FIELD OF THE INVENTION

The present invention relates to a transducer for use with a rotary bearing, and more particularly to such a transducer comprising a piezoelectric body and configured to be located intimately to the rotary bearing. BACKGROUND

In a rotating machine, rolling element bearings have a primary role of creating a low friction rotation and carrying the major load of the shaft. Due to cyclic load on the bearing, some imperfections in the normal working condition of bearings can gradually lead to fatigue stress, crack propagation, spalling, corrosion, and failure [1]. Therefore, it is desirable to diagnose bearing incipient fault for maintenance actions prior to reaching a severe damage level which can lead to abrupt failure [2],

A solution to prevent a machine from premature failure is implementing an appropriate condition monitoring technique. So far, vibration analysis and using piezoelectric accelerometers have been the most common technique for condition monitoring of rotating machines. The main problem that arises during the vibration analysis of bearings is the low energy of impacts generated by defects compared with the overall vibration of the system and noises from surrounding components or machines. The reason why fault symptoms have a low energy level is related to the transmission path of the vibration signal. By installing the transducer on the housing, the vibration signal goes through different paths to reach the transducer. A combination of signals from different components, whether healthy or faulty, will lose their energy on the path to reach the transducer due to the structural damping. Consequently, early fault symptoms with low energy become weaker once they reach the transducer [3].

For over three decades, various signal processing techniques have been implemented for fault diagnosis applications, such as singular value decomposition de-noising (SVD) [4] and variational mode decomposition (VMD) [5] for early degradation monitoring. Despite all these advances in signal processing techniques, there have been several efforts to implement or develop embedded sensors in bearings. If the sensor is mounted closer to the bearing, condition monitoring and fault detection are more efficient [6]. These types of bearings are called intelligent or smart bearings. The current trend toward the internet of things (loT), big data processing, and industry 4.0 makes intelligent bearings an undeniable part of future industries [7], The fundamental parts of a smart bearing are an embedded sensor, a battery, or energy harvested to provide a power supply for wireless data transmission [8][9], the receiver module, and a fault detection technique such as artificial intelligence (Al) methods to extract the fault symptoms. A comprehensive review of the latest approaches in Al methods for fault detection is presented in reference [10]. In 1997, Holm-Hansen and Gao [11]— [13] initiated a study about the performance of sensor-integrated ball bearings. In their model, a slot was created on the outer ring of the ball bearing, and a piezoelectric load sensor was embedded inside the slot. The finite element (FE) model and experimental tests confirmed that this integrated sensor could detect ball pass frequency. However, the performance of the sensor for fault diagnosis was not investigated and creating the slot on the outer ring surface can damage the bearing. Several researchers have proposed using displacement probes to monitor the bearings’ dynamic behavior. To illustrate more, Rasolofondraibe et al. [14]— [17] utilized an embedded capacitive probe inside the bearing and housing by machining a slot. Different parameters could be measured from the signal through the outer ring displacement, such as static load and bearing vibration signatures. Besides these technologies, there have been some efforts to use triboelectric nanogenerators to harvest energy from the kinetic energy of a bearing and meanwhile use this technique as a self-powered sensor with different functions [18]. As a few examples of the triboelectric effect in bearings, Meng et al. [19] developed an enclosed bearing-structured self-powered speed sensor by using the triboelectric effect. Han et al. [7] proposed using comb-shaped electrodes on the outer ring of the bearing to detect missing balls and damaged electrodes through the output electricity. In subsequent research, this bearing was tested for localized fault detection, and an accuracy of 92% in fault classification was achieved [20]. However, one of the main drawbacks of triboelectric nanogenerators is the requirement of having two different materials in contact for electrification, which may not be possible in most industrial bearings made of a single material. Other than these methods, sounds and acoustic emission-based approaches have attracted more attention in recent years. For example, in 2020, Nicholas et al. [18] used embedded piezoelectric patches on the cylindrical roller’s outer ring to monitor the radial load and lubricant behavior through the reflected ultrasonic pulses. Even though acoustic emission (AE) methods have been remarkably successful in early fault detection, fault localization, and friction/oil monitoring, but this method is subjected to background noise and is more suitable for electric fault detection rather than mechanical faults [21], A comprehensive review of the latest advances using AE methods for fault diagnosis in induction motors and their bearing is provided in reference [21],

Despite the aforementioned sensors and techniques, several researchers have suggested using optical fiber such as fiber Bragg grating (FBG) strain sensor. In 2019, Alian et al. [6] implemented fiber optic sensors in bearing fault monitoring. According to the results, local measurement of mechanical strain compared with acceleration is less subjected to the surrounding noise, and the signal-to-noise ratio (SNR) of the measured signal was significantly enhanced. They claimed that not only FBG sensors can detect spall-like defects, but also the size of the spall can be detected. Even though FBG sensors are precise strain sensors, their fragile structure and low- frequency bandwidth can be one of the main drawbacks. Besides FBG strain sensors, several authors have proposed using piezoelectric strain sensors or strain gauges. Hou and Wang [22] embedded several strain gauges on the other ring of a cylindrical roller bearing. The geometry of the housing was modified to ease installing sensors and wiring. The bearing load was measured through the finite element (FE) model and experimental tests, which can be used for load monitoring and fatigue life assessment.

Several authors have proposed using piezoelectric sensors for bearing condition monitoring. Piezoelectric materials operate under the piezoelectric effect that generates an electric charge in response to applying a mechanical strain. However, compared with strain gauges, they have several superiorities in monitoring dynamic systems, such as self-powered, sensitivity over a high strain bandwidth, superior SNR, high-frequency noise rejection, and less bulky electronic devices for signal conditioning [23]. Table 1 present the advantages and disadvantages of the most common sensor types. As a few examples, Gama et al. [24], [25] utilized piezoelectric strain sensors for misalignment detection in bearing test systems. Even though piezoelectric materials are not a new discovery but introducing various types and compact shapes into the market with low prices and high capabilities has attracted more attention to these materials. Wang et al. [26] instrumented a piezoelectric/elastic ring inserted in the inner bearing ring to monitor raceways’ wear. Since 2021 , Dou et al. [27] proposed using a piezoelectric strain sensor on the outer raceway of the bearing to measure the oil-film thickness. However, creating a slot on the outer raceway and direct contact of rollers with the sensor is prone to fatigue and subsequent damage or spalling. Russel et al. [28] investigated piezoresistive pressure sensors in the bearing-housing interface to measure load distribution in different clearances and housing fitting loads. In contrast with piezoelectric ceramics, these piezoresistive materials require an external power supply to generate a voltage signal in response to resistance changes.

In the most recent studies in 2022, Nguyen et al. [29] created a smart sensor made of a multilayered thin-film piezoelectric. This sensor was designed for condition monitoring of the bearing, and the effect of temperature on the output of the sensor was investigated. In the previous studies, there are a few works that piezoelectric transducer is used for fault detection, and in most of these studies, the oil thickness and load measurement are the focus. In one of the latest studies, Zhang et al. [8] used an instrumented bearing housing with integrated piezoelectric sheets. This experiment used the harvested energy from the piezoelectric sheets for self-powered and wireless data transmission. In addition, the generated signal was investigated in faulty conditions and fault characteristics were observable in time and frequency domain signals. Their Lead Zirconate Titanates (PZT) transducer is a curved thick sheet that is mounted at the bottom half of the bearing by modifying the bearing housing. Therefore, the major applied load from the shaft to the bearing is transferred to PZT sheet. This causes higher electric power for the energy harvesting and selfpowering the wireless module. However, considering the brittleness of piezoelectric ceramics, this design can lead to high stresses on the transducer in high shaft radial loads and possibly the breakage of the piezoelectric. The transducer is excited by a combination of strain changes by several rollers at the bottom half of the bearing. When there is a local damage, one roller that passes through the damaged area generates a weak fault symptom because all other rollers are not affected by the local damage. The weak fault symptom generated by this PZT sheet is a disadvantage. Last but not least, the majority of previous studies were conducted in a noise and vibration-free laboratory setting. However, a typical work setting of bearing includes noise and vibration from other machines and surrounding components.

SUMMARY OF THE INVENTION

It is an aspect of the invention to provide a compact and small sized piezoelectric transducer to detect local faults in a cylindrical roller bearing. The transducer is embedded inside the bearing housing at the middle which is in direct contact with the bearing outer ring. When rollers are rotating, the generated radial strains in the thickness of the outer ring will induce the transducer. Therefore, a voltage signal proportional to the carried force by rollers is obtained which can be used for condition monitoring. To test the transducer performance, three different tests including simulation and experimental tests are considered. In the first test, the dynamic forces on the transducer are simulated in healthy and faulty conditions to demonstrate the maximum force amplitude compared with the shaft radial load for the durability of the transducer. In the second test, the performance of the transducer for fault detection on the outer ring and rollers is investigated. Both simulation and experimental tests are adopted to investigate the fault detection ability of the transducer. In the third test, artificial background noise and vibration through an air motor are generated to test the performance of the transducer in a noisy setting both at low and high rotational speeds.

According to an aspect of the invention there is provided a transducer for use with a rotary bearing arranged to provide relative rotation between an inner member and an outer member; wherein the rotary bearing has an inner ring encompassing an axis of the bearing and configured to receive the inner member, an outer ring encompassing the inner ring and arranged to be supported by the outer member and a plurality of rotational elements between the inner and outer rings and arranged to provide relative rotation of the inner and outer rings around the axis of the bearing; the transducer comprising: a piezoelectric body comprising piezoelectric material and configured to generate an electrical signal in response to physical deformation thereof, wherein the piezoelectric body has opposite faces lying along a body axis of the piezoelectric body and a periphery of the piezoelectric body encompassing the opposite faces; a pair of electrodes electrically connected to the piezoelectric body and configured to transmit the electrical signal; a force-transmission member in operative mechanical engagement with a first one of the opposite faces of the piezoelectric body, wherein the force-transmission member is disposed along the body axis, wherein the force-transmission member defines an exterior contact surface of the transducer distal to the first opposite face and arranged in mechanical contact with the rotary bearing to receive vibratory motion thereof, wherein the force-transmission member comprises incompressible rigid material so as to transmit force exerted thereon from the vibratory motion of the rotary bearing and to the piezoelectric body, wherein the force-transmission member is substantially electrically nonconductive; electrical insulation arranged around the piezoelectric body and configured to prevent transmission of the electrical signal generated by the piezoelectric body to a proximal electrically conductive body; and a base disposed along the body axis and in opposite relation to the forcetransmission member for covering a second one of the opposite faces of the piezoelectric body, wherein the base is substantially electrically nonconductive.

