Online validation of software for cylindrical involute gears

AbstractThe manufacturing of case-hardened gears usually consists of several complex and expensive steps to ensure high load carrying capacity. The load carrying capacity for the main fatigue failure modes pitting and tooth root breakage can be increased significantly by increasing the near surface compressive residual stresses. In earlier publications, different shear cutting techniques, the near-net-shape-blanking processes (NNSBP’s), were investigated regarding a favorable residual stress state. The influence of the process parameters on the amount of clean cut, surface roughness, hardness and residual stresses was investigated. Furthermore, fatigue bending tests were carried out using C-shaped specimens. This paper reports about involute gears that are manufactured by fineblanking. This NNSBP was identified as suitable based on the previous research, because it led to a high amount of clean cut and favorable residual stresses. For the fineblanked gears of S355MC (1.0976), the die edge radii were varied and the effects on the cut surface geometry, hardness distribution, surface roughness and residual stresses are investigated. The accuracy of blanking the gear geometry is measured, and the tooth root bending strength is determined in a pulsating test rig according to standardized testing methods. It is shown that it is possible to manufacture gears by fineblanking with a high precision comparable to gear hobbing. Additionally, the cut surface properties lead to an increased tooth root bending strength.

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Cylindrical Gears with Increased Contact Area – Proposal of Application in Watercrafts Power Transmission Systems

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.236.26 ◽

2015 ◽

Vol 236 ◽

pp. 26-30 ◽

Cited By ~ 2

Author(s):

Michał Batsch ◽

Tadeusz Markowski ◽

Wojciech Homik

Keyword(s):

Power Transmission ◽

Point Contact ◽

Surface Strength ◽

Hertz Theory ◽

Cylindrical Gears ◽

Position Errors ◽

Power Transmission Systems ◽

Involute Gears ◽

Maximum Contact ◽

Two Bodies

Paper presents the method for obtaining maximum contact pressure of Novikov gears. Described surface strength calculation method is based on Hertz theory of two bodies being in point contact. What’s more the influence of gear position errors on maximum contact stresses has been presented. Also the comparison of Hertz stresses for Novikov and involute gears has been made.

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Transmission Error Analysis of Conical Involute Gears

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C ◽

10.1299/kikaic.78.2624 ◽

2012 ◽

Vol 78 (791) ◽

pp. 2624-2634 ◽

Cited By ~ 6

Author(s):

Kunihiko MORIKAWA ◽

Masaharu KOMORI ◽

Masanori NAGATA ◽

Izumi UEDA ◽

Zhonghou WANG

Keyword(s):

Error Analysis ◽

Transmission Error ◽

Involute Gears

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Derivation of the Explicit Solution of the Inverse Involute Function and its Applications

6th International Power Transmission and Gearing Conference: Advancing Power Transmission Into the 21st Century ◽

10.1115/detc1992-0020 ◽

1992 ◽

Author(s):

Harry Hui Cheng

Keyword(s):

Series Solution ◽

Asymptotic Series ◽

Explicit Solutions ◽

Series Solutions ◽

Perturbation Techniques ◽

Pocket Calculator ◽

Practical Applications ◽

Involute Gears ◽

Simple Expansion ◽

Explicit Series Solutions

Abstract The involute function ε = tanϕ – ϕ or ε = invϕ, and the inverse involute function ϕ = inv−1(ε) arise in the tooth geometry calculations of involute gears, involute splines, and involute serrations. In this paper, the explicit series solutions of the inverse involute function are derived by perturbation techniques in the ranges of |ε| < 1.8, 1.8 < |ε| < 5, and |ε| > 5. These explicit solutions are compared with the exact solutions, and the expressions for estimated errors are also developed. Of particular interest in the applications are the simple expansion ϕ = inv−1(ε) = (3ε)1/3 – 2ε/5 which gives the angle ϕ (< 45°) with error less than 1.0% in the range of ε < 0.215, and the economized asymptotic series expansion ϕ = inv−1 (ε) = 1.440859ε1/3 – 0.3660584ε which gives ϕ with error less than 0.17% in the range of ε < 0.215. The four, seven, and nine term series solutions of ϕ = inv−1 (ε) are shown to have error less than 0.0018%, 4.89 * 10−6%, and 2.01 * 10−7% in the range of ε < 0.215, respectively. The computation of the series solution of the inverse involute function can be easily performed by using a pocket calculator, which should lead to its practical applications in the design and analysis of involute gears, splines, and serrations.

