Effect of Variations in the Ring Thickness on the Dynamic Performance of the Bimetal Gears

Bikramjit Singh , Pawan Kumar , S. P. Harsha

International Journal of Mechanical System Dynamics ›› 2026, Vol. 6 ›› Issue (1) : 86 -105.

PDF (7005KB)
International Journal of Mechanical System Dynamics ›› 2026, Vol. 6 ›› Issue (1) :86 -105. DOI: 10.1002/msd2.70035
RESEARCH ARTICLE
Effect of Variations in the Ring Thickness on the Dynamic Performance of the Bimetal Gears
Author information +
History +
PDF (7005KB)

Abstract

This study used a six-degrees-of-freedom dynamic model to analyze the dynamic response of bimetal spur gears. Aluminum alloy forms the core of the bimetal gears, and a uniform-thickness steel ring surrounds the teeth. Gear mesh stiffness of bimetal gears and the transmission error have been assessed using a numerical approach based on finite element contact analysis. The system steady-state dynamic response is examined in both the frequency and temporal domains. Results indicate a 25%–48% decrease in gear mesh stiffness alongside a rise of 35%–90% in bimetal-gear static transmission error with a weight reduction of 30%–55% compared with an identical steel-gear pair for 2–9 mm ring thickness. Bimetal gears show a reduction of nearly 10%–12% in dynamic factor and 4%–15% in peak-to-peak extreme displacement amplitude compared with steel gears.

Keywords

bimetal gear / dynamic factor / dynamic response analysis / gear mesh stiffness / transmission error

Cite this article

Download citation ▾
Bikramjit Singh, Pawan Kumar, S. P. Harsha. Effect of Variations in the Ring Thickness on the Dynamic Performance of the Bimetal Gears. International Journal of Mechanical System Dynamics, 2026, 6 (1) : 86-105 DOI:10.1002/msd2.70035

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

D. Jelaska, Gears and Gear Drives (John Wiley & Sons, 2012).

[2]

D. W. Dudley, Handbook of Practical Gear Design & Manufacture, 2nd ed. (CRC Press, Taylor & Francis Group, 2012).

[3]

L. Chang, G. Liu, and L. Wu, “A Robust Model for Determining the Mesh Stiffness of Cylindrical Gears,” Mechanism and Machine Theory 87, no. March (2015): 93–114, https://doi.org/10.1016/j.mechmachtheory.2014.11.019.

[4]

S. Li, “Gear Contact Model and Loaded Tooth Contact Analysis of a Three-Dimensional, Thin-Rimmed Gear,” Journal of Mechanical Design 124, no. 3 (2002): 511–517, https://doi.org/10.1115/1.1485290.

[5]

B. Guilbert, P. Velex, and P. Cutuli, “Quasi-Static and Dynamic Analyses of Thin-Webbed High-Speed Gears: Centrifugal Effect Influence,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 21–22 (2019): 7282–7291, https://doi.org/10.1177/0954406219855411.

[6]

A. Toso, F. Van Wermeskerken, N. Cappellini, and G. Heirman, “On the Effect of Lightweight Gear Blank Topology on Transmission Dynamics,” Proceedings of the ASME Design Engineering Technical Conference 10 (2015): 1–7, https://doi.org/10.1115/DETC201547646.

[7]

R. F. Handschuh, K. E. Laberge, S. Deluca, and R. Pelagalli, Vibration and Operational Characteristics of a Composite-Steel (Hybrid) Gear, NASA Technical Report NASA/TM-2014-216646 (2014).

[8]

R. F. Handschuh, G. D. Roberts, R. R. Sinnamon, D. B. Stringer, B. D. Dykas, and L. W. Kohlman, Hybrid Gear Preliminary Results—Application of Composites to Dynamic Mechanical Components, NASA Technical Report NASA/TM—2012-217630 (2012).

[9]

K. E. LaBerge, R. F. Handschuh, G. Roberts, and S. Thorp, “Performance Investigation of a Full-Scale Hybrid Composite Bull Gear,” Annual Forum Proceedings—AHS International 3 (2016): 2591–2597.