This provides a transducer for sensing various conditions of a rotary bearing by way of direct contact therewith.

Preferably, the base comprises incompressible rigid material.

Preferably, the transducer is used with a biasing element arranged to bias the transducer towards the rotary bearing to urge the transducer into mechanical contact with the rotary bearing.

In one arrangement, the base is asymmetrically shaped around the body axis.

In one arrangement, the base comprises a circular portion coaxial with the body axis and a projecting portion extending therefrom in a transversely outward direction relative to the body axis.

In one such arrangement, the base is cylindrically shaped about the body axis.

In one arrangement, the exterior contact surface is planar.

In one arrangement, the force-transmission member is cylindrically shaped about the body axis.

In one arrangement, the piezoelectric body is cylindrically shaped about the body axis.

In one arrangement, the force-transmission member is sized and shaped substantially the same as the piezoelectric body.

In one arrangement, the force-transmission member comprises a body of the incompressible rigid material.

In one arrangement, the electrodes cover full surface areas of the opposite faces of the piezoelectric body. In one arrangement, the incompressible rigid material comprises a ceramic material.

In one arrangement, the ceramic material comprises alumina.

In one arrangement, the incompressible rigid material is substantially electrically nonconductive.

According to another aspect of the invention there is provided a rotary assembly comprising: an inner member disposed along a rotational axis of the rotary assembly; an outer member encompassing at least a portion of the inner member and the rotational axis; wherein the inner and outer members are arranged for rotation relative to one another around the rotational axis; a rotary bearing rotatably interconnecting the inner and outer members, wherein the rotary bearing comprises an inner ring receiving the inner member and encompassing a bearing axis of the rotary bearing coaxial with the rotational axis, an outer ring encompassing the inner ring and supported by the outer member and a plurality of rotational elements between the inner and outer rings and arranged to provide relative rotation of the inner and outer rings around the bearing axis; wherein the outer member comprises a bearing receptacle configured to receive the rotary bearing; and a transducer configured to sense vibration of the rotary bearing; and wherein the outer member further includes a transducer receptacle in communication with the bearing receptacle and receiving the transducer therein such that the transducer is disposed in operative mechanical engagement with the rotary bearing to receive the vibration thereof.

This enables the transducer to be less affected by noise.

Preferably, the transducer is in direct contact with the rotary bearing.

Preferably, when the bearing axis is generally horizontally oriented, the transducer receptacle is below the bearing axis.

Preferably, when the bearing axis is substantially horizontally oriented, the transducer receptacle is vertically in-line with the bearing axis.

Preferably, the rotary assembly further includes a biasing element in the transducer receptacle and configured to bias the transducer in a crosswise direction generally towards the bearing axis to urge the transducer into operative mechanical engagement with the rotary bearing.

Preferably, when the transducer receptacle extends in the crosswise direction to the bearing axis, the biasing element is threadably supported in the transducer receptacle and configured for threadable movement in said crosswise direction. Preferably, when the biasing element is configured for movement in the crosswise direction to the bearing axis by rotation of the biasing element along an axis thereof oriented in said crosswise direction, the transducer comprises an anti-rotation member shaped asymmetrically about the axis of the biasing element and the transducer receptacle includes a keyway portion shaped to receive the anti-rotation member of the transducer, so as to resist rotation of the transducer relative to the transducer receptacle upon movement of the biasing element in said crosswise direction.

Preferably, when the transducer comprises a piezoelectric body configured to generate an electrical signal in response to deformation thereof, the anti-rotation member of the transducer is disposed between the piezoelectric body and the biasing element.

In one arrangement, when (i) the outer ring comprises an inner surface in engagement with the rotational elements and an outer surface opposite to the inner surface and (ii) the bearing receptacle has a peripheral surface which encompasses the outer surface of the outer ring and is in intimate contact therewith, the transducer receptacle opens at the peripheral surface so that the transducer is disposed in operative mechanical engagement with the outer surface of the outer ring to receive the vibration of the rotary bearing.

In one arrangement, when the transducer receptacle extends transversely of the bearing axis, the transducer comprises a linear configuration of a piezoelectric body configured to generate an electrical signal in response to deformation thereof and a force-transmission member in operative mechanical engagement with the piezoelectric body and defining a contact surface in operative mechanical engagement with the rotary bearing, and the linear configuration of the piezoelectric body and the force-transmission member lie along an axis transverse to the bearing axis.

Preferably, in such an arrangement, the transducer receptacle and the linear configuration of the piezoelectric body and the force-transmission member lie along an axis radially oriented to the bearing axis.

In one such arrangement, when the outer ring of the rotary bearing comprises a cylindrical outer surface, the contact surface is planar and tangentially oriented to the outer surface of the outer ring.

Preferably, the outer ring of the rotary assembly is stationary and the inner ring is rotatable relative thereto.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in conjunction with the accompanying drawings in which:

Figure 1 is a perspective view of an arrangement of rotary assembly according to the present invention; Figure 2 is an end view of the arrangement of Figure 1 ;

Figure 3 is a cross-sectional view along line 3-3 in Figure 2;

Figure 4 is a cross-sectional view of the arrangement of Figure 1 as if it were taken along line 4-4 in Figure 3;

Figure 5 is a perspective view of an arrangement of transducer in the arrangement of rotary assembly of Figure 1 ;

Figure 6 is a side view of the arrangement of transducer of Figure 5;

Figure 7 is a cross-sectional view along line 7-7 in Figure 6;

Figure 8 is a bottom plan view of the arrangement of transducer of Figure 5;

Figure 9 is an enlarged view of the area indicated at I in Figure 3;

Figure 10 is an enlarged view of the area indicated at II in Figure 4;

Figure 11 is a schematic diagram of a piezoelectric disc under radial mechanical force;

Figure 12 is a flowchart of the designing process, simulation, and experimental tests of transducer according to the present invention;

Figure 13A is an exploded view of the transducer of Figure 5;

Figure 13B is another perspective view of the transducer of Figure 5;

Figure 14A is a finite element (FE) model of the transducer of Figure 5 for modal analysis;

Figure 14B is a graph comparing frequency response functions of the novel transducer and accelerometer;

Figure 15A shows an apparatus for testing the novel transducer;

Figure 15B shows a housing of the apparatus of Figure 15A and an enlarged partial view showing a slot in the housing for positioning the sensor;

Figure 16A is an exploded view of a roller bearing installed on a drive train of a mining conveyor;

Figure 16B shows an equivalent 4-DOF LPM of one bearing;

Figures 17A through 17C respectively show the FE model of the bearing outer ring and the housing; an enlarged view of the fine mesh area; and an illustration of the contact widths and mesh transition;

Figure 18 shows FE modeling of the novel transducer in contact with the bearing outer ring and close-up view of the local fault;

Figures 19A and 19B show deformation contour and maximum principal stress distribution, respectively, on the bearing outer ring;

Figures 20A through 20C respectively show simulated interface forces in different conditions, namely healthy; outer ring fault at 270° and outer ring fault at 260°; Figures 21 A and 21 B respectively show dimensions of artificial faults on the outer ring and the roller;

Figures 22A and 22B are graphs showing experimental time domain voltage signals of the novel transducer in healthy and faulty conditions, respectively;

Figures 22C and 22D are graphs showing frequency domain analyses of the voltage signals of Figures 22A and 22B, that is in healthy and faulty conditions, respectively;

Figures 22A and 22B are graphs showing experimental time domain acceleration signals of the bearing in healthy and faulty conditions, respectively;

Figures 23C and 23D are graphs showing frequency domain analyses of the acceleration signals of Figures 23A and 23B, that is in healthy and faulty conditions, respectively,

Figures 24A through 24C are graphs showing voltage signals in different positions of the fault on the outer ring, namely 270°, 260° and 250°, respectively;

Figures 25A and 25B show voltage signals of the novel transducer in time and frequency domains, respectively, and Figures 25C and 25D show acceleration signals in time and frequency domains, respectively, of a faulty roller;

Figures 26A and 26B respectively show time domain voltage signal and frequency domain of the novel transducer while having a faulty roller and outer ring fault at 270°;

Figures 27A and 27B respectively show acceleration signals and voltage signals in impacting and impact-free conditions;

Figures 28A and 28B are short-time Fourier transforms (STFTs) of the acceleration signals in impact-free and impacted conditions, respectively, and Figures 28C and 28D are STFTs of the voltage signal in impact-free and impacted conditions at 1000 rpm, respectively;

Figures 29A and 29B show envelope spectrum of the acceleration signals in impact- free and impacted conditions, respectively, and Figures 29C and 29D show envelope spectrum of the voltage signal in impact-free and impacted conditions at 250 rpm. Respectively;

Figures 30A and 30B respectively show power spectrum density (PSD) of the acceleration signal and of the novel transducer in impact-free and impacted conditions;

Figure 31 is a graph showing interface contact between the novel transducer and the outer ring under different shaft radial loads;

Figure 32A shows voltage signal amplitude changes due to speed variations, and Figures 32B and 32C respectively show zoomed view of the signal in a healthy condition and having a faulty outer ring;

Figures 33A and 33B are graphs showing measured speed by the novel transducer vs the encoder and PZT voltage variations over time, respectively;

Figures 34A and 34B show normalized signals in healthy and faulty conditions, respectively; Figures 35A and 35B show time-frequency representation (TFR) of the voltage signal in healthy and faulty conditions, respectively; and

Figures 36A and 36B show of the novel transducer in healthy and faulty roller condition, respectively; Figures 36C and 36D show TFR of the voltage signal in healthy and faulty roller condition, respectively; and Figures 36E and 36F show the frequency spectrum in healthy and faulty roller condition, respectively.

In the drawings like characters of reference indicate corresponding parts in the different figures.

DETAILED DESCRIPTION

There is shown in the accompanying figures a transducer, generally indicated at 20 and more clearly shown in Figures 5-8, for use with a rotary bearing 1 arranged to provide relative rotation between an inner member 3 and an outer member 4, which are typically components of a rotary assembly 6. The rotary assembly 6 is an arrangement of components configured in a manner to provide rotation between at least a pair of the components or groupings of the components.