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On Satisfaction of the Fifth Necessary Condition of Proper Part Surface Generation in Design of Plunge Shaving Cutter for Finishing of Precision Involute Gears

Journal of Mechanical Design ◽

10.1115/1.2748452 ◽

2006 ◽

Vol 129 (9) ◽

pp. 969-980 ◽

Cited By ~ 7

Author(s):

Stephen P. Radzevich

Keyword(s):

Gear Tooth ◽

Numerical Control ◽

Proper Part ◽

Surface Generation ◽

Tooth Surface ◽

Necessary Condition ◽

Analytical Mechanics ◽

Part Surface ◽

Involute Gears ◽

Novel Design

In this paper, a novel modified scheme and effective computer representation for design of a plunge shaving cutter is presented. The paper aims to develop a novel design of shaving cutter for plunge shaving of precision involute gears. The study is carried out on the premise of satisfaction of the fifth necessary condition of proper part surface generation (PSG) when designing the plunge shaving cutter. In the current study, the author’s earlier developed DG/K method of surface generation is used together with the principal elements of analytical mechanics of gears. (The DG/K method is based on fundamental results obtained in differential geometry of surfaces, and on kinematics of multi-parametric motion of a rigid body in the E3 space. The interested reader may wish to go for details to the monograph: Radzevich, S.P., Fundamentals of Surface Generation, Monograph, Kiev, Rastan, 2001, 592 pp., and to: Radzevich, S.P., Sculptured Surface Machining on Multi-Axis NC Machine, Monograph, Kiev, Vishcha Schola, 1991, 192 pp.) In the particular case under consideration, the method employs (a) an analytical description of the gear tooth surface to be machined, (b) configuration of the plunge shaving cutter relative to the involute gear, (c) analytical representation of the coordinate systems transformations, and (d) the fifth condition of proper PSG that is adapted to finishing of precision involute gears. The fifth condition of proper PSG is investigated in the paper. On the premise of the obtained results of the investigation, a novel design of plunge shaving cutter for finishing of precision involute gears is proposed. The developed novel design of plunge shaving cutter can be used on shaving machines available on the market, e.g. on Gleason’s new Genesis™ 130SV computer numerical control (CNC) shaving machine.

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A parameterized numerical method for generating discrete helical gear tooth surface allowing non-standard geometry

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes799 ◽

2008 ◽

Vol 222 (6) ◽

pp. 1033-1038 ◽

Cited By ~ 4

Author(s):

J Hedlund ◽

A Lehtovaara

Keyword(s):

Gear Tooth ◽

Numerical Approach ◽

Helical Gear ◽

Tooth Surface ◽

Tool Profile ◽

Standard Geometry ◽

Gear Manufacturing ◽

Involute Gears ◽

Gear Geometry ◽

Tooth Flank

Gear analysis is typically performed using calculation based on gear standards. Standards provide a good basis in gear geometry calculation for involute gears, but these are unsatisfactory for handling geometry deviations such as tooth flank modifications. The efficient utilization of finite-element calculation also requires the geometry generation to be parameterized. A parameterized numerical approach was developed to create discrete helical gear geometry and contact line by simulating the gear manufacturing, i.e. the hobbing process. This method is based on coordinate transformations and a wide set of numerical calculation points and their synchronization, which permits deviations from common involute geometry. As an example, the model is applied to protuberance tool profile and grinding with tip relief. A fairly low number of calculation points are needed to create tooth flank profiles where error is <1 μm.

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