Analytical Crack Propagation Scenario for Gear Teeth and Time-Varying Gear Mesh Stiffness
In this paper an analytical crack propagation scenario
is proposed which assumes that a crack propagates in the tooth root in
both the crack depth direction and the tooth width direction, and
which is more reasonable and realistic for non-uniform load
distribution cases than the other presented scenarios. An analytical
approach is used for quantifying the loss of time-varying gear mesh
stiffness with the presence of crack propagation in the gear tooth root.
The proposed crack propagation scenario can be applied for crack
propagation modelling and monitoring simulation, but further
research is required for comparison and evaluation of all the
presented crack propagation scenarios from the condition monitoring
point of view.
[1] O. F. Chaari, T. Fakhfakh, M. Haddar. Analytical modelling of spur gear
tooth crack and influence on gearmesh stiffness, European journal of
mechanics A/Solids. 28 (2009) 461-468.
[2] Z. Chen, Y. Shao. Dynamic simulation of spur gear with tooth root crack
propagating along tooth width and crack depth, Eng.Failure Anal. 18
(2011) 2149-2164.
[3] F. Chaari, W. Baccar, M. Abbes, M. Haddar. Effect of spalling or tooth
breakage on gearmesh stiffness and dynamic response of a one-stage
spur gear transmission, European journal of mechanics A/Solids. 27
(2008) 691-705.
[4] C. Weber. The deformation of loaded gears and the effect on their load
carrying capacity, Sponsored research (Germany). British Dept.of Sci.
and Ind. Res. (1949).
[5] Y. Attia. Deflection of spur gear teeth cut in thin rims, ASME paper 63-
WA-14. (1963).
[6] R. Kasuba, J.W. Evans. Extended model for determining dynamic loads
in spur gearing. Journal of mechanical design. 103 (1981) 398-409.
[7] R. W. Cornell. Compliance and stress sensitivity of spur gear teeth.
Journal of mechanical design. 103 (1981) 447-459.
[8] D. C. H. Yang, J.Y. Lin. Hertzian damping, tooth friction and bending
elasticity in gear impact dynamics. Journal of mechanisms,
transmissions, and automation in design. 109 (1987) 189-196.
[9] S. Sirichai. Torsional properties of spur gears in mesh using nonlinear
finite element analysis, PhD thesis, Curtain University of Technology.
(1999).
[10] L. Jianfeng, X. Mingtian, W. Shouyou. Finite element analysis of
instantaneous mesh stiffness of cylindrical gears (with and without
flexible gear body), Communications in numerical methods in
engineering. 15 (1999) 579-587.
[11] J. Wang. Numerical and experimental analysis of spur gears in mesh,
PhD thesis, Curtain University of Technology. (2003).
[12] D. Lewicki. Gear crack propagation path studies-guidelines for ultrasafe
design, Journal of the American Helicopter Society. 47 (2002) 64-
72.
[13] D. Lewicki, B. Ballarini. Effect of rim thickness on gear crack
propagation path, Journal of mechanical design. 119 (1997) 88-95.
[14] D. Lewicki, R. Ballarini. Gear crack propagation investigations,
Tribotest. 5 (1998) 157-172.
[15] F. K. Choy, V. Polyshchuk, J. J. Zakrajsek, R. F. Handschuh. Analysis
of the effects of surface pitting and wear on the vibration of a gear
transmission system, Tribol.Int. 29 (1996) 77-83.
[16] C. D. Begg, C. S. Byington, K. P. Maynard. Dynamic simulation of
mechanical fault transitions, Proceedings of the 54th Meeting of the
Society for Machinery Failure Prevention Technology, Virginia Beach,
USA. (2000).
[17] I. Yesilyurt, F. Gu, A. Ball. Gear tooth stiffness reduction measurement
using modal analysis and its use in wear fault severity assessment of
spur gears, NDT E international. 36 (2003) 357-372.
[18] X. Tian. Dynamic simulation for system response of gearbox including
localized gear faults, MSc. thesis, University of Alberta, Edmonton,
Alberta, Canada, 2004. (2004).
[19] S. Wu, M. Zuo, A. Parey. Simulation of spur gear dynamics and
estimation of fault growth, J.Sound Vibrat. 317 (2008) 608-624.
[20] S. Zouari, M. Maatar, T. Fakhfakh, H. Haddar. Three-dimensional
analyses by finite element method of a spur gear: Effect of cracks in the
teeth foot on the mesh stiffness, Journal of failure analysis and
prevention. 7 (2007) 475-481.
[21] P. Sainsot, P. Valex, O. Duverger. Contribution of gear body to tooth
deflections - A new bidimensional analytical formula, Journal of
mechanical design. 126 (2004) 748-752.
[22] D. C. H. Yang, Z. S. Sun. Rotary model for spur gear dynamics. Paper -
American Society of Mechanical Engineers. (1985).
[23] S. Glodez, S. Pehan, J. Flasker. Experimental results of the fatigue crack
growth in a gear tooth root, Int.J.Fatigue. 20 (1998) 669-675.
[24] P. Orlov, Fundamentals of machine design, Mir Publishers, Moscow,
Russia, 1979.
[25] S. C. Mohanty. Tooth load sharing and contact stress analysis of high
contact ratio spur gears in mesh, Journal of the Institution of Engineers.
India. Mechanical Engineering Division. 84 (2004) 66-70.
[26] G. Maitra, Handbook of gear design, Second edition ed., Tata McGraw
Hill, New Delhi, India, 1994 (Seventeenth reprint, 2010).
[1] O. F. Chaari, T. Fakhfakh, M. Haddar. Analytical modelling of spur gear
tooth crack and influence on gearmesh stiffness, European journal of
mechanics A/Solids. 28 (2009) 461-468.
