SYSTEM, APPARATUS AND METHOD FOR ESTIMATING REMAINING USEFUL

LIFE OF AT LEAST ONE BEARING

The present invention relates to a field of bearing monitoring systems and more particularly relates to estimating remaining useful life of at least one bearing .

Bearings are used in several machinery in an indust ry for the purpose of reducing friction between two rotating part s . These bearings also re strict relative motion between the rotating part s to a desired motion . However, bearings may fail unex- pectedly due to factors such as poor lubrication and contami- nation within a structure of the bearing . For example , lubri- cation within the bearing may fail during an operat ional phase of the bearing due to exces sive temperatures . Contamination may occur due to entry of foreign particles , moisture etc . into the structure of the bearing . The above factors lead to failure modes such as corrosion, spalling, pitting, electrical erosion, plastic deformation and the like , in the bearing . As a result , an expected fatigue life of the bearing as sembly is reduced and eventually failures occur . Consequently, bearing failures may cause unexpected downtime of the machinery, re- sulting in production and financial los s . In safety-critical applications , bearing failures may also put human lives at risk .

In light of the above , there exist s a need for estimating remaining useful life of a bearing .

Therefore , it is an ob j ect of the present invention to provide a system, apparatus and method for estimating remaining useful life of at least one bearing . The ob j ect of the present invention is achieved by a method for estimating remaining useful life of at least one bearing .

The method comprises receiving a request for analysing a defect in the at least one bearing . The term ' defect ' as used herein refers to any structural deformities within the at least one bearing that result in abnormal operation of the bearing . The request comprises operational data as sociated with the at least one bearing . In one embodiment , the operational data comprises an output of at least one sensing unit as sociated with the bearing in real-time . It must be understood that the term ' sensing unit ' as used herein includes both transducers and sensors . In addition to the above , the request may also specify one or more bearing parameters .

Advantageously, the present invent ion faciliates estimation of remaining useful life of bearings of any size based on the respective operational data .

The method compri ses determining vibration spectrum of the at least one bearing from the received operational data . Advan- tageously, the conversion of the operational data f rom time domain to frequency domain helps in enveloping the signal and protect s from the unneces sary vibrations that are caused by the sources from external physical factors . Furthermore, the determination of remaining useful life of the at least one bearing based on the vibration spectrum improves accuracy and

The method comprises monitoring an impact of the de fect on the at least one bearing over a period of time based on the deter- mined vibration spectrum . The term ' impact ' as used herein refers to deviat ions from a normal operation of the bearing resulting from the defect . In an embodiment , in monitoring the impact of the defect , the method comprises monitoring anoma- lies in the output of the at least one sensing unit . Advantageously, the present invention facilitates continuous monitoring of impact s due to defect s in a bearing in real- time .

The method comprises determining one or more charateristic values from the vibration spectrum for which the impact of the defect on the bearing is above a threshold range . In an exam- ple , determining the one or more charateristic values compirses analyzing the operational data as scoaited with the at least one bearing .

The method comprises determining an impact force during an operation of the at least one bearing based on the determined one or more charateristic values and one or more parameters obtained from a virtual bearing model . The term ' impact force ' as used herein refers to a contact force or maximum com- pires sion force experienced by the ball upon entering an edge of the defect .

In an embodiment , determining an impact force during an oper- ation of the at least one bearing comprises generat ing the virtual bearing model for a group of bearings comparable with the at least one bearing .

In an embodiment , generating the virtual bearing model com- prises determining test operation profiles based on test op- eration data as sociated with the group of bearings . Further, the method coprises simulating the predetermined de fect s on a predefined bearing model compris ing dataset pursuant to dy- namic load rating standards and rating life standards as soci- ated with the group of bearings . Further, the method comprises generating simulated operation profiles in frequency domain as sociated with the group of bearings based on the simulation of the predetermined defect s on the predefined bearing model . In a preferred embodiemnt , determining the impact force during an operation of the at least one bearing comprises determining calibrated impact force for the group of bearings based on a correlation model obtained from frequency spectrum of simula- tion vibration signals and the generated simulated operation profiles in frequency domain as sociated with the group of bearings .

In an embodiment , the virtual bearing model is generated based on one or more of simulation data, experimental data and math- ematical data as sociated with the group of bearings .

In an embodiment , determining the impact force further com- pirses optimizing the one or more parameters in the determined calibrated impact force for the group of bearings using a machine learning model .

In an embodiemnt , determining the impact force further com- prises determining dynamic parameter for the at least one bearing based on the one or more parameters determined for each of the bearings in the group of bearings .

Advantageously, the present invention uses impact froce during the time period to obtain remaining useful life of the bearing .

The method compri ses determining the remaining useful life of the at least one bearing based on the imapct force and the operational data during the time period . The term ' remaining useful life ' as used herein, refers to a duration between initiation of a detectable failure mode and a funct ional fail- ure of the bearing . In a preferred embodiment , in determining the remaining useful life , the method comprises computing a dynamic parameter as sociated with the bearing based on the impact force using the virtual model of the bearing . In one embodiment , the dynamic parameter is a dynamic equivalent load on the bearing .

