Mathematical modelling and experimental validation of electrostatic sensors for rotational speed measurement

Recent research has demonstrated that electrostatic sensors can be applied to the measurement of rotational speed with excellent repeatability and accuracy under a range of conditions. However, the sensing mechanism and fundamental characteristics of the electrostatic sensors are still largely unknown and hence the design of the sensors is not optimised for rotational speed measurement. This paper presents the mathematical modelling of strip electrostatic sensors for rotational speed measurement and associated experimental studies for the validation of the modelling results. In the modelling, an ideal point charge on the surface of the rotating object is regarded as an impulse input to the sensing system. The fundamental characteristics of the sensor, including spatial sensitivity, spatial filtering length and signal bandwidth, are quantified from the developed model. The effects of the geometric dimensions of the electrode, the distance between the electrode and the rotor surface and the rotational speed being measured on the performance of the sensor are analyzed. A close agreement between the modelling results and experimental measurements has been observed under a range of conditions. Optimal design of the electrostatic sensor for a given rotor size is suggested and discussed in accordance with the modelling and experimental results

Electrostatic Sensors – Their Principles and Applications

Over the past three decades electrostatic sensors have been proposed, developed and utilised for the continuous monitoring and measurement of a range of industrial processes, mechanical systems and clinical environments. Electrostatic sensors enjoy simplicity in structure, cost-effectiveness and suitability for a wide range of installation conditions. They either provide unique solutions to some measurement challenges or offer more cost-effective options to the more established sensors such as those based on acoustic, capacitive, optical and electromagnetic principles. The established or potential applications of electrostatic sensors appear wide ranging, but the underlining sensing principle and resultant system characteristics are very similar. This paper presents a comprehensive review of the electrostatic sensors and sensing systems that have been developed for the measurement and monitoring of a range of process variables and conditions. These include the flow measurement of pneumatically conveyed solids, measurement of particulate emissions, monitoring of fluidised beds, on-line particle sizing, burner flame monitoring, speed and radial vibration measurement of mechanical systems, and condition monitoring of power transmission belts, mechanical wear, and human activities. The fundamental sensing principles together with the advantages and limitations of electrostatic sensors for a given area of applications are also introduced. The technology readiness level for each area of applications is identified and commented. Trends and future development of electrostatic sensors, their signal conditioning electronics, signal processing methods as well as possible new applications are also discussed

Simultaneous Measurement of Belt Speed and Vibration Through Electrostatic Sensing and Data Fusion

Accurate and reliable measurement of belt speed and vibration is of great importance in a range of industries. This paper presents a feasibility study of using an electrostatic sensor array and signal processing algorithms for the simultaneous measurement of belt speed and vibration in an online, continuous manner. The design, implementation, and assessment of an experimental system based on this concept are presented. In comparison with existing techniques, the electrostatic sensing method has the advantages of non-contact and simultaneous measurement, low cost, simple structure, and easy installation. The characteristics of electrostatic sensors are studied through finite-element modeling using a point charge moving in the sensing zone of the electrode. The sensor array is arranged in a 2 × 3 matrix, with the belt running between two rows of three identical sensing elements. The three signals in a row are cross correlated for speed calculation, and the results are then fused to give a final measurement. The vibration modes of the belt are identified by fusing the normalized spectra of vertically paired sensor signals. Experiments conducted on a two-pulley belt-driven rig show that the system can measure the belt speed with a relative error within ±2% over the range 2-10 m/s. More accurate and repeatable speed measurements are achieved for higher belt speeds and a shorter distance between the electrode and the belt. It is found that a stretched belt vibrates at the harmonics of the belt pass frequency and hence agrees the expected vibration characteristics

Radial Vibration Measurement of Rotary Shafts through Electrostatic Sensing and Hilbert-Huang Transform

