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Improving functional performance characteristics of spur gears through flank modifications by non-contact advanced finishing process

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This paper describes reduction in noise, vibrations, total and tooth-to-tooth, and longwave transmission errors, total and tooth-to-tooth composite errors, and radial runout of spur gears by imparting them flank modifications and their combinations by a non-contact advanced finishing process referred to as pulsed electrolytic dissolution. Eight spur gears were modified using innovatively developed 5 cathode gears and apparatus by imparting them 5 flank modifications (i.e. tip relief, root relief, end relief, profile crowning, lead crowning) individually and their 4 selected combinations. Vibrations at all rotational speeds and noise at 900 and 1200 rpm are reduced for all modified spur gears at all the values of applied loads. End relieved spur gear showed maximum reductions in noise and vibrations by 5 dBA and 3.77 m/s2 respectively for 1200 rpm speed. Reduction amount in noise and vibrations of modified gears increase with rotary speed. Lead crowned gear showed maximum reductions of 146 µm in total transmission error, 109 µm in total composite error, and 102 µm in radial runout. End relieved gear showed maximum reductions of 37 µm in tooth-to-tooth and 139 µm longwave transmission errors. Tip relieved, and tip and root relieved gear showed maximum reduction of 121 µm in tooth-to-tooth composite error. This work proves that the developed non-contact process can very effectively impart different flank modifications individually and their combinations to spur gears without any twist error. Lead crowning, end relieving, tip relieving, and tip and root relieving are main flank modifications that significantly improve functional performance characteristics of spur gears. It will result in their enhanced operating performance and service life, which will help their manufacturers and end-users.

Graphical Abstract


  • Non-contact process developed to impart 5 flank modifications and their combinations to spur gears.

  • Study on decrease in total, tooth-to-tooth, and longwave transmission error by single flank roll test.

  • Reduction study in total and tooth-to-tooth composite errors, radial runout, noise and vibrations.

  • All flank modifications of spur gears improved their functional performance characteristics.

  • Lead crowned and tip+root relieved gears yielded max reduction in double flank testing parameters.

  • End relieved gear gave max reduction in noise and vibrations and single flank testing parameters.

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\({{\varvec{F}}}_{{\varvec{i}}}^{\mathbf{^{\prime}}}\) :

Total transmission error (µm)

\({{\varvec{f}}}_{{\varvec{i}}}^{\mathbf{^{\prime}}}\) :

Tooth-to-tooth transmission error (µm)

\({{\varvec{F}}}_{{\varvec{l}}}^{\mathbf{^{\prime}}}\) :

Longwave tangential composite error (µm)

\({{\varvec{F}}}_{{\varvec{i}}}^{"}\) :

Total composite error (µm)

\({{\varvec{f}}}_{{\varvec{i}}}^{"}\) :

Tooth-to-tooth composite error (µm)

\({{\varvec{F}}}_{{\varvec{r}}{\varvec{f}}}^{\mathbf{^{\prime}}}\) :

Radial runout determined from double flank roll testing (µm)

r wp :

Pitch circle diameter of workpiece gear (mm)

Z m :

Number of teeth in master gear

Z w :

Number of teeth in workpiece gear

θ m :

Angle rotated by the master gear (radians)

θ w :

Angle rotated by the workpiece gear (radians)

ΔNGi :

Change in noise level for ith modified gear with respect to unmodified gear (dBA)

ΔVGi :

Change in vibrations for ith modified gear with respect to unmodified gear (m/s2)


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The authors acknowledge DST-FIST Center of Excellence in Gear Engineering at IIT Indore and other labs for providing the research facilities for the present work. The first author wishes to thank the Department of Science and Technology (DST), Govt. of India, for funding him as DST-INSPIRE Research Fellow to pursue this research work.

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All authors contributed to the study conception and design. Planning design and conduct of experiments, data collection, and analysis were performed by Vivek Rana. The first draft of the manuscript was written by Vivek Rana. Prof. Neelesh Kumar Jain and Dr. Sunil Pathak commented on the previous versions of the manuscript. All authors approved the final manuscript.

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Correspondence to Neelesh Kumar Jain.

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Table 5

Table 5 S1ound pressure level for unmodified and modified spur gears for different rotational speed and applied load

Table 6

Table 6 RMS values of vibrations for unmodified and modified spur gear for different rotational speed and applied load

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Rana, V., Jain, N.K. & Pathak, S. Improving functional performance characteristics of spur gears through flank modifications by non-contact advanced finishing process. Int J Adv Manuf Technol 124, 1787–1811 (2023).

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