This calculator inverts a peak-to-minimum speed ratio for an assumed two-lobe sinusoidal angular-speed law. It does not synthesize non-circular gears, predict machine vibration or estimate screening performance.
Irregular Vibratory Motion Interactive Calculator
Explore modulation depth and peak-to-mean speed implied by an assumed normalized law omega/omega_mean=1+m cos(2 theta).
Equation Used
- Positive normalized law omega/omega_mean=1+m cos(2 theta), with 0<m<1.
- Entered R values are peak/minimum angular-speed ratios, not acceleration or g-force ratios.
- Mean speed is the angular average of the assumed profile.
- No pitch curves, center distance, conjugate tooth profiles, contact ratio, undercut, backlash, torque, inertia, machine mass/stiffness/damping, forcing, amplitude, resonance, particle transport, throughput, screening efficiency, structure, strength or safety model.
The entered ratios mean peak angular speed divided by minimum angular speed under the stated law. If the high-case ratio is entered below the low-case value, it is raised to the low-case value for calculation. Neither result predicts screening efficiency.
Assumed normalized speed law
The calculator assumes omega/omega_mean = 1+m cos(2 theta), where omega_mean is the average over angle rather than time. Its two lobes create two maxima and two minima per revolution. Inverting the peak/minimum ratio gives m=(R-1)/(R+1).
The plot shows this assumed speed law against angle. Constructing a compatible gear pair or calculating machine vibration requires additional geometry and dynamics.
Use as dimensionless profile arithmetic
The outputs can check the algebra between an already-chosen speed ratio and modulation depth. They cannot establish that a gear pair is manufacturable or predict vibration, material transport, throughput or separation efficiency.
Ratio inversion
For omega/omega_mean=1+m cos(2 theta), normalized maximum and minimum are 1+m and 1-m. Therefore R=(1+m)/(1-m), and solving gives m=(R-1)/(R+1). The other two tiles report 100(1+m), the peak speed as a percentage of mean.
Worked examples
For R=1.4, m=0.1667, so modulation is 16.67% and peak speed is 116.67% of mean. For R=2.2, m=0.375, giving 37.50% modulation and peak speed 137.50% of mean.
Limits of the speed-profile comparison
The profile supplies neither a gear shape nor a machine response. Gear geometry must satisfy conjugate rolling and closure, while vibration depends on the forces and the structure’s mass, stiffness and damping. Material-screening performance must be established independently of this ratio calculation.
Questions
Does the ratio describe acceleration or g-force?
No. Here it is peak angular speed divided by minimum angular speed under the stated law.
Does the plot define a non-circular gear shape?
No. It is only a speed profile.
Does modulation predict screening efficiency?
No. The calculator contains no material, screen or separation model.
References & Further Reading
- Wikipedia contributors. Non-circular gear. Wikipedia
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