Mesh stiffness modeling considering actual tooth profile geometry for a spur gear pair

Abstract

Some tooth profile geometric features, such as root fillet area, flank modification and wear are of nonnegligible importance for gear mesh stiffness. However, due to complexity of analytical description, their influence on mesh stiffness was always ignored by existing research works. The present work derives analytical formulations for time-varying gear mesh stiffness by using parametric equations of flank profile. Tooth geometry formulas based upon a rack-type tool are derived following Litvin's vector approach. The root fillet area and tooth profile deviations can therefore be fully considered for spur gear tooth stiffness evaluation. The influence of gear fillet determined by tip fillet radius of the rack-type tool is quantified parametrically. The proposed model is validated to be effective by comparing with a finite element model. Further, the model is applied to investigate the stiffness variations produced by tooth addendum modification, tooth profile nonuniform wear and modification.

Stress analysis of coated spur and helical gears considering load distribution

“…The parametric equations of gear root fillet, generated by tip fillet of the cutting tool, can be expressed in coordinate system S ( x , y ) as follows (refer to Yang et al. 33 for more details). where t∈[0,ρcosα], s=|OO'|=rfcosθ, h=hf-(1-sinα)ρ, h f is the dedendum of gear tooth, r denotes the reference radius, ρ and α are tip fillet radius and tooth profile angle of the tool, respectively.…”

“…The parametric equations of involute profile of gear tooth in the coordinate system S ( x , y ) can be expressed as follows. 33 where t∈[ρcosα,(mha*+h)tanα+ρcosα]. t can also be expressed as a function of ϕ …”

“…We have noticed that gear body-induced tooth deflections have been incorporated in elastic potential and mesh stiffness evaluations of gear pairs in many previous studies. 30,32,33 In all of these papers, the gear body-induced tooth deflections were calculated by employing equation (17) of Sainsot et al. 39 Nevertheless, the body-induced deflection is not taken into account in this paper for two reasons.…”

“…The tangency point of tooth fillet and root circle (point A) is on the y axis. The parametric equations of gear root fillet, generated by tip fillet of the cutting tool, can be expressed in coordinate system S(x, y) as follows (refer to Yang et al 33 for more details).…”

Analytical approach and numerical simulation to investigate the stress field and the dynamic stress intensity factors of a cracked tooth subjected to a periodic loading

“…Meanwhile, the effect of these three types of cracks on the equivalent stress, the tooth displacement and contact pressure were analyzed by using the FE method. Recently, Yang et al [14] proposed analytical formulations, validated by a finite element model, to investigate the influence of the tip fillet radius of rack-type tools and tooth addendum modification on gear mesh stiffness for a spur gear pair.…”