Upgraded Kalman Filtering of Cutting Forces in Milling

Advanced piezoelectric dynamometers with a wide frequency bandwidth are required for cutting force measurement in high-speed milling and micromilling applications. In many applications, the signal bandwidth is limited by the dynamic response of the mechanical system, thus compensation techniques are necessary. The most effective compensation techniques for a full 3D force correction require an accurate and complex identification phase. Extended Kalman filtering is a better alternative for input force estimation in the presence of unknown dynamic disturbances. The maximum bandwidth that can be currently achievable by Kalman filtering is approximately 2 kHz, due to crosstalk disturbances and complex dynamometer’s dynamics. In this work, a novel upgraded Kalman filter based on a more general model of dynamometer dynamics is conceived, by also taking into account the influence of the force application point. By so doing, it was possible to extend the frequency bandwidth of the device up to more than 5 kHz along the main directions and up to more than 3 kHz along the transverse directions, outperforming state-of-the-art methods based on Kalman filtering.

Effect of Cutting Speed and Depth on the Course of Resultant Force Acting on a Cultivator Tine

The paper presents research results on the effect of cutting depth and speed on the resultant force tilt angle and location of its application point on a flexible tine ended with a cultivator point. The studies were carried out in field conditions in sandy clay with the gravimetric moisture of 11.2% and volumetric density of 1470 kg·m−3. Tines whose flexibility coefficient was 0.0061; 0.0711; 0.0953 and 0.1406 m·kN−1 were used. It was found out that that the resultant force tilt angle raises at the increase of the cutting speed and drops at the increase of depth but this angle and its gradient at the increase of the cutting depth grow along with the decrease of the flexibility coefficient of tines. The increase of the cutting speed and depth causes the decrease of both the distance of the resultant force application point on the tool from the bottom of a furrow and a proportion of this parameter to the cutting depth. The courses of the distance of the resultant force application point on the tool from the bottom of a furrow and courses of proportion of this parameter to the cutting depth as the function of cutting do not differ significantly for tines with higher flexibility coefficients while for the most rigid tine values of these parameters and their gradients are higher. All obtained courses of the analysed values as a function of depth and cutting speed were described with regression equations.

Influence Functions of a Point Force for Kirchhoff Plates with Rigid Inclusions

A semi-analytic method is proposed for two problem settings for a Kirchhoff plate containing an absolutely rigid circular inclusion and undergoing a transverse point force. The settings differ by the location (within and out of inclusion) of the force application point. In both cases, the plate's stress-strain state is simulated with a boundary value problem for the biharmonic equation stated over a doubly connected region whose inner contour represents the edge of the inclusion. Boundary conditions imposed on the inner contour bring some parameters which are found via the equations of static equilibrium of the inclusion. A modification of the Kupradze'smethod of functional equationsis proposed for obtaining influence functions of a point force for such plates. Green's functions of the biharmonic equation for appropriately shaped simply connected regions are employed. Numerical differentiation is never required in the computing of stress components and the latter are subsequently found with accuracy level comparable with that attained for the deflection function.