Meshing Characteristics of Profile Shifted Cylindrical Quasi-Involute Arc-Tooth-Trace Gears. Part 1. Theoretical Base (original) (raw)
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2015
Abstract: This paper presents a novel method of synthesis of cylindrical gears having opposite curvatures on the contacting flanks. The method is an improved variant of cylindrical gears having Archimedean spiral curved toothline – developed by the author [3, 4]. Due to the increased cutting capacity of the milling head used in the technological variant that will be presented the kinematics of the meshing results more sophisticated like in the simplest case where a single radial feed is applied. Due to the fact that the present technology uses a cutter head with three cutter groups that executes a tangential feed motion the meshing process can be discussed in three variants: single parameter meshing, bi-parametric meshing and a novel method developed by the author – the double meshing model. This paper discusses the most widely used method in the theory of gear meshing, the single parametric method. The model of the improved cutting tool, the kinematics of meshing, and the mathemati...
Innovative Systems Design and Engineering, 2012
In order to achieve any design study on a gear tooth or to carry out any type of analysis on a complete gear drive, the first step is the representation of the actual form of this tooth under consideration. In this work, a mathematical simulation of generation process for the symmetric involute gear teeth shapes based on the principle of the gear shaping process with a rack-shaped cutter has been developed to take into account the effect of asymmetric tooth profiles and the use of profile correction on each side of tooth with different design parameters for each side of tooth. As a result of this work, a computer program based on this mathematical simulation has been built to represent graphically step-by-step the actual form of symmetric and asymmetric gear teeth shapes with and without profile correction for different gear design parameters.
2014
In general, the circular-arc tooth-trace (CATT) gears are considered as a special type of spiral bevel gears whose shaft-angle is zero. The CATT gears were manufactured using the conventional circular face-mill cutters. In this paper, the new CATT gears have been developed using 3D-CAD/CAM; the tooth profile of pinion gears has the same involute curve at the any section through the face-width. Similarly the tooth profile of the CATT's rack is a straight line at the both sides of the face-width.
Arched Gears Teeth Geometry Within Reference Profile Shift
2019
Teeth geometry of cylindrical arched gears generated by rack tool which is profiled in normal cross-section and in longitude direction by arbitrary curves taking into account reference profile shift has been researched. Meshing of arched rack’s and gear’s teeth within reference profile shift considering as an analogue of the teeth generating process by rack tool by means of generating method. The essence of this method is that teeth surfaces of the rack tool envelop the gear’s teeth surfaces. The equations of teeth surfaces coordinates were obtained in X1Y1Z1 and X2Y2Z2 coordinate systems connected with pinion and gear respectively. In common case these equations are equations of helical surfaces of variable height. Using these equations, the surfaces coordinates of pinion convex tooth side and gear concave tooth side can be determined. These equations can be also used for the determination of meshing field borders, appropriate to the tops of the pinion and gear teeth. The equations...
The Influence of the Tooth Profile Shape on the Stress-Strain State in the Gear
2018
The shape of the tooth profile affects the stress-strain state in the gear. In the case of a fatigue failure the stress state is a decisive criterion for the lifetime of the gear. The shape of the tooth flank affects the magnitude of the contact pressure in the contact of the meshing teeth. The consequence of which are surface cracks and pitting. The shape of the tooth root influences the magnitude of the root stress, which, when limit is exceeded, leads to root cracks and teeth breakage. Many different types of gearing are known, but in the practice most widely used is the involute one. Other types of gearing become interesting especially when polymer materials are being used. If the gears are injection molded the type of gearing does not affect the cost of the tool. In the case of metal gears, standardized tools for involute gearing make the use of other special types of gearing economically unjustified. Our research is focused on the S-gears, which got their name from the S-shape...
Utilization of Computer Programs in Modelling of Gears with Asymmetric Involute Teeth
2008
This paper studies the equations of rack cutters for generating helical gears with asymmetric involute teeth. By applying profile equations of the rack cutter, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing, the mathematical models of involute helical gear is given. The paper presents aspects regarding the utilisation of computer programmes for computer aided design graphical modelling of cylindrical gears with asymmetric involute teeth. Software applications in the domain of computing the points that define the profile and the line of tooth flanks, as well as their 2 and 3 D representation are performed.
2019
Today, involute spur gears are the most common in mechanical engineering. However, besides of the benefits, involute teeth present several disadvantages. To overcome those disadvantages, designers resort to changes that increase the complexity of equipment, cutting tools that lead to the expensive cost. On another hand, gear and transmission, namely sinusoidal gear and transmission is known by higher properties. The results of the simulation of involute and sinusoidal gearing are described in the article. Proved that, sinu-soidal gears have higher performance parameters. Simulation confirmed that sinusoidal gear have higher bending strength, lower contact stress, reduced contact friction and tension in the edging contact, improved performance indicators of transmission. The advantages are due to the following features of the sinusoidal gears geometry: gear tooth profile outlined by a smooth sine wave curve; greater teeth thickness on the pitch circle; wide range of coast flank pressure angle. A new method of gears machining is described. This technology makes it possible to reduce number of expensive and complex gears cutting tools and gears machine tools, greatly simplifies technology of tooth cutting and reduces the cost of gears manufacturing by a numerous times. The method has a wide versatility, provides the opportunity to produce a variety of gears types including, gears with asymmetric teeth.
GEARS WITH THE ASYMMETRIC TOOTH PROFILES AND A NEW ALTERNATIVE METHOD OF ITS MANUFACTURING
Ukrainian Journal of Mechanical Engineering and Materials Science, 2017
The article presents a new gears cutting process - radial circular generating method and describes its multiple benefits to makers of transmissions. The overall increase in efficiency realized through the using a simple tool and the conventional gear tool machine for cutting gears of different types. In particular, this new method was used for cutting gears with the asymmetric profiles of wheel teeth, that allows considerably amplifying power transmission density, increasing load capacity, and reducing size and weight
Optimisation of the Tooth Flank Geometry for Non-Standard Spur Gear
In order to increase the transmissible power level of the plastic spur gears, a non-standard tooth is designed, with a variable geometry along the gear facewidth. The variation of the tooth flank geometry, generated by a simple kinematics, is a consequence of a specific cutting-tool geometry and position. Due to the gear tooth complex geometry, the traditional numerical modeling and analysis of the 3D surfaces is replaced by the solid modeling technique. The non-standard gear generation process is simulated and the virtual gears are further used to investigate the gear basis formats and other criteria of gear quality. The data base unable the selection of the tooth flank geometry that would lead to a proper gear mesh.
MACRo 2015, 2015
Some cutting tools work in kinematic conditions that differ consistently from the hypothetical conditions admitted in the phase of project. Especially in case of gear cutting the difference between the main cutting velocity vector and total cutting velocity vector can't be neglected. The present paper analyses the constructive and the functional geometry of the milling head's arbitrary cutting edge and emphasizes the dependence of the real cutting geometry of the constructive elements and the kinematic peculiarities of the cutting process, where the relative position of cutting tool and cut gear becomes a severe factor of influence.