Tooth Surface Modelling and Mesh Behaviors for Paralleled Beveloid Gears

Abstract

This paper proposed a new tooth surface modeling method for beveloid gear based on the real cutter surface using two orthogonal variables. Then, the analytical mesh model with and without misalignments were derived and solved to study the influences of geometry design parameters on contact behaviors for paralleled beveloid gear pair. Loaded tooth contact analysis is used to validate the proposed mesh model by abaqus software, and the error is below 5%. Results suggest that the increase in pressure, cone, and helical angles enlarge the contact area for meshing without misalignments. The addendum coefficient has unsubstantial impacts on the contact behaviors. For meshing with axis error in the horizontal direction, the growth of pressure angle, cone angle, helical angle, and addendum coefficient improves the carrying capacity of single tooth. But the transmission error deteriorates with the increase in pressure, cone, and helical angles. All three types of misalignments have little influence on the size of the contact ellipse. The growth of axis errors in horizontal and vertical directions significantly increases the transmission error, but the center distance error has a little influence on the transmission precision.

Kremayer tipi takımla imal edilen evolvent dişli çarkların genelleştirilmiş matematik modeli

“…Brauer, ayrıca takım yüzey parametrelerin değişim aralıklarının analitik tayinini de incelemiştir. Sun ve arkadaşları konikvari pinyon-çark mekanizmasının matematik modelini sunmuşlar ve ayrıca temas kuvvetinin büyüklük ve dağılımını hesaplamak için bir yaklaşım geliştirmişlerdir [6,7]. Şentürk ve Fetvacı konikvari dişli çarkların modellerini elde etmişler ve çeşitli tasarım parametrelerin temas gerilmelerinin üzerindeki etkilerini incelemişlerdir [8].…”

“…Sun ve diğ. tarafından yapılan çalışmada ise, konikvari dişliler için bir yüzey modelleme yöntemi sunulmuş ve geometrik dizayn parametrelerinin paralel eksenlerde temas durumlarına etkisi eksenel sapma olan ve olmayan dişli çiftleri için test edilmiştir [24]. Konikvari evolvent dişliler uygulamada, yat şanzımanlarında yaygın olarak kullanılmaktadır.…”

Numerical study on contact force of paralleled beveloid gears using minimum potential energy theory

“…The beveloid gear is processed with gear hobbing technique by an inline hobbing cutter which is shown in Figure 1. The tooth surface equation taking gear 1 as example in O o − x o y o z o based on former research 10 can be expressed as…”

“…where X s 1 j i is the initial point coordinate of the potential energy calculation, t x | − p c 4 + m n tan α n is the t x value of cutter top side, 10 then the height of contact point on slice s i can be expressed as…”

“…Li et al 9 carried out research for non-involute beveloid gears based on the space curve meshing theory, he built the tooth profile equation and used computer-aided design (CAD) system to get the three-dimension model. Sun et al 10 proposed a new tooth surface modeling method based on the real cutter surface and the analytical mesh model with and without misalignments were derived to study the contact behaviors for paralleled beveloid gear pair.…”