Effects of off line of action contact on static behavior of the high contact ratio spur gear mechanism

Mekanizmalardan beklenen çalışma hızı ve güç/ağırlık oranı her geçen gün artmaktadır. Özellikle redüktör gibi kimi ekipmanlarda bu istek sadece malzeme ya da tribolojik gelişmelerle değil aynı zamanda güç iletim sistemine ait tasarımının geliştirilmesi ile mümkün olabilmektedir. Bu amaca ulaşmak için kullanılan yöntemlerden biri Yüksek Kavrama Oranına (YKO) sahip dişli çark mekanizmalarından faydalanmaktır. Burada amaç, yükün daha fazla diş tarafından paylaşımı sonucu mekanizmada aşırı bir ağırlık artışı olmaksızın iletilen gücün arttırılmasıdır. Dişli çark mekanizmalarında yüksek kavrama oranı, kavrama oranının 2'den büyük olması anlamına gelir. Bunun anlamı, mekanizmada her an için en az iki diş çiftinin temasta olmasıdır. Dişli çark mekanizmasının kendine özgü davranışını görebilmek için doğru olarak modellenmesine ihtiyaç duyulmaktadır. Bu makalede dişli çarkların analizi için kullanılan model, Yücenur tarafından geliştirilen ve uç girişiminin etkisini de içeren bir modeldir. Uç girişimi olayı; diş çiftinin dişlinin çalışma şartlarından kaynaklanan yük altında elastik şekil değişimi ya da dişlerde bulunan hatalar nedeniyle diş çiftinin temasının kavrama kıtasının öncesinde başlaması ve dışında da sürmesidir.  Modelde; dişlerde eğilme ve kayma deformasyonları, dişin gövdeye bağlandığı bölgelerdeki deformasyonlar ve temas bölgesi deformasyonları ayrı ayrı hesaplanmakta ve ilgili konum için dişin yaylanma sayısı bulunmaktadır. Uç temasının olduğu bölgelerde yaylanma sayısı için ayrıca hesap yapılmamakta, bu bölgeler için yaylanma sayısı değerleri iki uçtan lineer olarak ekstropole edilmektedir. Bu makalede uç girişiminin yüksek kavrama oranlı dişli çark mekanizmasında statik zorlanmalara olan etkisi incelenmiştir. Anahtar Kelimeler:  Yüksek kavrama oranı, uç teması, dişli çark modeli. Expected performance and power to weight ratio of power transmission systems have been steadily increasing. Especially for the equipments like speed reducers, this requirement can be met only by improvement of power transmission design. Another approach to meet this requirement is to use high contact ratio (HCR) gears. The purpose of using the HCR gears is distribution of the total load to more than one tooth pair; as a result, an increase in the power transmission capacity of the mechanism can be achieved without significant increase in mechanism weight. It is known that, single teeth load on the HCR spur gear is approximately 2/3 of the standard gear teeth for the same working condition. To this end, precise determination of the performance of gears in design phase is crucial. For gear mechanism situation is same. Unfortunately, there is no easy solution algorithm that is valid for the behavior of all gear mechanisms. For that reason, proper gear models are required to observe the specific behavior of each gear mechanism. Although, the studies on gear mechanisms go back to the beginning of the 20th century, there are still some uncertainties even for the standard gears. One of them is premature contact of the teeth; due to heavy tooth load or pitch deviations, tooth pair can meet outside the theoretical first contact point (similarly, contact may continue outside of the last theoretical contact point due to same reasons). This action is known as off line of action contact or corner contact. Many researchers have been trying to adopt this phenomenon to their models, but they could not succeed. In this study, the model utilized for gears also includes the off line of action contact effect, developed by Yücenur and he also represented a paper that included the effect of corner contact to a standard gear mechanism. Author showed that especially for moderately and heavily loaded spur gears, there is a significant effect of corner contact and this effect can not be neglected. In the study, the effect of off line of action contact on the static behavior of a HCR spur gear mechanism has been examined. The load carrying and related stress value for a gear which rotates at low speeds can be assumed as static. HCR can be expressed as; spur gears which have contact ratio larger than two. For the standard spur gears, contact ratio is normally smaller than two. If the change of pressure angle having small effect on contact ratio is neglected, only possibility to achieve HCR is using the extended teeth. It is clear that, of course, these gears can be manufactured only by using special cutting tools; however, this increases the manufacturing cost. In this study, to examine the effect of HCR, mechanisms having extended teeth (namely, mechanisms have HCR) are compared with standard mechanism; both mechanisms have involute teeth. Special efforts have been performed to select mechanisms that have the same characteristic values (such as the same module, the same pressure angle, and the same pitch circle). In this way, objective comparisons can be achieved. In this study, associated gear models are prepared with the aid of a computer program. Analyses are performed for many mechanisms. Then, the results are compared with each other on the same ground. In the analyses, all teeth are assumed to be geometrically perfect. At the end of the study, it is observed that real contact ratio slightly greater than the theoretical contact ratio due to the effect of off line of action. This effect is related with the working condition (transmitted power), and when the tooth load increases, the contact ratio also increases. Hence, it is shown that HCR can be achieved without excessive extension of the addendum circle radius value. In the study, in order to make a reliable comparison, the mechanism with real contact ratio is equal to 2 is also investigated and this mechanism is also compared with the others. In the analyzed examples, it is found that HCR mechanisms have the static tooth load value less than almost 1 / 3 of the standard mechanism value. It is also observed that bending stress at the root of both HCR gear and pinion teeth are reduced as the same degree of the load value. On the other hand, at the point of Hertzian stress, no significant advantages of HCR mechanism have been observed. In some applications, on the other hand, this stress values are slightly greater than those of the standard gears. Keywords: High Contact Ratio (HCR), off line of action, spur gear model.