Further, a remaining useful life model of the bearing is con- figured based on the dynamic parameter . The remaining useful life model is a dynamic model that relates the dynamic param- eter to a life of the bearing . Further, the remaining useful life of the bearing is computed based on the configured re- maining useful life model and the operational data .

Advantageously, the present invention facilitates use of im- pact force to determine a dynamic parameter that influences degradation of the bearing .

The method compri ses generating a notification indicating the remaining useful life of the bearing on an output device . In addition to the remaining useful life , the notif ication may further include diagnostic information as sociated with the bearing . For example , the diagnostic information may indicate the impact force curve , the RUL curve , time and spectral domain velocity curves , and an indication of the state of degradation on the RUL curve .

The ob j ect of the present invention is achieved by an apparatus for estimating remaining useful life of a bearing . The appa- ratus comprises one or more proces sing unit s , and a memory unit communicatively coupled to the one or more proces sing unit s . The memory unit comprises a bearing management module stored in the form of machine-readable instructions executable by the one or more proces sing unit s . The bearing management module is configured to perform method steps described above .

The execution of the condition management module may also be performed using co-processors such as Graphical Processing Unit (GPU) , Field Programmable Gate Array (FPGA) or Neural Processing/Compute Engines.

According to an embodiment of the present invention, the ap- paratus can be an edge computing device. As used herein "edge computing" refers to computing environment that is capable of being performed on an edge device (e.g., connected to sensing units in an industrial setup and one end and to a remote server (s) such as for computing server (s) or cloud computing server (s) on other end) , which may be a compact computing device that has a small form factor and resource constraints in terms of computing power. A network of the edge computing devices can also be used to implement the apparatus. Such a network of edge computing devices is referred to as a fog network .

In another embodiment, the apparatus is a cloud computing sys- tem having a cloud computing based platform configured to pro- vide a cloud service for analyzing analyzing defects in a bearing. As used herein, "cloud computing" refers to a pro- cessing environment comprising configurable computing physical and logical resources, for example, networks, servers, stor- age, applications, services, etc., and data distributed over the network, for example, the internet. The cloud computing platform may be implemented as a service for analyzing defects in a bearing. In other words, the cloud computing system pro- vides on-demand network access to a shared pool of the config- urable computing physical and logical resources. The network is, for example, a wired network, a wireless network, a com- munication network, or a network formed from any combination of these networks.

Additionally, the object of the present invention is achieved by a system for estimating remaining useful life of a bearing. The system comprises one or more sources capable of providing operational data as sociated with a bearing and an apparatus as described above , communicatively coupled to the one or more sources . The term ' sources ' as used herein, refer to electronic devices configured to obtain and transmit the operational data to the apparatus . Non-limiting examples of sources include sensing unit s , controllers and edge devices .

The ob j ect of the present invention is also achieved by a computer-readable medium, on which program code sections of a computer program are saved, the program code sections being loadable into and/or executable by a proces sor which performs the method as described above when the program code sections are executed .

The above-mentioned attributes , features , and advantages of this invention and the manner of achieving them, will become more apparent and understandable ( clear ) with the following description of embodiment s of the invention in con j unction with the corresponding drawings . The illustrated embodiment s are intended to illustrate , but not limit the invention .

FIG 1A illustrates a block-diagram of a system for estimat- ing remaining useful life of at least one bearing, in accordance with an embodiment of the present inven- tion ;

FIG 1B illustrates a block-diagram of an apparatus for es- timating remaining useful life of at least one bear- ing, in accordance with an embodiment of the present invention ;

FIG 2A illustrates structure of a ball bearing;

FIG 2B illustrates a defect in an outer race of the ball bearing; FIG 3 illustrates an experimental test set-up for building a virtual model of a bearing, in accordance with an embodiment of the present invention ;

FIG 4A is a Graphical User Interface view showing an example time-velocity curve of the operational data obtained from the sensing unit , in accordance with an embodi- ment of the present invention ;

FIG 4B is a Graphical User Interface view showing peak am- plitudes values when signal is pas sed through band- pas s filter, in accordance with an embodiment of the present invention ;

FIG 5 depict s a flowchart of a method for estimating re- maining useful life of the bearing, in accordance with an embodiment of the present invention ;

FIG 6 is an exemplary web-based interface that enables a user to provide values for the one or more bearing parameters from a client device , in accordance with an embodiment of the present invention ;

FIG 7 is a Graphical User Interface view showing an example of determined output , in acccordance with an embodi- ment of the present invention ;

FIG 8 is a Graphical User Interface view showing an example of impact force and speed curve , in accordance with an embodiment of the present invention ;

FIG 9A is a Graphical User Interface view showing an example of ball velocity as obtained from operational data in time domain, in accordacne with an embodiment of the present invention ; FIG 9B is a Graphical User Interface view showing an example of power spectrum in frequency domain, in accordance with an embodiemnt of the present invention ;

FIG 10 is a Graphical User Interface view showing degrada- tion in remaining useful life , in accordance with an embodiment of the present disclosure .

Hereinafter, embodiment s for carrying out the present inven- tion are described in detail . The various embodiment s are de- scribed with reference to the drawings , wherein like reference numerals are used to refer to like element s throughout . In the following description, for purpose of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiment s . It may be evident that such embodiment s may be practiced without these specific details .