[10]

T. G. Yilmaz, O. Doğan, and F. Karpat, “A Numerical Investigation on the Hybrid Spur Gears: Stress and Dynamic Analysis,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 1 (2022): 354–369, https://doi.org/10.1177/0954406220982007.

[11]

K. E. LaBerge, J. P. Johnston, R. F. Handschuh, and G. D. Roberts, “Evaluation of a Variable Thickness Hybrid Composite Bull Gear,” AHS International 74th Annual Forum & Technology Display, Phoenix, Arizona (2018).

[12]

A. Karthik Pandian, S. S. Gautam, and S. Senthilvelan, “Experimental and Numerical Investigation of the Bending Fatigue Performance of Symmetric and Asymmetric Polymer Gears,” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 234, no. 6 (2020): 819–834, https://doi.org/10.1177/1464420720909486.

[13]

M. Kodeeswaran, A. Verma, R. Suresh, and S. Senthilvelan, “Effects of Frequency on Hysteretic Heating and Fatigue Life of Unreinforced Injection Molded Polyamide 66 Spur Gears,” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 233, no. 5 (2019): 781–789, https://doi.org/10.1177/1464420717702176.

[14]

A. J. Mertens and S. Senthilvelan, “Durability Enhancement of Polymer Gear Using Compressed Air Cooling,” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 230, no. 2 (2016): 515–525, https://doi.org/10.1177/1464420715581195.

[15]

A. K. Singh, I. Siddhartha, and P. K. Singh, “Polymer Spur Gears Behaviors Under Different Loading Conditions: A Review,” Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 232, no. 2 (2018): 210–228, https://doi.org/10.1177/1350650117711595.

[16]

P. K. Singh, Siddhartha, and A. K. Singh, “An Investigation on the Thermal and Wear Behavior of Polymer Based Spur Gears,” Tribology International 118, no. February (2018): 264–272, https://doi.org/10.1016/j.triboint.2017.10.007.

[17]

A. S. Wadleigh and C. Torrance, “Multi-Metal Composite Gear/Shaft. Patent 5271287,” Yeast 2, no. 19 (1993): 4–6.

[18]

D. J. Politis, J. Lin, T. A. Dean, and D. S. Balint, “An Investigation Into the Forging of Bi-Metal Gears,” Journal of Materials Processing Technology 214, no. 11 (2014): 2248–2260, https://doi.org/10.1016/j.jmatprotec.2014.04.020.

[19]

D. J. Politis, N. J. Politis, J. Lin, T. A. Dean, and D. S. Balint, “An Analysis of the Tooth Stress Distribution of Forged Bi-Metallic Gears,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 1 (2018): 124–139.

[20]

P. Wu, B. Wang, J. Lin, B. Zuo, Z. Li, and J. Zhou, “Investigation on Metal Flow and Forming Load of Bi-Metal Gear Hot Forging Process,” International Journal of Advanced Manufacturing Technology 88, no. 9–12 (2017): 2835–2847, https://doi.org/10.1007/s00170-016-8973-x.

[21]

T. G. Yılmaz, O. Doğan, and F. Karpat, “A Comparative Numerical Study of Forged Bi-Metal Gears: Bending Strength and Dynamic Response,” Mechanism and Machine Theory 141, no. March (2019): 117–135, https://doi.org/10.1016/j.mechmachtheory.2019.07.007.

[22]

B. Singh, R. S. Mulik, and S. P. Harsha, “Static and Vibration Analysis of Functionally Graded Gears,” Mechanics Based Design of Structures and Machines 51, no. 12 (2023b): 6928–6946, https://doi.org/10.1080/15397734.2022.2081176.

[23]

A. Harsha and P. Kumar, “Thermoelectric Elastic Analysis of Bi-Directional Three-Layer Functionally Graded Porous Piezoelectric (FGPP) Plate Resting on Elastic Foundation,” Forces in Mechanics 8, no. August (2022): 100112, https://doi.org/10.1016/j.finmec.2022.100112.

