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Gear axial pitch $p_x$ is the axial repeat distance between corresponding flanks of successive teeth of a cylindrical helical gear. The measurement follows a line parallel to the rotation axis on a concentric cylinder. It is not the axial advance of one tooth helix through an entire revolution; that larger distance is gear lead $L$. For $N$ equally spaced teeth, $L=N{p}_x$.^[ref]

On the developed cylinder, neighboring tooth traces separated transversely by gear transverse pitch $p_t$ intersect a fixed circumferential coordinate at axial positions separated by $p_x$. Their slope givesFor $d=60\mathrm{mm}$, $N=30$ and gear helix angle $|\beta |=30{}^{\circ }$, $p_t=2\pi \mathrm{mm}$ and $p_x=2\pi \sqrt{3}\mathrm{mm}\approx 10.8828\mathrm{mm}$. The corresponding gear normal pitch is only $5.4414\mathrm{mm}$. These two distances differ by a factor of two in this example because $\sin 30{}^{\circ }=1/2$.

For an engaged gear face width $b=20\mathrm{mm}$, the ideal gear overlap ratio is $b/p_x\approx 1.8378$: successive tooth-contact traces span about1.84 axial pitches across the face. Holding $p_t$ fixed while letting $\beta$ tend to zero makes $p_x$ diverge. Straight spur gear tooth traces do not cross an axial generator successively, so a finite axial-pitch interpretation does not survive that limit. Helix hand determines orientation; the positive pitch magnitude alone does not specify hand.

Gear effective face width is the usable axial width participating in a stated cylindrical gear mesh. It must be distinguished from each component's nominal gear face width, and from a claim that every part of that width carries equal load. The normal/transverse tooth geometry and gear overlap ratio use this engaged width, while gear face load distribution describes how the load actually occupies it.^[ref]

An elementary geometric model treats the two toothed widths as intervals $I_1=[a_1,b_1]$ and $I_2=[a_2,b_2]$ on their common axial coordinate. Their available overlap isFor one20mm-wide gear occupying $[-10,10]\mathrm{mm}$ and a16mm-wide mate centered at $6\mathrm{mm}$, the second interval is $[-2,14]\mathrm{mm}$. Their overlap is only12mm. The mean line load for a hypothetical uniformly shared normal force of1200N is then100N/mm, rather than the60N/mm obtained by using the first gear's entire nominal width.

With gear normal module $m_n=2\mathrm{mm}$ and gear helix angle $|\beta |=30{}^{\circ }$, gear axial pitch is $p_x=4\pi \mathrm{mm}$. The12mm overlap gives geometric gear overlap ratio $b_{\mathrm{eff}}/p_x=3/\pi \approx 0.9549$, compared with $5/\pi \approx 1.5915$ for20mm. Axial positioning can therefore alter overlap without changing the ideal gear ratio.

The interval calculation assumes the flanks remain usable throughout their common extent. Relief, damaged regions or partial contact can require a more specific working-width convention. Uneven loading is not generally corrected by shrinking width until a uniform-load formula looks plausible; a stated load-distribution model is needed to predict local loading.

Gear face load distribution describes how tooth-contact load is spread across the engaged gear face width. Equal total transmitted force can produce different local loads when shafts tilt, supports deform or tooth traces are imperfect. A geometrically available gear effective face width therefore does not establish uniform loading. The manufacturer's tooth-flank gear face load factor accounts for support arrangement and the expected quality of contact under load.^[ref]

For a simple axial line-load model, let $w(z)$ have units $N/mm$ over $0\le z\le b$. Its total normal force isUniform loading gives $w=F_n/b$. An illustrative tilted distribution isIts integral remains $F_n$, while its largest line load is $(1+\lambda )F_n/b$. With $F_n=1000\mathrm{N}$, $b=20\mathrm{mm}$ and $\lambda =0.6$, the two edges carry20 and80N/mm, compared with the50N/mm mean. The peak-to-mean ratio1.6 characterizes this constructed model; it is not a substitute for the manufacturer's standard factor calculation.

The gear contact pattern can reveal where mating tooth flanks touch, but an unloaded marking test alone does not measure the operating force density. A loaded comparison must specify applied torque, shaft positioning and support deformation. In helical gears, changing tooth-contact lines and multiple simultaneous contacts also require a consistent choice of time and projected width. A wider tooth can reduce mean load per width while still suffering a concentrated edge load; width and alignment must be considered together.