Referring to Figures 1-4, and generally speaking, the rotary assembly 6 comprises the inner member 3, which is disposed along a rotational axis R of the rotary assembly, and the outer member 4, which encompasses at least a portion of the inner member 3 and the rotational axis R. That is, the outer member 4, which surrounds the inner member 3 in a circumferential direction of the rotational axis R, at least partially overlaps the inner member 3 in an axial direction of axis R. The inner and outer members 3, 4 are arranged for rotation relative to one another around the rotational axis R.

As shown more clearly in Figures 3-4, the rotary bearing 6 rotatably interconnects the inner and outer members 3, 4 for relative rotation. The rotary bearing 6 generally comprises an inner ring or race 8 encompassing an axis of the bearing B and configured to receive the inner member 3; an outer ring or race 9 of the bearing encompassing the inner bearing ring 8 and arranged to be supported by the rotary assembly’s outer member 4; and a plurality of rotational elements 10 between the inner and outer rings 8, 9 and arranged to provide relative rotation of the inner and outer rings 8, 9 around the bearing axis B. In the illustrated arrangement, the outer bearing ring 9 is substantially fully overlapped with the inner bearing ring 8 relative to an axial direction of bearing axis B. When implemented in the rotary assembly 6, the bearing axis B is coaxial with the rotational axis R of the assembly 6. In the illustrated arrangement, the rotary bearing 6 is a cylindrical roller bearing in which both of the races 8, 9 are circular cylindrically shaped around the bearing axis B, and the rotational elements 10 that provide relative rotation of the races are substantially circular cylindrical rollers with axes oriented parallel to the bearing axis.

To sense various conditions of the bearing 6, for example speed thereof or a fault or damage developed in the bearing, the transducer 20 is configured to sense vibration of the rotary bearing, which it achieves by being in operative mechanical engagement with the bearing 1 . In this manner the vibration or vibratory motion of the bearing is received by the transducer 20 directly without passing through other components of the rotary assembly 6, for example the outer member 4, which may impart noise to the signal sensed or detected by the transducer.

Turning now to Figures 5-8, and particularly Figure 7, the transducer 20 comprises a piezoelectric body 22 comprising piezoelectric material and configured to generate an electrical signal in response to physical deformation thereof. That is, when an external mechanical force is applied to the piezoelectric body 22, causing any degree of deformation of the body 22, the body 22 generates or outputs an electrical signal, which can be processed or analyzed to interpret the applied force. The piezoelectric body 22 has opposite faces 24, 25 lying along a body axis A of the piezoelectric body and a periphery 27 of the piezoelectric body encompassing the opposite faces 24, 25. The transducer 20 also comprises a pair of electrodes 29 electrically connected to the piezoelectric body 22 and configured to transmit the electrical signal. In the illustrated arrangement, the electrodes 29 are in electrical contact with the opposite faces of the piezoelectric body 22, and the electrodes 29 are planar. Furthermore, in the illustrated arrangement the electrodes 29 cover full surface areas of the opposite faces 24, 25 of the piezoelectric body 22.

The transducer 20 further includes a force-transmission member 32 in operative mechanical engagement with a first one of the opposite faces of the piezoelectric body, generally a proximal one of the faces in relation to the rotary bearing 1 , and in this case the one indicated at 24. When the electrodes 29 are in electrical contact with the opposite faces 24, 25, the forcetransmission member 32 is not in direct contact with the proximal face 24 over a full surface area thereof, rather they are mechanically interconnected to transmit mechanical forces therebetween by a corresponding one of the electrodes 29 (that is in electrical contact with the proximal face 24). Regardless, the force-transmission member 32 is substantially electrically nonconductive, so as not to interfere with the electrical signal generable thereby.

Furthermore, it will be appreciated that the force-transmission member 32 is disposed along the body axis A, so as to transmit mechanical force to the piezoelectric body substantially therealong.

The force-transmission member 32 defines an exterior contact surface 34 of the transducer 20 distal to the proximal face 24 and arranged in mechanical contact with the rotary bearing 1 to receive vibratory motion thereof. That is, the contact surface 34 is exposed to an environment of the transducer 20 to be available for mechanical contact with the bearing 1. Moreover, the force-transmission member 32 comprises incompressible rigid material so as to transmit force exerted thereon, and more specifically substantially all of the force applied thereto, from the vibratory motion of the rotary bearing 1 and to the piezoelectric body 22. As such, the received force from the bearing 1 is substantially not attenuated during transmission to the piezoelectric body 22 through member 34. Furthermore, the force-transmission member 32 is substantially electrically nonconductive so as not to transmit the electrical signal generated by the piezoelectric body through the member 34 and to the rotary bearing, which typically is metallic, or to the surrounding rotary assembly 6. In the illustrated arrangement, the force-transmission member comprises a body of the incompressible rigid material, meaning that the member 32 has a unitary composition. Preferably, the incompressible rigid material is substantially electrically nonconductive so as to ascribe this attribute to the force-transmission member 34.

To prevent short circuiting of the piezoelectric body during physical deformation, the transducer 20 further includes electrical insulation 36 arranged around the piezoelectric body 22 and configured to prevent transmission of the electrical signal generated by the piezoelectric body to a proximal electrically conductive body, for example belonging to the rotary assembly 6. In the illustrated arrangement, the electrical insulation 36 comprises a tubular body configured to surround the periphery 27 of the piezoelectric body, which is otherwise uncovered by other components of the transducer recited herein. In other words, in the illustrated arrangement the electrical insulation 36 comprises a tubular body, which is generally cylindrical, encompassing the piezoelectric body 22 around the body axis A of the transducer.

To support the piezoelectric body 22 during physical deformation, the transducer 20 further includes a base 39 disposed along the body axis A and in opposite relation to the forcetransmission member 32, such that the piezoelectric body is substantially sandwiched therebetween. The base 39 acts to cover a second one of the opposite faces of the piezoelectric body, in this case indicated at 25. The base 39 is substantially electrically nonconductive so as not to interfere with the electrical signal generable thereby or transmit the electrical signal to the surrounding environment, for example the rotary assembly 6.

To enhance the sandwiching effect and ensure the (vibratory) force transmissible to the piezoelectric body is substantially not attenuated, the base 39, like the force-transmission member 32, comprises incompressible rigid material. In the illustrated arrangement, the incompressible rigid material of both the base and the force-transmission member comprises a ceramic material, and more specifically the ceramic material comprises alumina. In the case of both the base and the force-transmission member, it is the incompressible rigid material that is substantially electrically nonconductive, so as to ascribe this characteristic to the corresponding transducer component.

In the illustrated arrangement, and with particular reference to Figure 8, the base 39 is asymmetrically shaped around the body axis A. More specifically, the base 39 comprises a generally circular portion 40A coaxial with the body axis A and a projecting portion 40B extending therefrom in a transversely outward direction relative to the body axis A. The circular portion 40A of the base is registered with the piezoelectric body 22, relative to the body axis A, and the projecting portion 40B is disposed radially outwardly of same, such that the transducer’s body axis A is eccentric to the base 39. Thus, the base 39 is shaped in a manner suitable to prevent rotation of the transducer about the body axis A, as will be better appreciated later. Furthermore, the base 39 is cylindrically shaped about the body axis A, so as to be of constant cross-section (size and shape).

Similarly to the base 39, each of the piezoelectric body 22 and the forcetransmission member 32 is cylindrically shaped about the body axis A of the transducer. However, in contrast to the base, the force-transmission member 32 is sized and shaped substantially the same as the piezoelectric body 22, which is circular cylindrical in shape. As such, the forcetransmission member 32 is substantially identically registered with the piezoelectric body relative to the axis 22 to enhance transmissibility of the force applied to the outer member 32. Furthermore, the exterior contact surface 34 is planar and normal or perpendicular to the body axis A.

As the piezoelectric body 22 of the illustrated arrangement is cylindrical in shape, the periphery 27 thereof is in the form of an annular surface and the opposite faces 24, 25 are planar end faces of the body 22.

In order to locate the transducer 20 in operative mechanical engagement with the rotary bearing 1 to receive the vibration thereof, so that the transducer can generate the electrical signal in response thereto, the outer member 4 of the rotary assembly 6 includes a transducer receptacle 12 configured to receive the transducer 20 therein and which is in communication with a bearing receptacle 14 formed in the outer member 4 and configured to receive the rotary bearing 1 . In the illustrated arrangement, the bearing receptacle 14 is a cavity in the outer member 4 sized and shaped to intimately receive the outer race 9 of the bearing 1 , so as to support the rotary bearing 1 , and such that the outer member 4 is maintained in fixed rotational relation to the outer race 9.

When the bearing axis B is generally horizontally oriented, meaning it is oriented more horizontally than upright, the transducer receptacle 12 is disposed below the bearing axis B. In other words, within the rotary assembly 6, the transducer receptacle 12 is disposed at a lower elevation than the bearing axis B. Furthermore, when the bearing axis is substantially horizontally oriented, as in the illustrated arrangement in which it is horizontal, the transducer receptacle 12 is vertically in-line with the bearing axis. That is, the transducer receptacle 12 is under the bearing axis B so as to lie in a common vertical plane therewith.

In the illustrated arrangement, the transducer 20 is in direct contact with the rotary bearing 1 , meaning that there are no intervening bodies therebetween across which force from the vibration of the bearing is transferred on path to the transducer. Furthermore, the transducer 20 is in direct contact with the outer ring 9 of the bearing 1 . More specifically, the outer ring 9 comprises an inner surface 9A in engagement with the rotational elements 10 and an outer surface 9B opposite to the inner surface; and the bearing receptacle 14 has a peripheral surface 14A which encompasses the outer surface 9B of the outer ring and is in intimate contact therewith. The transducer receptacle 12 opens at end 12A at the peripheral surface 14A so that the transducer 20 received in the receptacle 12 is disposed in operative mechanical engagement, in particular direct contact, with the outer surface 9B of the outer ring to receive the vibration of the rotary bearing 1 .