Radial vibration measurement of rotary shafts plays a significant part in condition monitoring and fault diagnosis of rotating machinery. This paper presents a novel method for radial vibration measurement through electrostatic sensing and HHT (Hilbert-Huang Transform) signal processing. The foundational characteristics of the electrostatic sensor in the vicinity of a drifting shaft are studied through Finite Element Modelling. Experimental tests were conducted on a purpose-built test rig to characterize the operating condition of the rotor at different rotational speeds (400 rpm and 600 rpm). A normal working shaft and an eccentric shaft were tested and the output signals from the electrostatic sensors were analyzed. Through empirical mode decomposition (EMD) on the electrostatic signals, the intrinsic mode functions (IMF) including the vibration information of the shaft are identified and further analyzed in the time-frequency domain. Experimental results suggest that the electrostatic sensing technique in conjunction with HHT provides a simple and cost-effective approach to radial vibration measurement of rotary shafts

Instantaneous Rotational Speed Measurement Using Image Correlation and Periodicity Determination Algorithms

Dynamic and accurate measurement of instantaneous rotational speed is desirable in many industrial processes for both condition monitoring and safety control purposes. This paper presents a novel imaging based system for instantaneous rotational speed measurement. The low-cost imaging device focuses on the side surface of a rotating shaft without the use of a marker, entailing benefits of non-contact measurement, low maintenance and wide applicability. Meanwhile, new periodicity determination methods based on the Chirp-Z transform and parabolic interpolation based auto-correlation algorithm are proposed to process the signal of similarity level reconstructed using an image correlation algorithm. Experimental investigations are conducted on a purpose-built test rig to quantify the effects of the periodicity determination algorithm, frame rate, image resolution, exposure time, illumination conditions, and photographic angle on the accuracy and reliability of the measurement system. Experimental results under steady and transient operating conditions demonstrate that the system is capable of providing measurements of a constant or gradually varying speed with a relative error no greater than ±0.6% over a speed range from 100 to 3000 RPM (Revolutions Per Minute). Under step change conditions the proposed system can achieve valid speed measurement with a maximum error of 1.4%

Time Domain Analysis and Spectral Methods for Determining Rotational Speed of Rotary Machines

Accurate estimation of rotational speed of rotary machines has usually high priority in technical applications. This information should be calculated for many diagnostic algorithms, control or regulation processes. Incorrectly estimated values could occur serious disturbances in the operation of machines. Additional instrumentation often may be obstructed due to lack of space, but the construct of the machine may also affect the accuracy of measurement. In such cases, vibration diagnostic tools can be the disposal of difficulty. Mounting an acceleration sensor onto the outer surface of the measured device is not a major challenge. In most cases using time, frequency or quefrency domain analysis, it is possible to estimate the rotational speed of the analysed rotary machine. The calculated spectra and cepstra can help to determine the rotational speed more easily and more accurate than the time domain methods. This paper presents the comparison of these methods in terms of their usability and rotational speed estimation accuracy. A possible error of traditional optical measurement due to misalignment and benefits of the other methods are illustrated in this article via measured data series of a Brushless DC (BLDC) motor driven system

A review of electrostatic monitoring technology: The state of the art and future research directions

Electrostatic monitoring technology is a useful tool for monitoring and detecting component faults and degradation, which is necessary for system health management. It encompasses three key research areas: sensor technology; signal detection, processing and feature extraction; and verification experimentation. It has received considerable recent attention for condition monitoring due to its ability to provide warning information and non-obstructive measurements on-line. A number of papers in recent years have covered specific aspects of the technology, including sensor design optimization, sensor characteristic analysis, signal de-noising and practical applications of the technology. This paper provides a review of the recent research and of the development of electrostatic monitoring technology, with a primary emphasis on its application for the aero-engine gas path. The paper also presents a summary of some of the current applications of electrostatic monitoring technology in other industries, before concluding with a brief discussion of the current research situation and possible future challenges and research gaps in this field. The aim of this paper is to promote further research into this promising technology by increasing awareness of both the potential benefits of the technology and the current research gaps

Non-Contact Vibration Monitoring of Power Transmission Belts Through Electrostatic Sensing