FIG 1A illustrates a block-diagram of a system 100 for esti- mating remaining useful life of a bearing 105 , in accordance with an embodiment of the present invention . For example , the bearing 105 may be part of a rotating equipment such as an industrial motor (not shown ) . Non-limiting examples of bear- ings include deep groove ball bearings , cylindrical roller bearings , a tapered roller bearing, thrust bearing, angular contact ball bearing, needle ball bearing and the like . In the present embodiment , the bearing 105 comprises an inner race , an outer race and a plurality of rolling element s disposed in a gap between the inner race and the outer race . The bearing 105 further comprises a cage positioned between the inner race and the outer race for maintaining a symmetric radial gap between the rolling element s . An example of a bearing is de- scribed later in the present disclosure with reference to FIG

2A . The system 100 comprises an apparatus 110 communicatively cou- pled to one or more edge devices 115. The one or more edge devices 115 are connected to the apparatus 110 via a network 120, for example, local area network (LAN) , wide area network (WAN) , WiFi, etc. Each of the edge devices 115 is configured to receive sensor data from at least one sensing unit 125 associated with the bearing 105. The at least one sensing unit 125 may include, for example, a vibration sensor, a velocity sensor, an acceleration sensor and a force sensor. The sensor data corresponds to an output of the at least one sensing unit 125. For example, the output from the at least one sensing unit 125 may be in the form of vibration data, velocity data, acceleration data or force data. In an embodiment, the sensor data are obtained through data acquisition interfaces on the edge device 115. The edge device 115 provides the sensor data in real-time to the apparatus 110.

In addition, the edge device 115 is also configured to provide one or more bearing parameters associated with the bearing 105 to the apparatus 110. The one or more bearing parameters in- clude, but are not limited to, a standard bearing number, a ball size, bearing static load, density of material, angular velocity, internal clearance, bearing diameter, number of rolling elements, radius of rolling element, diameter of inner race, diameter of outer race, defect size, fatigue load limit, and type of lubricant used in the bearing 105. It must be understood that the standard bearing number is indicative of certain specifications such as a ball size, bearing static load, density of material, internal clearance, bearing diame- ter, number of rolling elements, radius of rolling element, diameter of inner race, diameter of outer race, fatigue load limit, bearing width and the like, as provided by a manufac- turer of the bearing 105. Therefore, in an embodiment, the standard bearing number as sociated with the bearing 105 may be provided in place of the above bearing parameters .

The one or more bearing parameters may be stored in a memory of the edge device 115 or may be input to the edge device 115 by an operator . For example , the edge device 115 may be com- municatively coupled to a client device 130 . Non-limiting ex- amples of client devices include , personal computers , work- stations , personal digital as sistant s , human machine inter- faces . The client device 130 may enable the user to input values for the one or more bearing parameters through a web- based interface . Upon receiving the one or more bearing param- eters from the user, the edge device 115 transmit s a request for analysing a defect in the bearing 105 to the apparatus 110 . The defect s occur due to initiation of a failure mode in the bearing 105 . Non-limiting examples of failure modes in- clude spalling, pitting, plastic deformation, abras ion, elec- trical erosion and corrosion typically on an outer race of the bearing 105 . The defect s may occur due to presence of contam- inant s or due to properties of a lubricant used within the bearing 105 . The request comprises the one or more bearing parameters along with the sensor data .

In the present embodiment , the apparatus 110 is deployed in a cloud computing environment . As used herein, "cloud computing environment" refers to a proces sing environment comprising configurable computing physical and logical resources , for ex- ample , networks , servers , storage , applications , services , etc . , and data di stributed over the network 120 , for example , the internet . The cloud computing environment provides on- demand network acces s to a shared pool of the configurable computing physical and logical resources . The apparatus 110 may include a module that estimates remaining useful life of a given bearing based on the corresponding sensor data and the one or more bearing parameters. Additionally, the apparatus 110 may include a network interface for communicating with the one or more edge devices 115 via the network 120.

The apparatus 110 comprises a processing unit 135, a memory unit 140, a storage unit 145, a communication unit 150, the network interface 155 and a standard interface or bus 160, as shown in FIG IB. The apparatus 110 can be a computer, a work- station, a virtual machine running on host hardware, a micro- controller, or an integrated circuit. As an alternative, the apparatus 110 can be a real or a virtual group of computers (the technical term for a real group of computers is "cluster", the technical term for a virtual group of computers is "cloud") .

The term 'processing unit' 135, as used herein, means any type of computational circuit, such as, but not limited to, a mi- croprocessor, microcontroller, complex instruction set compu- ting microprocessor, reduced instruction set computing micro- processor, very long instruction word microprocessor, explic- itly parallel instruction computing microprocessor, graphics processor, digital signal processor, or any other type of pro- cessing circuit. The processing unit 135 may also include em- bedded controllers, such as generic or programmable logic de- vices or arrays, application specific integrated circuits, single-chip computers, and the like. In general, a processing unit 135 may comprise hardware elements and software elements. The processing unit 135 can be configured for multi-threading, i.e. the processing unit 135 may host different calculation processes at the same time, executing the either in parallel or switching between active and passive calculation processes.

