validation of assembly ergonomics. Nevertheless, this feature force diminishing effect has a bigger impact on the disassembly forces, which could potentially fail the retention evaluation stages. 4. Conclusions The employment of the proposed methodology for snap-fit systems design permitted to further analyze the detail design stages of a previously 3D-printed ensemble of a model for a 1-gallon plastic container that could not be printed in a single job due to 3D-printing building chamber limitations. Overall results could indicate that the currently available snap-fit system design formulae can predict the feature strain behavior to some extent, and, deflection failure regarding material overstraining can be avoided by following the design considerations. However, the deflection forces greatly depend on part geometry and feature location, and the effects of the initially calculated forces does not correlate to the simulated responses. In addition, feature location affects the necessary deflection forces. Table 3 results shows the variance in feature deflection forces, which are directly proportional to assembly forces, and, more importantly, to the feature-specific retention forces. Future work aims to consider a more in-depth analysis of snap-fit features location, and its effects on deflection mechanism dimensioning. Furthermore, different part scenarios finite element analysis are needed in order to account for case studies in which the part with the retention features does not have a rigid behavior. Acknowledgements The authors would like to thank the Advanced Machining and Prototype Laboratory CAMPRO, from ESPOL Polytechnic University, for its contribution to this work.



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Jorge Luis Amaya et al. / Procedia CIRP 84 (2019) 680–687 Amaya et al./ Procedia CIRP 00 (2019) 000–000

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