= Gear tooth engagement threshold
A \b[gear tooth engagement threshold] is the relative approach or total load at which a previously separated tooth pair starts carrying compressive contact force in a stated model. Geometric overlap from the <gear contact ratio> does not guarantee that every potentially overlapping pair already carries load. Gaps, errors and <deformation> affect the <gear mesh active-contact set>.
For an original unilateral linear-spring model, write
$$
F_j(\delta)=k_j\max(\delta-e_j,0),\qquad
F(\delta)=\sum_j F_j(\delta),
$$
with $k_j>0$, common approach $\delta$ and initial gap $e_j$. Pair $m$ begins to carry load as $\delta$ rises above $e_m$. The corresponding total-load threshold is
$$
F_{{\rm th},m}=\sum_j k_j\max(e_m-e_j,0).
$$
This threshold includes the forces already carried by earlier contacts. It is not generally obtained by multiplying pair $m$'s own stiffness by its gap.
Take $k_1=80$, $k_2=120\,\mathrm{N/\mu m}$, $e_1=0$ and $e_2=3\,\mathrm{\mu m}$. The second pair begins at total load $80\cdot3=240\,\mathrm N$. At $200\,\mathrm N$, approach is $2.5\,\mathrm{\mu m}$ and the second pair remains unloaded. At $600\,\mathrm N$,
$$
80\delta+120(\delta-3)=600
$$
gives $\delta=4.8\,\mathrm{\mu m}$, forces $384$ and $216\,\mathrm N$, and <gear tooth load fractions> $0.64$ and $0.36$.
At the ideal threshold itself, the new contact contributes zero force but changes the one-sided <gear mesh tangent stiffness>. The force is continuous while its slope can jump. Finite contact geometry and nonlinear local <Hertzian contact> can smooth or alter this elementary linear-spring picture.
A controlled quasistatic test can increase total mesh load at approximately fixed contact position while measuring relative displacement and individual tooth-root <strain>. A change in response slope suggests a contact transition, but support motion and measurement resolution must be considered before assigning it uniquely to a tooth pair. Primary dynamic gear analysis couples tooth <stiffness> and calculated loads as contact position changes, underscoring that engagement cannot be inferred from tooth count alone.<Predicted Effect of Dynamic Load on Pitting Fatigue Life for Low-Contact-Ratio Spur Gears by David G. Lewicki>[Summary and Introduction, printed p. 1, stiffness–load iteration and contact-position dependence]{ref}
Back to article page
