predicting and validating assembly forces of cylindrical
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Predicting and Validating Assembly Forces of Cylindrical Snap-Fit Joints by Comparing Closed-Form Solutions to Computational Methods
2016 ASME V&V Symposium Track 9: Validation Methods for Solid Mechanics and Structures
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ASME V&V 10 [1]
• Motivation • Configuration used in this example • Material properties • Closed-form solution • Computational Model • Verification • Comparison of closed-form & simulation
results • Variability of material properties • Geometry with draft • Experimental data • Uncertainty quantification • Validation • Conclusion
Outline
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• Cylindrical snap-fit joints are commonly used for connections and fastening • Typical questions
– What is the maximum assembly force for a given snap-fit design? – How do closed-form solutions compare to simulation results? – How much do material property variations influence the results? – Do printed parts provide useful feedback? – How long will it take to get meaningful results?
• Concerns – Closed-form equations are for assemblies with:
• simple geometry • uniform wall thickness • one rigid component and one elastic component
– FEA for complex geometry is time consuming – Rapid prototyping with PolyJet RGD720 has:
• different E than production thermoplastic • rough surface finish
Motivation
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• V&V 10 defines a framework and common terminology to address the questions and concerns [1], [2]
V&V Framework
V&V questions Application-specific responses
Description of the top-level reality of interest
Cylindrical snap-fit joint between 2 thermoplastic parts
Intended use of the top-level model
Determine maximum assembly force for given dimensions of snap-fit joint geometry
System Response Quantity (SRQ)
Winsert = applied axial load during assembly
Model accuracy requirement Computed results predict Winsert to within 10% of experimental measurements
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• Customer asked for redesign of a slip-fit, epoxy-bonded connection in a medical device to a less costly, permanent, cylindrical snap-fit joint
Configuration
Dimensions in mm
Proposed snap-fit
O.D. of receptacle is fixed dimension, Ø18.5 mm
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• Evonik CYRO XT® Polymer 250 Clear [3], [4], [5]
– Acrylic-based multipolymer compound, impact-modified Polymethyl Methacrylate Acrylic (PMMA)
– for molding and extrusion – for medical devices, pharmaceutical packaging, and rigid medical device
packaging
• Secant Modulus at permissible short-term strain
• Poisson’s Ratio
• Coefficient of Friction
Material Properties
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Closed-Form Solution [6]
• Strain-controlled • Deflection equals the undercut • Results give
– one value for mating force
FEA • Nonlinear static • Allows complex or varying geometry • Results show
– stress distribution – mating force vs. displacement
Comparison of Methods
Assumptions • Single joining operation • Nominal geometry dimensions • Properties at room temperature
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• Define dimensions – Use values from
proposed geometry • Define material • Create Mathcad calculation • Solve
Closed-Form Solution
[6]
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Free Body Diagram of mating force based upon • Classical beam theory for
cantilever snap-fit [7]
• Theory of a beam of infinite length resting on a resilient foundation [6]
Closed-Form Solution
Evaluate transverse force ‘P’ at transverse deflection ‘y’ [6]
fremote = factor based on joint’s distance from end X = geometric factor
Plot ‘P’ vs. insertion distance for outer and inner mating parts Evaluate insertion force [6]
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• Prepare the model – Create simplified assembly – Simplify the individual parts – Check for interference and coincident
interference • Define material • Set up nonlinear simulation • Run
Nonlinear FEA of Cylindrical Snap-Fit Joint
Dimensions in mm
Proposed Simplified for Analysis
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Assembly Force
Win
sert
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Mesh quality check • Aspect ratio < 2.6 in area
of interest • Global aspect ratio < 5
Verification of Simulation Results
Solution of Winsert converges • Goal is to have simulation error less
than 2% of the 10% required model accuracy
• Simulation convergence error < 0.2% • Finest mesh identical mesh control
used for subsequent simulations
