A Generalised Mathematical Model of Involute Gears Generated by Rack Type Cutters

Öz

In this study, a mathematical model of beveloid gears is developed based on the vector expression of the cutting tool. Coordinate transformations, differential geometry and gear theory were applied to obtain the fabricated surfaces. In addition, the ranges of the helical design parameter are also examined. Depending on the angular displacement of the contact point on the line of action of the rack gear mechanism, a generalized expression is proposed to determine the boundary point between the involute profile and the end circle. Numerical examples were prepared to investigate the effect of design parameters on the fabricated gear geometry. For the accuracy and validity of the presented model, a comparison was made with a beveloid gear model in the literature. In addition, undercut and zero topland were investigated in various sections of spur and helical beveloid gears.

Anahtar Kelimeler

• Beveloid Gears
• Rack Cutter
• Undercutting Analysis
• Addendum Modification

Kremayer Tipi Takımla İmal Edilen Evolvent Dişli Çarkların Genelleştirilmiş Matematik Modeli

Öz

Bu çalışmada, kesici takımın vektör ifadesinden hareketle beveloid dişlilerin matematiksel modeli geliştirilmiştir. İmal edilen yüzeyleri elde etmek için koordinat dönüşümleri, diferansiyel geometri ve dişli teorisi uygulanmıştır. Ayrıca, evolvent tasarım parametresinin sınırları da incelenmiştir. Kremayer dişli mekanizmasının kavrama doğrusu üzerindeki temas noktasının açısal yer değiştirmesine bağlı olarak, evolvent profil ile uç daire arasındaki sınır noktasını belirlemek için genelleştirilmiş bir ifade önerilmiştir. Tasarım parametrelerinin imal edilen dişli geometrisi üzerindeki etkisini araştırmak için sayısal örnekler hazırlanmıştır. Sunulan modelin doğruluğu ve geçerliliği için literatürdeki bir beveloid dişli modeli ile karşılaştırma yapılmıştır. Ayrıca, düz ve helisel beveloid dişlilerin çeşitli kesitlerinde alttan kesme ve sivri tepe incelenmiştir.

Anahtar Kelimeler

• beveloid dişli
• kremayer takım
• alttan kesme analizi
• profil kaydırma

Kaynakça

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