Asimetrik Dişlilerde Diş Dibi Gerilmelerinin Hesaplanması için Yeni Bir Yöntem

Öz

Günümüzde asimetrik diş profillerine sahip dişli tasarımları, dişlilerin diş kökü gerilmelerinin azaltılmasında önemli çözümler sunmaktadır. Asimetrik diş profiline sahip dişlilerde diş dibi gerilmelerini hesaplamak için sayısal, analitik ve deneysel çalışmalar yapılmasına rağmen literatürde standart veya basitleştirilmiş bir denklem veya ampirik ifadeye rastlanmamıştır. Bu çalışmada hem DIN3990 standardı hem de sonlu elemanlar yöntemi kullanılarak asimetrik diş profillerine sahip dişliler için yeni bir diş dibi gerilmesi hesaplama prosedürü geliştirilmiştir. Simetrik profilli dişlilerin diş dibi gerilmeleri geliştirilen sonlu elemanlar modeli ile belirlenmiş ve sonuçlar DIN 3990 standardı ile karşılaştırılarak doğrulanmıştır. Doğrulanmış sonlu elemanlar modeli kullanılarak, süren taraf basınç açısı 20° ile 30° arasında ve diş sayısı 18 ile 100 arasında değiştirilerek 66 farklı durum incelenmiş ve asimetrik profile sahip dişlilerdeki diş dibi gerilmeleri belirlenmiştir. Analizler sonucunda yeni bir asimetriklik faktör elde edilmiştir. Elde edilen faktörün DIN 3390 formülüne eklenmesiyle asimetrik profilli dişlilerin diş dibi gerilmelerinde kullanılmak üzere yeni bir denklem türetilmiştir. Bu denklem sayesinde tasarımcılar, asimetrik diş profiline sahip dişlilerde sonlu elemanlar analizine ihtiyaç duymadan diş dibi gerilmelerini yüksek hassasiyetle hesaplayabilecektir.

Anahtar Kelimeler

• Diş dibi gerilmesi
• Asimetrik düz dişli çarklar
• DIN3990
• Sonlu elemanlar yöntemi

A Novel Method for Tooth Bending Stress Calculation of Gears with Asymmetric Teeth

Abstract

Today, gear designs with asymmetric tooth profiles offer essential solutions in reducing tooth root stresses of gears. Although numerical, analytical, and experimental studies are carried out to calculate the bending stresses in gears with asymmetric tooth profiles a standard or a simplified equation or empirical statement has not been encountered in the literature. In this study, a novel bending stress calculation procedure for gears with asymmetric tooth profiles is developed using both the DIN3990 standard and the finite element method. The bending stresses of gears with symmetrical profile were determined by the developed finite element model and was verified by comparing the results with the DIN 3990 standard. Using the verified finite element model, by changing the drive side pressure angle between 20° and 30° and the number of teeth between 18 and 100, 66 different cases were examined and the bending stresses in gears with asymmetric profile were determined. As a result of the analysis, a new asymmetric factor was derived. By adding the obtained asymmetric factor to the DIN 3390 formula, a new equation has been derived to be used in tooth bending stresses of gears with asymmetric profile. Thanks to this equation, designers will be able to calculate tooth bending stresses with high precision in gears with asymmetric tooth profile without the need for finite element analysis.

Keywords

• Gear bending stress
• Asymmetric spur gears
• DIN3990
• Finite element method

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