An interface between the transducer 20 and bearing 1 is thus formed by the transducer contact surface 34 and the outer surface 9B of the bearing’s outer ring 9. In the illustrated arrangement, the outer surface 9B is cylindrical and the contact surface 34 is planar and tangentially oriented to the outer surface 9B of the outer ring 9. Thus, the interface 34 is relatively small, effectively being in the form of a line parallel to the bearing axis B. When the transducer 20 is arranged vertically in-line with the bearing axis B, and specifically under the same, weight of the bearing 1 may increase the total force transmitted from the bearing 1 to the transducer upon vibration of the former.

Since the transducer 20 is in contact with the outer ring 9 of the bearing 1 , the outer ring 9 of the rotary bearing is stationary and the inner ring 8 is rotatable relative thereto, such that there is substantially no shear force exerted on the transducer during rotation of the bearing 1 . Accordingly, the outer member 4, which is fixed rotational relation to the outer ring 9, is stationary, and the inner member 3, which is in fixed rotational relation to the inner ring, rotates.

To maintain the transducer 20 in operative mechanical engagement with the bearing 1 , in this case direct contact therewith, the rotary assembly 6 further includes a biasing element 16 in the transducer receptacle 12 and configured to bias the transducer 20 in a crosswise direction generally towards the bearing axis B to urge the transducer into operative mechanical engagement with the rotary bearing. As such, the biasing element 16 is disposed in the transducer receptacle 12 in opposite relation to the bearing 1 , so that the transducer 20 is intermediate. In the illustrated arrangement, the biasing element 16 is threadably supported in the transducer receptacle 12 and configured for threadable movement in the crosswise direction. More specifically, the biasing element is configured for movement in the crosswise direction to the bearing axis B by rotation of the biasing element along an axis thereof Z oriented in this crosswise direction.

More specifically, in the illustrated arrangement, the transducer receptacle 12 extends transversely crosswise of the bearing axis B, meaning a path along which the receptacle 12 extends, if continued, would cross the axis B. Furthermore, the transducer 20 comprises a linear configuration of a piezoelectric body 22 configured to generate an electrical signal in response to deformation thereof and a force-transmission member 32 in operative mechanical engagement with the piezoelectric body 22 and defining a contact surface 34 in operative mechanical engagement with the rotary bearing 1 . In other words, the piezoelectric body 22 and the force-transmission member 34 are arranged substantially end-to-end along an axis; in the illustrated arrangement, there is an intervening electrode 29 between the force-transmission member 34 and the piezoelectric body such that they are not in touching end-to-end relation.

Since the receptacle 12 extends along a transverse path to the bearing axis B, the linear configuration of the piezoelectric body and the force-transmission member lie along an axis transverse to the bearing axis, too. This may enhance sensing capability of the transducer, as vibratory force is stronger in a transverse direction of the bearing axis. Preferably, as in the illustrated arrangement, the transducer receptacle and the linear configuration of the piezoelectric body and the force-transmission member lie along an axis radially oriented to the bearing axis B, a direction in which a captured vibratory force may be strongest.

Since the transducer 20 of the illustrated arrangement is generally asymmetrically shaped about the body axis A because wires 43 electrically connected to the electrodes 29 lie to the side of the axis, in generally parallel relation thereto, the transducer 20 comprises an antirotation member shaped asymmetrically about the axis of the biasing element Z, and the transducer receptacle 12 includes a keyway portion 17A shaped to receive the anti-rotation member of the transducer, so as to resist rotation of the transducer relative to the transducer receptacle upon movement of the biasing element in the crosswise direction. That is, the transducer receptacle 12 comprises a primary cylindrical passageway 17B in which the transducer 20 and the biasing element 16 are substantially located and which can be traversed thereby to suitably engage the bearing 1 , and the keyway portion 17A which is in communication with the passageway 17B and extends parallel to the primary passageway. The keyway portion 17A extends only a partial depth of the transducer receptacle 12 from an open end thereof 12A at the bearing receptacle. Furthermore, the keyway 17A is shaped in a circumferential direction of the transducer’s body axis, when received in the primary portion of the transducer receptacle 12, to substantially mate with the anti-rotation member. In the illustrated arrangement, the transducer base 39 provides or forms the anti-rotation member, which is disposed between the piezoelectric body 22 and the biasing element 16 to protect the former from the latter. Furthermore, in the illustrated arrangement, the keyway portion 17A is substantially rectangular cylindrical.

This provides a transducer for sensing various conditions of a rotary bearing by way of direct contact therewith and enables the transducer to be less affected by noise.

PRINCIPLE OF PIEZOELECTRIC TRANSDUCERS

With respect to the fundamentals of piezoelectric materials for sensing applications, the piezoelectric effect refers or relates to generating an electric charge in response to a mechanical strain. One of the most common materials for sensing applications or energy harvesting is Lead Zirconate Titanates, known as PZT ceramics. Their constitutive equations determine the electromechanical response of piezoelectric materials. Various forms of constitutive equations are available depending on the application and target parameters that can be implemented, such as stress-charge or strain-charge modes [36]. The strain-charge mode is adopted to measure the generated output voltage in response to a mechanical force. For a piezoelectric material, such as the disc in Figure 11 , the constitutive equations in strain-charge mode are as follows [25]: where S _p and T _q present the strain and stress, respectively. Here, s _pq denotes the elastic compliance matrix at a constant electric field. Also, Di and d, _q illustrate the electric displacement and piezoelectric matrix, respectively. The electric field is denoted by E, and sl _k stands for the permittivity matrix in constant stress. Due to the anisotropic structure of piezoelectric materials, the properties are defined based on the direction. Here, the subscripts of / and k demonstrate the numbers 1 to 3. Also, p and q indicate numbers 1 to 6. According to Figure 11 , numbers 1 to 3 represent the normal directions in the coordinate system, and numbers 4 to 6 stand for the shear planes. The electric field (E ₃ ) equals V/h, where V and h stand for the generated voltage and the piezoelectric height, respectively. Once a piezoelectric material is under mechanical force in an open circuit condition (D ₃ = 0), the constitutive equation can be rewritten to obtain the output voltage value [25]: where F denotes the applied radial force over the piezoelectric disc top area (A). If the connected measurement instrument to the PZT disc has infinite resistance, the voltage from the experimental tests matches well with Eq (3). The measurement instrument has a finite resistance, and the generated electric charge immediately finds the path with the lowest resistance. This phenomenon reduces the voltage amplitude in the experiment compared with the voltage from Eq (3) [37], Therefore, the equivalent resistance and capacitance of the circuit can be considered in the voltage equation to simulate charge dissipation. A universal approach is explained in [37] for stress-charge mode, and the strain-charge mode [36] is disclosed herein. By rearranging Eq (1), the following equation is obtained [35]:

The generated electric displacement (D ₃ ) is equal to Q/A, in which Q denotes the electric charge over the electrode. In addition, the piezoelectric capacitance (C _p ) is expressed by C _p = s ₃₃ A/h. Considering these equations and the relationship between current and electric charge (/' = dQ/dt), the derivative of Eq (4) gives the following equation [35]: Eq (5) is a first-order non-homogeneous linear differential equation that includes the circuit resistance (R) and capacitance. By changing the stress (T ₃ ) into applied force over the PZT area (F/A), the Eq (6) can be obtained through the general solution to the first-order non- homogeneous differential equation as follows [35]:

Through Eq (6), the generated voltage signal with charge dissipation can be calculated. In contrast with the open-circuit voltage by Eq (3), the voltage by Eq (6) has a lower amplitude due to charge dissipation. The voltage value for different frequencies can be obtained through this equation, and subsequently, the sensitivity and linearity can be reported for low- frequency ranges. This procedure is further discussed in the next section, and the designing procedure, the experimental setup, and the FE modeling of the transducer are explained. The designing process and tests for analyzing the performance of the novel transducer, which may be referred to hereinafter as PZT transducer for convenience, as for example schematically shown in Figure 11 , are summarized in Figure 12. These steps will be explained in detail later.

Referring to Figure 11 , there is shown the transducer having a disc-shaped PZT material 1102 and electrodes 1104. The electrodes are connected to a voltmeter 1107 to measure voltage generated upon compaction of the transducer due to externally applied forces indicated by arrows 1109 and 1110.

TRANSDUCER MODELING AND EXPERIMENTAL SETUP

This section explains the details of the transducer structure, the experimental setup, and the transducer's dynamic FE model. Piezoelectric materials generate an electric charge in response to a mechanical strain. When these materials are being used under dynamic excitation, special caution is taken for selecting the materials in contact with the PZT element. In fact, it is preferable to use highly stiff materials in contact with the PZT to have a sensitive voltage.

TRANSDUCER STRUCTURE DESIGN

Figures 13A and 13B demonstrate the structure of the designed transducer. As shown in Figure 13A, two alumina discs, a top one 1302 and a bottom key-shaped one 1303, are placed on the top and bottom of a PZT disc 1305. The top alumina disc 1302 has a diameter and height of 3 mm and 1.5 mm, respectively. Beneath the top alumina disc 1302, the PZT disc 1305 with a diameter and height of 3 mm and 2 mm, respectively, has been attached to copper electrodes 1308, 1309. These parts are mounted on the key-shaped bottom alumina disc 1303 with a diameter and height of 5 mm and 1.5 mm, respectively. The key-shaped bottom alumina disc 1303 is used to prevent transducer rotation once a preload is applied to it. In addition, protective heat-shrink tubes 1311 , 1312 cover the circumference of the PZT disc 1305 and the connection point of wires 1313 to the copper electrodes 1308, 1309. In Figure 13B, the assembled transducer is shown, which illustrates the small dimensions of the transducer, which measure 9.5 mm in a first dimension 1315 and 5.2 mm in a second dimension 1316. The total dimension of the transducer is

9.5x5.2x5 mm, weighing about 0.4 gr. To prevent damping and soft materials in between the components, super glue is applied only to the edges of the components to fix the structure. Two 28 AWG wires are soldered to the copper electrodes, and the other ends are connected to a low-noise coaxial cable model PCB-003 connected directly to the data acquisition system (DAQ) model Spider 80-Xi. The output of this transducer is an analog output and different sampling frequencies can be selected for the DAQ to digitalize the output.

