Geometry Design and Tooth Contact Analysis of Crossed Beveloid Gears for Marine Transmissions

Beveloid gears,also known as conical gears,gain more and more importance in industry practice due to their abilities for power transmission between parallel,intersected and crossed axis.However,this type of gearing with crossed axes has no common plane of action which results in a point contact and low tooth durability.Therefore,a geometry design approach assuming line contact is developed to analyze the tooth engagement process of crossed beveloid gears with small shaft angle for marine transmission applications.The loaded gear tooth contact behavior is simulated by applying a quasi-static analysis to study the effects of gearing parameters on mesh characteristics.Using the proposed method,a series of sensitivity analyses to examine the effects of critical gearing parameters such as shaft angle,cone angle,helix angle and profile-shift coefficient on the theoretical gear mesh is performed.The parametric analysis of pitch cone design shows that the dominant design parameters represented by the angle between the first principle directions（FPD） and normal angular factor are more sensitive to the shaft and cone angles than they are to the helix angle.The theoretical contact path is highly sensitive to the profile-shift coefficient,which is determined from the theoretical tooth contact analysis.The FPD angle is found to change the distribution of contact pattern,contact pressure and root stress as well as the translational transmission error and the variation of the mesh stiffness significantly.The contact pattern is clearly different between the drive and coast sides due to different designed FPD angles.Finally,a practical experimental setup for marine transmission is performed and tooth bearing test is conducted to demonstrate the proposed design procedure.The experimental result compared well with the simulation.Results of this study yield a better understanding of the geometry design and loaded gear mesh characteristics for crossed beveloid gears used in marine transmission.

Research on meshing theory of noninvolute beveloid gears

A mathematical model has been developed using the space engagement theory and the differential geometry for the line contact of noninvolute beveloid gears with intersecting axes with their tooth profile equations and engagement equations established for the first time and their meshing theory analysed. It can be seen from the fact that the tooth profile equation finally derived is no longer a standard involute helicoid and standard involute beveloid gears with intersecting axes have no way to satisfy the line contact requirement. However, the noninvdute beveloid gears derived in this paper satisfy the line contact requirement very well. All these work will inevitably facilitate further investigations into gear tooth generation, stiffness, backlash and efficiency of transmission.

Continuous generating grinding method for beveloid gears and analysis of grinding characteristics

Continuous generating grinding has become an important gear processing method owing to its high efficiency and precision.In this study,an adaptive design model is proposed for the continuous generation of beveloid gears in common gear grinding machines.Based on this model,a method for determining the installation position and grinding kinematics is developed alongside an analytical meshing model for grinding contact trace and derivation of key grinding parameters.By combining these aspects,a general mathematical model for the continuous generation of beveloid gears is presented,comprising the entire grinding process from worm wheel dressing to the evaluation of grinding deviation.The effects of the worm and dressing wheel parameters on the grinding deviation were analysed,facilitating the development of an approach to improve the grinding accuracy.The presented procedure represents a novel design method for the continuous generation of beveloid gears in common gear grinding machines,facilitating the appropriate selection of worm and dressing wheel parameters.