The speed at which the rack travels based on the pinion's rotational speed. $$v = \frac\pi \times d \times n1000$$
To move the load, the motor must provide 14.7 Nm of torque at 318 rpm driving a 20-tooth Module 3 pinion. rack and pinion calculations pdf
$$S_F = \frac\sigma_limit\sigma_calculated$$ A Safety Factor $> 1.5$ to $2.0$ is typical for industrial applications. The speed at which the rack travels based
| Symbol | Parameter | Unit (SI) | Unit (Imperial) | | :--- | :--- | :--- | :--- | | $z$ | Number of teeth (Pinion) | - | - | | $m$ | Module | mm | - | | $P$ | Circular Pitch | mm | in | | $d$ | Pitch Diameter | mm | in | | $d_a$ | Tip Diameter (Outer Diameter) | mm | in | | $d_f$ | Root Diameter | mm | in | | $a$ | Center Distance | mm | in | | $v$ | Linear Speed | m/s | ft/min | | $n$ | Rotational Speed | rpm | rpm | | $T$ | Torque | Nm | lb-in | | $F_t$ | Tangential Force | N | lbf | | $F_a$ | Axial Force | N | lbf | | $F_r$ | Radial Force | N | lbf | | $\alpha$ | Pressure Angle | degrees | degrees | To move the load, the motor must provide 14
To ensure the system does not fail, the Lewis Formula (for bending stress) is often used as a baseline check.
The module is the defining metric for gear teeth size. It represents the pitch diameter divided by the number of teeth. $$m = \fracdz$$