Question

(c) A titanium hip replacement ball joint of 23.000 mm diameter was precision ground and required to be finished to a tolerance of +/- 0.002 mm The inspection procedure resulted in the parts being measured whilst still hot at 80 C after grinding. If the coefficient of linear expansion of titanium is 10 microns/metre deg C, determine 1) The linear expansion relative to the reference temperature of 20 deg C 2) The overall result of measuring parts hot on the finished size and the type of engineering fit that may result Comment on the likelihood of the +/- 0.002 mm tolerance being obtainable and should a correction factor be applied to the measurement ?

Answer 1

co-efficient of linear expantion of the titanium is 10 micron/ meter

that is 0.01 mm/ 1000 mm = 0.00001 / ⁰c .

if the titanium ball is finished to the size of 23 mm at 80^oC .

while ambient is at 20^oC .

linear expantion of BALL DIAMETER is = 0.00001 X 23 X (80-20)

= 0.0138 mm

leniar expantion of titanium b all relative to the reference temprature of 20^oC is 0.0138mm .

2)

there fore after the presision grinding of the titanium ball , ball is at 80^oC .

DUE TO THIS BALL WILL QUENCH BY THE 0.0138 mm at 20^oC .

there fore nominal size of ball will reduce to 23-0.0138 = 22.9862 mm.

with the nominal sise the tolerance zone over the ball diameter will also shift inword.

size of the ball will be 22.9862 ⁺_- 0.002 mm  

as we see , the thermal contraction is larger than the toleranceover the nominal ball sise of the 23 mm.

ther fore the general CLEARENCE FIT WILL BE PRODUCED ON THE BALL FOR

TOLERANCE LIMIT OF ⁺_- 0.002 mm ..

THANK YOU.