= Idler bearing load sharing
<Idler bearing load sharing> determines how an <idler support reaction> is divided among the shaft's supporting <bearing (mechanical)> elements. Zero net <torque> on an ideal steady <idler gear> does not remove its mesh-induced transverse <force>. The bearing loads additionally depend on axial positions and the supported-shaft arrangement. Manufacturer guidance separates a radial load between two bearings from an overhung load and treats gear loads as applications of those cases.<Shafts and Bearings by SDP-SI>[§4.0, “Bearing Loads”, cases(a), (b) and (f): between-support, overhung and external-spur-gear loading]{ref}
Model the shaft as a <simply supported beam> with supports A and B at axial coordinates $z=0$ and $z=L$. Let a gear resultant $P$ act upward at $z=a$, and take upward reactions as positive. <Static equilibrium> requires
$$
R_A+R_B+P=0,\qquad R_BL+Pa=0,
$$
so
$$
R_A=-P\left(1-\frac aL\right),\qquad R_B=-P\frac aL.
$$
For a200N mesh resultant at $a=40\,\mathrm{mm}$ between supports100mm apart, the downward reactions are120N and80N. Equal division occurs only for the centered load in this symmetric ideal support model.
For <overhung idler loading> at $a=130\,\mathrm{mm}$ with the same support span and resultant, $R_A=+60\,\mathrm N$ and $R_B=-260\,\mathrm N$. The farther support's force reverses direction, and the nearer bearing carries more than the applied resultant. This does not violate <force> balance: $60-260+200=0$. If a particular support cannot provide the required reaction direction, the assumed support model must change.
For loads in two transverse directions, solve each component balance before forming the resultant at each <bearing (mechanical)>. <Helical gears> add <gear axial force>; allocating that thrust requires the actual bearing constraints and cannot be inferred from the transverse lever rule. More than two effective supports generally require deformation compatibility as well as equilibrium. These calculations estimate support forces, rather than directly determining bearing life or internal rolling-element contact loads.
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