[2] Z. Chen, Y. Shao. Dynamic simulation of spur gear with tooth root crack
propagating along tooth width and crack depth, Eng.Failure Anal. 18
(2011) 2149-2164.
[3] F. Chaari, W. Baccar, M. Abbes, M. Haddar. Effect of spalling or tooth
breakage on gearmesh stiffness and dynamic response of a one-stage
spur gear transmission, European journal of mechanics A/Solids. 27
(2008) 691-705.
[4] C. Weber. The deformation of loaded gears and the effect on their load
carrying capacity, Sponsored research (Germany). British Dept.of Sci.
and Ind. Res. (1949).
[5] Y. Attia. Deflection of spur gear teeth cut in thin rims, ASME paper 63-
WA-14. (1963).
[6] R. Kasuba, J.W. Evans. Extended model for determining dynamic loads
in spur gearing. Journal of mechanical design. 103 (1981) 398-409.
[7] R. W. Cornell. Compliance and stress sensitivity of spur gear teeth.
Journal of mechanical design. 103 (1981) 447-459.
[8] D. C. H. Yang, J.Y. Lin. Hertzian damping, tooth friction and bending
elasticity in gear impact dynamics. Journal of mechanisms,
transmissions, and automation in design. 109 (1987) 189-196.
[9] S. Sirichai. Torsional properties of spur gears in mesh using nonlinear
finite element analysis, PhD thesis, Curtain University of Technology.
(1999).
[10] L. Jianfeng, X. Mingtian, W. Shouyou. Finite element analysis of
instantaneous mesh stiffness of cylindrical gears (with and without
flexible gear body), Communications in numerical methods in
engineering. 15 (1999) 579-587.
[11] J. Wang. Numerical and experimental analysis of spur gears in mesh,
PhD thesis, Curtain University of Technology. (2003).
[12] D. Lewicki. Gear crack propagation path studies-guidelines for ultrasafe
design, Journal of the American Helicopter Society. 47 (2002) 64-
72.
[13] D. Lewicki, B. Ballarini. Effect of rim thickness on gear crack
propagation path, Journal of mechanical design. 119 (1997) 88-95.
[14] D. Lewicki, R. Ballarini. Gear crack propagation investigations,
Tribotest. 5 (1998) 157-172.
[15] F. K. Choy, V. Polyshchuk, J. J. Zakrajsek, R. F. Handschuh. Analysis
of the effects of surface pitting and wear on the vibration of a gear
transmission system, Tribol.Int. 29 (1996) 77-83.
[16] C. D. Begg, C. S. Byington, K. P. Maynard. Dynamic simulation of
mechanical fault transitions, Proceedings of the 54th Meeting of the
Society for Machinery Failure Prevention Technology, Virginia Beach,
USA. (2000).
[17] I. Yesilyurt, F. Gu, A. Ball. Gear tooth stiffness reduction measurement
using modal analysis and its use in wear fault severity assessment of
spur gears, NDT E international. 36 (2003) 357-372.
[18] X. Tian. Dynamic simulation for system response of gearbox including
localized gear faults, MSc. thesis, University of Alberta, Edmonton,
Alberta, Canada, 2004. (2004).
[19] S. Wu, M. Zuo, A. Parey. Simulation of spur gear dynamics and
estimation of fault growth, J.Sound Vibrat. 317 (2008) 608-624.
[20] S. Zouari, M. Maatar, T. Fakhfakh, H. Haddar. Three-dimensional
analyses by finite element method of a spur gear: Effect of cracks in the
teeth foot on the mesh stiffness, Journal of failure analysis and
prevention. 7 (2007) 475-481.
[21] P. Sainsot, P. Valex, O. Duverger. Contribution of gear body to tooth
deflections - A new bidimensional analytical formula, Journal of
mechanical design. 126 (2004) 748-752.
[22] D. C. H. Yang, Z. S. Sun. Rotary model for spur gear dynamics. Paper -
American Society of Mechanical Engineers. (1985).
[23] S. Glodez, S. Pehan, J. Flasker. Experimental results of the fatigue crack
growth in a gear tooth root, Int.J.Fatigue. 20 (1998) 669-675.
[24] P. Orlov, Fundamentals of machine design, Mir Publishers, Moscow,
Russia, 1979.
[25] S. C. Mohanty. Tooth load sharing and contact stress analysis of high
contact ratio spur gears in mesh, Journal of the Institution of Engineers.
India. Mechanical Engineering Division. 84 (2004) 66-70.
[26] G. Maitra, Handbook of gear design, Second edition ed., Tata McGraw
Hill, New Delhi, India, 1994 (Seventeenth reprint, 2010).
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:57093", author = "Omar D. Mohammed and Matti Rantatalo and Uday Kumar", title = "Analytical Crack Propagation Scenario for Gear Teeth and Time-Varying Gear Mesh Stiffness", abstract = "In this paper an analytical crack propagation scenario
is proposed which assumes that a crack propagates in the tooth root in
both the crack depth direction and the tooth width direction, and
which is more reasonable and realistic for non-uniform load
distribution cases than the other presented scenarios. An analytical
approach is used for quantifying the loss of time-varying gear mesh
stiffness with the presence of crack propagation in the gear tooth root.
The proposed crack propagation scenario can be applied for crack
propagation modelling and monitoring simulation, but further
research is required for comparison and evaluation of all the
presented crack propagation scenarios from the condition monitoring
point of view.", keywords = "Crack propagation, Gear tooth crack, Time varying
gear mesh stiffness.", volume = "6", number = "8", pages = "1575-6", }
