China
Africa
Explore chapters and articles related to this topic
Helical, Bevel, and Worm Gears
Published in Ansel C. Ugural, Youngjin Chung, Errol A. Ugural, Mechanical Engineering Design, 2020
Ansel C. Ugural, Youngjin Chung, Errol A. Ugural
Intersection of the normal plane N–N and the pitch cylinder of diameter d is an ellipse (Figure 12.4). The shape of the gear teeth generated in this plane, using the radius of curvature of the ellipse, would be a nearly virtual spur gear having the same properties as the actual helical gear. From analytic geometry, the radius of curvature rc at the end of a semi-minor axis of the ellipse is rc=d/2cos2ψ
Interaction of Gear Teeth: Contact Geometry of Interacting Gear and Pinion Teeth Flanks
Published in Stephen P. Radzevich, Advances in Gear Design and Manufacture, 2019
In most cases of gear meshing, the degree of conformity at a point of contact of the tooth flanks, 𝒢 and 𝒫, is not of a constant value, and it alters as coordinates of the contact point change. Degree of the surfaces conformity to one another depends on the orientation of the normal plane section through the contact point, K, and changes as the normal plane section spins about the common perpendicular, ng. This statement immediately follows from the above made conclusion that the degree of conformity at a point of contact of the tooth flanks, 𝒢 and 𝒫, yields interpretation in terms of radii of normal curvature, Rg and Rp.
Gear Types and Nomenclature
Published in Stephen P. Radzevich, Dudley's Handbook of Practical Gear Design and Manufacture, 2016
Normal plane—The normal plane is the plane through the plane-of-action apex Apa perpendicular to the centerline ℄ of the gear pair. In the case of Ia gearing, the Nln plane is a plane perpendicular to the gear and pinion axes of rotation Og and Op, respectively. In the case of Pa gearing, the Nln plane is a plane perpendicular to the gear and pinion axes of rotation Og and Op, respectively.
Calculus of pasta, sausages, and bagels: can their surface areas be derivatives of their volumes?
Published in International Journal of Mathematical Education in Science and Technology, 2020
On the other hand, a disk is not the only possible figure that may be slid along a closed curve to provide solids with similar properties. (For the sake of integrity, we point out that the case of planar curves has already been mentioned in [Dorff & Hall, 2003]). In fact, the same considerations concerning surface area and volume are valid for any regular polygon whose centre is on a curve of length L and that slides without rotation along this curve in its normal plane. Formulas similar to (11) can be derived by replacing (‘pie’!!!) with the suitable constant for the given type of polygon and interpreting as the inradius. Figure 7 presents two examples of such bodies, suggesting, perhaps, a chocolate ring cake or a jelly mold!
Classification and selection of sheet forming processes with machine learning
Published in International Journal of Computer Integrated Manufacturing, 2018
Elia Hamouche, Evripides G. Loukaides
The principal curvatures for a given surface describe how the surface bends by different amounts in different directions at each point (Guggenheimer 1977). By calculating the principal curvatures at every point of a 3D surface, a 2D representation of the geometry can be generated in order to describe fully the curvature to the classifier. For a given 3D differentiable surface in Euclidean space, a unit normal vector can be drawn at each point on the surface. The normal plane will contain a normal vector and a tangent vector to the surface which cuts the surface in a plane curve. This curve will have different curvatures for different normal planes at each point. The principal curvatures for each point are denoted as and and refer to the maximum and minimum values of this curvature.
An integrated CAD/CAM system for hyperboloidal-type normal circular-arc gear
Published in Journal of Industrial and Production Engineering, 2020
Guangwen Yan, Houjun Chen, Xiaoping Zhang, Chang Qu, Zhilan Ju
The tooth surface of HNCG, engaging in the meshing activity, is a tubular surface whose cross-section at any location in the normal plane of the helix midline is the circular arc with constant radius. From the point of view of geometry, it can be created by extruding the circular arc along the helix midline. Due to its unique shape of tooth profile, the existing software programs provided by the OEMs cannot yet directly support the design and machining of HNCG. To solve this problem, an integrated CAD/CAM system for the design and machining of HNCG is developed to solve this problem. The main purpose of this system is to achieve the design and machining of HNCG efficiently, and to share the interaction of computer-aided design part and simulation machining part.