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• Closed-Form Solution – 19.3 lbf
• Nonlinear FEA – 24.5 lbf
Comparison of Closed-Form & Simulation Results
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Uncertainty Quantification of Stress-Strain Data
[3]
Evonik CYRO XT® Polymer 250 Clear [3], [4], [5]
test data
data sheet
test data
Secant Modulus
at permissible short-term strain
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Sensitivity Analysis of Secant Modulus
Winsert is directly proportional to Esecant
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Sensitivity Analysis of Poisson’s Ratio
Poisson’s ratio has a small effect on Winsert
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Sensitivity Analysis of Friction Coefficient
Winsert is proportional to coefficient of friction, μ
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• Geometric features not considered in closed-form solution – Length of snap boss – Location of snap boss – Closed ends – Non-uniform walls – Draft
Manufacturing Design
Dimensions in mm No Draft Draft
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Parts with Draft
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• 3D Printed Parts with PolyJet RGD720 Full Cure [8], [9]
• Measured parts w/ calipers • Modified CAD geometry to match
Printed Parts
Dimensions in mm
15° 30°
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• Mark-10 Force Tester with 50 lbf load cell
Test Set-Up
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Experimental Results
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Validation
• Estimate the Probability Densities from Uncertainty Estimates • Probability density at x (SRQ) of a normal distribution with
– mean μ – standard deviation σ
System Response Quantity
Prob
abili
ty D
ensit
y Fu
nctio
n
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• Cumulative distributions at x (SRQ) of the normal probability distributions
• Use the Area Metric to determine accuracy
• The simulation is validated because “the relative difference between the simulation outcomes and the validation experiments” is within 10% [2]
Validation – Assessing Accuracy
System Response Quantity Cum
ulat
ive
Dist
ribut
ion
Func
tion
ASME V&V 10.1 [2]
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• Uncertainty quantification of secant modulus and friction in – Simulation results – Experimental data
• Validation – Quantitative comparison between simulation and experimental outcomes – 10% target accuracy was met
• Efficient method for predicting the assembly force of cylindrical snap-fits – Get test data for material – Get coefficient of friction test data for representative configuration – Limit simplifications to geometry – Run 2D nonlinear FEA
• Notes – Include large fillet radii on lead-ins to reduce initial force
Conclusion
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[1] Guide for Verification and Validation in Computational Solid Mechanics, ASME V&V10, 2006.
[2] An Illustration of the Concepts of Verification and Validation in Computational Solid Mechanics, ASME V&V 10.1, 2012.
[3] Evonik XT® Polymer 250 Compound [Online]. Available: http://www.cyrolite.com/product/cyrolite-compounds/us/products/xt-polymer/pages/default.aspx
[4] Michelle Irvine. (2015, Oct. 22). Evonik XT® Polymer Compounds 250-000: Tensile Stress/Strain Curve, Medical Performance Materials/Acrylic Polymers [email].
[5] Justin Grumski, Technical Service Engineer (2015, Nov. 9). Evonik XT® Polymer Compounds 250-000: Stress Strain Curve, Medical Performance Materials/Acrylic Polymers [email].
[6] Snap-Fit Joints for Plastics – A Design Guide, Bayer MaterialScience LLC, Pittsburgh, PA, 2000 pp. 6-7 and pp. 20-26.
[7] Snap-Fit Design Manual – Technical Expertise, BASF Corporation, 2007.
[8] Statasys (2015). PolyJet Material Properties [Online]. Available: http://www.stratasys.com/materials/material-safety-data-sheets/polyjet/transparent-materials and http://usglobalimages.stratasys.com/Main/Files/Material_Spec_Sheets/MSS_PJ_PJMaterialsDataSheet.pdf?v=635785205440671440
[9] Gaurav Goenka. "Modeling and investigation of elastomeric properties in materials for additive manufacturing of mechanistic parts.“ Thesis submitted for Master of Engineering, Department of Mechanical Engineering, National University of Singapore, 2011.
[10] Design calculations for snap fit joints in plastic parts, Ticona, A Business of Celanese, Florence, KY, 2009.
[11] Paul A. Tres, Designing Plastic Parts for Assembly, Hanser Publishers, 2014.
[12] Gunter Erhard, Designing with Plastics, Hanser Publishers, 2005.
[13] Designing with Engineering Plastics, Tech. Rep. PLA-748-REV3-0806, GE Plastics, Exton, PA, 2006.
References
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