FEA Simulation of the 22LR Vibration Test Hardware
www.VarmintAl.com

The FEA model includes the following:
1. Base Plate of aluminum with the aluminum block tied to the plate and the locations of the plate to bench bolts fixed in xyz.
2. Aluminum block with the barrel clamped with a tied surface to surface to simulate the attachment of the barrel to the block.
3. The 22LR stainless steel barrel is 24.68" long with a diameter of 1.063" inches. The barrel extends 18 inches past the block.
4. The steel action is simulated with a solid cylinder merged to the barrel.
5. The Polaroid card is simulated by 40 mil thick polycarbonate plastic shell elements and is 2.5 by 2.5 inches set back 0.5 inches from the muzzle.

PRESSURE CURVES.... The chamber pressure curves were generated from strain gauge data. The data was scaled for the pressure amplitude to generate the given muzzle velocities for a 40 gr 0.224 caliber bullet in a 24.75 inch barrel. The assumption for these calculations are that higher velocity bullets will exit earlier than lower velocity bullets. For some markedly different pressure curves with early high pressures that drop off to a very low value later, lower velocity bullets could exit earlier that higher velocity bullets but this is highly unlikely with a single lot of ammo.

Excitation:
The mesh in zero gravity is horizontal. The first step of the calculation is to apply 1 G of gravity. Then the chamber is loaded with the pressure curve that will launch a 40 22LR bullet at 1075 fps from a 24.75 inch barrel. There is no pressure traveling up the barrel.

This view shows the mesh details. The model has a vertical plane of symmetry down the axis of the bore. The x direction is into the plane of the paper and the y direction is up. The z direction is down the barrel from the breach to the muzzle.

This view shows the symmetry plane where nodes on the x plane were allowed to move in the y and z directions but constrained to x=0.

For reference, this is your plot of mv vs time.

The red curve is the last 0.5 inches of the muzzle projected to a 50 yard target. It includes both rotation and vertical displacement. The bullet exit time is 0.00259 ms. The blue curve is the projection of two points half way up the Polaroid card a quarter of an inch from the front and back edge projected to the 50 yard target. The card appears to be vibrating fore and aft while constrained to remain in the x=0 plane.
Note. With more information on the Polaroid card's size and properties, I can make a better mesh of the card and determine only the average rotation of the sum of the two locations of the light sensing instrumentation.

Movie showing the motion of the test setup FEA. The displacements have been amplified by 200x.

Movie of the muzzle and card motion. The deformations are amplified by 200x. The card appears to be vibrating is the fore/aft direction as would a cantilever beam. The red fringe is 100 psi. Only the chamber is excited by the pressure curve. I have been working on the complicated mesh to break up the barrel into 0.25" segments and run the pressure up the barrel as that section of the barrel is pressurized behind the bullet. This is a work in progress.

I have included the LS-DYNA keyword input file so that you can also run it. fea-model-keyword-file.zip

Good Hunting... from Varmint Al

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