Lubricant film thickness measurement and condition monitoring of bearings

Abstract

Examples are directed to detecting an oil film state of a bearing device. An arrangement obtains background impedance, background admittance, static and dynamic admittance, and determines electrical contact resistance for a rolling element. When the electrical contact resistance is greater than the high resistance value, the arrangement calculates inner capacitance and outer capacitance from the impedance or the admittance; calculates central film thickness in the contact region; and calculates inlet distance and dimensionless meniscus distance. The arrangement determines when the inlet distance is not less than the dimensionless meniscus distance and stores the central film thickness. When the inlet distance is less than the dimensionless meniscus distance, the arrangement recalculates the central film thickness. When the electrical contact resistance is not greater than the high resistance value, the arrangement calculates inner capacitance and outer capacitance from the impedance or the admittance; and determines and stores the central film thickness.

Description

Attorney Docket No.023644-0009-WO01 LUBRICANT FILM THICKNESS MEASUREMENT AND CONDITION MONITORING OF BEARINGS RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 698,953, filed September 25, 2024, the entire content of which is hereby incorporated by reference. BACKGROUND

[0002] Various systems and methods for determining lubricant film thickness and monitoring lubrication condition in bearing devices are known.

[0003] U.S. Patent Publication No.2023 / 0366781 discloses a method for detecting a state of a bearing device by applying an alternating current voltage to an electric circuit including an outer member, rolling element, and an inner member while a predetermined load is applied to the bearing device. An oil film thickness and a metal contact ratio between the inner member and the rolling elements is derived based on the impedance and phase angle.

[0004] U.S. Patent Publication No.2023 / 0251075 discloses a monitoring method that measuring total capacitance of a bearing, a first calculation step for determining a film thickness of a lubricant based on a measured capacitance of the bearing and for determining whether the lubrication condition is fully flooded or starved, and when the lubrication condition is fully flooded, and a second calculation step for correcting the film thickness determined in the first calculation step.

[0005] The above patents do not individually address or provide a capacitive film thickness measurement model, which covers all three lubrication regimes, fully flooded, starved, and mixed. SUMMARY

[0006] The arrangement is directed to a method, a monitoring system, and a non-transitory computer-readable storage medium storing a computer program for causing an electronicAttorney Docket No.023644-0009-WO01 processor to determine an oil film thickness under fully flooded, starved, and mixed lubrication regimes.

[0007] One arrangement is directed to a method for detecting an oil film state according to a lubricant in a bearing device including an inner race, an outer race, and rolling elements. The method comprises: obtaining background impedance and / or background admittance; obtaining both static and dynamic impedance and / or both static and dynamic admittance; and determining electrical contact resistance for a rolling element. When the electrical contact resistance is greater than a high resistance value, the method assumes that the bearing device is in a fully flooded regime and operates to: calculate inner capacitance and outer capacitance from the impedance or the admittance; calculate central film thickness (hc) in the contact region; calculate inlet distance (m) and dimensionless meniscus distance (m*); and determine whether the inlet distance (m) is less than the dimensionless meniscus distance (m*); when the inlet distance (m) is not less than the dimensionless meniscus distance (m*), store the central film thickness. When the inlet distance is less than the dimensionless meniscus distance, the method recalculates the central film thickness in the contact region using a starved regime. When the electrical contact resistance is not greater than the high resistance value, the bearing device is in a mixed regime and the method operates to: calculate inner capacitance and outer capacitance from the impedance or the admittance; determine the central film thickness for the bearing device in the mixed regime; and store the central film thickness.

[0008] Another arrangement is directed to a monitoring system for detecting an oil film state according to a lubricant in a bearing device including an inner race, an outer race, and rolling elements. The monitoring system includes an electronic processor; a memory; and a sensing arrangement including an impedance / admittance sensor. The electronic processor is configured to: obtain background impedance and / or background admittance; obtain both static and dynamic impedance and / or both static and dynamic admittance; and determine electrical contact resistance for a rolling element. When the electrical contact resistance is greater than a high resistance value, the electronic processor assumes that the bearing device is in a fully flooded regime and: calculates inner capacitance and outer capacitance from the impedance or the admittance; calculates central film thickness (hc) in the contact region; calculates inlet distance (m) and dimensionless meniscus distance (m*); and determines whether the inlet distance (m) isAttorney Docket No.023644-0009-WO01 less than the dimensionless meniscus distance (m*). When the inlet distance (m) is not less than the dimensionless meniscus distance (m*), the electronic processor stores the central film thickness. When the inlet distance is less than the dimensionless meniscus distance, the electronic processor recalculates the central film thickness in the contact region using a starved regime. When the electrical contact resistance is not greater than the high resistance value, the bearing device is in a mixed regime and the electronic processor is configured to: calculate inner capacitance and outer capacitance from the impedance or the admittance; determine the central film thickness for the bearing device in the mixed regime; and store the central film thickness.

