MET 425 - FEA Applications II

Prof. Dave Johnson, psuprofdj@psu.edu, Penn State Erie, The Behrend College

Homework Assignment: Modal Analysis

Concepts: Modal Analysis by FEA symmetry in dynamic analysis constraints in dynamic analysis animation of mode shapes free vibration pre-stressed modal Problem: A cheap fan for electronics cooling is made from a sheet metal stamping.  It is expected to spin at 0 - 3600 RPM during operation.
The repeatable-sector geometry is shown at the right.  All dimensions are given in mm. The part is a 32 gage galvanized steel. Thickness = 0.34036 mm Elastic Modulus = 207,000 MPa density = 7800 kg/m3 Poisson's ratio = 0.3 A 10 mm RADIUS washer holds the center of the fan to the motor shaft. Basic geometry (in mm dimensions) is given at this link for the mid-surface of the sheet metal part.

To do:

Use FEA modal analysis to determine the natural frequencies of this part in the frequency range of interest.
(The link above gives you ANSYS commands to generate the geometry and output an IGES file which can be loaded into Workbench.)

• Determine 2D or 3D modeling ?
• Determine symmetry ?
• Linear or nonlinear ? WHY ?
• Determine proper constraint at washer ?
• Use SI units, but meters or millimeters, and what units for material properties (list the material properties you used)?

Turn in:

• Answers with discussion to the list of questions above
• Calculations to estimate one natural frequency of a simple disc (try "umbrella mode"), compared to the FEA model results.
  Required: you must use MathCAD for this calc. (with units on every term)
  See hand calc reference.
• Estimate of the mass of the disk, compared to the FEA model Mass Summary
• A plot showing the mesh - document the no. of nodes and elements and the element type used.
• An environment plot that shows ALL applied boundary conditions.
• A contour plot of the normal deflection to show each mode shape in the frequency range of concern (0-3600 RPM).  Also, show your instructor an animation of one of the modes.
• A contour plot of the normal deflection to show the "umbrella" mode shape
• ANSYS tabular output listing of all modes you discovered
• Discuss: A customer inquired about running this fan up to 5,000 RPM.  Could he have other vibration problems in the 0 - 5000 RPM speed range ?
• LL Question:  What is "modal cyclic symmetry" ?  Could we use Modal Cyclic Symmetry for this analysis ?  If appropriate for this problem, would it be easier or harder to use than the full 3D model method ?

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• 2nd FEA Simulation: If this model was evaluated with NO constraints (FREE Vibration), are the real modes any different (In free vibration, the first six modes are zero) ?  List the first six "real" natural frequencies for free vibration.  Why are they different ?

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• 3rd FEA Simulation:If the fan with proper constraints was spinning at 3600 RPM, what are the natural frequencies ? List the first six "pre-stressed modal" natural frequencies.  Why are they different ?
• Finally, WHAT answer is appropriate for the customers (3600 and 5000 RPM) ?