A gear face load factor quantifies the effect of nonuniform load across the engaged gear face width. For the contact-load convention in ISO 6336-1:2006, $K_{H\beta }$ compares maximum line-load intensity with the mean intensity over the stated width:Here $F_m$ is the total load represented by that distribution and $b$ is its evaluation width. A uniform distribution gives1; an edge-concentrated distribution gives a larger value. The numerator and denominator must refer to the same load convention and operating condition.^[ref]

For an original illustrative distribution over $b=20\mathrm{mm}$,total load is1000N, mean line load is50N/mm and maximum line load is80N/mm. Thus $K_{H\beta }=1.6$. A uniform distribution with the same width and total load gives1. The gear contact pattern can cover the whole width in both cases.

For ideal elastic line contact at fixed geometry and material, Hertzian contact pressure scales with the square root of line load. The corresponding gear contact-stress load factor is therefore $\sqrt{1.6}\approx 1.265$ in this simplified comparison. Multiplying the contact pressure itself by1.6 would confuse a load-intensity ratio with a stress ratio. This scaling does not replace a complete gear-rating calculation.

The manufacturer's treatment connects face-load assessment to shaft-support placement, shaft stiffness and loaded contact quality.^[ref] A value inferred from a toy line-load profile is consequently useful for understanding the factor, while a real design must obtain the relevant distribution or factor from a method appropriate to its geometry and load state.

Gear face width $b$ describes the width of the toothed portion. For a cylindrical spur gear or helical gear, it is measured parallel to the rotation axis, rather than along the slanting tooth trace. A projecting hub need not be part of the toothed width. Manufacturer drawings distinguish face width, hub width and total length as separate dimensions.^[ref]

The available width of one gear is not necessarily the gear effective face width of a pair. For two aligned cylindrical gears with equal width $b$ and relative axial offset $e$, a simple interval-overlap model givesAn original $b=20\mathrm{mm}$ pair offset by $4\mathrm{mm}$ has only $16\mathrm{mm}$ of common axial extent. If a hypothetical normal load $1000\mathrm{N}$ were uniformly spread across that extent, mean load per axial width would rise from $50$ to $62.5N/mm$. This is bookkeeping for an ideal uniform load, not a tooth-strength prediction. Actual gear face load distribution also depends on alignment and deformation.

For helical gears, width also enters gear overlap ratio:With gear normal module $m_n=2\mathrm{mm}$ and gear helix angle $|\beta |=30{}^{\circ }$, reducing engaged width from $20$ to $16\mathrm{mm}$ reduces ideal overlap from $1.5915$ to $1.2732$. The overall gear ratio is unchanged. Width therefore affects engagement and loading even when tooth counts and shaft speeds remain the same.^[ref]

Gear overlap ratio measures the additional engagement overlap caused by a helical gear's tooth inclination across its gear face width. It is distinct from the transverse gear contact ratio, which measures contact length within one transverse section. For face width $b$, reference gear helix angle $\beta$ and gear normal module $m_n$,where $m_t$ is gear transverse module and $p_x$ is gear axial pitch.^[ref]

Unwrapping the reference cylinder explains the ratio: moving across axial width $b$ shifts the tooth pattern circumferentially by $b\tan |\beta |$. Dividing this shift by gear transverse pitch $\pi m_t$ counts how many tooth spacings the engagement progresses across the face.

For an original example, $b=20\mathrm{mm}$, $m_n=2\mathrm{mm}$ and $|\beta |=30{}^{\circ }$ giveDoubling the face width doubles this geometric overlap if the other parameters stay fixed. At the spur gear limit $\beta =0$, the overlap contribution tends to zero.

In the ideal cylindrical-helical model, total geometric contact ratio is the sum of transverse and axial contributions, ${ϵ}_{\gamma }={ϵ}_{\alpha }+{ϵ}_{\beta }$. This does not specify a uniform division of load: flexibility, alignment and the usable flank region affect actual contact. Increasing helix angle can improve overlap while also increasing gear axial force; increasing width also changes the alignment and support demands. These are related geometric tradeoffs, not a guarantee of a specified noise level or load capacity.