The reason behind selecting alumina ceramic for the discs is that if the contact surface of the transducer is made of a stiff and nonporous material, the voltage response is more sensitive to the applied strain. However, if the transducer structure has a low module of elasticity or there is a hyperplastic substance, such as glue, in between the components, the applied strain is not properly inducing the PZT element. Therefore, the transducer will not be capable of capturing small variations or excitations. The structure of the transducer is designed with stiff materials to prevent the aforementioned problem. Therefore, by using nonporous alumina ceramic (aluminum oxide, AI2O3), which has a module of elasticity of 330 GPa, it is tried to majorly induce the PZT disc to capture small excitation or impacts in the applied dynamic force.

The PZT type of the illustrated arrangement of transducer is PIC255. The material properties are given below in the form of matrices that were provided by the supplier. The total cost of this PZT element and alumina ceramics is about $14, excluding the cables. 1.606 - 0.5 68 -0.745 0 0

-0.568 1 ,6C )6 -0.745 0 0

-0.745 - 0.7 45 1.909 0 0

I ^s ] PZT ^— 0 0 0 4.6S 0

0 0 0 0 4.699 0 0 0 0 0

A determinative parameter in the output voltage of PZT materials is the frequency of excitation and the amount of dynamic force. In fact, the sensitivity abruptly changes in lower frequencies by increasing the excitation frequency. In a specific frequency range, the sensitivity shows most likely a linear behavior which is defined as the frequency bandwidth of the transducer. This phenomenon is relevant if the transducer measures a specific parameter such as force or strain to measure the value accurately. However, in the illustrated arrangement, the PZT element is being used just as a transducer to analyze its performance for fault detection. A modal analysis using ANSYS and an experimental impact test is conducted to estimate the first natural frequency and observe that resonance is not happening in a specific frequency range suitable for bearing applications.

Figure 14A shows the FE model of the PZT transducer, which was previously shown in Figure 13B. Thus, there is generally shown in Figure 14A the top alumina disc, now indicated at 1402; the bottom alumina disc, now indicated at 1403; and the PZT disc, now indicated at 1405. The material properties of the Alumina ceramic are applied to the top and bottom parts using element type SOLID185, and the PZT material properties from Eqs (7) to (8) are applied to the middle part using element type SOLID226. By constraining the bottom surface in Z-direction, the modal analysis is performed. Ignoring the first three rigid-body mode shapes, the first natural frequency equals 127.3 kHz. This natural frequency is far beyond the typical frequency range for vibration sensors for bearing applications, which mostly go up to 10 kHz or 15 kHz. An impact hammer test is conducted to experimentally verify that no resonance is happening in the PZT transducer up to 15 kHz. The PZT transducer is mounted inside the bearing housing, the procedure for which is described later. An accelerometer is installed in the close vicinity of the bearing housing to estimate the resonances of the bearing pedestal and its assembly. Therefore, comparing the FRF of the accelerometer and PZT transducer demonstrates whether resonances in the FRF come from the bearing assembly or the PZT transducer. By using the impact hammer, a rapid force pulse is applied to the PZT top surface. The FRFs of this impact test are obtained by considering the force signal as the input and PZT and accelerometer signals as the outputs. These two FRFs are shown in Figure 14B, and it can be observed that all resonances in the PZT FRF happen exactly in the accelerometer FRF as well, and these resonances are related to the bearing assembly. The result shows that the PZT transducer has no resonance up to 15 kHz and is suitable for bearing application.

EXPERIMENTAL SETUP

Figure 15A illustrates a bearing test apparatus, which includes a 1-1/2 HP AC motor 1502, three bearings 1504-1506, and a loading mechanism 1508. The middle bearing 1504 is a self-aligning bearing used as the loading mechanism 1508 on the shaft, and the bearing 1505 on pedestal 1 indicated at 1510 is a double-row cylindrical roller bearing. On pedestal 2 indicated at 1512, a cylindrical roller bearing type SKF N305 ECP and indicated at 1506 is mounted, which is used as the test bearing 1506 for fault detection. The specification of this bearing type is presented in Table 2. In the illustrated arrangement, the transducer is implemented inside the housing of the test bearing 1506. The housing type is a split housing model SNL 506-605, and the cross-sectional view is shown in Figure 15B. In order to embed the PZT transducer inside the housing, an M6 threaded hole 1515 is created in the middle of the housing, and by machining a narrow slot, the wire path 1516 to the outside of the bearing is formed. The key-shaped part of the bottom disc is placed inside the wire path to prevent the rotation of the transducer. Also, an M6 bolt keeps the PZT transducer in direct contact with the outer ring surface. However, a moderately low preload is applied to the bolt by tightening the bolt using a hand just to keep the sensor in contact with the outer. Through this experiment, it is expected that the dynamic force of each individual roller excites the PZT, and the measured voltage signal can be used for condition monitoring. A DAQ measures the outputs of the implemented sensors and the PZT transducer.

DYNAMIC FINITE ELEMENT MODELING OF THE EMBEDDED TRANSDUCER

During the rotation of the bearing, the dynamic forces from the rolling element excite the transducer resulting in the generation of a voltage signal. In the case of a faulty bearing, dynamic forces are affected due to the impact between rolling elements and the faulty area. These forces can be simulated to visualize the effect of local fault on the dynamic forces. In order to model the PZT transducer inside the bearing housing 1602, which is of the split type, and simulate applied forces on the transducer, a bearing finite element (FE) model reported in [36], [38] is adopted for further studies of the embedded transducer. This model includes a 4 degree-of-freedom (DOF) bearing lumped-parameter model (LPM) and an FE model in ANSYS. In this dynamic model, contact forces of rollers 1605 in healthy and faulty conditions are obtained employing LPM and are used as the input data of a bearing FE model in ANSYS Mechanical APDFL. Figures 16A and 16B present the exploded view of the bearing and the equivalent 4-DOF bearing LPM. Here, F _r refers to the radial load from the shaft to the inner ring or raceway 1608. A cage of the bearing is indicated at 1610. The shaft and the inner ring 1608 displacements are defined by shaft stiffness (K _s ) and damping (C _s ) in horizontal and vertical directions, respectively. The inner ring and shaft with a total mass of m _Si interact with the outer ring raceway 1616 through the rolling elements 1605. The angular position of each individual roller is denoted by <pj and their interactions with the outer raceway 1616 are defined by the contact stiffness (K) and viscous damping (C _r ). The outer ring, housing, and pedestal together have an equivalent mass of m _p (the values for the horizontal and vertical directions are different based on their different natural frequencies). Therefore, 4-DOF equations of motion are created in MATLAB and solved by the 4 ^th -order Runge-Kutta method. For further details about the model parameters estimation and modeling details, readers are encouraged to refer to the reference [38].

The forces from the LPM model are used in an FE model and applied to the outer raceway to simulate rollers rotation. In fact, instead of modeling all the bearing components and contact elements among rolling elements, only the housing and the outer ring are modeled. Therefore, the input contact forces from the bearing LPM are applied to small areas on the outer ring, which are generated based on the contact width CW (2b) by Hertz contact theory. This model is a computationally efficient method with fewer modeling complexities compared with nonlinear bearing FE models that include contact elements among the components [38]. By creating a vertical hole in the housing of the FE model, the PZT transducer is modeled inside the hole same as the experimental setup. A comparatively accurate subsurface stress distribution is achieved by applying the contact forces over the small contact areas, which overlaps the theoretical models. The subsurface stress and strain changes through this model have been previously verified in references [36] and [38].

Figures 17A through 17C illustrate the bearing FE model developed in ANSYS. This model includes the bearing outer ring and the housing with an integrated PZT transducer. Since the bearing is radially loaded and there is no axial loading, the symmetric boundary condition is applicable to the modeling. Therefore, only half of the housing and the outer ring has been modeled in the axial direction, and displacements of the nodes on the symmetric plane are constrained in the x-direction (Ux = 0). Due to having a thick steel-made pedestal, it is assumed that the deformation of the pedestal is negligible. Hence, the displacement of the nodes at the bottom of the housing has been constrained (Uz = 0). As shown in Figure 17A, the model is made by a combination of coarse and fine elements. Basically, the target section for this simulation is the load zone of the bearing where maximum contact forces are applied to the outer ring. Therefore, a fine mesh is applied to the outer ring's load zone, which covers 75 degrees of the bottom half. The enlarged view of the fine mesh section is illustrated in Figure 17B where the small contact widths are illustrated as well. The width of these contact areas is individually generated based on the input data of the bearing LPM. The rollers' contact forces are applied over these narrow contact widths in the form of uniform pressure. To compensate for the difference between semielliptical pressure and uniform pressure, a constant pressure multiplier is proposed in reference [38] to minimize the error in subsurface stresses. Subsequently, all the pressure values over the contact areas are multiplied by 0.78, which causes identical subsurface stresses as the theoretical solution [38]. In Figure 17C, the close view of the contact widths and mesh transition from the coarse to fine elements have shown. The element type for the housing and the outer ring is SOLID185, and the material properties of the FE model are presented in Table 3.

As shown in Figure 15B, an M6 threaded hole is created in the middle of the bearing housing to position the PZT transducer. Therefore, in the FE model, a vertical section is removed from the housing to simulate the hole, and the PZT transducer is modeled in direct contact with the outer ring. Figure 18 presents the modeled PZT transducer with the outer ring. However, the housing has not been shown to better visualize the transducer. The transducer includes the top alumina disc 1802 and the PZT element 1803. Since a moderately low preload is applied to the transducer, the preload in the FE model is ignored, and instead, the radial displacement of the sensor bottom surface is constrained (Uz = 0). In addition, for a faulty condition, a local line spalling is demonstrated and further details about the dimension and position of the fault are explained in the next section. The element type for the alumina disc is SOLID185, and for the PZT disc, the element type of SOLID226 is selected. For the PZT material, the material properties in Eqs (7) to (9) are adopted, and the interaction between the top alumina disc and the outer ring is defined by frictional contact type. This model has been solved with the same time increment as the reference [38], which is 0.392 (ms) or the sampling frequency of 2551 (Hz). The radial load of the test bearing is considered to be 800 N and the bearing is operating under 1000 rpm rotational speed. Please refer to the reference [38] for further details about time increment selection.

