Proposed solution to eliminate pitch fluctuation in case of conical screw surface machining by apex adjustment

Balajti, Zsuzsa; Mándy, Zoltán

doi:10.1016/j.promfg.2021.10.038

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…In order to eliminate the pitch fluctuation in the case of machining the conical worm with axis displacement, it was examined with the affine geometrical relations demonstrated with the descriptive geometry toolbox [21]. The goal was to determine the equation of the profile curve of the drive pin in an explicit form in order to correct the pitch error [22].…”

Section: Methodsmentioning

confidence: 99%

Selection of Optimal Profile Shift Coefficients in Terms of Bending Stress for Spur Gears

Tomori

2023

Preprint

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The various methods used to choose the profile shift coefficients, primarily the so-called equalizations, were based on assumed advantages without physical evidence proving them. In this paper a new calculation method is presented for determining profile shift coefficient. The procedure gives the pair of values of the profile shift coefficients, in which case, under the given load, the resulting bending stress will be of the lowest possible value.

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Section: Methodsmentioning

confidence: 99%

Selection of Optimal Profile Shift Coefficients in Terms of Bending Stress for Spur Gears

Tomori

2023

Preprint

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“…𝑎 𝑤 +𝑝 tan 𝜆 𝑥 ±√(𝑎 𝑤 +𝑝 tan 𝜆 𝑥 ) 2 −4(𝑎 𝑤 𝑝𝜑 tan 𝜆 𝑥 −𝑝 2 𝜑 sin 𝜑) cos 𝜑 2 cos 𝜑 (12) In order to decide which solution corresponds to the geometric reality of the grinding operation, a numerical approach is necessary. Let's consider the case of a gear-hob originating from an involute worm.…”

Section: The Theoretical Equations Of the Helical Rake Facementioning

confidence: 99%

“…Trying to eliminate the undercut by limiting the grinding wheel diameter, another phenomenonthe transectionappears. This phenomenon occurs when the real body of the generating tool, a grinding wheel for example, or the subspace generated by the cutting edge in its relative motion, intersects the surface obtained with the application of the meshing theory [9], [10], [11], [12], [13].…”

Section: Introductionmentioning

confidence: 99%

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Peculiarities of the Grinding Process of a Gear Hob Helical Rake Face

Hodgyai

Máté

Tolvaly-Roșca

et al. 2021

Acta Universitatis Sapientiae, Electrical and Mechanical Engineering

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This paper presents a study regarding the gear hob’s rake face grinding possibilities and its consequences. A simple theoretical lined surface is considered. The mathematical model of the reciprocate meshing of surfaces was applied. It was proven that the proposed form of the rake face cannot be obtained because an undercut of inacceptable extent occurs. It is also proven and sustained by CAD modeling that using a simplified, flat grinding disk, the undercut is avoided, but the phenomenon of transection appears.

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“…In the corresponding views, the radius drawn from the momentary pole to the moving point is perpendicular to the trajectory tangent. By selecting the appropriate length of the tangent, the drive pin profile can be constructed, namely accurately calculated, in an explicit form [23].…”

Section: Introductionmentioning

confidence: 99%

Challenges of Engineering Applications of Descriptive Geometry

Balajti

2023

Symmetry

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Descriptive geometry has indispensable applications in many engineering activities. A summary of these is provided in the first chapter of this paper, preceded by a brief introduction into the methods of representation and mathematical recognition related to our research area, such as projection perpendicular to a single plane, projection images created by perpendicular projection onto two mutually perpendicular image planes, but placed on one plane, including the research of curves and movements, visual representation and perception relying on a mathematical approach, and studies on toothed driving pairs and tool geometry in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, for which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Our aim was to examine the spatial variation in the wear of the tool edge and the machining of the components of toothed drive pairs using two cameras. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the searching for the right projection direction, and positioning cameras appropriately. A special method of enumerating the possible infinite viewpoints for the reconstruction of tool surface edge curves is presented in the second part of this paper. In the case of the monitoring the shape geometry, taking into account the interchangeability of the projection directions, i.e., the property of symmetry, all images made from two perpendicular directions were taken into account. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. A new criterion was formulated for the tested tooth edge of the hob to take into account the shading of the tooth next to it. The analysis and some of the results of the Monge mapping, suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, namely defining the conditions for camera placements that ensure reconstructibility are also presented. Taking physical shadowing into account, conclusions can be drawn about the degree of distortion of the machined surface from the spatial deformation of the edge curve of the tool reconstructed with correctly positioned cameras.

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Proposed solution to eliminate pitch fluctuation in case of conical screw surface machining by apex adjustment

Cited by 3 publications

References 8 publications

Selection of Optimal Profile Shift Coefficients in Terms of Bending Stress for Spur Gears

Selection of Optimal Profile Shift Coefficients in Terms of Bending Stress for Spur Gears

Peculiarities of the Grinding Process of a Gear Hob Helical Rake Face

Challenges of Engineering Applications of Descriptive Geometry

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