1. Why Geometric Progression (GP) is Used: The primary reason for using a
Geometric Progression is to ensure a
constant percentage increase between consecutive speed steps.
If speeds followed an Arithmetic Progression ($100, 200, 300$), the percentage jump from 100 to 200 is 100%, but from 200 to 300 it is only 50%. This would result in poor coverage at lower speeds and unnecessary density at high speeds.
2. Mathematical Advantage: In a GP ($N_1, N_1\phi, N_1\phi^2, ...$), the ratio between any two successive speeds is constant ($\phi$). This allows the machinist to maintain a nearly constant cutting speed regardless of the workpiece diameter.
The "step ratio" ($\phi$) is usually chosen based on Preferred Numbers (Renard series), such as 1.26, 1.41, or 1.58.
3. Practical Implications: Using GP steps minimizes the "speed loss"—the maximum possible difference between the ideal theoretical cutting speed and the closest available speed on the machine. This ensures that tools are used efficiently and that the surface finish remains consistent across various operations.