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

Syncroness Proprietary and Confidential

2 Listen. Respond. Deliver.

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



• 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



• 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



• 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



• 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


Listen. Respond. Deliver. 7

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



• Define dimensions – Use values from

proposed geometry • Define material • Create Mathcad calculation • Solve

Closed-Form Solution

[6]



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]



• 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



Assembly Force

Win

sert



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



• Closed-Form Solution – 19.3 lbf

• Nonlinear FEA – 24.5 lbf

Comparison of Closed-Form & Simulation Results



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



Sensitivity Analysis of Secant Modulus

Winsert is directly proportional to Esecant



Sensitivity Analysis of Poisson’s Ratio

Poisson’s ratio has a small effect on Winsert



Sensitivity Analysis of Friction Coefficient

Winsert is proportional to coefficient of friction, μ



• 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



Parts with Draft



• 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°



• Mark-10 Force Tester with 50 lbf load cell

Test Set-Up



Experimental Results



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



• 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]



• 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



[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

http://www.cyrolite.com/product/cyrolite-compounds/us/products/xt-polymer/pages/default.aspx

http://www.cyrolite.com/product/cyrolite-compounds/us/products/xt-polymer/pages/default.aspx

http://www.stratasys.com/materials/material-safety-data-sheets/polyjet/transparent-materials

http://www.stratasys.com/materials/material-safety-data-sheets/polyjet/transparent-materials

http://usglobalimages.stratasys.com/Main/Files/Material_Spec_Sheets/MSS_PJ_PJMaterialsDataSheet.pdf?v=635785205440671440

http://usglobalimages.stratasys.com/Main/Files/Material_Spec_Sheets/MSS_PJ_PJMaterialsDataSheet.pdf?v=635785205440671440

predicting and validating assembly forces of cylindrical

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