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Disk Mill Gear Cutters
Published in Stephen P. Radzevich, Gear Cutting Tools, 2017
The clearance surface Cs of a disk mill gear cutter is a type of relieved surface. It is shaped using an Archimedean spiral curve as the relieving curve. The outer diameter do.c of the disk mill gear cutter and the clearance angle αo at the top cutting edge are given. The rake angle γo at the top cutting edge of the disk mill gear cutter tooth is equal to zero. The parameters of the involute tooth profile to be machined are also known. It is necessary to determine the normal clearance angle αN.y at a point of interest m of the cutting edge CE. The cutting edge point m is located on a circle of an arbitrary diameter dy.c, the value of which is specified.
Advances in DTM Technology
Published in R. Balasubramaniam, RamaGopal V. Sarepaka, Sathyan Subbiah, Diamond Turn Machining, 2017
R. Balasubramaniam, RamaGopal V. Sarepaka, Sathyan Subbiah
A new spiral tool path generation method is reported [97]. Instead of projecting a planar Archimedean spiral on the work surface, which leads to the problem of unequal spiral spacing, a surface of revolution close to the surface of the work-piece is first generated. An Archimedean spiral is then generated on this surface of revolution with equal spacing. This surface spiral is then projected along its normal surface direction on the desired work-piece surface. This way, the spacing variation is reduced considerably. Detailed algorithms for automating the surface of revolution, spiral generation and projection are developed and tested on actual work surfaces with encouraging results.
High-Conformal Parallel-Axes Gearing
Published in Stephen P. Radzevich, Theory of Gearing, 2018
It should be stressed here that none of the feasible profiles, Pia, of the pinion addendum intersect the boundary N-circle. The pinion addendum profile is entirely located within the interior of the boundary N-circle. Therefore, no arc of a smooth regular curve can be used as tooth profile of the pinion addendum. The circular arc, an arc of an ellipse (at one of its apexes), and a cycloidal profile containing its apex are examples of applicable curves for addendum tooth profiles. Spiral curves (involute of a circle, Archimedean spiral, logarithmic spiral, and so forth) are examples of smooth regular curves of which no arc can be used in designing a pinion tooth addendum. This is because the radius of curvature of a spiral curve (as well as many other curves) changes uniformly when a point travels along the curve. This is schematically illustrated in Figure 10.10. In Figure 10.10a, an ellipse-arc, ab, is shown; the ellipse-arc is entirely located within the interior of the boundary N-circle. The ellipse-arc, ab, can be selected as the tooth addendum profile of a conformal gear pair. An ellipse-arc, cd (Figure 10.10a), is entirely located in the exterior of the boundary N-circle. The ellipse-arc, cd, can be selected as the tooth dedendum profile of a conformal gear pair. Finally, an ellipse-arc, ef (Figure 10.10b), intersects the boundary N-circle. The ellipse-arc, ef, cannot be used as the tooth profile in a conformal gear pair. The same is valid for all spiral curves.
A novel wideband reflectarray using sub-wavelength Archimedes spiral unit cell
Published in Electromagnetics, 2022
Zhiyuan Yang, Jie Zhang, Yufeng Liu, Wenmei Zhang, Qiang Zhang, Yang Gao, Zongwei Tong
The Archimedes spiral is a trajectory formed by a point leaving a fixed point evenly while rotating around the fixed point at a fixed angular velocity. Traditional Archimedean spiral is applied to antenna design with two symmetrical arms and requires balanced excitations. Figure 1 depicts the schematic diagram of a single-arm Archimedes spiral structure. The polar coordinate equation of the Archimedes spiral is