“…Oda et al. 36 have proposed the practical formula for tooth deformations of internal involute spur gears considering various numbers of teeth and addendum modification coefficients. They have used the two-dimensional elasticity theory and the mapping function.…”
Section: Formulation For Tooth Deformation and Load Sharing In Internmentioning
confidence: 99%
“…The results are also compared with those of two-dimensional FEM. Considering the comprehensive geometric model proposed by Oda et al., 36 shown in Figure 5, all deformations of the engaged tooth under the action of load F , can be formulated as follows:…”
Section: Formulation For Tooth Deformation and Load Sharing In Internmentioning
Involute toothed internal−external standard gear sets are modeled for load-sharing by the teeth pairs in mesh along the line of contact. An analytical solution is proposed. Considering the rigid body in rotation, it is assumed that angular rotation of a gear with respect to the other gear due to deformation along the line of contact is equal. The sum of the normal loads in all tooth pairs in contacts, which equals to the total transmitted load, is considered constant. All possible deformations such as, tooth bending deflection, tooth compressive (contact) deformation, tooth foundation deflection and tooth shearing deflection are considered in analyses. Detailed tooth geometries are incorporated in modeling. Ultimately, the map of load sharing by tooth pairs in contacts, at different angular position, over a cycle of similar contact pattern, is established. Finally, considering thin rimmed gears, the effects of the rim thickness on load sharing, which is the aim of the present investigation are analyzed and the results are presented in terms of backup ratios.
“…Oda et al. 36 have proposed the practical formula for tooth deformations of internal involute spur gears considering various numbers of teeth and addendum modification coefficients. They have used the two-dimensional elasticity theory and the mapping function.…”
Section: Formulation For Tooth Deformation and Load Sharing In Internmentioning
confidence: 99%
“…The results are also compared with those of two-dimensional FEM. Considering the comprehensive geometric model proposed by Oda et al., 36 shown in Figure 5, all deformations of the engaged tooth under the action of load F , can be formulated as follows:…”
Section: Formulation For Tooth Deformation and Load Sharing In Internmentioning
Involute toothed internal−external standard gear sets are modeled for load-sharing by the teeth pairs in mesh along the line of contact. An analytical solution is proposed. Considering the rigid body in rotation, it is assumed that angular rotation of a gear with respect to the other gear due to deformation along the line of contact is equal. The sum of the normal loads in all tooth pairs in contacts, which equals to the total transmitted load, is considered constant. All possible deformations such as, tooth bending deflection, tooth compressive (contact) deformation, tooth foundation deflection and tooth shearing deflection are considered in analyses. Detailed tooth geometries are incorporated in modeling. Ultimately, the map of load sharing by tooth pairs in contacts, at different angular position, over a cycle of similar contact pattern, is established. Finally, considering thin rimmed gears, the effects of the rim thickness on load sharing, which is the aim of the present investigation are analyzed and the results are presented in terms of backup ratios.
“…In case of internal teeth (Figure 15) Hertzian contact deformation, δci and bending deflection, δbi are determined according to Oda et al. 30 as Figure 15.Internal teeth (CS gear) model.…”
Section: Sharing Of Interference (Overlapping) At Secondary Contact Amentioning
confidence: 99%
“…Internal teeth (CS gear) stiffness. In case of internal teeth ( Figure 15) Hertzian contact deformation, c i and bending deflection, b i are determined according to Oda et al 30 as…”
Section: Interference (Overlap) Sharing By Mating Teethmentioning
confidence: 99%
“…Solving equations (29) and (30) simultaneously, the solution in quadratic equation of x is in the form as follows…”
Originally fixed and uniform circular pitches of flex spline (FS) teeth of a ‘Strain Wave Gearing’ or ‘Harmonic Drive’ (HD) experience variations in pitch lengths when teeth move on ‘strain wave generating’ oval-shaped cam. This is due to varying root deformations of teeth. In case of teeth with widely used involute profile, away from the contacts on line of action through pitch point, they definitely experience force closeness to or separation from the circular spline’s (CS) originally conjugate tooth. We have estimated the deformed pitch distances at no load considering that FS teeth remain rigid while the rim deforms. The geometry of the oval-shaped pitch curve which is parallel to the elliptical outer profile of the cam is also defined. Similarly to maintain an elliptical pitch curve of FS, the oval cam is also defined. Both cases of tooth mesh of undeformed FS with CS and tooth mesh of deformed FS with CS, with involute teeth, are considered to find out tooth positions. Geometries of involute teeth profiles in mesh are examined and compared considering oval-shaped (on deformation) base drum of FS, whereas the base circle of the CS remained circular.
Strain Wave Gear (SWG) or Harmonic Drive (HD) shows moderate performance under symmetrical involute teeth. Teeth interference, excessive teeth meshing, vibration due to improper teeth engagement are the major drawbacks of strain wave gear under symmetrical involute teeth. In the present paper, an attempt has been made to improve the performance of strain wave gear by replacing the symmetrical involute teeth with asymmetrical involute teeth. Present investigation finds that under ‘asymmetric toothed strain wave gear’, aspects such as teeth interference, teeth engagement and teeth contact stress of strain wave gear are improving clearly and as a consequence some other aspects such as individual teeth strength, load carrying capacity, tooth endurance are also improving inherently. In the present analysis for symmetrical teeth 20°–20° pressure angle and for asymmetrical teeth, three different combinations of pressure angles such as 25°–20°, 30°–20° and 35°–20° are taken.
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