The memory unit 140 may be volatile memory and non-volatile memory. The memory unit 140 may be coupled for communication with the processing unit 135. The processing unit 135 may execute instructions and/or code stored in the memory unit 140 . A variety of computer-readable storage media may be stored in and acces sed f rom the memory unit 140 . The memory unit 140 may include any suitable element s for storing data and machine- readable instructions , such as read only memory, random acces s memory, erasable programmable read only memory, electrically erasable programmable read only memory, a hard drive , a remov- able media drive for handling compact disks , digital video disks , diskettes , magnetic tape cartridges , memory cards , and the like .

The memory unit 140 comprises a bearing management module 1 65 in the form of machine-readable instructions on any of the above-mentioned storage media and may be in communication to and executed by the proces sing unit 135 . The bearing management module 1 65 comprises a preproces sing module 170 , an impact monitoring module 175 , an impact force computation module 180 , a life estimation module 185 and a notification module 1 90 . The preproces sing module 170 is configured for receiving a request for analyzing a defect in the bearing 105 . The request comprises the operational data as sociated with the bearing 105 and the one or more bearing parameters . The preproces sing mod- ule 170 is configured for determining vibration spectrum of the at least one bearing from the received operational data . The impact monitoring module 175 is configured for monitoring an impact of the defect on the bearing 105 over a period of time . The impact monitoring module 175 is further configured for determining one or more frequencies from the vibration spectrum for which the impact of the defect on the bearing is above a threshold range . The impact force computation module 180 is configured for determining an impact force during an operation of the at least one bearing based on the determined one or more frequencies and one or more parameters obtained from the virtual bearing model . The life estimation module 185 is configured for determining a remaining useful life of the bearing 105 based on the impact force and the operational data during the time period. The notification module 190 is config- ured for generating a notification indicating the remaining useful life of the bearing 105 on an output device. In the present embodiment, the output device may be the client device 130.

The storage unit 145 comprises a non-volatile memory which stores default bearing parameters associated with standard bearing numbers. The storage unit 145 includes a database 195 that comprises default values of bearing parameters and one or more look-up tables comprising predetermined values for fac- tors that vary with operating conditions of the bearing 105. The bus 160 acts as interconnect between the processing unit 135, the memory unit 140, the storage unit, and the network interface 155. The communication unit 150 enables the appa- ratus 110 to receive requests from the one or more edge devices 115. The communication module may support different standard communication protocols such as Transport Control Protocol/In- ternet Protocol (TCP/IP) , Profinet, Profibus, and Internet Protocol Version (IPv) .

Those of ordinary skilled in the art will appreciate that the hardware depicted in FIG 1A and IB may vary for different implementations. For example, other peripheral devices such as an optical disk drive and the like, Local Area Network (LAN) / Wide Area Network (WAN) / Wireless (e.g., Wi-Fi) adapter, graphics adapter, disk controller, input/output (I/O) adapter, network connectivity devices also may be used in addition or in place of the hardware depicted. The depicted example is provided for the purpose of explanation only and is not meant to imply architectural limitations with respect to the present disclosure . FIG 2A illustrates structure of a ball bearing 200. The ball bearing 200 comprises an outer race 210 of diameter D, a plu- rality of balls 215 each of radius r _ball , a cage 220 and an inner race 225 of diameter d. The plurality of balls 215 are disposed in a gap between the outer race 210 and the inner race 225. The cage 220 maintains a symmetric radial spacing between the balls 215. FIG 2B illustrates a defect of defect size ddefect on a wall of the outer race 210 in contact with the balls 210. In the present example, the defect is an indentation in the outercase due to pitting. The defect size may be defined as a distance travelled by a ball of the ball bearing 200 between entering and leaving the defect. The defect subtends an angle θ _center at the center of a ball 215A among the plurality of balls 215 as shown. The angular velocity of a shaft on which the ball bearing 200 is mounted, is indicated as 0) .

FIG 3 illustrates an experimental test set-up 300 for building a virtual model of a bearing, in accordance with an embodiment of the present invention. In the present embodiment, the vir- tual model corresponds to ball bearings. It must be understood by a person skilled in the art that the virtual model may be built for other types of bearings in a similar manner.

The virtual model may be based on one or more of physics-based models, Computer-Aided Design (CAD) models, Computer-Aided En- gineering (CAE) models, one-dimensional (ID) models, two-di- mensional (2D) models, three-dimensional (3D) models, finite- element (FE) models, descriptive models, metamodels, stochas- tic models, parametric models, reduced-order models, statis- tical models, heuristic models, prediction models, ageing mod- els, machine learning models, Artificial Intelligence models, deep learning models, system models, surrogate models and the like . In the present embodiment, the virtual model is built based on test operation data such as simulation data, experimental data and mathematical data associated with a plurality of bearings under a plurality of operating conditions. The plurality of operating conditions may be generated based on a Design Of Experiments (DOE) for varying values of load, angular velocity and defect size. Here, the term 'load' indicates bearing static load. For example, the defect size may be selected as one of 0.1 mm, 0.2 mm, 1 mm, 2 mm, 3 mm, 4 mm and 5 mm. The load may be one of 400 N and 500 N. The angular velocity may be one of 1000 rad/s, 1200 rad/s, 1400 rad/s and 1600 rad/ s . In the present embodiment, simulation data, experimental data and mathematical data associated with a group of bearings compris- ing three standard ball bearings are used. For example, a first bearing among the three bearings may have a standard bearing number 6205, a second bearing may have a standard bearing number 6213 and a third bearing may have a standard bearing number 6319.

