Statistical Analysis for Transmission Error of Gear System with Mechanical and Thermal Deformation Uncertainties
Source abstract
Abstract
We establish a robust algorithm to analyze the influence of system uncertainties on the transmission error of a spur gear pair under 2D simplification. The algorithm provides a way of generating smooth cutter profiles with machining uncertainties and measuring the thermal deformation through the uncertainties in material properties. Then, it produces realizations of gear tooth profiles based on the analytical method for accuracy and computational efficiency. Numerical investigations show the statistical analysis on the tooth contact analysis by comparing steel and plastic gears. It is worthwhile remarking that the plastic gear is susceptible to the geometric error caused by thermal deformation. Moreover, although the impact of thermal deformation on steel gear may seem slim, it can have a noticeable influence when it exists with mechanical uncertainties together.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Gear and Bearing Dynamics Analysis · Advanced machining processes and optimization · Advanced Measurement and Metrology Techniques
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Robotics and Mechatronics, Korea Institute of Machinery and Materials, 156, Gajeongbuk-Ro, Yuseong-gu, Daejeon 34103, Korea
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309-429, USA
Department of Smart Industrial Machine Technologies, Korea Institute of Machinery and Materials, 156, Gajeongbuk-Ro, Yuseong-gu, Daejeon 34103, Korea
Department of Mechanical Engineering (Integrated Engineering), Kyung Hee University 1732, Deogyeong-daero, Giheung-gu, Yongin-si 17104, Gyeonggi-do, Korea
Funding
Ministry of Trade, Industry and Energy
References (38)
Show source-provided references
1. Krawiec, P., Walus, K., Warguła, Ł., and Adamiec, J. (2017, January 5–8). Wear evaluation of elements of V-belt transmission with the application of optical microscope. Proceedings of the MATEC Web of Conferences Machine Modelling and Simulations, Sklené Teplice, Slovak Republic.10.1051/matecconf/201815701009 ↗
2. Konczak, M., Kukla, M., Warguła, Ł., and Talaska, K. (2019, January 21–23). Determination of the vibration emission level for a chipper with combustion engine. Proceedings of the IOP Conference Series: Materials Science and Engineering, Kazimierz Dolny, Poland.
3. Radial and tangential error analysis of double-flank gear measurement10.1016/j.precisioneng.2017.10.011 ↗
4. Calibration and uncertainty evaluation of single pitch deviation by multiple-measurement technique10.1016/j.precisioneng.2009.05.009 ↗
5. Krawiec, P., Warguła, Ł., Walus, K., and Adamiec, J. (2018, January 4–7). Wear evaluation study of the multiple grooved pulleys with optical method. Proceedings of the MATEC Web of Conferences XXIII Polish-Slovak Scientific Conference on Machine Modelling and Simulations, Rydzyna, Poland.10.1051/matecconf/201925401004 ↗
6. Krawiec, P., Domek, G., Warguła, Ł., Walus, K., and Adamiec, J. (2018, January 5–8). The application of the optical system ATOS II for rapid prototyping methods of non-classical models of cogbelt pulleys. Proceedings of the MATEC Web of Conference, Machine Modelling and Simulations, Sklené Teplice, Slovak Republic.10.1051/matecconf/201815701010 ↗
7. A proposal of measurement methodology and assessment of manufacturing methods of nontypical cog belt pulleys10.1016/j.measurement.2018.09.039 ↗
8. Krawiec, P., Czarnecka-Komorowska, D., Warguła, Ł., and Wojciechowski, S. (2021). Geometric Specification of Non-Circular Pulleys Made with Various Additive Manufacturing Techniques. Materials, 14.10.3390/ma14071682 ↗
9. Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears10.1016/j.mechmachtheory.2006.06.002 ↗
10. Analytical method for coupled transmission error of helical gear system with machining errors, assembly errors and tooth modifications10.1016/j.ymssp.2017.01.005 ↗