[0009] One arrangement is directed to a non-transitory computer-readable storage medium for storing a computer program for execution by an electronic processor. The electronic processor is configured to: obtain background impedance and / or background admittance; obtain both static and dynamic impedance and / or both static and dynamic admittance; determine electrical contact resistance for a rolling element; and when the electrical contact resistance is greater than a high resistance value, assume that a bearing device is in a fully flooded regime and operate to: calculate inner capacitance and outer capacitance from the impedance or the admittance; calculate central film thickness (hc) in the contact region; calculate inlet distance (m) and dimensionless meniscus distance (m*); and determine whether the inlet distance (m) is less than the dimensionless meniscus distance (m*). When the inlet distance (m) is not less than the dimensionless meniscus distance (m*), the electronic processor stores the central film thickness; and when the inlet distance is less than the dimensionless meniscus distance, recalculates the central film thickness in the contact region using a starved regime. When the electrical contact resistance is not greater than the high resistance value, the bearing device is in a mixed regime and the electronic processor is configured to: calculate inner capacitance and outer capacitance from the impedance or the admittance; determine the central film thickness for the bearing device in the mixed regime; and store the central film thickness. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG.1 is a block illustration of a bearing monitoring system for monitoring the thickness of a lubricant within a lubricated bearing, according to some aspects.Attorney Docket No.023644-0009-WO01

[0011] FIG.2A is a partial cross-sectional view of a lubricated bearing device that is electrically connected to an alternating current generator, according to some aspects.

[0012] FIG.2B is a partial cross-sectional view of a different lubricated bearing device that is electrically connected to an alternating current generator, according to some aspects.

[0013] FIG.3A is an electronic network model for capacitance of a series of rolling elements in a lubricated bearing device, according to some aspects.

[0014] FIG.3B is a front view of a contact region of a single contact of a lubricated bearing device, according to some aspects.

[0015] FIG.3C is an electronic network model for capacitance of the single contact arrangement shown in FIG.3B, according to some aspects.

[0016] FIG.4A is a front view of a fully flooded contact region of a lubricated bearing device, according to some aspects.

[0017] FIG.4B is a top view of a fully flooded contact region shown in FIG.4A, according to some aspects.

[0018] FIG.5 is an electric network model for an outlet region that has two oil films adhering to each raceway and air therebetween.

[0019] FIG.6A is a front view of a starved contact region of a lubricated bearing device, according to some aspects.

[0020] FIG.6B is a top view of a starved contact region shown in FIG.6A, according to some aspects.

[0021] FIG.7A is an illustration of a mixed mode for a lubricated bearing device, according to some aspects.

[0022] FIG.7B is an electric network model for a mixed mode of a lubricated bearing device, according to some aspects.Attorney Docket No.023644-0009-WO01

[0023] FIG.8A is a front view of a mixed mode contact region of a lubricated bearing device, according to some aspects.

[0024] FIG.8B is a top view of a mixed mode contact region shown in FIG.8A, according to some aspects.

[0025] FIG.9 is a flow chart showing operation of the monitoring system shown in FIGS.1- 8B, according to some aspects. DETAILED DESCRIPTION

[0026] Before any arrangements, examples, aspects, or features are explained in detail, it is to be understood that those arrangements, examples, aspects and features are not limited in their application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. Other arrangements, examples, aspects, and features are possible and are capable of being practiced or of being carried out in various ways.

[0027] Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The terms “mounted,” “connected” and “coupled” are used broadly and encompass both direct and indirect mounting, connecting, and coupling. Further, “connected” and “coupled” are not restricted to physical or mechanical connections or couplings, and can include electrical connections or couplings, whether direct or indirect. Also, electronic communications and notifications may be performed using any known means including wired connections, wireless connections, etc.