SIMULATION AND EXPERIMENTAL RESULTS

Three tests to test the transducer performance, including simulation and experiments. In the first test, the forces on the transducer are simulated to observe how different fault locations cause abnormal excitations in the force signals. Through experimental tests, the transducer performance in the faulty detection for two types of faults are investigated. The second test in this disclosure explores the effect of external noise and excitation on the fault detection ability of the transducer by creating artificial noises and excitation in the test apparatus. In the third test, a preliminary analysis of the transducer durability is conducted employing FE modeling.

FAULT DETECTION PERFORMANCE OF THE TRANSDUCER

During the rotation of the bearing, the force carried by each roller causes a radial strain in the thickness of the outer ring. Since the transducer touches the outer ring through a preloaded bolt, the radial strain changes cause an interface contact force between the transducer and the outer ring at a transducer interface contact 1902. The interface forces on the PZT generate an electric charge which can be analyzed as a voltage signal for fault detection. For better visualization, Figures 19A and 19B illustrate the FE model created in ANSYS. Through running the transient analysis, the radial strain changes by rotating rollers excite the embedded transducer. For a moment when a roller is positioned exactly above the transducer, the deformation contour and Hertzian stress are illustrated in Figure 19A and Figure 19B, respectively. The maximum deformation and stress are at the contact area between the roller and the outer ring and gradually reduce through the thickness. The interface forces on the transducer can be obtained in each time step of the FE model to create the dynamic force signal. This dynamic force excites the PZT transducer and generates an electric charge. In the faulty condition, it is expected to have abnormal impulses in the dynamic forces and subsequently in the voltage signal.

Here, the dynamic interface force is simulated in healthy and faulty conditions to investigate the effect of the outer ring fault on the transducer. Through performing a transient analysis in ANSYS, the contact force on the interface of the transducer is simulated as shown in Figures 20A through 20C. The rotational speed is 1000 rpm, and the radial load on the bearing is 800 N. In this figure, three different bearing conditions are considered. In Figure 20A, a healthy bearing is demonstrated. The peaks of the signal refer to a situation when a roller is positioned right above the transducer, and the maximum force is applied to the transducer. When each roller gets further from the transducer, the force amplitude decreases. In faulty conditions, in addition to amplitude modulation of the dynamic force signal, small impulses are generated due to contact between rolling elements with the sharp edges of the fault. By artificially making a local fault on the outer ring, the contact forces in the faulty conditions are simulated as well. Figure 20B presents the interface forces when the outer ring fault is positioned at 270°. According to this figure, some periodic impulses are generated at the peak of the force signal where the maximum contact force passes over the transducer. However, if the position of the fault is changed to 260°, the fault impulses happen farther from the signal peak as shown in Figure 20C. This illustrates that not only it is expected to capture fault symptoms by the transducer but also the signal is sensitive to the fault location, and fault location can be estimated too. In the following, the experimental results are investigated in different conditions.

Typically, in a faulty bearing, due to the impact between the rolling elements and the faulty area, the resonant frequency of the bearing is excited which causes abnormal impulses in the signal. For a situation where the outer ring of the bearing is fixed, the bearing frequencies are presented in Table 4. In this table, f _s refers to the shaft rotational frequency, and for two different rotational speeds that are investigated in this disclosure, Table 5 presents the values of fundamental frequencies. In the faulty condition of the bearing, it is expected to capture these frequencies according to the location of the local fault. In the following experiments, two types of faults, including outer ring and roller faults, are investigated. These two faults are created by electric discharge machining (EDM), and their dimensions are shown in Figures 21 A and 21 B, where, with respect to a first fault shown in Figure 21 A, a first dimension 2105 in a circumferential direction is 0.35 mm and a second dimension 2110 in a depthwise direction is 0.23 mm; and with respect to a second fault shown in Figure 21 B, a first dimension 2115 in a circumferential direction is 1 mm and a second dimension 2120 in a depthwise direction is 1 mm.

Figures 22A through 22D illustrates the experimental voltage signals in time and frequency domains in the healthy condition and faulty outer ring. For the faulty case, the local fault shown in figure 21 A is positioned at 260° counter-clockwise on the outer raceway. The bearing is operating under 1000 rpm rotational speed and 800 N radial load. In Figure 22A, due to the healthy condition of the bearing, there is only amplitude modulation by the BPFO. However, having a local fault on the outer raceway causes periodic fault symptom impulses which are illustrated in Figure 22B. Since in the healthy condition of the bearing, the voltage amplitude is modulated by BPFO, the frequency domain of the healthy signal obtained by the envelope spectrum includes low amplitude BPFO and its harmonics. This situation is illustrated in Figure 22C with a magnified view of the fundamental frequencies. Finally, in the faulty condition, the envelope spectrum faces a significant amplitude elevation in BPFO and its harmonics compared with the healthy condition, as shown in Figure 22D.

To compare the performance of the transducer versus a commercial accelerometer, the acceleration signal is recorded simultaneously with the voltage signal of the PZT transducer. The type of accelerometer in this experiment is PCB 352C33 with a frequency range of 0.5 Hz to 10 kHz. Figures 23A through 23D give the experimental acceleration signals of the test bearing measured by a commercial accelerometer. In Figure 23A, there is a low amplitude acceleration signal in the healthy condition due to background noise and varying compliance of the bearing. However, having the local fault has created several periodic impulses in the signal as shown in Figure 23B. The envelope spectrum of the healthy condition in Figure 23C does not include any fault frequency component. However, the local fault on the outer ring led to a significant elevation in the BPFO and its harmonics in the envelope spectrum, as shown in Figure 23D. So far, it can be concluded that both the accelerometer and the PZT transducer can detect the fault on the outer raceway. In the following, the effect of fault location on the outer ring is investigated.

Figures 24A through 24C present the voltage signal of the PZT transducer corresponding to three different positions of the local fault on the outer ring. According to Figure 24A, if the fault is positioned at 270° on the outer ring above the transducer, there will be a sharp impulse at the peak of the amplitude-modulated voltage signal. Once the fault is positioned farther from the outer ring center, such as 260° in Figure 24B, the fault symptoms shift away from the peaks. This condition is more obvious in Figure 24C where the fault is positioned at 250° and is almost close to the ending of the bearing load zone. The same conclusion as the simulation results in Figures 20A through 20C can be obtained according to these experimental results. In fact, the generated voltage signal is also sensitive to the location of the fault, and if the fault is positioned on the outer ring, it can be used to estimate the location of a fault on the outer ring. When it comes to a fault on the rollers or the inner ring, the fault's position changes during the rotation. Therefore, the excitation caused by the fault may not be significant enough when the fault is away from the bearing load zone. A faulty roller has been investigated in the following to investigate this condition.

Figures 25A through 25D demonstrate the voltage and acceleration signals in case of a local fault on one of the rollers. The faulty roller is tested in the bearing test apparatus by machining a line spall with a width and depth of 1 mm as shown in Figure 21 B. Due to slippage and rotation of the rollers, the behavior of the fault-generated impulses is not as predictable as the outer ring with a fixed position of the fault. As an example, Figure 25A illustrates the voltage signal and fault symptoms due to the faulty roller. The fault symptoms appear once the roller is positioned in the bearing load zone. Also, there is a gap with no impulse in between the fault symptoms since the roller is away from the load zone. This phenomenon causes that instead of observing BSF and its harmonics in the spectrum, the FTF of the bearing is excited and observed in lower frequencies. In fact, the time gap between the impulses of the faulty roller have lowered the frequency range of the faulty roller during each full rotation. It can be observed in the frequency-domain spectrum in Figure 25B that FTF and its harmonics indicate the faulty roller and BPFO shows the amplitude modulation of the signal through the roller pass over the transducer. The same process has been investigated for the acceleration signal in Figures 25C and 25D. In these figures, the faulty roller has created impulses in the signal which are detectable in the frequency spectrum. In addition, once the roller is away from the load zone, more impulses are generated in the acceleration signal contrary to the voltage signal. Therefore, the BSF and its harmonics are elevated by a faulty roller in the acceleration signal. It can be concluded that the proposed PZT transducer is also capable of detecting faults on the rotating rollers. To further investigate the fault detection performance, a composite fault case has been investigated in the following.

Figures 26A and 26B illustrate the composite fault condition when the outer ring fault and roller fault exist at the same time. The rotational speed of 1000 rpm and 800 N radial load is considered for this experiment. Figure 26A shows the PZT voltage signal, and the fault symptoms of the faulty roller and outer ring are indicated. Since the outer ring fault is positioned at 270°, the fault symptoms are detectable at the peaks of the voltage signal. Meanwhile, once the faulty roller enters the load zone, several impulses from the faulty roller appear in the signal. These fault symptoms are demonstrated in the frequency domain spectrum in Figure 26B. The faulty roller leads to high amplitude FTF and its harmonics in the frequency response, and the outer ring fault has elevated the BPFO and its harmonics. As a result, the transducer demonstrates an acceptable performance under composite fault conditions. In the following, the effect of external vibration and impact on the transducer output is investigated.

EFFECT OF EXTERNAL MECHANICAL EXCITATION

In the previous section, the fault detection performance of the PZT transducer in noise and impact-free situations was investigated. According to the results, the proposed transducer has been successful in detecting bearing faults similar to a commercial accelerometer. In this section, the effect of external vibration excitation is investigated to further compare the performance of the PZT transducer versus the accelerometer. Typically, the effect of bearing fault compared to the overall vibration level is weak in the early stages [6]. Therefore, in some applications where there is high background noise or external excitation to the structure, the collected vibration data can be affected by some frequencies or impulses that are not related to faulty components. For example, this situation can happen in mining industries where there are heavy impacts during the operation, or in gearboxes where gear meshing frequencies can mask the bearing fault symptoms [39]. In this section, the effect of external excitation by means of artificial excitation on the bearing pedestal is investigated.

To create high-frequency excitations to the test apparatus and bearing pedestal, an air motor with magnetic mounting is attached to the apparatus. This air motor can provide a maximum excitation frequency of 200 Hz in response to a supplied pressure of 413.685 kPa (60 PSI). The input pressure can be adjusted using a regulator, but there is not any explicit information in the product datasheet to achieve the desired frequency at a certain pressure level. Therefore, by manually adjusting the pressure regulator, it is tried to create an excitation frequency of 50 Hz to the bearing pedestal.

