Probabilistic Simulation Approach to Evaluate the Tooth-Root Strength of Spur Gears with FEM-Based Verification

EL-Sayed S. Aziz, Constantin Chassapis

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DOI: 10.4236/eng.2011.312142                

Abstract

Dependency on deterministic design techniques without attention to inherent process variations and uncertainties in gear design and manufacturing processes can lead to unreliable results and affect the performance of a gearing system. A better understanding of the impact of uncertainty associated with the system input on the system output can be achieved by including reliability techniques to accomplish a reliable design methodology. This emerged the need to consider the probabilistic behavior of the stress distribution on the gear tooth during the design phase. The present effort reports on the application of the SSI theory within the context of a “Design for Reliability” approach in support a detailed gear design methodology for the evaluation the tooth-root strength with FEM-based verification. The SSI theory is formulated to predict the effect of the root fillet generated by a rack or hob tool with and without protuberance on the gear system reliability. The results obtained from the probabilistic analysis strongly agreed with the FEM’ results across a range of different gear tooth fillet profiles. A quantitative assessment of the investigated gear sets showed the highest tooth-root stress was associated with the lowest tip radius of the generating tool. This approach helps with making the decision by quantifying the impact of stress and strength variations during the gear design stage.

Keywords

Gear Design, Design for uncertainties, Probabilistic Design, Reliability, FEM

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Vlahinos, S. Kelkar, S. Reh, R. Secaur and S. Pliz, “Reliability Based Optimization within the CAD Environ- ment,” 2002. http://www.aes.nu/publications/2002-ReliabilityBasdOptimiz-bmx-ANSYS.pdf
[2]	G. Cooper and G. Thompson, “Concept Design and Reli- ability,” Acta Polytechnica, Vol. 42, No. 2, 2002, pp. 3-12.
[3]	O. P. Yadav, S. S. Bhamareb and A. Rathoreb, “Reliabil- ity-Based Robust Design Optimization: A Multi-Objec- tive Framework Using Hybrid Quality Loss Function,” Quality and Reliability Engineering International Journal, Vol. 26, No. 1, 2010, pp. 27-41. doi:10.1002/qre.1027
[4]	X. He and S. O. Oyadiji, “A Study of Practical Reliability Estimation Method for a Gear Reduction Unit,” IEEE SMC’99 Conference Proceedings, Vol. 1, 1999, pp. 948- 953.
[5]	X. Du and W. Chen, “Sequential Optimization and Reli- ability Assessment Method for Efficient Probabilistic De- sign,” Journal of Mechanical Design, Vol. 126, No. 2, 2004, pp. 225-233. doi:10.1115/1.1649968
[6]	D. P. Townsend, “Dudley’s Gear Handbook,” McGraw- Hill, New York, 1992.
[7]	A. Kawalec, J. Wiktor and D. Ceglarek, “Comparative Analysis of Tooth-Root Strength Using ISO and AGMA Standards in Spur and Helical Gears with FEM-Based Verification,” Journal of Mechanical Design, Vol. 128, No. 3, 2006, pp. 1141-1158. doi:10.1115/1.2214735
[8]	A. L. Kapelevich and T. M. McNamara, “Direct Gear Design for Automotive Applications,” SAE World Con- gress & Exhibition, Detroit, 2005.
[9]	S. Xiaogen and D. R. Houser, “Characteristics of Tro- choids and Their Application to Determining Gear Teeth Fillet Shapes,” Journal of Mechanism and Machine Theory, Vol. 35, No. 2, 2000, pp. 291-304. doi:10.1016/S0094-114X(99)00004-X
[10]	V. B. Math and S. Chand, “An Approach to the Determi- nation of Spur Gear Tooth Root Fillet,” Journal of Mechanical Design, Vol. 126, No. 2, 2004, pp. 336-340. doi:10.1115/1.1666891
[11]	J. Brauer, “Analytical Geometry of Straight Conical Invo- lute Gears,” Journal of Mechanism and Machine Theory, Vol. 37, No. 1, 2002, pp. 127-141. doi:10.1016/S0094-114X(01)00062-3
[12]	M. Savage, K. L. Rubadeux and H. H. Coe, “Bending Strength Model for Internal Spur Gear Teeth,” NASA Lewis Research Center, Cleveland, 1995.
[13]	AGMA 930-A05, “Calculated Bending Load Capacity of Powder Metallurgy (P/M) External Spur Gears,” American Gear Manufacturers Association, Alexandria, 2005.
[14]	AGMA Information Sheet 908-B89, “Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,” American Gear Manufacturers Association, Alexandria, 1989.
[15]	K. Stoker, A. Chaudhuri and N. H. Kim, “Safety of Spur Gear Design under Non-Ideal Conditions with Uncertainty,” Proceedings of the ASME 2010 IDETC/CIE, Montreal, 15-18 August 2010, pp. 1-11.
[16]	T. J. Dolan and E. L. Broghame, “A Photoelastic Study of Stresses in Gear Tooth Fillets,” University of Illinois Engineering Experiment Station Bulletin 335, 1942.
[17]	E. S. Aziz and C. Chassapis, “Knowledge-Based Geome- try Generation for Spur and Helical Gears,” Concurrent Engineering: Research & Applications (CERA) Journal, Vol. 10, No. 3, 2002, pp. 251-261.
[18]	E. S. Aziz and C. Chassapis, “An Intelligent Design Sys- tem for Agile Design and Manufacturing of Mechanical Transmission Systems,” The 9th International ASME Power Transmission and Gearing Conference, Chicago, 2-6 September 2003.
[19]	E. S. Aziz and C. Chassapis, “A Decision-Making Frame- work Model for Design and Manufacturing of Mechanical Transmission System Development,” Engineering with Computers Journal, Vol. 21, No. 2, 2005, pp. 164- 176. doi:10.1007/s00366-005-0320-z
[20]	B. Bertsche, “Reliability in Automotive and Mechanical Engineering: Determination of Component and System Reliability,” VDI-Buch, Springer-Verlag, Berlin, 2008.
[21]	R. C. Kuczera and Z. P. Mourelatos, “On Estimating the Reliability of Multiple Failure Region Problems Using Ap- proximate Metamodels,” Journal of Mechanical Design, Vol. 131, No. 12, 2009, pp. 1-11. doi:10.1115/1.4000326
[22]	E. G. Haugen, “Probabilistic Mechanical Design,” John Wiley and Sons, New York, 1980.
[23]	P. Martin, “A Review of Mechanical Reliability,” Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, Vol. 212, No. 4, 1998, pp. 281-287. doi:10.1243/0954408981529484