A device that controls rifle barrel vibration and improves bullet accuracy was evaluated and designed by computer simulation. A computer program was written by the authors to solve the transient form of the elastic beam vibration equation for any given driving function. Output consists of binary files containing transverse velocity and displacement profiles. These files are readable by FFT post-processing codes and by PV-WAVE^® procedure files, which display animations of the system. FFT post-processing was performed to benchmark and verify the simulator with analytical solutions of mode shapes and frequencies. The simulator then was used to optimize a design for a set of rifle barrel modifications that alter the vibrational response to minimize the angular dispersion, or slope, at the muzzle. Bullets will thus exit the barrel always pointing in the same direction (parallel to the barrel baseline axis). This minimizes the sensitivity of precision (measured by group size) to bullet exit time and vibration initiators. Rifle accuracy is thereby improved for a wide range of loads for a given rifle. Introduction

Barrel vibration is one of the factors affecting the accuracy of rifles. Variations in loads (propellant charge weights and bullet masses) cause different times-of-flight from primer ignition to the point in time when the bullet leaves the muzzle. These variations cause the bullet to impact in different locations around the point of aim. The size of the bullet dispersion is called group size. Handloaders have typically reduced bullet group size by "tuning" (or adjusting) the powder load to the barrel so that minimum bullet group size results. The goal is to get the bullet to exit the barrel at a point of maximum barrel deflection, as this represents a point of minimum time-rate-of-change in barrel slope at the muzzle. This minimizes the sensitivity of bullet dispersion to statistical muzzle velocity variation. A new approach was investigated that improves firearm precision by significantly reducing the magnitude of the angular dispersion of the muzzle over a window of relevant bullet exit times.

Proposed modifications to the barrel control the shape of the vibrational response so that the barrel slope at the muzzle is minimized. The first modification (addition of a mass to the barrel between the breech and the muzzle) isolates the muzzle from much of the vibrational energy initiated between it and the chamber through inertial damping (reflection). The second modification (addition of a flexible cylindrical extension and mass attached to the muzzle) acts as a cantilever harmonic oscillator, providing a periodic bending moment to alter the shape of the vibrational response associated with the transmitted vibrational energy. This flexible extension is designed so that the barrel slope is minimized at the point where the bullet leaves physical contact with the barrel, and its flight is determined. The barrel extension has an inner diameter larger than the bore diameter and gas release slots to reduce the effect of gas upsetting the bullet after it has left the muzzle. The design goal is to optimize the positions of the two masses, the radial dimensions and length of the extension, and the configuration of lengthwise slots in the extension to minimize the slope of the muzzle over a window of bullet exit times. This is accomplished when the barrel and flexible extension forms a resonating segment between the masses so that any vibrational energy transmitted past the first mass forms a symmetrical standing wave. The location of zero barrel slope (half the standing wavelength) is designed to coincide with where the bullet enters the extension and leaves physical contact with the barrel. The bullet exits the barrel parallel to the baseline axis for an extended window of bullet exit times, resulting in significantly less sensitivity to variations in exit times.

Rifle barrel vibration is initiated by mechanical interaction between the barrel and the bullet accelerating down the bore, as well as by the severe pressure transient arising from the burning propellant. Barrel vibrations are considered, for this application, to be a superposition of transverse vibrational modes initiated at a continuum of points along the barrel. The short-term vibrational response includes a particular solution arising from the specific characteristics of the driving function (the operating deflection shape), but this response will rapidly transition into the natural modes for the barrel itself. Although this transition takes longer to occur than the time required for the bullet to exit the barrel, comparisons with natural mode shapes and frequencies allow independent verification of the simulator.