Through testing different rotational speeds of 1000 rpm and 250 rpm under 800 N radial load, the simultaneous acceleration and voltage signal are recorded in three conditions. First, the test apparatus is in an impact/excitation-free condition. In the second the third conditions, the air motor has been attached to pedestals 1 and 2, respectively. In fact, it is tried to investigate the effect of external excitation close and far from the test bearing. As an example, Figure 27A illustrates the acceleration signal for both impact-free and impacted conditions under 1000 rpm rotational speed with impact on pedestal 2 while having the local defect at 270°. According to Figure 27A, the vibration level of the acceleration signal has significantly increased due to the external excitations. To compare the performance of the acceleration signal versus the proposed transducer, Figure 27B demonstrates the voltage signal of the transducer for impact-free and impacted conditions. According to Figure 27B, the voltage signal of the embedded transducer is not significantly affected by the external excitation which demonstrates the superiority of local measurement rather than global measurement by accelerometers. However, this requires more investigations, such as comparing the signal statistical indicators, testing lower speeds, and analyzing frequency domain spectrums which are discussed in the following.

Table 6 and Table 7 are provided to compare the effect of external vibration on the signal characteristics at different speeds and locations of the air motor. The peak-to-peak comparison is meant to be used for comparing the maximum amplitude changes. The RMS and Kurtosis are meant to be used to compare the signal's energy and impulsiveness, respectively. At low rotational speed (250 rpm), the impact between rolling elements and the faulty area has low energy. This causes more troublesome fault detection in low-speed machines, especially at the early stages of the fault. According to Table 6, having an external impact on the test apparatus has significantly increased the acceleration signal level and impulsiveness at 250 rpm. Obviously, the impact on pedestal 2 which is closer to the test bearing, has affected the signal more than the impact on pedestal 1. The same conclusion is ascertained for the rotational speed of 1000 rpm. In fact, having an impact on the pedestals, especially pedestal 2, has significantly increased the level of the measured acceleration signal. Contrary to the accelerometer, the PZT transducer has shown a consistent performance considering that all signal statistical indicators remained almost constant at different rotational speeds or different locations of the air motor according to Table 7. Therefore, it can be concluded that the local measurement by the PZT transducer creates more consistent data in a noisy environment compared with accelerometers. To further investigate these observations, the time-frequency domain of the signal for fault detection in case of external excitation is investigated in the following.

Figures 28A through 28D illustrate the short-time Fourier transform (STFT) of the acceleration and voltage signals envelope in impact-free and impacted conditions, respectively. The same rotational speed of 1000 rpm with 800 N radial load is considered, and the fault is positioned at 270°. According to Figure 28A, the BPFO and its harmonics are visible in the timefrequency spectrum of the acceleration signal without having external excitation to the apparatus. By turning on the air motor on pedestal 2 and vibrating the apparatus with a frequency of 50 Hz, the BPFO and its harmonics are masked by the strong frequency component of the air motor as shown in Figure 28B. In contrast, the voltage signal of the PZT transducer clearly shows the BPFO and its harmonics in both impact-free and impacted conditions. In the impact-free condition, the BPFO and its harmonics are illustrated in Figure 28C. By having the excitation through the air motor, the voltage signal still shows a distinguishable BPFO and its harmonics from the frequency components of the air motor as shown in Figure 28D. Therefore, it can be concluded that the PZT transducer has a better performance in detecting fault symptoms even if there is an external excitation with a frequency near the bearing frequency components. Other than the rotational speed of 1000 rpm, a lower speed needs to be investigated to analyze the PZT performance for low-speed applications.

Figures 29A through 29D presents the envelope spectrum of the acceleration and voltage signals at the rotational speed of 250 rpm with an 800 N radial load. It is worth mentioning that bearing fault frequencies for 250 rpm rotational speed were mentioned in Table 5. By magnifying the low-frequency range of the frequency spectrum, the BPFO and its harmonics are visible in the envelope spectrum of the acceleration signal without any excitation as shown in Figure 29A. By applying the impact through the air motor, the BPFO, and its harmonics are comparatively masked since the signal is majorly dominated by the 50 Hz excitation of the air motor according to Figure 29B. There is only a low amplitude BPFO in the frequency domain and all other harmonics are masked by other frequency components. For the impact-free condition, the voltage signal of the PZT transducer clearly demonstrates the BPFO and its harmonics in the frequency domain as shown in Figure 29C. Once the air motor is working, the air motor frequency still is observable in the frequency spectrum of the voltage signal, however, there are not any interferences with the bearing fault frequency components, according to Figure 29D. Figure 29D shows that using an embedded piezoelectric transducer for local measurement also performs better than an accelerometer at low rotational speed for detecting outer ring fault. In order to conclude the effect of external vibration and noise on the PZT transducer compared with an accelerometer, Figures 30A and 30B give the power spectrum density (PSD) of the accelerometer and PZT transducer in impact-free and impacted conditions. According to Figures 30A and 30B, a wide frequency range of the accelerometer is affected by the external impact which also has a high amplitude. In contrast, the external impact affects a narrower frequency range of the PZT transducer. In addition, the affected frequencies of the PZT transducer have low amplitudes compared with the impact-free condition. Hence, it can be concluded that detection bearing local faults by an embedded PZT transducer is less challenging, especially in a noisy setting. Even though various advanced and successful filtering methods have been proposed in the literature to detect bearing faults from the acceleration signal in noisy settings [34], using embedded sensors can significantly ease the fault detection process. The proposed method herein also may be suitable for low-speed machines in which the fault symptom do not adequately excite the natural frequency of the machine to be captured by the accelerometer.

DURABILITY ANALYSIS OF THE TRANSDUCER

As previously explained, it is desired to provide a small-size PZT transducer that is less subjected to direct load from the shaft. In previous studies, such as [8], the PZT transducer was mounted on the lower half of the housing which covers about 180° of the outer ring. Any radial load to the shaft is directly applied to the PZT transducer. Considering that in some applications, there could be a heavy load on the shaft, the cyclic load can lead to fatigue of the transducer over time since piezoelectric materials are brittle. Therefore, by means of simulation in ANSYS Mechanical APDL, the bearing dynamic model referenced hereinbefore is run for different radial loads to estimate the interface force between the transducer and the outer ring. The interface force between the top alumina disc causes radial stress in the thickness of the PZT transducer and is preferred to be less than the shaft radial load. The designated loads are from 1000 N to 4000 N, close to the fatigue load limit of the bearing provided by SKF (4550 N).

Figure 31 illustrates the interface contact force between the transducer and the outer ring under different radial loads. Figure 31 shows that the interface force is about 3-4% of the shaft radial load, which is much less than the total shaft radial load. In fact, the radial load from the shaft is transferred to the inner ring and rollers. Then, summation of the rollers forces creates the same amount of load on the outer ring of the bearing. Since the outer ring is tightened inside the split housing of the bearing, the load is distributed on the inner curved surfaces of the housing. Obviously, having a small slot or hole in the housing and mounting the PZT transducer inside it does not significantly influence this load distribution, and the transducer captures only a small portion of the load. Therefore, it can be concluded that the proposed PZT transducer and the mounting location can be safer compared to the previous designs. For the implemented PZT ceramic in the illustrated arrangement, the compressive strength of 600 MPa is reported by the supplier. If the radial load of 4,000 N is applied to the bearing, The compressive stress on the PZT disc is equal to 18 MPa which is much smaller than the compressive strength.

Based on this disclosure, the small size and the good performance of the designed transducer are promising for future industries where smart bearings with integrated sensors are implemented, particularly for condition monitoring. It will be appreciated that the transducer is preferably sealed to prevent penetration of lubricant between the layers. Although performance of the novel transducer is discussed with specific reference to the cylindrical roller bearing, it is expected that for bearings without angular contact regions, such as deep groove ball bearings, needle bearings, or double-row roller/ball bearings, the novel transducer will perform substantially similarly because the transducer is directly excited by maximum strain in the radial direction. For bearings with angular contact area, such as angular contact ball bearings or tapered roller bearings, the fault symptoms might be a bit weaker since the maximum strain is not in the radial direction due to the angular contact region. In addition, for thrust bearings, the position of the transducer is preferably modified since the strain changes from the rolling elements are in the axial direction along the shaft axis.

CONCLUSIONS

As described herein, there is disclosed a piezoelectric transducer for local fault detection in a cylindrical roller bearing. The transducer is embedded inside the bearing housing by creating a small slot. Compared to common techniques of using accelerometers mounted on the housing of the bearing, it is expected to have more obvious fault symptoms through the piezoelectric transducer due to the shorter transmission path to the bearing. In addition, the developed transducer is less expensive compared with a typical accelerometer. Both FE modeling and experimental tests are considered to analyze the transducer performance. Through modal analysis and impact test it is verified that the first natural frequency happens much beyond the frequency range of 0-15 kHz. This frequency range is enough for the application of bearing condition monitoring. In this disclosure, three tests are conducted to evaluate the transducer performance.

In the first test, the fault detection ability of the transducer is investigated using simulation and experiment. Through dynamic FE modeling of the bearing with an embedded piezoelectric transducer, the excitation forces on the transducer are modeled in healthy and faulty conditions. The existence of local faults at different locations of the outer ring affected the excitation force on the transducer, which in the experiment, caused spikes in the voltage signal. To validate the observations from the simulation, the transducer was experimentally tested in a bearing test apparatus for two faulty cases of the outer ring and roller faults. In both cases, the transducer gives signals with clear fault symptoms both in the time and frequency domain, similar to a commercial accelerometer. Through this test, the location of the fault on the outer ring can be estimated by the PZT transducer. Also, a faulty outer ring, faulty roller, or combination of both faults at the same time is detectable through the transducer.

In the second test, an air motor with an excitation frequency of 50 Hz was attached to the bearing apparatus to investigate the performance in a more realistic environment with noise and vibration. Comparing the results in two rotational speeds of 250 and 1000 rpm demonstrated that the bearing fault frequencies in the acceleration signal are masked in the frequency spectrum since the air motor excitation dominated the vibration signal. Nevertheless, in the voltage signal of the proposed transducer, both bearing fault frequencies and air motor frequencies are detectable. In fact, fault frequencies and air motor frequencies are easily distinguishable. For further investigation, the PSD of the accelerometer and piezoelectric transducer demonstrated that a wide frequency range of the accelerometer is affected by the air motor, which shows the superiority of using embedded sensors in a noisy environment.

