Abstract
There are ample literature addressing the dynamic analysis for gears. In this paper, some important literature on dynamics of both healthy gears and gears with defects have been reviewed. Dynamic analysis of gears is significant from the condition monitoring point of view. Single degree of freedom dynamic model for spur gears has been detailed first. Dynamic study for worm gear with force analysis has been reported. Also, the effect of defects like crack and spall on dynamic behavior of gears studied by researchers has been included in this review. The study of defect model can be utilized in improving the efficiency of the system and preventing the failures in industries as well.
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Abbreviations
- c1, c2:
-
Damping coefficients of first and second tooth pair in mesh, respectively
- c m :
-
Mesh damping coefficient
- D(t):
-
Instantaneous defect width along the contact line
- e(t):
-
Static transmission error
- e 1, e 2 :
-
Displacement excitations due to gear error
- F 0 :
-
External torque load
- Fx, Fy, Fz:
-
Three orthogonal force components
- F(t):
-
Defect morphology
- G(t):
-
Time-periodic defect excitation generated by tooth shape deviations and errors
- I1, I2:
-
Mass moments of inertia of gear no. 1 and 2, respectively
- Jw, Jg, J4:
-
Moment of inertias of the worm, worm gear, and the flywheel, respectively
- Kw, Kg:
-
Elastic constants of the worm shaft and the worm gear shaft, respectively
- k :
-
Total mesh stiffness of the gear pair
- k 0 :
-
The mesh stiffness per unit contact length
- k1, k2:
-
Stiffness of first and second tooth pair in mesh, respectively
- k a :
-
Axial compressive stiffness
- k m :
-
Mean mesh stiffness of one pair contacted with healthy teeth
- k t :
-
Stiffness of a single tooth
- \( k_{f} \), \( k_{b} \), \( k_{s} \):
-
Fillet-foundation, bending, shear stiffness, respectively
- k i :
-
Mesh stiffness of the ith tooth pair
- k tooth :
-
Total mesh stiffness due to teeth deformation of N tooth pairs
- \( k_{{s\_{\text{crack}}}} \), \( k_{{b\_{\text{crack}}}} \):
-
Shear and bending stiffness of cracked tooth, respectively
- m e :
-
Equivalent mass
- T1, T2:
-
Input and output torques, respectively
- P(η):
-
Defect depth along the contact line
- R1, R2:
-
Base radii of gear
- rw, rg:
-
Pitch radii of the worm’s helical tooth and the worm gear, respectively
- W0:
-
Static load
- Wf, Wn:
-
Friction force, normal force
- ɸ1, ɸ2:
-
Angular displacements of gear number 1 and 2, respectively
- ɸ’, ɸ”:
-
First- and second-order derivatives of ɸ, respectively
- θ1, θ2, θ3, θ4:
-
The rotation angles of worm shaft, worm’s body, worm- gear body, and flywheel, respectively
- \( \phi_{n} \) :
-
The pressure angle
- λ :
-
The worm’s lead angle
- λ1, λ2:
-
Correction coefficients of the fillet-foundation stiffness for driving and driven gears, respectively
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Gautam, S., Khanam, S., Tandon, N. (2021). Dynamic Analysis for Healthy and Defective Gears: A Review. In: Singh, M., Rafat, Y. (eds) Recent Developments in Acoustics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5776-7_18
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DOI: https://doi.org/10.1007/978-981-15-5776-7_18
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