Gear teeth act like small cantilever beams. The Lewis Bending Stress equation helps determine if the teeth can handle the load without snapping. Lewis Formula for Rack Teeth
$$RPM = \frac\textVelocity \times 1000\pi \times d = \frac20 \times 1000\pi \times 40 \approx 159 \text RPM$$
Use these mathematical relationships to calculate the physical dimensions of your system. 1. Metric Calculations (Based on Module) rack and pinion calculations pdf
The ratio of the pitch diameter to the number of teeth. It is the most critical factor for gear compatibility. Pressure Angle (
): The distance from a point on one tooth to the corresponding point on the next tooth. Formula: 2. Linear Travel and Velocity Gear teeth act like small cantilever beams
T = (Fr × d) / 2000
Assume efficiency ( \eta = 0.92 ): ( T = (1098.1 \times 75) / (2000 \times 0.92) = 44.76 ) Nm Pressure Angle ( ): The distance from a
The linear speed of the rack is determined by the pinion's module, tooth count, and rotational speed:
For a reliable design, you must perform several calculations, including kinematics and load capacity. A. Geometrical Calculations dp=m×zpd sub p equals m cross z sub p Linear Velocity (v):