[0028] It should also be noted that a plurality of hardware and software based devices, as well as a plurality of different structural components may be utilized in various implementations. Aspects, features, and instances may include hardware, software, and electronic components or modules that, for purposes of discussion, may be illustrated and described as if the majority of the components were implemented in hardware. However, one of ordinary skill in the art, and based on a reading of this detailed description, would recognize that, in at least one instance, the electronic based aspects of the invention may be implemented in software (for example, stored on non-transitory computer-readable medium) executable by one or more electronic processors.Attorney Docket No.023644-0009-WO01 As a consequence, it should be noted that a plurality of hardware and software based devices, as well as a plurality of different structural components may be utilized to implement the invention. For example, “computing devices” and “controllers” described in the specification can include one or more electronic processors, one or more memory modules including a non-transitory computer-readable medium, one or more input / output interfaces, and various connections (for example, a system bus) connecting the components. It should be understood that although certain drawings illustrate hardware and software located within particular devices, these depictions are for illustrative purposes only. In some instances, the illustrated components may be combined or divided into separate software, firmware and / or hardware. For example, instead of being located within and performed by a single electronic processor, logic and processing may be distributed among multiple electronic processors. Regardless of how they are combined or divided, hardware and software components may be located on the same computing device or may be distributed among different computing devices connected by one or more networks or other suitable communication links.

[0029] For ease of description, some or all of the example systems presented herein are illustrated with a single exemplar of each of its component parts. Some examples may not describe or illustrate all components of the systems. Other instances may include more or fewer of each of the illustrated components, may combine some components, or may include additional or alternative components.

[0030] FIG.1 illustrates a block illustration of a bearing monitoring system 20 for monitoring the thickness of a lubricant within a lubricated bearing device. The monitoring system 20 includes a computing device 24 that analyzes information to determine central film thickness based on received data. The computing device 24 includes an electronic processor 28 and one or more non-transitory, computer-readable memory modules. In the example of FIG.1, the computing device 24 includes a random access memory (“RAM”) module 32 and a read-only memory (“ROM”) module 36. The computing device 24 also includes an input / output interface 40 that transmits and receives data over a controller area network (“CAN”) or other communication bus 44. It should be understood that the computing device 24 can include multiple electronic processors, additional computer-readable memory modules, multiple I / OAttorney Docket No.023644-0009-WO01 interfaces, and / or additional components or modules (e.g., hardware, software, or a combination thereof).

[0031] The electronic processor 28 receives information from the I / O interface 40 and processes the information by executing instructions for one or more software modules (which may also be referred to as a “calculator” or “calculators”) stored to a memory module of the computing device 24, such as the ROM 36. The electronic processor 28 stores information to and retrieves information from the RAM 32 (e.g., information received from other subsystems or sensors through the communication bus 44 and information generated by modules executed by the electronic processor 28). The non-transitory computer readable memory modules of the computing device 24 include volatile memory, non-volatile memory, or a combination thereof and, in various constructions, may also store operating system software, applications / instructions data, and combinations thereof.

[0032] Various other arrangements are also connected to the communication bus 44 and communicate with the computing device 24. In the example of FIG.1, a sensing arrangement 48 includes an AC generator 52 for providing an AC voltage to one of an inner race and an outer race for sensing electrical properties, and especially capacitance for a rolling element / bearing(s) via the inner race and the outer race. The sensing arrangement 48 includes an impedance / admittance sensor 56 for sensing impedance in response to an AC voltage provided through the inner race, rolling element and outer race. Finally, the sensing arrangement 48 includes a phase angle sensor 60 to determine a phase angle for the bearing device. In another example, the impedance / admittance sensor 56 is a component of an inductance, capacitance, resistance (LCR) meter that measures inductance, capacitance and resistance. The LCR meter also is capable of measuring quality factor, dissipation factor, voltage, current, conductance, phase angle, and susceptance of sensed electrical signals.

[0033] FIG.1 further illustrates a temperature sensor 64 for providing a bearing temperature to the computing device 24 and a load sensor 68 for providing a load for a rolling element to the computing device 24. Finally, an optional pressure sensor 72 may be provided for providing a pressure value to the computing device 24 via the communication bus 44. Other sensingAttorney Docket No.023644-0009-WO01 arrangements 48 are contemplated wherein computer programs utilize calculations and assumptions to determine various values. Other monitoring systems 20 are contemplated.