[24]

P. Kumar and S. P. Harsha, “Vibration Response Analysis of Exponential Functionally Graded Piezoelectric (EFGP) Plate Subjected to Thermo-Electro-Mechanical Load,” Composite Structures 267, no. March (2021a): 113901, https://doi.org/10.1016/j.compstruct.2021.113901.

[25]

P. Kumar and S. P. Harsha, “Vibration Response Analysis of PZT-4/PZT-5H Based Functionally Graded Tapered Plate Subjected to Electro-Mechanical Loading,” Mechanics Research Communications 116, no. July (2021b): 103765, https://doi.org/10.1016/j.mechrescom.2021.103765.

[26]

P. Kumar and S. P. Harsha, “Electroelastic Static and Vibration Response Analysis of Sigmoid PZT-5A/Pt-Based Smart Functionally Graded Plate,” International Journal of Structural Stability and Dynamics 22, no. 14 (2022b): 2250155, https://doi.org/10.1142/S0219455422501553.

[27]

P. Kumar and S. P. Harsha, “Static Analysis of Porous Core Functionally Graded Piezoelectric (PCFGP) Sandwich Plate Resting on the Winkler/Pasternak/Kerr Foundation Under Thermo-Electric Effect,” Materials Today Communications 32, no. June (2022c): 103929, https://doi.org/10.1016/j.mtcomm.2022.103929.

[28]

P. Kumar and S. P. Harsha, “Response Analysis of Functionally Graded Piezoelectric Plate Resting on Elastic Foundation Under Thermo-Electro Environment,” Journal of Composite Materials 56, no. 24 (2022d): 3749–3767, https://doi.org/10.1177/00219983221122925.

[29]

P. Kumar and S. P. Harsha, “Static and Vibration Response Analysis of Sigmoid Function-Based Functionally Graded Piezoelectric Non-Uniform Porous Plate,” Journal of Intelligent Material Systems and Structures 33, no. 17 (2022e): 2197–2227, https://doi.org/10.1177/1045389X221077433.

[30]

A. Harsha and P. Kumar, “Impact of the Porosity and Elastic Foundation on Frequency and Buckling Response of Bidirectional Functionally Graded Piezoelectric Porous Plate,” International Journal of Structural Stability and Dynamics 2450077 (2023): 1–35, https://doi.org/10.1142/S0219455424500779.

[31]

P. Kumar and A. Harsha, “Vibration Response Analysis of the Bi-Directional Porous Functionally Graded Piezoelectric (BD-FGP) Plate,” Mechanics Based Design of Structures and Machines 52, no. 1 (2024): 126–151, https://doi.org/10.1080/15397734.2022.2099418.

[32]

P. Kumar and S. P. Harsha, “Dynamic Analysis of Porosity Dependent Functionally Graded Sigmoid Piezoelectric (FGSP) Plate,” Structures 46, no. October (2022a): 1737–1752, https://doi.org/10.1016/j.istruc.2022.11.021.

[33]

P. Kumar and S. P. Harsha, “Vibration Response Analysis of Sigmoidal Functionally Graded Piezoelectric (FGP) Porous Plate Under Thermo-Electric Environment,” Mechanics Based Design of Structures and Machines 51, no. 8 (2023a): 4604–4634, https://doi.org/10.1080/15397734.2021.1971090.

[34]

P. Kumar and S. P. Harsha, “Thermoelectric Nonlinear Vibration and Buckling Analysis of the Smart Porous Core Sandwich Plate (SPCSP) Resting on the Elastic Foundation,” Journal of Intelligent Material Systems and Structures 34, no. 14 (2023b): 1587–1616, https://doi.org/10.1177/1045389X221142085.