On-line vibration monitoring plays an important role in the fault diagnosis and prognosis of industrial belt drive systems. This paper presents a novel measurement technique based on electrostatic sensing to monitor the transverse vibration of power transmission belts in an on-line, continuous, and non-contact manner. The measurement system works on the principle that variations in the distance between a strip-shaped electrode and the naturally electrified dielectric belt give rise to a fluctuating current output. The response of the sensor to a belt moving both axially and transversely is numerically calculated through finite-element modeling. Based on the sensing characteristics of the sensor, the transverse velocity of the belt is characterized through the spectral analysis of the sensor signal. Experiments were conducted on a two-pulley belt drive system to verify the validity of the sensing technique. The belt vibration at different axial speeds was measured and analyzed. The results show that the belt vibrates at well-separated modal frequencies that increase with the axial speed. A closer distance between the electrode and the belt makes higher order vibration modes identifiable, but also leads to severer signal distortion that produces higher order harmonics in the signal. On-line vibration monitoring plays an important role in the fault diagnosis and prognosis of industrial belt drive systems. This paper presents a novel measurement technique based on electrostatic sensing to monitor the transverse vibration of power transmission belts in an on-line, continuous, and non-contact manner. The measurement system works on the principle that variations in the distance between a strip-shaped electrode and the naturally electrified dielectric belt give rise to a fluctuating current output. The response of the sensor to a belt moving both axially and transversely is numerically calculated through finite-element modeling. Based on the sensing characteristics of the sensor, the transverse velocity of the belt is characterized through the spectral analysis of the sensor signal. Experiments were conducted on a two-pulley belt drive system to verify the validity of the sensing technique. The belt vibration at different axial speeds was measured and analyzed. The results show that the belt vibrates at well-separated modal frequencies that increase with the axial speed. A closer distance between the electrode and the belt makes higher order vibration modes identifiable, but also leads to severer signal distortion that produces higher order harmonics in the signal

On-line Continuous Measurement of the Operating Deflection Shape of Power Transmission Belts Through Electrostatic Sensing

The measurement of the operating deflection shape (ODS) of power transmission belts is of great importance for the fault diagnosis and prognosis of industrial belt drive systems. This paper presents a novel method based on an electrostatic sensor array to measure the ODS of a belt moving both axially and transversely. Finite element simulations are performed to study the sensing characteristics of a strip-shaped electrode and the results reveal that the transverse velocity determines the sensor signal. Construction of the ODS is achieved in the frequency domain using the ODS frequency response function. Experiments conducted on a purpose-built test rig show that the belt vibrates at resonant frequencies that are well separated and identifiable using a peak picking method. The ODSs for different vibration modes exhibit similar deformation patterns and the axial motion of the belt determines that the ODSs propagate along the belt length, rather than stay fixed in space

An Improved Method for the Processing of Signals Contaminated with Strong Common-Mode Periodic Noise in Correlation Velocity Measurement

Electrostatic sensors have been successfully used for the velocity measurement of pneumatically conveyed particles and the rotational speed measurement. However, the signal from an electrostatic sensor is usually vulnerable and susceptible to contamination in a hostile environment. The acquired original signal may be contaminated by different types of noise that can be within or outside the frequency range of the signal. This paper presents a novel correlation signal processing method to minimise the impact of noise in the signal through a de-noising process and hence improve the performance of correlation-based measurements in general. The method is applied to the rotational speed measurement based on electrostatic sensors in particular. The de-noising process is an essential task in digital signal processing to improve the signal-to-noise ratio before implementing the measurement algorithm. A hybrid de-noising method is proposed to combine a cut-off frequency method to remove the noise components outside the signal bandwidth and a median filter to smooth the signal. Subsequently, the signal is de-noised in the time domain by employing an advanced digital filtering method based on correlation techniques to suppress the noise frequency components mixed with the original signal. The rotational speed measurement system with the proposed technique has proven to be effective in de-noising signals that are buried in noise with which they are correlated. Moreover, the technique is capable of producing more accurate and repeatable measurements with a wider measurement range than the existing system. Experimental results suggest that the relative error of the improved system is mostly within ±0.1% over the speed range of 300 rpm - 3000 rpm and within ±0.2% over the speed range of 40-300 rpm