[0034] FIG.2A illustrates a partial cross section of a bearing device 80 having an outer race 82 and an inner race 84 along with insulated ribs 86. The AC generator 52 connects to the outer race 82 and the inner race 84 to sense the impedance across the races 82, 84 and a rolling element (not shown).

[0035] FIG.2B illustrates a partial cross section of a bearing device 90 having an insulated outer race 92 and an inner race 94 along with ribs 96. The AC generator 52 connects to the rib 96 and the inner race 94 to sense the impedance across the inner race 94, a rolling element (not shown) and the rib 96.

[0036] Fully Flooded Model

[0037] In a fully flooded condition / regime, the total bearing capacitance Ctotal is a sum of bearing capacitance Cbearingand background capacitance Cbackgroundas follows:

[0038] Ctotal = Cbearing + Cbackground

[0039] Background capacitance is measured with a ceramic ball bearing with a same geometry in the arrangements of FIGS.2A and 2B. Assuming inner and outer race capacitance is connected in series and capacitance of different ball bearings are connected in parallel: z Cbearing= ----------------- 1 1 ------ + ------- Cinner Couter

[0040] In the above equation, z represents the number of rolling elements or balls disposed in a bearing device. Cinnerrepresents the capacitance of the inner race film and Couterrepresents the capacitance of an outer race film.

[0041] The relationship between inner race film and outer race film is calculated based on the contact geometry and temperature difference using a film thickness equation. This equation is also assumed to work for both fully flooded and starved condition.Attorney Docket No.023644-0009-WO01

[0042] The following discussion focused on the inner raceway contact only. There are five regions: inlet, Hertzian contact, outlet, and two side leakage areas. Due to the small area of side leakage, the side leakage is typically ignored. This simplification is also adopted in the present equation below. In this equation, the inlet region, contact region (Hertz) and outlet region (cavitation) are connected in parallel. An electric network model is shown in FIGS.3A-3C. FIG.3A shows a capacitance representation model 98 for multiple balls or rolling elements in a bearing device. Each ball includes a Cinnerand Coutervalue when contacting an inner race and an outer race.

[0043] FIG.3B represents a model 100 of film thickness in the contact region that also provides a capacitance as shown in FIB.3C. The inlet region 102, contact region (Hertz) 104 and outlet region (cavitation) 106 shown in FIG.3B are connected in parallel. FIGS.3B and 3C represent a single contact. FIG.3C represents a model 110 of capacitance for the single contact regions shown in FIG.3B. FIG.3C results in the following equation:

[0044] Cinner = Cinlet + CHertz + Coutlet

[0045] Cinner= ε0(εoilAinlet / hinlet+ εHertzAHertz / hHertz+ εoutletAoutlet / houtlet)

[0046] Cinner= ε0(εoil∬ Ainletdxdy / (hinlet(x,y) ) + 1 / hc∬ AHertzεHertzdxdy +∬ Aoutletεoutletdxdy) / (houtlet(x,y))

[0047] In the above equations, Cinlet is capacitance in the inlet region shown in FIG.3B, CHertz is capacitance in the Hertz region shown in FIG.3B, and Coutlet is capacitance in the outlet region shown in FIG.3B. ε0is dielectric constant in a vacuum, εoilis dielectric constant of lubricant oil or grease at an ambient pressure and temperature, εoutlet is dielectric constant at great pressure and temperature as a ball or rolling element contacts the film thickness in contact region Aoutlet, and εHertzis dielectric constant at great pressure and temperature as a ball or rolling element contacts the film thickness in contact region AHertz. Ainlet is the contact area (m2) in the inlet region 102, AHertz is the contact area in the Hertz region 104, and Aoutlet is the contact area in the outlet region 106. hinletis a height of the inlet region 102, hHertzis a height in the Hertz region 104, and houtletis a height in the outlet region 106. hcis the central film thickness in the contact region during contact by a ball or rolling element in the bearing device. The inlet section isAttorney Docket No.023644-0009-WO01 assumed full of oil under a fully flooded condition. The geometry bounding may be set as hinlet = 51hc. An example equation for inlet height is as follows:

[0048] hinlet= hc- b2 / 2R + x2 / 2R, wherein hinletrepresents a height of an inlet region, b represents half of a length of a Hertzian contact region as shown in FIG.4A, R represents a contact radius, and x represents a length of the inlet region 102 and half of the length of the Hertzian contact region 104 as shown in the model of film thickness 114 shown in FIG.4A.

