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Optimisation of polymer spur gear pairs with experimental validation

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Abstract

This study aims to present a procedure for optimisation of polymer gear pairs, along with the rough design guidelines. Multi-objective optimisation of polymer spur gear pairs was carried out. The gear pair module, face width, pinion number of teeth, and profile shift coefficients of both gears served as design variables. Two objective functions were used to rate the designs—volume and frictional power losses. Compared with well-researched steel gear pair optimisation, additional boundary conditions were necessary: tooth flank and root temperatures, abrasion wear, and tooth addendum displacement. Two arbitrary datasets were used as examples, each made of polyoxymethylene. For each of the sets, a Pareto optimal solution was manufactured to enable the experimental validation. For this purpose, an open-circuit experimental rig was designed. As no literature was found on the polymer gear pair optimisation, results were compared with ones for steel gear pairs. The results have shown that changes in macro-geometry affect polymer gears significantly different. The lower volume pairs made of polymer had greater face widths, while the opposite was observed in steel gears. The differences between the analytical and experimental results were up to 21%.

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Abbreviations

α w :

Working transverse pressure angle

b :

Face width

d a1 :

Tip diameter (pinion)

d a2 :

Tip diameter (wheel)

ED :

Relative duty ratio

f 1 :

First objective function (volume)

f 2 :

Second objective function (frictional power losses)

i :

Transmission ratio

F Nmax :

Maximum normal load acting upon the gear flank

F t :

Tangential load

K A :

Application factor

K F :

Dynamic factor (root)

K H :

Dynamic factor (flank)

λ :

Tooth addendum displacement

μ :

Friction coefficient between the meshing gear pairs

m :

Gear module

n 1 :

Rotational speed (pinion)

P loss :

Frictional power losses

P lossB :

Bearing power losses

P lossΣ :

Overall power losses (measured value)

ψ :

Curvature radius at point i on the line of action

R M :

Load sharing ratio

ρ :

Density (steel)

ρ rel :

Radius of relative curvature

T 1 :

Input torque

ϑ Flank :

Tooth flank temperature

ϑ Root :

Tooth root temperature

v s :

Sliding velocity

x :

Design variable vector

x 1 :

Profile shift coefficient (pinion)

x 1max :

Maximal allowable profile shift coefficient (pinion)

x 2 :

Profile shift coefficient (wheel)

w :

Specific load

W m :

Mean linear wear

W P :

Permissible wear

z 1 :

Number of teeth (pinion)

z 2 :

Number of teeth (wheel)

References

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Acknowledgement

The authors would like to thank engineers Petar Koren and Milan Kovačević of KONČAR, Electrical Engineering Institute Inc., for valuable advice and assistance with the experimental measurements.

Funding

The experimental rig was partially financed by the Faculty of Mechanical Engineering and Naval Architecture through the competitive funds for doctoral students. This paper reports on work funded by the Croatian Science Foundation project IP-2018-01-7269: Team Adaptability for Innovation-Oriented Product Development - TAIDE.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10002, Zagreb, Croatia

    Daniel Miler, Matija Hoić, Stanko Škec & Dragan Žeželj

Authors
  1. Daniel Miler
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  2. Matija Hoić
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  3. Stanko Škec
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  4. Dragan Žeželj
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Corresponding author

Correspondence to Daniel Miler.

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Conflict of interest

The authors declare that they have no conflict of interest.

Replication of results

The experimental data and the recording of one test run are provided as the supplemental materials. For the objective functions, boundary conditions, and algorithm properties, please contact the corresponding author.

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Responsible Editor: Mehmet Polat Saka

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Appendix. PlossΣ—t diagrams

Appendix. PlossΣ—t diagrams

Fig. 7
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Miler, D., Hoić, M., Škec, S. et al. Optimisation of polymer spur gear pairs with experimental validation. Struct Multidisc Optim 62, 3271–3285 (2020). https://doi.org/10.1007/s00158-020-02686-1

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  • DOI: https://doi.org/10.1007/s00158-020-02686-1

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