Pin / Shaft Press Fit Force Equation

Pin / Shaft Press Fit Force Equation

The Force required to assemble (press fit) cylindrical parts depends on the allowance or clearance between the cylindrical parts for the fit, area of the positioned and fitted surfaces, the pressure increasing in proportion to the distance that the shaft feature is forced in.

The approximate ultimate force in tons can be determined by the following formula:

P = (A · a · F) / 2

Where:

P = Ultimate Force required, in tons
A = Area of surface in contact between the shaft and hole feature (in²)
a = Total allowance or actual material interfering between the shaft and hole feature in inches; (pin diameter - bore diameter) (in),
F = Pressure factor ( tons/in³ )

Assumptions:

Diameter of the hub (feature which force is applied to) is twice the diameter of the pin which is pressed into the bore)
Shaft is machine steel,
Hub is cast iron:

Shaft/Pin Diameter (Inches)	Pressure Factor (F)	Shaft/Pin Diameter (Inches)	Pressure Factor (F)
1.00	500	5.25	86
1.25	395	5.50	82
1.50	325	5.75	78
1.75	275	6.00	75
2.00	240	6.25	72
2.25	212	6.50	69
2.50	189	6.75	66
2.75	170	7.00	64
3.00	155	7.25	61
3.25	145	7.50	59
3.50	131	7.75	57
3.75	122	8.00	55
4.00	115	8.50	52
4.25	108	9.00	48.8
4.50	100	9.50	46.0
4.75	96	10.00	43.5
5.00	91	10.50	41.3