In this work, a model for the prediction of drilling stability against low-frequency lateral vibrations, named as whirling in the literature, is proposed. These vibrations are lateral displacements of the tool that arise at frequencies near multiples of the rotation frequency of the drill. The appearance of whirling vibrations leads to the generation of lobe-shaped holes. In order to predict whirling vibrations, the motion equation of the drill is deduced taking into account the modal characteristics of the drill and the cutting and process damping forces that act on it. In this paper, forces that arise in two different regions of the drill are considered: (1) forces on the main cutting edges and (2) forces on the chisel edge. Different force models are presented for each region that include both the regenerative effect of the vibration on the cutting area and the process damping. An oblique cutting model and an orthogonal model are employed for the calculation of cutting forces acting on the main cutting edges and on the chisel edge, respectively. The cutting force model for the main cutting edges takes into account the cutting angle (inclination angle, rake angle, and chip flow angle) variation along the main cutting edges. For the chisel edge region, where the feed speed is no longer negligible with respect to the cutting speed, the dynamic cutting angles are employed for the force model development. Concerning the process damping force model, previous works in the literature consider a constant value of the clearance angle for the calculation of the process damping coefficient. However, in this work, the variation of the normal clearance angle along the main cutting edges is considered. It is shown that, depending on the clearance face grinding parameters employed, the clearance angle can double its value along the main cutting edges. Considering the force models and through the semi-discretization of the motion equation of the drill, the appearance of low-frequency lateral vibrations is predicted regarding the drill geometry and cutting conditions such as drill rotation speed and feed. In addition, given cutting conditions at which whirling vibrations are expected to occur, the model is able to predict the vibration frequencies that are excited. The drilling model and the stability predictions are experimentally validated by means of drilling tests with different drill diameters and cutting conditions. In comparing the experimentally obtained results and the predictions obtained by the model, it is concluded that the model can reasonably predict the appearance of whirling vibrations as a function of drill geometry and cutting conditions. Generated hole shape is also analyzed through the measurement of hole roundness and bottom surface geometry. It is observed that, when drilling in the presence of whirling vibrations, holes with lobed shape and polygonal bottom surface are generated. It is also noticed that both the number of lobes and the number of sides of the polygonal bottom surface are directly related to the vibration frequencies that arise.

A model that predicts the appearance of low-frequency lateral vibrations in drilling with pilot hole is proposed in this work. These vibrations, called whirling in the literature, are responsible for the generation of lobe-shaped holes during drilling. The present model considers both the influence of the regenerative effect of vibrations on the cutting forces and the influence of the process damping phenomenon that appears along the main cutting edges. In order to model cutting forces, cutting edges are divided into discrete elements and for each of them oblique cutting model is employed. Specific cutting forces at each cutting edge element are calculated as function of cutting speed and normal rake angle value. A new methodology is developed to analyze the motion equation of the drill in the frequency domain in order to predict the appearance of whirling vibrations during drilling with pilot hole. Regarding the depth of cut and the spindle rotational speed, drilling stability limits against low-frequency lateral vibrations are obtained. Moreover, in the presence of vibrations, the model can predict the whirling frequencies that are excited depending on the established cutting conditions. In addition, the stability model is experimentally validated via drilling tests over pilot holes of different diameters for a wide range of cutting conditions. In order to study the appearance of low-frequency vibrations and to avoid the appearance of other vibrations such as regenerative chatter, the analysis is focused on low spindle speed values. A comparison between predicted vibration frequencies and actual frequencies in measured cutting forces during drilling tests is carried out and a good correlation between them is observed.

The geometric tolerances of cylindrical workpieces are highly influenced by clamping forces. This relation is of special importance in slender workpieces such as thin rings. Better tolerances are achieved with lower clamping forces, but the disadvantage is that friction is reduced and the risk of slipping increases. Thus, in order to control the process, a key factor is achieving the lowest possible clamping force while still ensuring safety. Cylindrical parts are usually machined in lathes that have concentric plate chucks that are fixed either mechanically with wrenches or hydraulically by controlling pressure with valves. This paper proposes a method for measuring clamping forces in lathes during the turning process. The method allows the clamping force to be calculated from the torque applied by a dynamometric wrench or from valve controlled hydraulic pressure.

Measuring the clamping forces on cylindrical workpieces is a key factor in the geometrical tolerances of such components, especially if they are slender as the case of thin rings. The lower the clamping force, better tolerances will be achieved, but with the disadvantage of reducing friction and, therefore, increasing the risk of slipping. Therefore, achieving a minimum but safe clamping force is a key factor to control the process. Usually, these parts are made in lathes that have concentric plate clutches and these are fixed mechanically by wrenches or hydraulically through the control of pressure by valves. A simple and economic method is proposed to measure the clamping forces in lathes, although it is necessary the use of a model for the ring deformation. This method allows knowing the clamping force from the torque applied by a dynamometric wrench, or from the hydraulic pressure controlled by valves.