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Influence of Geometric Parameters on the Dynamic Performance of Spiral Bevel Gear

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Abstract

Introduction and Background

Spiral bevel gears are ubiquitous in numerous power transmission systems. The exigent demands such as high performance, more strength and less noise in helicopter drives can be met by selecting the optimal geometrical design parameters. However, a comprehensive study on the influences of geometric parameters on the transmission system dynamics is not found in the literature.

Objective

Therefore, in this study, the effects of geometric design parameters such as spiral angle, pressure angle and pitch cone angle on the spiral bevel gear set dynamic characteristics for various boundary conditions are studied.

Method

Firstly, the analytical modelling of coupled lateral-axial–torsional vibrations of the spiral bevel gear set is derived theoretically under few assumptions. Then the emphasis on the effects of geometric parameters on the dynamic characteristics such as critical speeds, coupled mode shapes and unbalance vibration response of the gear pair supported by flexible and rigid boundary conditions are investigated numerically.

Results

Under rigid support conditions, it is observed that there is no remarkable influence of geometric parameters on the critical speeds. However, the unbalance response amplitudes at and around the resonance peaks are notably affected. Whereas the critical speeds and unbalance responses are essentially affected by the variation of axial and torsional stiffness at the supports. Meanwhile, the influence of geometric parameters on the critical speeds corresponding to torsional and axial modes is remarkable for the flexible support conditions. Furthermore, the steady-state response due to combined torsional and unbalance excitations is also studied, and the results show that the geometric parameters influence the axial, lateral and torsional responses.

Conclusion

The results obtained through this study are useful in the design of the spiral bevel gear set.

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Abbreviations

A:

Area of shaft

a, b, c, d:

Parameters determining the geometry of gears

C:

Damping coefficient

D:

Dissipation energy due to damping

E:

Young’s modulus

F:

Forces

fw:

Face width of gear

G:

Shear modulus

J:

Mass moment of inertia of gear

K:

Stiffness coefficient of bearing

KE:

Kinetic energy

L:

Length of shaft element

m:

Mass of gear

N:

Number of teeth on gear

PD:

Pitch diameter of gear

q:

Generalized coordinates

r:

Base radius of gear

T:

Torque

t:

Time

U:

Potential energy

Un:

Unbalance (mass*eccentricity)

x, y:

Lateral coordinates at nodes

z:

Axial coordinates at nodes

α :

Pressure angle of gear

β :

Mid spiral angle of gear

δ :

Pitch cone angle of gear

µ :

Poisson’s ratio

ω :

Running speed

ψ, φ :

Tilting angles at nodes

θ :

Torsional angle at nodes

0 :

Zero matrix

a, b, c, d :

Coefficients of the unbalance response

G :

Gyroscopic matrix

I :

Identity matrix

K :

Stiffness matrix

M :

Mass matrix

U :

Coefficients of the unbalance exciting force

d:

Diametrical direction

p:

Polar direction

1,2,3,4,5,6,7:

Nodes

c :

Cos component

s :

Sin component

a:

Axial direction

b:

Bearing

i:

Nodes

l:

Lateral direction

r1, r2:

Gear 1,2

s1, s2:

Shaft 1 and shaft2

s12, s23, s45, s56, s67:

Shaft elements

t:

Torsional direction

xx, yy:

Uncoupled bearing stiffness

xy, yx:

Coupled bearing stiffness

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Authors and Affiliations

  1. Department of Mechanical Engineering, IIT Madras, Chennai, Tamil Nadu, India

    Gollapudi Anuradha, Rathna Prasad Sagi, Piyush Shakya & A. Seshadri Sekhar

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  1. Gollapudi Anuradha
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  2. Rathna Prasad Sagi
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  3. Piyush Shakya
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  4. A. Seshadri Sekhar
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Correspondence to Piyush Shakya.

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Anuradha, G., Sagi, R.P., Shakya, P. et al. Influence of Geometric Parameters on the Dynamic Performance of Spiral Bevel Gear. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01327-x

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  • DOI: https://doi.org/10.1007/s42417-024-01327-x

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