Instantaneous angular speed monitoring of gearboxes under non-cyclic stationary load conditions

Abstract

Recent developments in the condition monitoring and asset management market have led to the commercialisation of online vibration-monitoring systems. These systems are primarily utilised to monitor large mineral mining equipment such as draglines, continuous miners and hydraulic shovels. Online monitoring systems make diagnostic information continuously available for asset management, production outsourcing and maintenance alliances with equipment manufacturers. However, most online vibration-monitoring systems are based on conventional vibration-monitoring technologies, which are prone to giving false equipment deterioration warnings on gears that operate under fluctuating load conditions. A simplified mathematical model of a gear system was developed to illustrate the feasibility of monitoring the instantaneous angular speed (IAS) as a means of monitoring the condition of gears that are subjected to fluctuating load conditions. A distinction is made between cyclic stationary load modulation and non-cyclic stationary load modulation. It is shown that rotation domain averaging will suppress the modulation caused by non-cyclic stationary load conditions but will not suppress the modulation caused by cyclic stationary load conditions. An experimental investigation on a test rig indicated that the IAS of a gear shaft could be monitored with a conventional shaft encoder to indicate a deteriorating gear fault condition.

Introduction

Conventional vibration-monitoring techniques are based on the assumption that changes in the measured structural response are caused by deterioration in the condition of the gearbox. However, this assumption is not valid under fluctuating load conditions since the fluctuating load will modulate the amplitude of the measured vibration signal and cause a change in the rotational speed of the system. The change in system speed results in a frequency modulation of the gear mesh signal.

The development of online gear vibration-monitoring systems therefore requires signal-processing procedures that compensate for the fluctuation in the shaft speed as well as the amplitude modulation caused by the varying load. The issue of fluctuating load conditions has generally been dealt with by enforcing constant load conditions on gearboxes during vibration measurements, through free rotational tests. However the online monitoring of large gearboxes under free rotational conditions contradicts the true objective of online vibration monitoring to monitor the equipment continuously under its operational conditions.

The influence of varying load conditions on gear vibration-monitoring signals has been described by authors such as Randall [1], Stander and Heyns [2]. Baydar and Ball [3] indicate that spectral analysis cannot track the degradation in the condition of a gear under different constant load conditions. They employed the Instantaneous Power Spectrum to detect local faults on the teeth of a gear under different constant load conditions.

Order tracking or order domain analysis traditionally deals with frequency modulation or the spectral smearing caused by the change in the rotational speed of rotating equipment. According to Fyfe and Munck [4] as well as Bossley et al. [5] order tracking methodologies are grouped into two main categories. The traditional hardware implementation entails the sampling of the vibration signal by adapting the sampling rate proportionally to a tachometer signal. The approach however cannot deal with rapidly changing shaft speeds. The computed order tracking (COT) method records the data at a constant sampling frequency or asynchronously, using conventional hardware. Once the data have been captured, it is interpolated to constant degrees of rotation based on a tachometer signal.

Stander and Heyns [6], [7] combined COT and the time-synchronous averaging or time domain averaging (TDA) developed by Braun and Seth [8], [9] and referred to the implementation as rotation domain averaging (RDA). The approach combines the properties of order tracking to avoid spectral smearing and the ability of TDA to filter out the vibration, which is non-synchronous with the rotation of the shaft. An experimental investigation on a gearbox test rig was conducted, which was able to apply fluctuating loads on a gearbox. The RDA procedure was applied to the measured data as well as a load demodulation normalisation (LDN) procedure, which were developed to suppress the amplitude modulation effect caused by the fluctuating load.

The monitoring of rotating equipment by utilising the instantaneous angular speed (IAS) has recently attracted greater interest. Yang et al. [10] utilised the IAS to detect fault conditions on a diesel engine. Sasi et al. [11] implemented the IAS to monitor the condition of electric motors.

A simplified mathematical model was consequently developed to determine whether the IAS of a shaft fitted with a gear would vary as the teeth meshed in and out of the gear mesh, and whether it could be used for diagnostic purposes under fluctuating load conditions. The model was based on the gear system modelling methodologies of Bartelmus [12] and Howard et al. [13]. Model simulations indicate that the IAS varies as the gear teeth mesh in and out of the gear mesh and that a fault condition in the form of reduced meshing stiffness can be detected by utilising the IAS.

The IAS is measured in order to compensate for the fluctuation in speed caused by the varying load conditions. Vibration signal is conventionally measured on gearbox casings for monitoring purposes but the IAS signal can be used as a substitute because the signal can reflect changes in the gear meshing stiffness for monitoring purposes. Gear monitoring measurements can therefore be taken with one less analogue-to-digital channel so as to indicate the deterioration in gear condition under fluctuating load conditions.

A distinction between cyclic stationary load conditions and non-cyclic stationary load conditions was proposed. It was found that non-cyclic stationary load modulation could be averaged out with RDA.

A test rig was built to apply non-cyclic stationary load conditions to a test gearbox. Measurements were taken with an accelerometer and a shaft encoder for three different levels of induced flank wear on the gear wheel in order to validate the postulates.