A quick and efficient algorithm for the calculation of gear profiles based on flank involutization (original) (raw)
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Fast modeling of conjugate gear tooth profiles using discrete presentation by involute segments
Mechanism and Machine Theory, 2007
This paper introduces the method of the discretization of the gear tooth flank in involute segments for the determination of conjugate gear tooth profiles. Instead of following a point-to-point analytical approach to the problem of determining the path of contact and the geometry of the generating rack and the mating wheel, the actual tooth flank is considered to be composed of infinitesimal local involutes and therefore a closed solution can be achieved. Due to its simplicity, the method is faster than the standard theory of gearing and this is particularly useful in problems requiring iterative calculations of the tooth geometry such as gear optimization. The method is implemented on modified involute as well as loboid gears used in lobe pumps and it is verified against existing theories.
[21]) on external modified involute gear teeth is presented in this technical report. The teeth in question are composed of an involute working profile from the outer to the form circle of the gear and of a circular fillet from the form to the root circle, replacing the conventional trochoidal fillet. This circular fillet has been proved to increase the bending strength of the gear without altering any other of its functional characteristics (Spitas et al. [22]) and therefore it can readily replace the corresponding conventional gears in a mechanism.
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.
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.
On the generation of conjugate flanks for arbitrary gear geometries
GAMM-Mitteilungen, 2009
In this paper, we present a novel approach to three-dimensional mathematical gearing theory. We start from a general formulation of the so called basic law of gear kinematics. Based on that we derive an analytic closed form solution for the generation of conjugate tooth flanks, given a (local) parametric representation for any prescribed flank profile. Also, we study the problem of constructing pairs of tooth flanks that give rise to a prescribed surface of action. Surfaces of action will be represented in an implicit global rather than in a parametric way. To illustrate the general theory, we consider a number of specific examples including the standard involute profile for spur gears as well as a more sophisticated three-dimensional generalization of that.
Interactive Involute Gear Analysis and Tooth Profile Generation Using Working Model 2D
Working Model 2D (WM 2D) is a powerful, easy to use planar multibody software that has been adopted by many instructors teaching Statics, Dynamics, Mechanisms, Machine Design, as well as by practicing engineers. Its programming and import-export capabilities facilitate simulating the motion of complex shape bodies subject to constraints. In this paper a number of WM 2D applications will be described that allow students to understand the basics properties of involutegears and how they are manufactured. Other applications allow students to study the kinematics of planetary gears trains, which is known to be less intuitive than that of fix-axle transmissions.
In this paper a new generation of asymmetric tooth profile gear is considered to enhance the dynamic behavior and vibroacoustic properties of toothed gear system. This paper presents a non linear dynamic model as a single degree of freedom equation for teeth meshing gear system which includes static and dynamic transmission error in order to investigate the influence of time varying mesh stiffness and periodic tooth errors on dynamic load factor for symmetric and asymmetric spur teeth profile. A new model of nonlinear time varying mesh stiffness is based on four types of deflections with consideration a small pressure angle for loaded tooth profile side and high pressure angle for another side. The complicated variation of meshing stiffness as a function of contact point along the mesh cycle is studied. Typical dynamic load factor equations are developed for symmetric and asymmetric tooth gear in single and double tooth contact by studied symmetrictooth with pressure angle (20 0 /20 0) and two pairs of asymmetric teeth (14.5 0 /25 0 & 20 0 /25 0). The effect of pressure of asymmetry and static transmitted load on transmission error and dynamic load factorare studied. The results indicate enhancement percentage in transmission error and dynamic load factor for asymmetric teeth profile compare with that symmetric tooth profile. 1. Introduction For the combination of high speeds and heavy loads encountered in modern engineering applications of the toothed gear, a precise analysis of the gear dynamic behavior is imperative. A New generation of asymmetric teeth gear play important role to increase load capacity, endurance ,long life and reduction vibration and noise. Transmission error (Tm) which is mean the difference between theoretical and actual angular position of driven gear when driver gear operating at constant speed ,therefore transmission error represent major excitation source for vibration and noise in geared system ,and reduction in transmission error represent major aim for researchers many decades ago, moreover gear vibration and noise level arise due to other several reasons [1] such as the error in the gear teeth profile at the contact point , misalignment between shaft axes , impact between mating teeth ,backlash, sliding and rolling friction between mating surface of gears ,bearing and housing ….etc. Most efforts to reduce the vibration and noise generation at the mesh have been directed towards improving the accuracy of manufacture. But, experience proves that the improving of manufacturing accuracy does not reduce the vibration and noise level considerably [2]. Several studies in literature have been conducted on the design and stress analysis of asymmetric tooth gear, little of them transact this approach dynamically, kaplelevich[3] present analytical method to design a gear with asymmetric tooth side surface, he consider a high pressure angle for the drive side and low pressure angle for the coast side teeth , Yang [4] provide geometrical modeling to design the asymmetric helical gear meshing when assembly errors are present, he constructed Stress analysis for the helical and the cylindrical form ,Mallesh et al. [5,6] generate asymmetric spur gear tooth geometry for different pressure angles on drive and coast side using computer programme to create a finite element model of gear tooth and investigate the effect of bending stress at the critical section for different pressure angles, different number of teeth and module , Ekwaro-Osire et al. [7] employ the inverse problem technique for asymmetric gear teeth which include photo elastic experimental work , Wang et al.[8] extend the edge – based smoothed point interpolation method (ES-IPM) in the bending strength analysis of asymmetric gear with various drive pressure angles side which generated by a special rack cutter , Agrawal et al. [9] Had been tested an asymmetric gear virtually with ANSYS code under a predefined loading and it has been investigated how bending stress changes at the fillet region of the asymmetric gear .Karpat et al. [10] present dynamic analysis of spur gear with symmetric and asymmetric teeth gear ,they consider high pressure angle for the drive side and low pressure angle profile for the coast side teeth ,they develop a MATLAB-based virtual tool to analyze dynamic behavior of spur gears with asymmetric teeth. In This work a new mathematical model for nonlinear mesh stiffness and dynamic load factor formula are developed for symmetric & asymmetric teeth meshing gear system then investigate the influence of asymmetry on dynamic load factor and transmission error .
The conjugate profile of the circular teeth of a spur gear. Part I: Problem statement
IOP Conference Series: Materials Science and Engineering, 2020
The paper presents the manner of finding the conjugate profile of a circular tooth of a spur gear. A synthesis of the method of enveloping applied to the cam mechanisms is presented in order to relate it the profile of the spur gears. The main argument of employing cam mechanisms is the possibility of obtaining any follower law of motion using a minimum number of parts-the cam and the follower. In the case of the mechanisms with flat face follower, the cam is obtained as an envelope of successive positions of the follower. The gear mechanisms are a particular case of cam mechanisms. The major requirement imposed to this mechanism is to transmit the rotational motion between two shafts with a constant transmission ratio. From here it results that the profile a geared wheel can be completely identified when there are known the distance between the axes, the transmission ratio and the profile of one of the wheels. The most used curve as tooth flank is the involute of a circle, due to the fact that this curve has as conjugate curve an involute, too. Although the involute profiles are common in most of the technical appliances, there are cases when they cannot satisfy the functional constraints of certain devices. As example, in the mechanical watches technology, large transmission ratios are needed and the gears with small number of teeth are used as routine. But this necessity is better fulfilled by cycloidal profiles than the involute ones. The circular profiles for the spur gear are the oldest gears due to the simple profile. The exact conjugate profile of a circular tooth obtained by enveloping by means of dedicated software is presented.