Said-Ball Cubic Transition Curve And Its Application To Spur Gear Design
| dc.contributor.author | Yahaya, Saifudin Hafiz | |
| dc.date.accessioned | 2017-01-09T07:17:14Z | |
| dc.date.available | 2017-01-09T07:17:14Z | |
| dc.date.issued | 2015-09 | |
| dc.description.abstract | Undoubtedly, gears are some of the most widely used elements in consumer and industrial machineries. Past studies have shown that an involute curve is the most common profile used in designing the spur gear tooth, developed based on the approximation theories such as Chebyshev approximation and the tracing points method. However, these employed methods are not accurate (or inexact) and only focusing on the approximation concepts. Gear noise reduction and tooth strength are continually being the focus of exploration and experimentation particularly the modification of the tooth shape or tooth profile. Therefore, this study is to design the S and C-shaped transition curves using Said-Ball cubic curve based on the third and fifth cases of circle to circle templates with some mathematical proofs. One of the objectives is to investigate the capability of this proposed S and C-shaped model in reducing sound or noise level through an acoustic experiment. In this study, spur gear is chosen as a case model due to its fundamental gear and the fact that it is simple to construct and manufacture. Based on the conducted experiment and simulation, results show that by using Said-Ball cubic curve, the theories of S and C-shaped transition curves have successfully developed. These curves have been mathematically proven, by using the concavity and second derivative tests and also Kneserās theorem. It is also revealed that S and C-shaped transition curves can be applied successfully in designing spur gear tooth. This proves that the solid model of spur gear can also be developed through the integrated use of mathematical and CAD software. When measured through linear static analysis, fatigue analysis and DE, the applicability of the proposed design and the material, AISI 304 shows that First-order Newton interpolating polynomial can be employed as a fatigue predictor for all design models. The new teeth design methods, S and C-shaped curves are the acceptable methods in designing the spur gear teeth where both methods have presented DE greater than 85% of the design effectiveness. All models have also been successfully measured via dynamic and acoustic response analyses. C-shaped model has been proven to have the lowest displacement when compared to S-shaped (transition) and EM models. By utilizing this model, it is proven that gear noise or sound can be reduced consistently. C-shaped model is more reliable than other models in accordance to PS. It is proven that tooth profile modification is the main factor in reducing sound or noise in a very significant and consistent way. The contribution of this study will be beneficial to the designers or manufacturers in designing the spur gear profiles where the above-mentioned curves can be applied as an alternate method of these profiles. For future research, the capability of C transition curve can be further explored in designing aerodynamic models for example, car, high-speed train, bullet etc. Study on gear design can also be further explored on other type of gears such as helical herringbone gear. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/3362 | |
| dc.subject | Mathematics | en_US |
| dc.title | Said-Ball Cubic Transition Curve And Its Application To Spur Gear Design | en_US |
| dc.type | Thesis | en_US |
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