An analysis and design of the mechanical characteristics of the knife edges used in the NPL watt balance

Of the seven base units of the international system of units, the SI, only the kilogram is still defined in terms of a material artefact. The watt balance is an experimental approach which supports a new definition of the kilogram in terms of constants of nature. Some watt balances, such as the NPL Mk II watt balance, use knives and flats for the balance pivots as they have the advantages of greater robustness over flexure pivots in this particular application. However, hysteresis in the knives can produce errors in the weighing through systematic shifts in the equilibrium point of the balance and it is desirable to investigate this effect as an aid to its elimination. This paper analyses the hysteresis mechanism using both finite element techniques and direct measurement. It was found that the cause of hysteresis is not normal stress but shear stress and that the deformation of the flat, rather than that of the knife, is an important factor. Problems that could not be analysed in a two-dimensional finite element model were investigated using a simplified stand-alone balance. The combined results from the finite element analysis and the stand-alone balance suggest that material properties and tip radius are more important than friction coefficient and tip angle. At loads where knife and flat distortion are low the straightness of the knife and the roughness of the surfaces can have a significant effect.