[0049] The length x is the square root of (100hcR + b2) or 10 times the square root of hcR. The equation for capacitance Cinlet is as follows: a -b 1

[0050] Cinlet= ε0εoil∫ ∫ -----------------------dxdy -a -10√(hcR) hc– b2 / 2R + x2 / 2R

[0051] For the Hertzian contact area, the film thickness is assumed equal to the central film thickness since it dominates. The dielectric constant in this region is determined by the average surface temperature and mean contact pressure. Total Hertzian contact area is πab. a represents a contact region length 116 shown in FIG.4B of the contact region.

[0052] Chertz = ε0 εHertz πab / hc

[0053] For the outlet / cavitation arrangement, we assume that the outlet section has two equal thickness oil layers or films adhering to each disk or raceway. The remainder of the outlet section is composed of air. One may assume that the composite dielectric constant of the two- phase fluids was a function of oil and air percentage. In this instance, it is assumed there are three layers at the outlet, two layers of oil and one layer of air in between as electrically represented in the electronic network model 120 shown in FIG.5. Each oil layer is assumed to be half of the central film thickness. The pressure in the cavitated region of the lubricant film will be approximately constant and near to the atmospheric or ambient pressure.

[0054] 1 / Coutlet= 1 / Coil+ 1 / Cair+ 1 / CoilAttorney Docket No.023644-0009-WO01 ^^ ^^^௨௧^^௧ ൌ ^^ ^ℎ ^^^^^^^^ ℎ^^^௨௧^^௧ି^^After applying the ^^ ൌ ^^ ^^^^^^ோఢబ^௨௧^^௧ ି^^^^ ^మష್మ^^^^^^^^ ^

[0057] For the starved condition / regime, the boundary of inlet regime will be determined by the meniscus for the model of film thickness 130 shown in FIG.6A and the length of contact region 136 shown in FIG.6B. The starvation condition is described with a dimensionless meniscus distance ratio m (m=x / b, x is the meniscus distance). Ratio m* is a critical location of m, which is a function of central film thickness: 20.58

[0058] m* = 1 + 3.06[(R / b) H ]x ff

[0059] H is the fully flooded film thickness, R is radius, and b is distance shown in FIG.ff x 6A. If the inlet distance m is less than m*, starvation is occurring. Otherwise, the bearing device is fully flooded. The starved central film thickness is expressed as: 0.29

[0060] H = H ((m-1) / (m*-1))c ffAttorney Docket No.023644-0009-WO01

[0061] The analytical results and the experimental results were also found in a good agreement for the film thickness reduction parameter (m−1) / (m*−1).

[0062] Similarly, the inlet capacitance C can be expressed as:inlet^ ି^ 1 ^^^^^^௧ ൌ ^^^^^^^^ ^ ^^^^^^^^^ ^^ଶ^^ ^^ଶ^

[0063] The flooded condition / regime.^ ି^ 1 ^^ ^^^^^^ு^^௧௭ ^^ ൌ ^^ ^^^ ^ ^ ^^^^^^^^ ^^^^^^ ^ ^^^^

[0064]

[0065] There are additional assumptions for mixed model / regime as compared to fully flooded and starved models.

[0066] For the mixed model, we assume that there will be sufficient lubricant supply in the mixed regime, otherwise it may cause premature bearing device damage. Further, we assume that there is no tribofilm formation on the surface. Tribofilms significantly increase the contact resistance.

[0067] Surface asperities contact occurs frequently in the mixed mode regime, as illustrated in the contact region 140 shown in FIG.7A. The contact area is modeled as a resistor and the separated area is modeled as a capacitor, as shown in the electric network model 146 of Figure 7b. Resistors and capacitors are connected in parallel in the electric network model 146. Breakdown ratio α is defined as:Attorney Docket No.023644-0009-WO01

[0068] α = (breakdown area) / (Hertzian contact area) = (contact resistance measured under static load) / (contact resistance measured under dynamic load)

[0069] α represents a breakdown ratio. Thus, there is no defined unit for the breakdown ratio α.