The experimental set-up 300 comprises a bearing 305, at least one force sensor 310 and at least one vibration sensor 315 attached to the bearing 305. The force sensor 310 and the vibration sensor 315 are communicatively coupled to an appa- ratus 320, similar to the apparatus 110. In an embodiment, the apparatus 320 may include a data acquisition interface for receiving signals from the force sensor 310 and the vibration sensor 315. The bearing 305 is mounted on a rotating shaft. In an example, the rotating shaft is part of a rotating equipment. Further, one or more defects are artificially introduced into an outer race of the bearing 305. Each of the defects is associated with a known defect size as specified in the oper- ating conditions. The force sensor 310 is configured to measure an impact force resulting from a ball of the bearing passing through the defect. The term 'impact force' as used herein refers to a contact force experienced by the ball upon entering an edge of the de fect . In an example , the force sensor 310 is a triaxial piezoelectric crystal . The vibration sensor 315 is configured to measure vibrations or acceleration values re- sulting from the ball pas sing through the defect . In an exam- ple , the vibration sensor 315 is an accelerometer . Further, the test or experimental data is recorded . The test operation data comprises the impact force measured by the force sensor 310 and respective acceleration values measured by the vibra- tion sensor 315 for each of the operating condit ions . Simi- larly, the experimental data corresponding to each of the three bearings are recorded .

The simulation data is generated by simulating a behaviour of the bearings based on a multi-physics simulation model . The operating conditions may be provided as input s to the mul- tiphysics simulation model in a simulation environment . For example , the simulation environment may be provided by a com- puter-aided simulation tool on the apparatus 320 . The simula- tion model comprises Finite-Element models of an outer race , a cage , a plurality of rolling element s , an inner race and a shield as sociated with the bearing . In the present example , the rolling element s are balls . Further, the simulation model corresponding to each of the standard ball bearings is config- ured to model a defect in the outer race of a defect size specified in the operating conditions . For example , the defect may be as sociated with one of spalling, pitting, plastic de- formation, abrasion, electrical erosion or corrosion or a com- bination thereof .

Based on the configured simulation model , simulation instances are generated . The simulation instances are executed in the simulation environment to generate the simulation data for the bearing corresponding to each of the simulation data is gen- erated for the same operating conditions that were used for generating the test operational data . The simulation data com- prises values of simulated maximum impact force corresponding to each of the operating conditions . Similarly, simulation data is generated for each of the three bearings .

The apparatus 320 further builds the virtual model of the bearing based on the simulation data, the experimental data and the mathematical data . In one embodiment , the virtual model is a surrogate model . The virtual model is further validated based on test data generated using the experimental set up 300 . The test data comprises a set of operating conditions of the bearing comprising known values of defect size , angular velocity and load . The output of the force sensor i s compared to the output of the virtual model in order to detect an error as sociated with the virtual model . Further, parameters of the virtual model are tuned in order to minimize the error . The tuned virtual model may be used to predict the maximum impact force as sociated with any bearing for any given set of oper- ating conditions .

FIG 5 depict s a flowchart of a method 500 for estimating re- maining useful life of a bearing, in accordance with an embod- iment of the present invention .

At step 505 , a request for analysing a defect in the bearing is received, by the proces sing unit 135 . The request comprises one or more bearing parameters as sociated with the bearing received from a client device , similar to client device 130 , along with sensor data received from at least one sensing unit attached to the bearing . The sensor data may compri se output of the at least one sensing unit as sociated with the bearing . Both the client device and the at least one sensing unit are communicatively coupled to an edge device , similar to edge device 115 . In the present embodiment , the at least one sensing unit comprises an accelerometer mounted on a bearing housing as sociated with the bearing . The output of the at least one sensing unit is an acceleration signal in time domain .

In an implementation, a user may initiate the reque st by providing the one or more bearing parameters through a web- based interface provided on the client device . For example , the one or more bearing parameters include ball radius , bearing static load, density of material , angular velocity, defect size and internal clearance . FIG 6 illustrates an exemplary web-based interface 600 that enables a user to provide values for the one or more bearing parameters from the client device , in accordance with an embodiment of the present invention .

In one embodiment , one or more of the bearing parameters are specified through a standard bearing number based on an inter- national standard such as I SO dimensional series . For example , if the standard bearing number is 6213 , the size of the bearing in mm is 65x120x23 , where 65 mm is a diameter of the inner race , 120 mm is a diameter of the outer race and 23 mm is a width of the bearing . The web-based interface may provide a drop-down menu for selecting a bearing number from a plurality of bearing numbers . In the present example , the bearing number may be selected as 631 9 .

Based on the bearing number, dimensions such as the ball radius and the bearing diameter may be automatically populated on the web-based interface . Similarly, the web-based interface may also provide the user an option to manually enter the bearing parameters , if the bearing number is not displayed in the drop- down menu . Further, the user may confirm the values of the one or more bearing parameters by pres sing a ' submit ' button on the web-based interface to initiate the request . In a preferred embodiment, the sensor data corresponds to real-time operating conditions of the bearing.

