This paper presents a general theory regarding the balancing of mechanisms. It starts with Stevenson’s theory , which proves that any mechanism can be dynamically perfectly balanced if there is a pair of counterweights that are eccentrically positioned in three reciprocating perpendicular axes, passing through the mass center of the body. The system of inertial forces are extended in Fourier series where only the first terms, the basic harmonics, are considered. The proposed goal is to stultify the effect of inertial forces and torques. This paper deals with a situation more appropriate to reality. In common cases there doesn’t exist the possibility of implementing counterweights in three perpendicular axes. In this situation only the minimization of inertial forces and torques remains as a possible solution. The method developed for this case is presented.
Márton Máté, Dénes Hollanda and Erzsébet Egyedfaluvégi
Some cutting tools work in kinematic conditions that differ consistently from the hypothetical conditions admitted in the phase of project. Especially in case of gear cutting the difference between the main cutting velocity vector and total cutting velocity vector can't be neglected. The present paper analyses the constructive and the functional geometry of the milling head's arbitrary cutting edge and emphasizes the dependence of the real cutting geometry of the constructive elements and the kinematic peculiarities of the cutting process, where the relative position of cutting tool and cut gear becomes a severe factor of influence.
Cylindrical gears with Archimedean spiral toothline represent a result of recent research. Similarly to the Öerlikon type bevel gears this type of gears cannot be grinded. This fact leads to the necessity of achieving best possible surface roughness while cutting using a specific cutter head. The paper presents the geometric model of the grinding technology applied for the main relief faces of the cutters and analyses the problems regarding the precision of the edge profile, its dependence with the technological setting parameters and the profile variation after the re-sharpenings. It concludes that the classic method of ground grinding allows a restricted number of resharpenings.
It is well known that straight teethed shaper cutters present a theoretical profile error. The side edges are situated on a common conical rack face with the result that they and their projection in the generating plane can’t be involute curves. The optimization of the cutter requires such a correlation of the edge defining parameters that the potential theoretical profile error is kept to the minimum possible. Thus the relevance of the edge equations is of great importance. This paper deals with the analysis of the edge equations, presenting two different forms of it. The comparison between the two different forms is realized by applying the numerical evaluation, by substitution of the edge point coordinates in the implicit equations of the originating surfaces. The obtained results present a difference of magnitude 10-E3. Finally, it can be concluded that the two forms of the edge equations cannot be used randomly but only in correlation with the goal proposed by the running application.
The side relief faces of the monolithic involute gear hob are machined through relieving. The resulting surfaces are bevel helical surfaces in which the side cutting edges result from the intersection of these with the helical rake face. Theoretically, the gear hob is derived from an involute worm. Resharpening decreases the diameter of the hob, thus the edges became closer to the axis, and as a consequence they will be situated on a smaller worm than the original. The present paper analyses the deviation of the re-sharpened gear hob’s carrying worm from the theoretically perfect involute worm whose characteristic dimensions were adjusted considering the re-sharpened gear hob characteristic diameters. It was proven that the evolution of the errors is significantly different from that described in the literature. Thus, increasing the new gear hob diameters in comparison with the calculated dimensions is unnecessary, because it cannot reduce the error to half with this procedure. The mathematical model was built up accepting that the edges result from the intersection of an involute worm with a helical rake face and the side relief faces result from the rototranslation of the edges on a bevel helix leading curve dressed by the relieving parameter.
Gear hobs are the most widely and frequently used gear cutting tools. During the time passed between the moment of invention (Schiele, 1876) and the present, gear hobs reached a considerable evolution regarding the geometry, the profile of the edge, the relieving technologies finalizing in the latest constructive and design solutions. This paper deals with the calculus of the edge profile in the case the basic worm of the hob has involute helicoid surfaces. In order to obtain a constant grinding allowance on the relief faces of the gear hob teeth it is necessary to compute the edge of the roughing relieving cutter. The equations are deduced considering that the provenience involute worm is a one teethed helical gear with shifted profile. The presented mathematical model proves that linearizing the relieving cutter profile is not an adequate solution if aspiring to higher precision.
Ferenc Tolvaly-Rosca, András Kakucs, Zoltán Forgó and Márton Máté
The paper proposes a comparative FEM analysis of gears solid model bodies, obtained with three different methods. The analytical method is based on the mathematical equations of the tooth flanks. It supposed to be the most accurate and precise solid modeling process. However, it reveals it’s limits by handling of surfaces that are not deduced mathematically, or in case of tooth geometries which needs to be modified in order to perform a quick test regarding the probably effects of the mentioned modifications. The solid subtraction- and the newly developed, mixed CAD method are pure CAD generating methods. As any discrete generating method, their precision is influenced by the fineness of the iteration steps. In case of the mixed CAD solution the precision is influenced by the filtering algorithm applied to the generated Points Cloud. The visual comparison of the three mentioned methods, was presented in previously published papers. The present paper validates the novel mixed CAD method comparing the FEA analysis of the generated solid models.