0
RESEARCH PAPERS

Comparative Analysis of Tooth-Root Strength Using ISO and AGMA Standards in Spur and Helical Gears With FEM-based Verification

[+] Author and Article Information
Andrzej Kawalec

 Rzeszów University of Technology, Department of Mechanical and Aerospace Engineering, ul. W. Pola 2, Rzeszów, PL-35-959, Polandak@prz.edu.pl

Jerzy Wiktor

 Rzeszów University of Technology, Department of Mechanical and Aerospace Engineering, ul. W. Pola 2, Rzeszów, PL-35-959, Poland

Dariusz Ceglarek

Department of Industrial and Systems Engineering, The University of Wisconsin-Madison, Madison, WIdarek@enger.wisc.edu

J. Mech. Des 128(5), 1141-1158 (Nov 18, 2005) (18 pages) doi:10.1115/1.2214735 History: Received July 21, 2004; Revised November 18, 2005

Current trends in engineering globalization require researchers to revisit various normalized standards that determine “best practices” in industries. This paper presents comparative analysis of tooth-root strength evaluation methods used within ISO and AGMA standards and verifying them with developed models and simulations using the finite element method (FEM). The presented analysis is conducted for (1) wide range of spur and helical gears manufactured using racks or gear tools; and for (2) various combinations of key geometrical (gear design), manufacturing (racks and gear tools), and performance (load location) parameters. FEM of tooth-root strength is performed for each modeled gear. FEM results are compared with stresses calculated based on the ISO and AGMA standards. The comparative analysis for various combinations of design, manufacturing, and performance parameters are illustrated graphically and discussed briefly. The results will allow for a better understanding of existing limitations in the current standards applied in engineering practice as well as provide a basis for future improvements and/or unifications of gear standards.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

The finite element model of a segment of a gear and two load cases: prescribed force applied at the tip and prescribed force applied at the highest point of single tooth contact (HPSTC)

Grahic Jump Location
Figure 2

The FEM model of a representative gear (z=45, mn=2.75mm, αn=20deg, b=32mm): segment of three-tooth made of 3D isoparametric 20-node brick finite elements; boundary conditions as in Fig. 1; load uniformly distributed along the line of contact at the HPSTC

Grahic Jump Location
Figure 3

The FEM model of a representative gear (z=45, mn=2.75mm, αn=20deg, b=32mm) made of 3D 20-node isoparametric and eight-node brick finite elements; all degrees of freedom on the internal cylinder of gear disk fixed; load uniformly distributed along the line of contact at the HPSTC; model of the whole gear (left); enlarged view of the loaded tooth (right)

Grahic Jump Location
Figure 4

Distribution of effective stress in the loaded part of the whole gear shown in Fig. 3

Grahic Jump Location
Figure 5

Distribution of the effective stress in the loaded tooth of the gear shown in Fig. 3

Grahic Jump Location
Figure 6

Comparison of effective stress distributions along tooth line and along fillet of the same gear computed with the use of different finite element models: (i) the whole spur gear built of 3D 20-node isoparametric and eight-node brick finite elements; (ii) segment of three teeth built of 3D 20-node isoparametric brick finite elements; and (iii) segment of three teeth built of eight-node plane stress finite elements; distance Δ describing location of transversal section of tooth is shown in Fig. 7 right

Grahic Jump Location
Figure 7

Absolute values of obtained differences in the effective stresses along fillet δσeff computed according to Eq. 1 for the 2D plane stress model with three teeth and for the model of the whole gear built of 3D 20-node isoparametric and eight-node brick finite elements in sections associated with Δ=2mm (left); explanation of the sections and the lines where the effective stresses are compared (right)

Grahic Jump Location
Figure 8

Comparative analysis of the effective stress distribution at tooth root for three magnitudes of rim thickness of gear (left); absolute values of the relative differences in the effective stresses along fillet Δσeff(1*,i*) computed according to Eq. 2 for the model of three-teeth segment of gear built of 3D 20-node isoparametric, for load applied at the HPSTC Fbn∕b=500N∕mm (right)

Grahic Jump Location
Figure 9

Determination of the critical section location, angle ζF and parameters of the critical section sFn, hFe, and ρF; according to the ISO and the AGMA standards (for comparison see Table 7 in the Appendix)

Grahic Jump Location
Figure 10

Influence of the number of gear teeth on the angle ζF between tooth centerline and tangent to fillet at the critical point F according to the ISO standard, AGMA standard, and FEM: load applied at the tip (left), load applied at the HPSTC (right); main parameters of the gear: mn=2.75, αn=20deg, s1=4.265, β1=0deg, main parameters of the rack: α0=20deg, s0=4.320, hfP=1.22mn, ρfP=0.18mn

Grahic Jump Location
Figure 11

Influence of the number of teeth z0 of the gear tool on the angle ζF between tooth centerline and tangent to fillet at the critical point F according to the ISO standard, AGMA standard, and FEM: load applied at the tip (left), load applied at the HPSTC (right); main parameters of the gear: mn=2.75, z1=45, αn=20deg, s1=4.265, β1=0deg, main parameters of the gear tool: α0=20deg, s0=4.320, hfP=1.22mn, ρfP=0.18mn