11. A model order reduction method for the simulation of gear contacts based on Arbitrary Lagrangian Eulerian formulation10.1016/j.cma.2018.03.039 ↗
12. Kinematic and geometric models of gear drives10.1115/1.2826926 ↗
13. Computerized simulation of meshing and contact of enveloping gear tooth surfaces10.1016/0045-7825(93)90054-2 ↗
14. Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness10.1016/j.euromechsol.2008.07.007 ↗
15. Improved analytical calculation model of spur gear mesh excitations with tooth profile deviations10.1016/j.mechmachtheory.2020.103838 ↗
16. Study on 3-D modification for reducing vibration of helical gear based on TCA technology, LTCA technology and system dynamics10.1016/j.ymssp.2020.106991 ↗
17. A new experimental approach for measuring thermal behaviour in the case of nylon 6/6 cylindrical gears10.1016/j.polymertesting.2010.09.002 ↗
18. Polymer gear surface thermal wear and its performance prediction10.1016/j.triboint.2009.07.006 ↗
19. Krawiec, P., Różański, L., Czarnecka-Komorowska, D., and Warguła1, Ł. (2020). Evaluation of the Thermal Stability and Surface Characteristics of Thermoplastic Polyurethane V-Belt. Materials, 13.10.3390/ma13071502 ↗
20. Krawiec, P., Warguła, Ł., and Różański, L. (2020, January 26–27). Diagnostics of the Thermal Condition of the Cable Gear Used in the Drive of a Wood Chipper. Proceedings of the IOP Conference Series: Materials Science and Engineering, Lviv, Ukraine.10.1088/1757-899X/1016/1/012013 ↗
21. Kashyap, S., Houser, D., Smith, Z., Selvaraj, S., Casella, J., and Bradway, J. (2021, January 28–31). Methods of describing plastic gear geometry after a temperature change with application to the prediction of gear load distribution. Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Washington, DC, USA.10.1115/DETC2011-47501 ↗
22. Geometric interference in cylindrical worm gear drives using oversized hob to cut worm gears10.1016/j.mechmachtheory.2016.02.002 ↗
23. Study of a harmonic drive with involute profile flexspline by two-dimensional finite element analysis10.1108/EC-03-2017-0086 ↗
24. Litvin, F.L., and Fuentes, A. (2004). Gear Geometry and Applied Theory, Cambridge University Press.10.1017/CBO9780511547126 ↗
25. Historical development of the Newton–Raphson method10.1137/1037125 ↗
26. A Newton–Raphson method for the solution of systems of equations10.1016/0022-247X(66)90115-6 ↗
27. ISO 1328-1 (2021, June 01). Cylindrical Gears—ISO System of Flank Tolerance Classification Part 1: Definitions and Allowable Values of Deviations Relevant to Flanks of Gear Teeth. Available online: https://www.iso.org/obp/ui/#iso:std:iso:1328:-1:ed-2:v1:en.
28. Analysis of thermal characteristic of spur/helical gear transmission10.1115/1.4041597 ↗
29. (2021, June 01). Abaqus Manual. Available online: http://dsk.ippt.pan.pl/docs/abaqus/v6.13/books/usi/default.htm.
30. Interval Monte Carlo methods for structural reliability10.1016/j.strusafe.2010.01.001 ↗
31. Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method10.1016/j.ymssp.2012.03.001 ↗
32. Evaluating a task-specific measurement uncertainty for gear measuring instruments via Monte Carlo simulation10.1016/j.precisioneng.2016.01.001 ↗
33. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems10.1016/S0951-8320(03)00058-9 ↗
34. Large sample properties of simulations using Latin hypercube sampling10.1080/00401706.1987.10488205 ↗
35. Weber, C. (1949). The Deformation of Loaded Gears and the Effect on Their Load-Carrying Capacity, British Department of Scientific and Industrial Research. Report No. 3.
36. Muskhelishvili, N.L. (1977). Some Basic Problems of the Mathematical Theory of Elasticity, Springer.10.1007/978-94-017-3034-1 ↗
37. Contribution of gear body to tooth deflections—A new bidimensional analytical formula10.1115/1.1758252 ↗
38. A rotary model for spur gear dynamics10.1115/1.3260759 ↗