[35]

A. Prakash, P. Kumar, V. H. Saran, and S. P. Harsha, “NURBS Based Thermoelastic Behaviour of Thin Functionally Graded Sigmoidal (TFGS) Porous Plate Resting on Variable Winkler's Foundation,” International Journal of Mechanics and Materials in Design 19, no. 4 (2023): 831–860, https://doi.org/10.1007/s10999-023-09654-9.

[36]

W. Bartelmus, “Mathematical Modeling and Computer Simulations as an Aid to Gearbox Diagnostics,” Mechanical Systems and Signal Processing 15, no. 5 (2001): 855–871, https://doi.org/10.1006/mssp.2001.1411.

[37]

H. Nevzat Özgüven and D. R. Houser, “Mathematical Models Used in Gear Dynamics—A Review,” Journal of Sound and Vibration 121, no. 3 (1988): 383–411, https://doi.org/10.1016/S0022-460X(88)80365-1.

[38]

S. Wu, M. J. Zuo, and A. Parey, “Simulation of Spur Gear Dynamics and Estimation of Fault Growth,” Journal of Sound and Vibration 317, no. 3–5 (2008): 608–624, https://doi.org/10.1016/j.jsv.2008.03.038.

[39]

O. D. Mohammed, M. Rantatalo, and J. O. Aidanpää, “Improving Mesh Stiffness Calculation of Cracked Gears for the Purpose of Vibration-Based Fault Analysis,” Engineering Failure Analysis 34, no. March (2013): 235–251, https://doi.org/10.1016/j.engfailanal.2013.08.008.

[40]

O. D. Mohammed, M. Rantatalo, and J. O. Aidanpää, “Dynamic Modelling of a One-Stage Spur Gear System and Vibration-Based Tooth Crack Detection Analysis,” Mechanical Systems and Signal Processing 54–55, no. March (2015): 293–305, https://doi.org/10.1016/j.ymssp.2014.09.001.

[41]

Z. Chen and Y. Shao, “Dynamic Simulation of Spur Gear With Tooth Root Crack Propagating Along Tooth Width and Crack Depth,” Engineering Failure Analysis 18, no. 8 (2011): 2149–2164, https://doi.org/10.1016/j.engfailanal.2011.07.006.

[42]

A. Kahraman and R. Singh, “Non-Linear Dynamics of a Spur Gear Pair,” Journal of Sound and Vibration 142, no. 1 (1990): 49–75, https://doi.org/10.1016/0022-460X(90)90582-K.

[43]

R. Maliha, C. U. gˇ Doǧruer, and H. N. Özgüven, “Nonlinear Dynamic Modeling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions,” Journal of Mechanical Design 126, no. 3 (2004): 534–541, https://doi.org/10.1115/1.1711819.

[44]

J. Wang, R. Li and, and X. Peng, “Survey of Nonlinear Vibration of Gear Transmission Systems,” Applied Mechanics Reviews 56, no. 3 (2003): 309–329, https://doi.org/10.1115/1.1555660.

[45]

B. Singh, R. S. Mulik, and S. P. Harsha, “Dynamic Response Analysis of Functionally Graded Gears,” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 237, no. 1 (2023a): 52–69, https://doi.org/10.1177/14644207221101694.

[46]

H. Ma, R. Song, X. Pang, and B. Wen, “Time-Varying Mesh Stiffness Calculation of Cracked Spur Gears,” Engineering Failure Analysis 44, no. March (2014): 179–194, https://doi.org/10.1016/j.engfailanal.2014.05.018.

[47]

Y. A. Tesfahunegn, F. Rosa, and C. Gorla, “The Effects of the Shape of Tooth Profile Modifications on the Transmission Error, Bending, and Contact Stress of Spur Gears,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 8 (2010): 1749–1758, https://doi.org/10.1243/09544062JMES1844.

[48]

Z. X. Zhang, Z. H. Fong, Y. H. Li, and H. S. Fang, “A Study of the Contact Stress Analysis of Cylindrical Gears Using the Hybrid Finite Element Method,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 1 (2013): 3–18, https://doi.org/10.1177/0954406212444383.