At step 510, vibration spectrum of the at least one bearing is determined from the received operational data. The operational data as received from the sensing unit 125 is in time domain. In a preferred embodiment, the ball velocity is obtained from the vibration sensor 315 and represented in time domain. FIG 4A is a Graphical User Interface view 400A showing an example time-velocity curve of the operational data obtained from the sensing unit 125, in accordance with an embodiment of the present invention. The time domain vibration signals are con- verted into frequency domain using signal processing tech- niques such as fourier transform, fast fourier transform (FFT) , continuous wavelet transform (CWT) , discrete wavelet transform (DWT) , and the like.

In an example, the continusos wavelet transform is given by: (1)

In particular, the time domain vibration signals are converted into frequency domain using Hilbert transform.

In an example, the Hilbert transform of a signal u(t) is given by : (2)

The Hilbert transform helps in enveloping the signal and pro- tects the signal from unnecessary vibrations that are caused by teh setup or sources from external physical factors.

At step 515, an impact of the defect on the bearing over a period of time is monitored. The impact of the defect is mon- itored based on anomalies present within the sensor data. The anomalies may be indicated by features of signals generated by the at least one sensing unit . The features may include , but are not limited to, amplitude , frequency, harmonics , spectral energy, RMS velocity, presence of shock pulses or t ransient s , repetitive pulses , and the like . In the present embodiment , the sensor data comprises vibration signal in time-domain which is converted into frequecny domain . The impact may be identi- fied from the vibration signal using kurtosis analysis . More specifically, kurtosis of the enevloped signal at dif ferent time intervals is performed to find the band with the highest noise signal . In an example , the kurtosis of the signal is performed using the following mathematical relation : (3)

Subsequent to kurtosis analysis , a bandpas s filter is applied to the signal to filter out the noise signal . The resulting signal is represented in FIG 4B . FIG 4B is a Graphical User Interface view 400B showing peak amplitudes values when signal is pas sed through bandpas s filter, in accordance with an em- bodiment of the present invention .

In an example , amplitude of the filtered signal may indicate periodic impact s of the defect . Upon identifying presence of such an impact , step 520 is performed .

At step 520 , one or more charateristic values are determined from the vibration spectrum for which the impact of the defect on the bearing is above a threshold range . The one or more characteristic values are indicative of impact s caused by the the defect s in the defined time period . More specif ically, the one or more charateristic values indicate the value s for which the rolling element has high impact casued by the defect . In a preferred embodiment , the characteristics values may be peak amplitude values of velocity signal , peak amplitude values of acceleration signal , or peak amplitude values of di splacement signal as obtained from the operation data . The threshold range may be predefined by the operator or may be based on specifi- cations provided by a manufacturer of the bearing . For example , the threshold value may be defined as 2mm/ s . Based on an out- come of the envelope analysis , if the amplitude of the velocity signal cros ses the threshold value , then the time period during which the amplitude of the amplitude of the envelope is greater than 2mm/ s is identified .

At step 525 , an impact force is determined during an operation of the at least one bearing based on the determined one or characteristic values and one or more parameters obtained from a virtual bearing model . The term ' impact force ' as used herein refers to a contact force or maximum compires sion force expe- rienced by the ball upon entering an edge of the de fect . The impact force for the at least one bearing for the requested defect is determined from for the one or more determined char- acteristic values . The impact force relation comprises dy- namic parameter that impact s the remaining useful life of the bearing . The dynamic parameter is determined based on deter- mined one or more parameters obtained for each bearing in the group of bearings i . e . the three standard bearings .

In an embodiment , determining an impact force comprises gen- erating the virtual bearing model for a group of bearings comparable with the at least one bearing . The group of bearings comprises three standard bearings as aforementioned . In an embodiment , the virtual bearing model is a hybrid model gen- erated based on one or more of simulation data, experimental data and mathematical data as sociated with the group of bear- ings . In an embodiment , generating the virtual bearing model comprises determining test operation profiles based on test operation data as sociated with the group of bearings . . Fur- ther, the method comprises simulating the predetermined de- fect s on a predef ined bearing model comprising dataset pursu- ant to dynamic load rating standards and rating life standards as sociated with the group of bearings . Further, the method comprises generating simulated operation profiles in frequency domain as sociated with the group of bearings based on the simulation of the predetermined defect s on the predefined bear- ing model . The simulated operation profiles are genrated by trans forming the simulated data into frequency domain . The simulated operation profiles in frequency spectrum is used to determined simulated impact force for the group of bearings . Subsequently, calibrated impact force is determined from the simulated impact force .

In a preferred embodiemnt , determining the impact force com- prises determining calibrated impact force for the group of bearings based on a correlation model obtained from velocity spectrum of vibration signals and the generated simulated op- eration profiles in frequency domain as sociated with the group of bearings . Furthermore , the correlation model is genrated from the velocity spectrum of the vibration signals and force on the bearing . The force is calculated from the mathmatical relation based on simulated data and various regres sion mdoels as below : ( 4 ) wherein,

F is the force excreted by the ball in the edge of the defect X is the maximum displacement of the ball bearing on interac- tion with the defect edge

P is the amplitude peak of the frequency spectrum obtained from the vibration signal of the bearing n, a, b, c are the equation constant s that are optimized using the simulation data that is obtained from the virtual bearing model .

