This paper deals with the geometric built-up of a theoretically profile errorless shaper cutter. Its proposed rake face is a cylindrical surface for each tooth. The setting parameters of this are the axis inclination angle and the grinding wheel’s radius. The possible domain of the setting parameters is computed from geometrical restrictive conditions. The proposed numerical evaluation consists in the computing of the orthogonal rake angle variation, together with the deviation of the generating pro-file from the perfect involute. The obtained results allow the formulation of some conclusions regarding the influence of the cylinder radius and the axis inclination: the best rake angle distributions are obtained when using increased radius values, while profile deviation becomes minimal when using smaller radii and axis inclination angles.
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.
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.
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.
The Mixed CAD Generating Method, developed by the first author and presented in previous papers, is able to generate gear teeth gaps from a special points cloud. The generation method requires only a few specific points from the cutting edges of the generating tools. These points can be obtained in a first approach through a simple drawing of the cutting edges. The drawings can use either mathematical equations, or simply the construction and design principles of the cutting tools. In the case of multi-edge cutting tools of a higher level of complexity, or in case of the absence of the edge equations, there exists a simpler approach. It consists in building a solid model, or obtaining the solid model of the tools from the tool’s designer or manufacturer. In these cases, the generating points are downloaded from the solid model. This paper presents two possibilities of obtaining these points with usual CAD methods.