Experimental techniques for the measurement of gear mesh stiffness

Abstract

Gearboxes are used for transmitting power in many industrial applications. Gearbox condition monitoring using vibration analysis is most commonly used technique for gear fault detection. Dynamic modeling of gearbox is done to predict the vibration. Mesh stiffness of gear pair is the main cause of gearbox vibration. A crack in the tooth of gear reduces the mesh stiffness. Researchers are evaluating the mesh stiffness of healthy and faulty gears by different techniques and modifying the existing techniques for the purpose of vibration based fault detection of the gearboxes. Generally, the mesh stiffness is evaluated statically for full mesh cycle and it is used for vibration analysis of the gearboxes. Mostly, analytical methods are being used to calculate the mesh stiffness. Very less work has been reported on experimental measurement of mesh stiffness. In this thesis, five experimental methods viz photoelasticity technique, strain gauge technique, laser displacement sensor technique, digital image correlation technique and experimental modal analysis technique have been proposed to measure the mesh stiffness of the gear pairs. The photoelasticity technique has been used for measuring the stress intensity factor (SIF) for cracked gear tooth. Subsequently SIF has been used to evaluate the gear mesh stiffness. The variations in the SIF and mesh stiffness have been quantified with angular displacements of the gears. Photoelasticity experiments have been performed for different crack lengths at the tooth root of the spur gear pair. Experimental results of mesh stiffness variation are compared with one of the analytical method i.e. potential energy method, which is widely used by researchers to calculate gear mesh stiffness. The strain gauge technique has been proposed to measure the gear mesh stiffness of healthy spur gear as well as of cracked spur gear pairs. Calculation of mesh stiffness of healthy and cracked spur gear tooth are based on strain energy and strain energy release rate respectively. The location of strain gauge plays an important role in calculation of strain energy stored in gear tooth. The locations of strain gauge on gear tooth are demonstrated for healthy and cracked gear. The SIF has been evaluated by strain gauge technique for calculating the stiffness of cracked tooth. The effect of crack length on mesh stiffness has been investigated by strain gauge technique and results are compared with the established analytical method. The experimental technique based on laser displacement sensor has been proposed to measure the mesh stiffness. In this technique, the deflection of the spur gear tooth is measured along the line of action by using the laser displacement sensor; consequently, gear mesh stiffness is evaluated. The experiment is also performed on cracked tooth pair to measure the mesh stiffness. For validating the experimental results, finite element method is used to estimate the mesh stiffness. The mesh stiffness evaluated by experiment is found in good agreement with the mesh stiffness evaluated by finite element method. The experimental technique based on digital image correlation (DIC) has been proposed to measure the mesh stiffness. The experiments have been performed on healthy as well as cracked gears. The deflection of the gear tooth has been measured by DIC technique. The deflection of the gear tooth along the line of action of force is used further to evaluate the mesh stiffness. This technique also includes the fillet-foundation deflection in the measurement of the mesh stiffness. The obtained mesh stiffness results have been compared with mesh stiffness obtained by finite element method and analytical method. The technique based on the experimental modal analysis (EMA) has been proposed to measure the mesh stiffness of spur gear pairs. In the EMA, frequency response functions (FRF) have been plotted. The FRF plots are then used to extract the mesh stiffness value of the gear pairs. EMA technique has also been used for measuring the mesh stiffness of cracked gear tooth pairs. The experimental mesh stiffness results are compared with the mesh stiffness results obtained by the analytical method. A comparative study of the above five proposed techniques have been done based on advantages and disadvantages of each technique. This comparative study is helpful in selecting the appropriate technique to evaluate mesh stiffness for given gear pair.