Shaft & bearing arrangement — force analysis

Analyze a typical gear/belt driven shaft with two bearings. Compute the radial reaction at each bearing and the axial load distribution for angular-contact or tapered arrangements.

F_r1 = √[ ((b·F_re + F_ae·d/2)/(a+b))² + (b·F_te/(a+b))² ] F_r2 = √[ ((a·F_re − F_ae·d/2)/(a+b))² + (a·F_te/(a+b))² ]

Input data

Bearing pair style

External axial force Fae (N)

Axial factor Y1 (taper)

Radial force from weight Fre (N)

Tangential force Fte (N)

Pitch / gear diameter d (mm)

Distance a — left (mm)

Distance b — right (mm)

Result

Radial at bearing 1 Fr1	— N
Radial at bearing 2 Fr2	— N
Induced axial Fd1	— N
Induced axial Fd2	— N
Axial at bearing 1 Fa1	— N
Axial at bearing 2 Fa2	— N

For deep groove ball bearings the external axial force splits equally: Fa1 = Fa2 = |Fae| / 2. For angular-contact / tapered rollers the bearing with the larger (Fd + external) side is the 'clocked' one.