Friction in a ball-cage linear guide
Hertzian contact stiffness and pressure of a single ball in a ball-cage linear guide (loaded at 45° to the guide axis), plus the resulting sliding friction force and coefficient.
Effective elasticity modulus, E'232.6 GPa
Effective contact radius, R'1.25 10⁻³ m
Hertzian normal load, F28.3 N
Contact radius, r0.08 10⁻³ m
Indentation, δ2.37 10⁻⁶ m
Incremental contact stiffness, S(dF)17.9 10⁶ N/m
Mean contact pressure, p_m1.52 GPa
Maximum contact pressure, p_max2.28 GPa
Vertical indentation, δ_slide3.35 10⁻⁶ m
Incremental stiffness, S_slide17.9 10⁷ N/m
Friction force, F_f,slide2.18 N
Friction coefficient, F_f,slide/P0.0054
Method & references
- Hertzian point contact of a ball loaded at 45° in a ball-cage linear guide.
The computation is a literal port of the original client-side JavaScript from /calculators/c4_8.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.