Modal and Harmonic Response Analysis of a Spur Gear System for Natural Frequency Prediction and Resonance Avoidance

Rajendra Wasnik; Manish Joshi; Suraj Prasad

Modal and Harmonic Response Analysis of a Spur Gear System for Natural Frequency Prediction and Resonance Avoidance

Author(s)	Rajendra Wasnik, Prof. Dr. Manish Joshi, Prof. Dr. Suraj Prasad
Country	India
Abstract	Because of their simplicity of geometry, high mechanical efficiency and fixed velocity ratio, spur gear transmissions are used in a wide variety of applications including power-train, machine-tool, robotics, compressor and material-handling applications. The principal disadvantage is a periodic excitation from the gear mesh which can be the same as one of the natural frequencies of the structure. In such cases, the dynamic displacement, stress at the root of the teeth, bearing load and acoustic emission may exceed significantly even if the static design seems safe. In this paper, two analytical methods, namely modal and harmonic response analysis, are discussed for the single-stage involute spur gear pair and presented in an IEEE format. The aim is to find natural frequencies of the system, to define the amplitude of the displacement response to the harmonic mesh excitation and to define the speed map for practical resonance avoidance. The data set was created with a defined gear geometry with the steel material properties, the extraction of the modes and with a harmonic frequency sweep from 100 to 1200 Hz for torque cases of 20, 40, and 60 N-m. Ten modes were found, the first of which was the dominant torsional mesh mode at 828 Hz. The relation between the mesh frequency and rpm, fmesh = Zp n/60, indicated that this mode is excited at about 2484 rpm with a 20-tooth pinion. In the low frequency region the harmonic response was enhanced from less than 2 um, to 37.21 um, close to resonance at 60 N-m. A statistical comparison of the near-resonance normalized response with the off-resonance response was performed and was found to be significantly higher (t = 7.86, p < 0.001). For continuous operation the study suggests that it is advisable to avoid the range of 2250-2750 rpm unless the design is retuned to the range by stiffness modification, damping addition or profile optimization. Academic use of the paper involves tables, figures, primary data and 60 IEEE references that are linked to the DOI.
Keywords	Spur gear, modal analysis, harmonic response, finite element analysis, natural frequency, resonance, mesh frequency, vibration, dynamic amplification.
Discipline	Engineering
Published In	Volume 4, Issue 5, September-October 2026
Published On	2026-10-12

View / Download Full-text Research PDF File

About AIJMR Fees & Payment Current Issue Publication Archive	Submit Research Paper Track Submission Status Publication Guidelines Publication Ethics Peer Review & Plagiarism	Join as a Reviewer Editors & Reviewers Reviewer Referral Program Get Reviewer Membership Certi.	Website/Journal Policies Usage Policy Content Policies Privacy Policy

Contact Us		+91-9687-828-838	editor@aijmr.com

Advanced International Journal of Multidisciplinary Research

An Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

Modal and Harmonic Response Analysis of a Spur Gear System for Natural Frequency Prediction and Resonance Avoidance

Share this