An Evaluation of the Rehbinder-Kuznetsov Pendulum Technique In Hardness Measurements
Authors: Heins Robert W. , Street Norman 
Published: December 2007

Abstract
An investigation was made of the Rehbinder- Kuznetsov pendulum as an instrument to aid in the study of rock drillability and of the effect of surface active agents on rock drillability. The "Critical weight", i.e., the pendulum weight at greatest sensitivity, was determined for several solids and it was shown that a change in surface environment changed the maximum value of the apparent hardness but not the critical weight, and the critical weight increased with increase of hardness of the solid used. Using silver halidies as the solid material, and solutions of either silver nitrate or the appropriate alkali halide, it was shown that there is a hardness maximum at the zero point of charge of the particular silver halide.
Introduction
The development of relative hardness measurement by the method of damped oscillations, or what has been caned the pendulum sclerometer is due largely to the Russian workers P. A. Rehbinder and V.D. Kuznetsov and their co-workers. The apparent simplicity of the method has led to its use in a number of fields, particularly those where relative hardness has to be determined on a brittle solid. As will be shown, the simplicity of the method belies its complexities.
THEORY OF THE PENDULUM SCLEROMETER
The operation of the pendulum is quite simple. Make a sharp point such as a diamond, hardened steel or tungsten carbide, as the fulcrum of a pendulum, with the center of gravity of the system below the point of support. The attenuation of this pendulum is a function only of air friction, provided no fragmentation, breakage or other work is performed by the point. However, when the solid surface breaks or disintegrates under the point, and the latter penetrates the solid, part of the energy of oscillation is absorbed in the work of creating new surface, and the rate of attenuation increases. In the case of brittle solids, the point of the pendulum produces fragmentary particles, whereas be point produces plastic deformation in a plastic solid; but in both cases damping occurs. This pendulum damping is a function of the hardness or strength of the solid. Whereas a pendulum oscillating on a hard material attenuates primarily by air friction, in the case of a soft material, the points penetrate the surface of the solid, producing new surface, and the pendulum damps much faster. Thus the attenuation rate is a function of the hardness or strength of a material in both plastic and brittle substances. Russian workers initially used a single support for the pendulum, but this created many problems because of oscillation of the pendulum in more than one plane. A revised version used two points, or sometimes a prism as support successfully confining oscillation to one plane. The version using two points was constructed and used throughout this investigation, making the recording of the attenuation as a function of time relatively easy. That both points should be in contact with the solid during the damping is implied. Rehbinder (c.f. Kuznetsov ) proposed that the hardness H as measured by this method could be expressed by a quantity which is inversely proportional to the relative initial rate of attenuation of amplitude.
(1)
where H = hardness parameter (arbitrary units)a = initial amplitudeda/dt = rate of attenuation of amplitude withtime.
In the simplest case of damping with a constant logarithmic decrement, H can be regarded as a constant for the duration of the whole damped oscillation process.
SPEJ
P. 177ˆ