Introduction to FEA Autodesk Simulation Presenter Bob Aldaz

Introduction to FEA (Autodesk Simulation) Presenter: Bob Aldaz

Agenda • How to apply FEA to Horns • Autodesk Simulation functionality • Work through actual problems 10/26/2020 2

What is FEA? • A solid model is broken into thousands of small simple elements. • Complex shapes can be evaluated by applying simple engineering mathematics to each of these smaller elements. 10/26/2020 3

How? Node (connection) Element (simple shape with stiffness and mass) Each small element is solved using simple equations 10/26/2020 4

What types of FEA are used at Dukane? Modal & Frequency response – horn and vibration Thermal – Hot plate Static – Support design 10/26/2020 5

How can it be applied to Horns? Typically two separate analysis will be run (Modal & Frequency Response) • Modal - Gives every possible resonant frequency. Use Modal analysis to determine which frequencies are critical to operation. • Frequency Response - Gives specific response at a given frequency. Includes stress results. 10/26/2020 6

Criteria • Stress limit • 2024 Aluminum 11, 000 psi (76 MPa) • 6 Al 4 V Ti 32, 000 psi (221 MPa) • Secondary Frequencies – Ideally not within 750 Hz for most horns • Amplitude Uniformity Across Face – Depends upon application but worse than +/- 20% from nominal tends to run poorly.

Options • How fine of a mesh? Very fine meshes give more accurate frequency and stress results but can greatly increase processing time. • Whole stack or just horn? Including booster and driver ensures all secondary frequencies are detected.

Typical setup Back slug – Stainless 302 CR Bolt – ASTM –A 572 Ceramics – EC 67 Front Slug – Al 2024 T 351 Booster – Al 2024 T 351 Horn – Al 2024 T 351 or Ti Al 6 4 V Grade 5 STA 10/26/2020 Omit studs 9

What can be learned from FEA? • Approximate tuned length. • Uniformity of amplitude. • Stress and maximum permissible booster gain. • The existence of secondary undesired resonant frequencies near running frequency.

What is not learned from FEA? • Will the horn run? A judgment call must be made based upon the amplitude uniformity, stress and presence of undesired secondary frequencies.

Risk FEA will can give incorrect results without warning for the following reasons. Operator must also rely upon expertise and experience to validate results. • Incorrectly entered loads, dimensions, material properties. • Effect of Nearby secondary frequencies (i. e. Cutting blades) • Effect of Distant secondary frequencies (i. e. Alcon example)

Application Example 1 Original 10/26/2020 Amplitude variation reduced After optimization 13

Application Example 2 Non uniform mode Original (click image to play) 10/26/2020 After optimization (click image to play) 14

Application Example 3 Stress reduction Original 10/26/2020 After optimization 15

Key areas of concern • Secondary frequency problems. • Stress concerns: • Surface finish critical? • Sharp transitions • Slot issues • Horn balancing 10/26/2020 16

Secondary frequencies Primary (click image to play) Secondary (click image to play) Generator can jump to secondary frequency when too close to primary frequency. This must be solved by a design modification. 10/26/2020 17

Stress Concerns Surface flaws can become critical issues when located in areas of high stress. 10/26/2020 18

Rougher surfaces create stress concentrations greater than expected in the original design. Therefore, if high stress is expected surface roughness must be minimized. 10/26/2020 19

Sharp steps create stress concentrations. Notice how when the radius is very small the stress multiplier becomes very large. 10/26/2020 20

Example – Low gain blade Maximum stress occurs at transition of nodal radius. This will be greatly increased if transition is rough or uneven. 10/26/2020 21

Example –Typical Food Blade Maximum stress occurs around the base of slots. If slot is not well rounded off here stress can further increase leading to crack formation. 10/26/2020 22

Example –Block with Apple Core These transitions create higher stress regions. Unfortunately such areas are also commonly rough, further increasing stress. 10/26/2020 23

Any feature that intersects the nodal area will increase the stress. Such features must be rounded off and smooth. 10/26/2020 24

In this case the tops of the slots are located near the nodal radius. 10/26/2020 25

Bell horn have critical areas both at nodal radius and inner bore. 10/26/2020 26

Full wave horns have critical areas in each of the two nodal regions. 10/26/2020 27

While typically the face isn’t a critical stress area, however when the face detail becomes deep enough to get closer to the nodal region, then high stress regions can be created. 10/26/2020 28

Horn Balancing • Fluttering • Singing 10/26/2020 29

Fluttering Created when a horn vibrates at a much lower frequency in addition to the desired frequency. This must be solved by a design modification. (click image to play) 10/26/2020 30

Singing Small manufacturing variations sometimes create a ripple along the edge of a blade. One solution is to dull the blade but this can reduce performance. 10/26/2020 31