This calculates the delfection of the outer race of a bearing when it is pressed into a housing.
These equations are from Shigley and Mischke “Mechanical Engineering Design” Fifth Ediion p.62-63
Modulus of Elasticity of Inner component (Ei)
Modulus of Elasticity of Outer component (Eo)
Inner Radius of Inner Component (land radius)(ri)
Outer Radius of Outer Component (ro)
Poisson’s Ratio of Inner Component (vi)
Poission’s Ratio of Outer Component (vo)
Radius at Press (interface) (R)
Radial Press (d)
Resulting Pressure (p)
Increase in Housing Outer Radius (delta ro)
Decrease in Bearing Inner Radius of OD (delta ri)
Both members have the same length.
Cross sections are uniform.
Radial interference is constant around the circumference.