geometry

Articles About geometry


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1 Homogeneous Geometry Calculation of Arbitrary Tooth Shapes: Mathematical Approach and Practical Applications (February 2016)

This paper provides a mathematical framework and its implementation for calculating the tooth geometry of arbitrary gear types, based on the basic law of gear kinematics. The rack or gear geometry can be generated in two different ways: by calculating the conjugate geometry and the line of contact of a gear to the given geometric shape of a known geometry (e.g., a cutting hob), or by prescribing the surface of action of two gears in contact and calculating the correspondent flank shapes.

2 A New Geometrically Adaptive Approach for Tooth Contact Analysis of Gear Drives (August 2015)

Tooth contact analysis (TCA) is an important tool directed to the determination of contact patterns, contact paths, and transmission errors in gear drives. In this work, a new general approach that is applicable to any kind of gear geometry is proposed.

3 Diametral Pitch Calculation (April 2015)

Circular pitch gives me the size of the teeth in my mind, but diametral pitch does not. What is the purpose of the diametral pitch concept? Does it merely avoid pi in calculation?

4 Axis of Rotation Metrology (August 2009)

In the history of machine tools, spindles have been very good relative to other bearings and structures on the machine. So quality professionals have developed a cache of tools—-ball bars, grid encoders displacement lasers, etc.—-to help them characterize and understand the geometry of the structural loop. But as machine tools have improved in their capability and precision, and the demands of part-geometry and surface finish have become more critical, errors in spindles have become a larger percentage of the total error.

5 Preventing Fretting Fatigue in Blade Dovetail Roots by Modifying Geometry of Contact Surfaces (August 2013)

Dovetails, gears and splines have been widely used in aero engines where fretting is an important failure mode due to loading variation and vibration during extended service. Failure caused by fretting fatigue becomes a prominent issue when service time continues beyond 4,000 hours. In some cases, microslip at the edge of a contact zone can reduce the life by as much as 40–60 percent.

6 Evolution of Worm Gear Standards and their Consequences on Load Capacity Calculation Approach (September 2014)

Beginning with a brief summary and update of the latest advances in the calculation methods for worm gears, the author then presents the detailed approach to worm gear geometry found in the revised ISO TR 10828. With that information, and by presenting examples, these new methods are explained, as are their possibilities for addressing the geometrical particularities of worm gears and their impact upon the behavior and load capacity of a gearset under working conditions based on ISO TR 14521 — Methods B and C. The author also highlights the new possibilities offered on that basis for the further evolution of load capacity calculation of a worm gearset based on load and contact pressure distribution.