Method of measuring

ZVUK devices are designed for non-destructive quality control of grinding tools as well as other products - refractories, metal castings, etc.

The individual inspection is based on comparing the results obtained for a specific product with the values of previous measurings which were taken for a group of identical products (statistical ensemble). Some deviation from the values outside the range of data acquired within the statistical ensemble indicates the different characteristics of the particular piece.

The functional principle of the device - theoretical basis of the method

For the evaluation of bodies, ZVUK devices use a correlational relationship which exists between the natural frequency of oscillations of the body and its physical-mechanical functional properties. The natural frequency of oscillations is influenced by the characteristics of the initial material, but also by the hardness of the individual components and the whole product, by porosity and other physical properties of bodies. Generally, therefore, the relationship between the natural frequency of oscillations of the body and the strength constants and dimensions, can be defined by this equation:


fi = Fi x Cl

fi – the natural frequency of oscillations which corresponds to the selected type of frequency "i"
Fi – the coefficient of the shape which is dependent on the shape of the measured body, its dimensions, the type of selected frequency and Poisson coefficient
Cl – the speed of propagation of sound waves by the measured body which is based on the formula Cl = √(E: ρ) and represents the speed of longitudinal sound waves in the axis of an infinitely long rod. In the formula, E is the value of E-modulus (Young's modulus), and ρ is the value of the specific weight of the measured body.

The shapes of the measured frequencies

The features of oscillations in individual bodies, when assessing the different types of frequencies, are shown in the following schematic image. The dashed lines indicate  nodal lines which - in the particular type of frequency - remain calm.

The frequencies f1 and f2 correspond to the deflection of the disc in a plane which is perpendicular to the axis of the disc, with two nodal diameters and nodal annuli (picture a, b).

The shapes of the measured frequencies

"Plus sign" and "Minus sign" refer to the movement of part of the body in a vertical plane upwards and downwards. In each half period there is an exchange in the direction of movement of these parts.

The frequency  fd corresponds to the moving direction of oscillations in the wheel across the diameter, with two nodal planes (picture c). The dashed lines show the movements of the body towards the hole in the wheel in different parts of the period.

ftorz  frequency indicates the frequency of torsional vibrations in the rod, with a nodal plane in the middle of the rod (picture d); The arrows indicate the direction of torque.

fpl  frequency corresponds to longitudinal oscillations in the rod, with two nodal planes (picture e); the dashed lines indicate the median values of oscillations for each half period. Another type of longitudinal oscillations fpl (picture f) corresponds to the oscillations in the rod with a single nodal plane wchich passes through the center of the  rod. The arrows indicate the directions of oscillations.

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