[49]

Z. Galym and C. Spitas, “Analysis of a Misalignment-Insensitive Spur Gear Transmission Using a Rzeppa Joint,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 235, no. 9 (2020): 0954406220950354, https://doi.org/10.1177/0954406220950354.

[50]

Z. Sun, S. Chen, X. Tao, and Z. Hu, “Research on Dynamic Characteristics of Gear System Considering the Influence of Temperature on Material Performance,” Journal of Vibration and Control 28, no. 13–14 (2022): 1792–1803, https://doi.org/10.1177/10775463211002616.

[51]

X. Q. Zheng, J. H. Hui, and H. Q. Lan, “Effect of Gear Body Temperature on the Dynamic Characteristics of Spiral Bevel Gears,” Lubricants 13, no. 2 (2025): 82.

[52]

Y. Benaïcha, J. Perret-Liaudet, J. D. Beley, E. Rigaud, and F. Thouverez, “On a Flexible Multibody Modelling Approach Using FE-Based Contact Formulation for Describing Gear Transmission Error,” Mechanism and Machine Theory 167, no. January (2022): 104505.

[53]

J. Zhan, M. Fard, and R. Jazar, “A Quasi-Static FEM for Estimating Gear Load Capacity,” Measurement 75 (2015): 40–49, https://doi.org/10.1016/j.measurement.2015.07.036.

[54]

Y. Wu, J. Wang, and Q. Han, “Contact Finite Element Method for Dynamic Meshing Characteristics Analysis of Continuous Engaged Gear Drives,” Journal of Mechanical Science and Technology 26, no. 6 (2012): 1671–1685, https://doi.org/10.1007/s12206-012-0416-5.

[55]

M. Autiero, G. Paoli, M. Cirelli, and P. P. Valentini, “The Effect of Different Profile Modifications on the Static and Dynamic Transmission Error of Spur Gears,” Mechanism and Machine Theory 201, no. July (2024): 105752, https://doi.org/10.1016/j.mechmachtheory.2024.105752.

[56]

X. Zheng, W. Luo, Y. Hu, Z. He, and S. Wang, “Study on the Mesh Stiffness and Nonlinear Dynamics Accounting for Centrifugal Effect of High-Speed Spur Gears,” Mechanism and Machine Theory 170, no. August 2021 (2022): 104686, https://doi.org/10.1016/j.mechmachtheory.2021.104686.

[57]

Q. Wang, K. Chen, B. Zhao, H. Ma, and X. Kong, “An Analytical-Finite-Element Method for Calculating Mesh Stiffness of Spur Gear Pairs With Complicated Foundation and Crack,” Engineering Failure Analysis 94, no. August (2018): 339–353, https://doi.org/10.1016/j.engfailanal.2018.08.013.

[58]

E. Hiroaki and S. Nader, “Gearbox Simulation Models With Gear and Bearing Faults,” in Mechanical Engineering, ed. M. Gokcek (CBS Publishers & Distributors, 2012), https://doi.org/10.5772/37687.

[59]

S. Du, R. B. Randall, and D. W. Kelly, “Modelling of Spur Gear Mesh Stiffness and Static Transmission Error,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 212, no. 4 (1998): 287–297, https://doi.org/10.1243/0954406981521222.

[60]

P. K. Meuleman, D. Walton, K. D. Dearn, D. J. Weale, and I. Driessen, “Minimization of Transmission Errors in Highly Loaded Plastic Gear Trains,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 9 (2007): 1117–1129, https://doi.org/10.1243/09544062JMES439.

[61]

J. D. Smith, Gear Noise and Vibration (Marcel Dekker Inc., 2003).

[62]

V. K. Tamminana, A. Kahraman, and S. Vijayakar, “A Study of the Relationship Between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs,” Journal of Mechanical Design 129, no. 1 (2007): 75–84, https://doi.org/10.1115/1.2359470.

RIGHTS & PERMISSIONS

2025 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.

PDF (7005KB)

1

Accesses

0

Citation

Detail

Sections
Recommended

/