MEASURING FORCES AND WEAR IN SWITCHIXG APPARATUS 471 



method. With the bariiini titanate transducer a bilUon cycles can be 

 ()l)t allied in 17 hours and a \'ery rapid wear test is obtained. 



If lubrication is not used, wear tests show that materials having a 

 hirge elastic strain limit will in general wear better than materials which 

 have a smaller elastic strain limit even though the latter may have a 

 higher yield stress; materials such as plastics and rubbers will outwear 

 materials such as metals and glasses. The volume of wear for one billion 

 operations is porportional to the product of static force times the length 

 of the stroke. The initial rate of wear is several times as large as the final 

 rate. Calculations show that only about one part in 10 of the energy 

 goes into producing wear, the rest going into heat production. 



As the length of slide is reduced, calcidations and measurements 

 show that there is a threshold of motion for which no gross slide occurs. 

 This condition occurs when the tangential force is less than the product 

 of the normal force times the coefficient of friction. The limiting dis- 

 placement for no slide increases as the two-thirds power of the normal 

 load and inversely as the two-thirds power of the shear stiffness. Hence 

 a heavily loaded material with a small shear elastic constant — such as 

 rubber — will have a large displacement for which no slide occurs, and 

 hence will wear considerably better than a stiff material such as a metal. 

 Wear tests in the region of no gross slide show that the rate of wear is 

 considerably less in proportion to the energy dissipated than in regions 

 of gross slide. 



A quantitative experimental and theoretical study of the region of 

 no gross slide has been made. Experimentally the results have been 

 obtained by mo\'ing a glass lens with a large radius of curvature on both 

 svu'faces between two glass lenses when the lenses are pressed together 

 with known normal forces. It was shown theoretically that slip should 

 occur between these lenses over a cii'cular annulus and experiments 

 verify this prediction ciuantitatively. Force-displacement curves have 

 been measured and it has been shown that the relation is a hysteresis 

 type loop whose area varies approximately as the square of the strain 

 amplitude. The small wear observed is related to the wear found in ball 

 bearings, where no gross slide occurs. This region is important in relays 

 for by introducing damping, long repeated vibrations — which are re- 

 sponsible for considerable wear — are quickly brought down to the low 

 wear, no gross slide region with a corresponding reduction in wear. The 

 mechanical resistance associated with the stress strain hysteresis curve 

 is of the same type that occurs in an assemblage of granular particles 

 such as in a telephone transmitter, where the motion is small enough 

 so that no gross slide occurs. 