In an example , the correlation model is a regres sion model that maps peaks obtained from the frequency spectrum of the simulation vibration signals to the force that is calculated from the mathemat ical equations . More specifically, a code is generated in an Integrated Development Environment ( IDE ) using any of the known programming languages . In an example , the code is developed in Python . The python code is configured to build an optimum curve which relates the vibration spectrum peaks with the force . Furthermore , a mathematical relation is generated relating the force with the peaks . Further, the sim- ulated impact force is determined for the group of bearings based on the output of the correlation model and the generated simulation operation profiles . More specifically, the simu- lated impact forces are predicted for the group of bearings by extracting peak values from the simulated operation profiles . Further, each peak value thus obtained from the experimental bearing setup is fit into the mathematical relation generated from the correlation model to obtain the predict ion for the corresponding force during the test operation for the group of bearings .

Once the simulated impact force is determined, we further ob- tain the calibrated impact force by impact force analysis . In an embodiment , determining the impact force further compirses optimizing the one or more parameters in the determined cali- brated impact force for the group of bearings using a machine learning model . In the calibrated impact force equation, Hert z- ian contact theory is used as the fundamental constant in the equation . Accordingly, the maximum compres sion of the ball on it s interaction with the defect in the race of the bearing or the impact force is obtained using Newtonian mechanics . The force can be calculated using the given mathe- matical relation ( 4 ) : wherein,

F is the force excreted by the ball in the edge of the defect

X is the maximum displacement of the ball bearing on interac- tion with the defect edge

P is the amplitude peak of the frequency spectrum obtained from the vibration signal of the bearing n, a, b, c are the equation constant s that are optimized using the simulation data that is obtained from the virtual bearing model .

It should be noted that apart from the fundamental constant , we also use other constant (n, a, b, c ) along with multiple powers of the amplitude peaks obtained from the fre- quency spectrum of the vibration signal .

The mathematical data for calculating the maximum impact force or the maximum compres sion in a ball bearing is based on a mathematical model of a bearing . The mathematical model is of the form : ( 5 ) which can be rearranged as : ( 6 ) where , X _imax is a maximum deflection of the ball in mm; (7)

(8) where v is Poisson' s ratio associated with a material of the bearing, E is Young' s modulus associated with material and Eeq is equivalent stiffness of the material. For example, if the bearing is made of EN31 steel, the Poisson' s ratio is 0.3 and Young's modulus is 210 GPa. r _eq = 0.5098 * r _ball (9) where r _ball is the radius of the ball

Qφ = Load * 4.37 (10) (11) , „ „ . (12) where nearing is a radius of the bearing given by: r _bearing = d _m + internal clearance/2 (13)

(14) where (n is angular velocity is the angular frequency with which the ball rotates about the edge of the defect .

In the above equation, parameters pl and p2 are tuned based on the bearing parameters. In an embodiment, the parameters are tuned using a trained machine learning model. The trained ma- chine learning model is an evolutionary algorithm. Similarly, the parameters p1 and p2 are obtained for the three beraings . In an embodiemnt , determining the impact force further com- prises determining dynamic parameter for the at least one bearing based on the one or more parameters determined for each of the bearings in the group of bearings . The dynamic parameter is calculated for the at least one bearing for which the defect is analysed in real-time . In an example , the ball radius is used as the normalizing scale in the bearing . That is , the parameters are related as a linear function of the ball diameter . Further, this relation is used to calculate the bearing parameter for any arbitrarily shaped bearing . It will be appreciated that this helps us in calculating the required bearing parameters for any arbitrary shaped bearing for which the remaining useful life needs to be predicted .

Further, the impact force F on the ball is calculated from Xtmax according to the following equation ( 4 ) :

Here F represent s the value of maximum impact force on the ball calculated mathematically . The maximum impact force is thus computed for the bearing for which the remaining useful life is to be calculated .

At step 530 , a remaining useful life of the bearing is deter- mined based on the determined inpact force and the operational data based on the determiend one or more frequencie s . In an example , the remaining useful life may be expres sed as number of revolutions be fore the failure occurs . In another example , the remaining useful life is expre s sed as number of operating hours at a constant speed before the failure . In a preferred embodiment , the remaining useful life model for the bearing is configured based on the following rating life model :

( 15 ) where, ai _SO is a life modification factor based on systems approach for life calculation given by:

(16) where, a ₁ is a life modification factor for reliability, Cu is fatigue load limit in Newtons, e _c is a contamination factor specific to the defect size, P _a is dynamic equivalent reference axial load in Newtons, C _a is basic dynamic equivalent axial load rating, K is viscosity ratio.

Therefre, the remaining useful life is a function of teh dyn- maic equaivalent load acting on the bearing P _a as shown:

(17)

Here, the dynamic parameter used for configuring the rating life model is the dynamic equivalent radial load.

