The Design of Polyurethane Parts: Using Closed Solutions and Finite Element Analysis to Obtain Optimal Results

Transcription

1 The Design of Polyurethane Parts: Using Closed Solutions and Finite Element Analysis to Obtain Optimal Results By: Richard Palinkas George Nybakken Ian Laskowitz Chemtura Corporation

2 Overview How does one predict performance in service? What is a closed solution (mathematical calculation)? What is the difference between linear and nonlinear materials (metals vs. urethanes)? What is Finite Element Analysis (FEA)? What are the steps in setting up an FEA? How is FEA useful? Real World Examples Concerns with FEA 2

3 How to predict performance in service? Field Testing Not practical in all cases Expensive Dangerous Difficult Liabilities FEA Theoretically predicts how a part will work Time Consuming Initial expense Closed Solution/Mathematical Equations Not as accurate as FEA but very useful Potential Issues Complex Geometries High Strain Go by the datasheet Would not recommend. Typical datasheets are very useful to compare materials but provide little useful data for design. 3

4 What is a closed solution? Mathematical Equations Industry proven formulas used to predict behavior of an entire design. Can provide relatively quick results Works very well for simple geometries and low strains Concerns: Simplifies complex geometries Does not account for nonlinear stress-strain curves. Boundary Conditions Simplest Form: Compression Equation Ec= Compression Modulus = Stress Strain (psi) Stress = Force (psi) Area Strain = Deflection Thickness 4

5 What is the difference between linear and nonlinear materials (metals vs. urethanes)? Young s Modulus (Linear) = Slope of a Stress Strain curve (Stress/Strain) 5

6 Closed Solution/Mathematical Equations Example: 6

7 What is FEA? Finite Element Analysis Breaks complex geometries into a more simplistic shapes. Each simple shape is now easier to solve Each node has 6 Degrees of freedom (DOF) Move in x, y, and z direction Rotate about the x, y, and z axis Solves each of the simplistic geometries for all 6 DOF s Combines the results from each simple geometry into the complex final shape. 7

8 What are the steps in setting up an FEA? Draw or import your model Create model from a print Import model directly from a customer Preprocess Mesh model Break model into many small parts Add boundary conditions (fixed displacements, symmetry, rotation points, ect) Add loads (displacements, pressures, force, ect) Add material properties Post Process Review Results (stress, strain, displacements, ect) 8

9 What are the steps in setting up an FEA? Preprocess (Mesh, Add Constraints/Loads, Material Properties) Mesh Constraints/Displacements 9

10 How is FEA useful? Simple vs. Complex Geometries Closed solutions often times require a simplified geometry. Potential to lose/overlook key characteristics of a part Equations can be very complex. Many times equations can not be used even when simplifying geometry Nonlinear Material Models More accurate prediction how a material will act Linear vs. Nonlinear Steel vs. Urethane Mooney Rivlin Material Model Uniaxial Tension Datasheet Data not always useful Predicts Localized Stress and Strain Very helpful in predicting failures Must understand materials and failure criteria 10

11 Uniaxial Stress vs. Strain: 5 th Cycle 90A/TDI/ETHER: Stress-Strain Curve Mooney-Rivlin Constants D E-5 C C Stress (psi) Strain (in/in) 11

12 Example 1: Compression Button Load vs. Deflection - FEA vs. Real World vs. Closed Solution Compression Button: Load vs. Deflection Load (Pounds Force) A TDI/ETHER Actual 90A TDI/ETHER Nonlinear Material Model FEA 90A TDI/ETHER Linear Closed Solution Deflection (inches) 12

13 FEA Example 2: Shear Spring Mesh Constraints/Displacements 13

14 FEA Example 2: Shear Spring - Issue: FEA Predicted 75% Strain in fatigue application - FEA predicted Local stress and strains - Understanding of the materials and performance FEA Compressed Real World Not Compressed Resolution: FEA used to redesign to lower strains but match spring rate 14

15 FEA Example 3: Off the Road Tire Deflected on a Rock Approximately 7,000 lb of Urethane Trial and error is not an option Carries 130,000 lbs over a rock 15

16 Concerns with FEA: Quality of input vs. Quality of output Understanding results and failure criteria Maximum Principal Strain and material limits Fatigue (compression and tension) Complex Geometries are difficult to setup and run time can be long. 16

17 Conclusions: FEA Considerations Predicts localized stresses and strains in complex geometries Closed solutions overlook localized stress and strain Need the understanding of materials and performance Failure to understand material properties such as maximum principal strain s relationship to fatigue failure Allows usage of Nonlinear effects Minimizes Field testing expensive, dangerous, not easy, ect Can be time consuming 17

18 Any Questions? Thank You! 18