In the third test, the preliminary durability analysis of the transducer is tested. Different shaft radial loads up to 4000 N were considered in the simulation. However, only 3-4% of this load was transferred to the transducer. As a result, the transducer is less subjected to load from the shaft than in the previous studies mentioned in the literature. According to the results, the transducer demonstrated promising performance in fault detection under various conditions. These may be innovations for smart bearings with integrated sensors.

SPEED MEASUREMENT AND FAULT DETECTION

In this section, the performance of the PZT transducer is investigated in two subsections. First, the speed measurement ability of the transducer is discussed. In the second section, the time-frequency domain of the normalized voltage signal is presented. In these conditions, the ball pass frequency on the outer ring (BPFO) is a parameter that is determinative in the modulation of the signal and speed measurement. The BPFO for a bearing with the fixed outer ring can be calculated by the following equation: where, f _s refers to the rotational frequency of the shaft, z stands for the number of rollers, D, and D _p indicate roller diameter and pitch diameter, and a is the contact angle of the bearing. For bearing type SKF N305 ECP, there are 11 rollers with a contact angle of zero. Also, the roller diameter and pitch diameter are equal to 10 and 44 mm, respectively. For varying rotational speed, f _s is variable, and it is not possible to calculate a constant BPFO. Therefore, by tracking instantaneous roller pass frequency (IRPF) in the time-frequency spectrum, the amplitude variations of the BPFO compared with the healthy condition can be investigated which is discussed in the next section.

SPEED MEASUREMENT

In order to interpret the behavior of the bearing frequency components for fault detection, knowing the speed variation helps with separating the vibration related to the rotational source from the random vibration. However, due to installation limitations and the expensive price of speed measurement devices, such as encoder and tachometer, it is preferred to detect the speed changes from the vibration sensor. As mentioned before, the novel transducer is excited by local strain changes by BPFO. Therefore, the time interval between two excitations (At) is equal to the inverse of the BPFO.

Figures 32A through 32C demonstrate the voltage signal of the transducer in healthy and faulty conditions. In Figure 32A, the voltage amplitude changes due to speed fluctuations are illustrated. The zoomed view of the signal in Figure 32B shows the time interval between two peaks that is equivalent to the inverse of the BPFO. Therefore, for sampled window length, the distance between these peaks gives the BPFO by assuming a constant speed in the sampled window length. If the speed fluctuations are not abrupt, by substituting the calculated BPFO in Eq (10), the shaft rotational frequency (f _s ) is extracted. By selecting adequately small window lengths and assuming constant speed in each window, the rotational speed of the shaft can be obtained. In Figure 32C, despite having a local fault on the outer ring, still, the interval between impulses represents the inverse of the BPFO. This technique is adopted to calculate speed changes in the bearing.

Figures 33A and 33B give the estimated rotational speed by the PZT transducer compared with a reference encoder that is installed on the AC motor. According to Figure 33A, the rotational speed of the bearing is accurately estimated by the PZT transducer. To achieve this, the signal is divided into window sizes of 5,000 samples with a sampling frequency of 27 kHz. This signal processing is conducted in MATLAB and for each window, the speed is estimated based on finding the interval between the peaks using the internal functions of MATLAB. By using sampling with a window size of 5,000 data points, the sampling frequency has been reduced by 5,000 times accordingly. To compensate for these changes, the vector size of the estimated speed is changed back to the original signal length by using linear interpolation. In addition, Figure 33B illustrates the voltage amplitude from the PZT transducer which is following the trend of speed variations. Assuming the encoder as the reference speed sensor, the absolute error of the speed measurement by the PZT transducer is 3.5%. Hence, this transducer can be successfully used as a speed sensor.

FAULT DETECTION IN THE SPEED VARYING CONDITION

By running the tests apparatus under 800 N radial load on the test bearing and randomly changing the rotational speed the voltage signal of the PZT transducer is recorded. Basically, the voltage of piezoelectric materials is highly dependent on the frequency of excitation. In addition, the preload on the transducer is a determinative parameter in the output voltage. If in several tests the preload on the PZT transducer is different, the output voltage will not be consistent in these cases. Therefore, both frequency of excitation and preload can interfere with the consistent data recording. To overcome this issue, the signal can be normalized to limit the amplitude between -1 and 1 v to ease the consistent data recording [40].

Figures 34A and 34B illustrate the normalized voltage signal. In Figure 34A, the raw signal in the healthy condition is given. Due to speed variation, the amplitude is modulated with speed fluctuations. However, if the signal is divided by the maximum amplitude in the recorded duration, the signal is normalized to the range of -1 to 1 V. This can be seen in Figure 34B as well, where the bearing is in the faulty situation and the normalized signal is dropped into the range of -1 to 1 v. This normalization simplifies the consistent data reading since the effect of preload bolt and bearing load reduces on the signal amplitude.

Figures 35A and 35B demonstrate the time-frequency representation of the normalized voltage signal in healthy and faulty conditions. By adopting a short-time Fourier transform (STFT) with a window size of 10,000 samples and using a Kaiser window, the timefrequency spectrum is created. As shown in Figure 35A, the roller pass frequency on the outer ring is the dominant frequency component in the frequency spectrum. Therefore, the dominant frequency over time is the IRPF and its second harmonic. Since this time-frequency representation (TFR) is made by the normalized signal, it can be used as the reference TFR for comparison. According to the literature [41], it was shown that the existence of a local fault can significantly elevate the harmonics of the IFCF in the TFR. Also, if the fault is on the outer ring, the dominant BPFO, and its harmonic face amplitude elevation. It can be observed in Figure 35B that the existence of local fault has significantly increased IRPF and its harmonics which indicate the elevation of BPFO in each window. By comparing the healthy and faulty conditions, it is concluded that the developed transducer can be successfully used in speed-varying conditions.

In addition to the fault on the outer ring, roller defect has also been investigated in this disclosure. Compared to the faulty outer ring, where the fault position is not rotating, the roller fault can be more challenging since the fault is rotating with the shaft. Figures 36A through 36F demonstrate the symptoms of the faulty roller compared to the healthy condition. In Figure 36A, the voltage signal of the healthy bearing is demonstrated which only includes amplitude elevation by the roller pass frequency. In case of having a faulty roller, some spikes in the signal are generated by the faulty roller as shown in Figure 36B. The TFR of these two signals in healthy and faulty conditions are presented in Figure 36C and 36D, respectively. The TFR of the healthy bearing only includes a dominant IRPF and its second and third harmonic, as already discussed with respect to Figure 35A. However, the faulty roller elevated the magnitude of the TFR over a wide frequency range after the 2 ^nd harmonic which demonstrates an abnormal condition. Even though the frequency domain by Fourier transform is not a suitable method for speed-varying conditions due to frequency smearing, but obtaining the frequency domain in Figures 36E and 36F can better clarify the effect of roller fault on the frequency spectrum here. According to Figure 36E, three ranges for IRPF and its 2 ^nd and 3 ^rd harmonics are demonstrated for the healthy bearing. In the faulty condition in Figure 36F, a wide frequency range including the range of the 3 ^rd harmonic is elevated up to 1500 Hz due to the faulty roller. Therefore, it can be concluded that the developed PZT transducer also is capable of detecting local faults under speed-varying conditions, whether the fault is on the stationary outer ring or the rotating parts like the rollers.

FURTHER CONCLUSIONS

As described hereinbefore, the performance of an embedded piezoelectric transducer for fault detection in variable speed conditions is investigated. These days, due to the current trend toward intelligent manufacturing and developing smart bearings for future rotating machines, it is preferred to have low-cost and self-sensing sensors. Moreover, by implementing the sensor in the close vicinity of the bearing, the effect of surrounding noise and vibration interferences can be significantly decreased. Therefore, a previously developed piezoelectric transducer embedded inside the housing of a cylindrical roller bearing has been adopted to further investigate the performance in speed monitoring and fault detection. According to the results, by instantaneously calculating the interval between voltage peaks in the signal, the roller pass frequency on the outer ring was calculated which can be converted into rotational speed by using the bearing fundamental frequencies. The results demonstrated a great correlation in the measured speed compared with a commercial encoder. Furthermore, by randomly changing the rotational speed in healthy and faulty conditions, the voltage signal was recorded and normalized into the range of -1 to 1 v by instantaneously sampling. Then, the normalized signal was converted into a time-frequency domain employing an STFT. Since this transducer is always excited by roller pass frequency, even in the healthy condition, the time-frequency spectrum in the faulty condition demonstrated an obvious elevation in the IRPF and its harmonics. According to the results, it can be concluded that this low-cost PZT transducer can be successfully used as a speed sensor and for detecting local faults, both in constant and variable speed conditions. However, these tests were conducted in an ideal laboratory setting with minimum background noise and vibration from other components, which simplified the fault detection process. Therefore, testing the transducer in real applications where several rotating components, such as gears, are involved can better demonstrate the performance of the transducer.

As described hereinbefore, the present invention relates to a transducer for use with a rotary bearing rotatably interconnecting an inner member along a rotational axis and an outer member supporting the rotary bearing. The transducer comprises a piezoelectric body arranged for physical deformation; a pair of electrodes arranged to receive an electrical signal generated by the piezoelectric body in response to physical deformation thereof; a substantially incompressible force-transmission member on one end of the piezoelectric body and defining an exterior contact surface for operative mechanical engagement with the rotary bearing to receive vibration therefrom; electrical insulation surrounding the piezoelectric body and arranged to prevent transmission of an electrical signal generated thereby to a proximal electrically conductive body; and a substantially electrically nonconductive base in opposite relation to the force-transmission member and covering a corresponding end of the piezoelectric body. In use, the transducer is mounted adjacent a receptacle receiving the bearing so as to be in operative mechanical engagement therewith.

The scope of the claims should not be limited by the preferred embodiments set forth in the examples but should be given the broadest interpretation consistent with the specification as a whole.

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Table 1 : Comparison of different sensor types for bearing fault detection.

Table 2: Specification of the cylindrical roller bearing SKF N305 ECP. Table 1 : Material properties of the components in the FE model.

Table 2: Bearing fundamental frequencies.

Table 3. Bearing frequencies in different rotational speeds.

Table 4: The signal characteristics of the accelerometer under external excitations at different speeds. Table 5. The signal characteristics of the PZT transducer under external excitations at different speeds.