Grahic Jump Location
Figure 12

Influence of the normal module mn on the angle ζF between tooth centerline and tangent to fillet at the critical point F according to the ISO standard, AGMA standard for load applied at the tip (Tip), and at the HPSTC; main parameters of the gear: z1=45, αn=20deg, β1=0deg; main parameters of the rack: α0=20deg, hfP=1.25mn, ρfP=0.5

Grahic Jump Location
Figure 13

Determination of parameters of the critical section: sFn, hFe, and ρF, according to the ISO standard (top) and according to the AGMA standard (bottom)

Grahic Jump Location
Figure 14

Influence of the number of gear teeth z1 on parameters of the critical section: sFn, hFe, ρF according to the ISO, AGMA for load applied at the tip (Tip), and at the HPSTC; main parameters of the rack (generating tool) and gear are the same as in Fig. 1

Grahic Jump Location
Figure 15

Influence of the number of teeth z0 of the gear tool on parameters of the critical section: sFn, hFe, ρF according to the ISO, AGMA for load applied at the tip (Tip) and at the HPSTC; main parameters of the gear tool (generating tool) and gear are the same as in Fig. 1

Grahic Jump Location
Figure 16

Influence of the range of sharpening of gear tool (parameter u) on parameters of the critical section: sFn, hFe, ρF according to the AGMA standard for load applied at the HPSTC (left), the range of sharpening of gear tool (right); main parameters of the gear tool (generating tool), and the gear in section 0-0 are the same as in Fig. 1

Grahic Jump Location
Figure 17

Influence of the normal module mn on parameters of the critical section: sFn, hFe, ρF according to the ISO and AGMA standards for load applied at the tip (Tip), and at the HPSTC; main parameters of the rack (generating tool) and gear are the same as in Fig. 1

Grahic Jump Location
Figure 18

Influence of the number of gear teeth z1 on tooth-root stress σF according to the ISO standard, AGMA standard, and FEM: for load applied at the tip Fbn∕b=250N∕mm (left) and for load applied at the HPSTC Fbn∕b=500N∕mm (right); main parameters of the rack (generating tool) and gear are the same as in Fig. 1

Grahic Jump Location
Figure 19

Influence of the number of teeth z0 of the gear tool on tooth-root stress σF according to the ISO standard, AGMA standard, and FEM: for load applied at the tip (left) and for load applied at the HPSTC (right); main parameters of the gear tool (generating tool) and gear are the same as in Fig. 1; magnitude of load is the same as in Fig. 1

Grahic Jump Location
Figure 20

Influence of the range of sharpening of gear tool (parameter u) on tooth-root stress σF according to the ISO, AGMA, and FEM: for load applied at the tip (left) and for load applied at the HPSTC (right); main parameters of the gear tool (generating tool) and the gear in section 0-0 are the same as in Fig. 1; magnitude of load is the same as in Fig. 1

Grahic Jump Location
Figure 21

Influence of the normal pressure angle αn on tooth-root stress σF according to the ISO, AGMA, and FEM: for load applied at the tip; main parameters of the gear: mn=2.75, z1=45, s1=4.265, β1=0deg; main parameters of the rack (generating tool): s0=4.320, ρfP=0.18mn; magnitude of load is the same as in Fig. 1

Grahic Jump Location
Figure 22

Influence of the addendum modification coefficient x1 on tooth-root stress σF according to the ISO, AGMA, and FEM: for load applied at the tip; main parameters of the gear: mn=2.75, αn=20deg, β1=0deg; main parameter of the rack (generating tool): ρfP=0.18mn; magnitude of load is the same as in Fig. 1

Grahic Jump Location
Figure 23

Influence of the helix angle β1 on tooth-root stress σF according to the ISO, AGMA, and FEM for load applied at the tip; main parameters of the gear: mn=5.0, z1=24, αn=20deg, magnitude of distributed load passing through the tip corner of helical tooth flank Fbn∕b=274N∕mm

Grahic Jump Location
Figure 24

Distribution of the effective stresses along tooth line passing through critical sections in various finite element models of helical gears with different helix angles β (left) and along fillet in various transversal sections of helical gear with helix angle β=17deg (right); main parameters of the gear: mn=5.0, z1=24; magnitude of distributed load passing through the tip corner of helical tooth flank Fbn∕b=274N∕mm; parameter Δ used for determination of location of transversal sections of tooth is illustrated in Fig. 7 left

Grahic Jump Location
Figure 25

Influence of the normal module mn on tooth-root stress σF according to the ISO and AGMA for load applied at the tip (Tip) and at the HPSTC; main parameters of the generating rack and gear are the same as in Fig. 1; magnitude of load is the same as in Fig. 1

Grahic Jump Location
Figure 26

Comparison of locations of the critical section and the angle between tangent to fillet and tooth centerline computed according to the ISO (left) and AGMA (middle) standards as well as according to the precise finite element analysis (right) of the gears with the same tooth profiles; magnitude of load is the same as in Fig. 1

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In