The life modification factor for reliability is a predefined value specified in ISO 281:2007 for a given value of reliabil- ity. For example, if the reliability may be considered to be 90%, al is taken as 1. The value of reliability is taken as 90% by default. In an embodiment of the present disclosure, the value of reliability may be modified by an operator through the client device. The life modification factor for reliabil- ity may be further obtained from a first lookup table stored in the database 195, based on the value of reliability. The fatigue load limit and the dynamic equivalent radial load rat- ing are obtained from the one or more bearing parameters as- sociated with the bearing. The contamination factor is determined based on the defect size. This is because, defects in the bearing result in removal of small, discrete particles of material from the structure of the bearing. These discrete particles increase the concentra- tion of contaminants inside the bearing. The contentration of contaminations further increases with increase in the defect size. The defect size is provided as input to a trained clas- sification model that classifies the defect size into one of a plurality of severity levels. For example, the plurality of severity levels may correspond to 'normal cleanliness', 'slight to typical contamination', 'severe contamination' and 'very severe contamination' . Based on the defect size, the trained classification model outputs a severity level. The severity level thus determined is further used to select an appropriate contamination factor from a second lookup table stored in the database 195. The second lookup table may com- prise values of contamination factor corresponding to each of the severity levels. It must be understood by a person skilled in the art that the classification model may be trained to classify the defect size into one of any number of severity levels .

The viscosity ratio is indicative of a lubrication condition of the bearing during operation. The viscosity ratio is cal- culated as the ratio of an operating viscosity of the lubricant to a rated viscosity of the lubricant. The operating viscosity is calculated based on a viscosity grade of the lubricant and an operating temperature. The viscosity grade of the oil may be obtained from a third look up table comprising viscosity grades corresponding to different types of lubricants. In one embodiment, the operating temperature of the bearing may be obtained from temperature sensors associated with the bearing. In another embodiment, a virtual model of the bearing may be used to determine a thermal profile of the bearing based on the sensor data. The rated viscosity is obtained from a fourth look up table based on dimensions of the bearing and angular velocity of the bearing.

The equation (17) for rating life is as below:

Here, the dynamic equivalent radial load P is the same as the impact force computed by the virtual model based on the sensor data. Therefore, the remaining useful life is a function of the determined impact force.

Therefore, the remaining useful life model is configured as below :

(18)

Based on the equation (18) , the remaining useful life (RUL) of the bearing is calculated.

At step 535, a notification indicating the remaining useful life of the bearing is generated on an output device. The output may be a notification that indicates the remaining use- ful life of the bearing as a dynamically changing parameter, based on real-time sensor data. For example, the notification may include a message 'The remaining useful life of bearing 6319 is 56 hours '. Furthermore, the output may also include values of peak amplitude values, force values, and remaining useful life as shown in FIG 7. FIG 7 is a GUI view 700 showing the peak amplitude values of the operation data received from the at least one bearing, the force exerted on the ball due to the defect, and the remaining useful life of the bearing in hours. The output may also include the impact force curve as shown in FIG 8 . FIG 8 is a Graphical User Interface view 800 showing an example of impact force and speed curve , in accord- ance with an embodiment of the present invention . The GUI view 800 depict s the relationship between the impact force on the bearing and the ball velocity for various defect si zes . Fur- thermore , the output may also include the operational data as represented in time domain and f requency domain . FIG 9A is a Graphical User Interface view 900A showing an example of ball velocity as obtained from operational data in time domain, in accordacne with an embodiment of the present invent ion . FIG 9B is a Graphical User Interface view 900B showing an example of power spectrum in frequency domain, in accordance with an em- bodiemnt of the present invention . Furthermore , the output may also include the RUL value further indicated on an RUL curve as shown in FIG 10 . FIG 10 is a GUI view 1000 showing degra- dation in remaining useful life ( shown as predicted life in hours ) , in accordance with an embodiment of the pre sent dis- closure . As may be seen from the curve , the RUL curve start s with potential failure in the at least one bearing and propa- gates till functional failure based on the vibration spectrum analysis , for example increase in velocity .

The present invention facilitates accurate calculat ion of re- maining useful life of a bearing based on the impact force computed from vibration spectrum of the real time s ignals from the sening unit 315 as sociated with the at least one bearing . The present invention continously monitors the real time op- eration data obtained from the bearing, covert s it into fre- quency domain and accurtely determine the remaining useful life of the bearing based on the relationship between imapct force and the frequency spectrum signal determined from the operation data of the bearing in real-time . The present invention is not limited to a particular computer system platform, processing unit, operating system, or net- work. One or more aspects of the present invention may be distributed among one or more computer systems, for example, servers configured to provide one or more services to one or more client computers, or to perform a complete task in a distributed system. For example, one or more aspects of the present invention may be performed on a client-server system that comprises components distributed among one or more server systems that perform multiple functions according to various embodiments. These components comprise, for example, executa- ble, intermediate, or interpreted code, which communicate over a network using a communication protocol. The present inven- tion is not limited to be executable on any particular system or group of system, and is not limited to any particular dis- tributed architecture, network, or communication protocol.

While the invention has been illustrated and described in de- tail with the help of a preferred embodiment, the invention is not limited to the disclosed examples. Other variations can be deducted by those skilled in the art without leaving the scope of protection of the claimed invention.