[0070] A simplified geometry model for the mixed model / regime is shown for the contact region 150 in FIG.8a. The inlet region 152 and the outlet region 156 are the same as in the fully flooded condition. Only the Hertz region 154 needs to be modified. This is shown by the equation for Cinner as follows: ^ ି^ 1^^ு^^ ^^^^^^^1 െ ^^^^^^^^^^ ൌ ^^ ^^^ ^ ^ ^^^^^^^^ ^ ௧௭^ ^^^obtain the admittance Y (inverse of impedance Z), since the capacitors connect in parallel with the resistor. The equation for Cinneris as follows:

[0072] Cinner = Cinlet + CHertz + Coutlet

[0073] Y = 1 / Z = 1 / ZR + 1 / ZCinner = 1 / Rc + jωCinner

[0074] 1 / Rc= |Y| cos θ

[0075] ωCinner= |Y| sin θ

[0076] Rc = 1 / |Y| cos θ

[0077] Cinner= |Y| sin θ / ωAttorney Docket No.023644-0009-WO01

[0078] Above, Rc is electrical contact resistance. ω is angular frequency. The resistance and capacitance are calculated as a function of admittance and phase angle in some examples. An inductance, capacitance, resistance (LCR) meter can measure inductance, capacitance and resistance. This meter also measures quality factor, dissipation factor, voltage, current, conductance, phase angle, and susceptance. FIG.8b is a top view of a mixed mode contact region 160.

[0079] OPERATION

[0080] FIG.9 illustrates a flow chart 200 showing operation of the film thickness monitoring system 20 for detecting an oil film state in a bearing device, according to one example. The steps provided within FIG.9 are merely examples, and may instead be conducted in a different order. Further examples of the method illustrated by flow chart 200 may include additional steps or may omit steps. At a first step 204, background impedance Zimpedance and / or background admittance Yadmittanceare measured by the sensing arrangement 48 for the bearing device 80, and specifically measured by an impedance / admittance sensor 56. The measurement can be performed using a hybrid bearing device under the same contact pressure in one example. The measured values are provided to the electronic processor 28 via a communication bus 44 and an input / output interface 36 shown in FIG.1. The computing device 24 advances to step 208.

[0081] At step 208, the monitoring system 24 measures both the static and dynamic impedance Ztotal, and admittance Ytotalfor the bearing device 80. The computing device 24 advances to decision step 212.

[0082] At decision step 212, the computing device 24 determines whether the electrical contact resistance Rcis greater than a high resistance value shown in FIG.9. If the electrical contact resistance Rcnot greater than the high resistance value, the bearing device 80 is in the mixed mode and the computing device 24 advances to step 216.

[0083] At step 216, the computing device 24 calculates values Cinner and Couter using admittance Ytotal. Then, the computing device 24 advances to step 220. At step 220, the breakdown ratio α and central film thickness hc are calculated by the computing device 24.Attorney Docket No.023644-0009-WO01 Thereafter, the computing device 24 advances to step 224 whereat the breakdown ratio α and central film thickness hc are stored, and the execution of the flow chart 200 ends.

[0084] Returning to decision step 212, when the electrical contact resistance Rcis greater than the high resistance value, meaning that the bearing device is in either fully flooded regime or starved regime, the computing device advances to step 228. At step 228, the computing device 24 assumes the fully flooded regime occurs and calculates values Cinnerand Couterusing impedance Ztotal. Then, the computing device 24 advances to step 232 and calculates central film thickness hc, m and m*.

[0085] Thereafter, the program executed by the computing device 24 advances to decision step 236. At decision step 236, the computing device 24 determines whether m < m*. When m is not less than m*, the computing device 24 advances to step 224 and the values for central film thickness hc, m and m* are stored in memory 32.

[0086] Returning to decision step 236, when m < m*, the computing device 24 advances to step 240. At step 240, the computing device 24 calculates the central film thickness hc using the starved model. Thereafter, the computing device 24 advances to step 224. At step 224, the central film thickness hcis stored in memory 32 by the computing device 24. Execution of the flow chart 200 ends.

[0087] Storage of calculated values in memory 32, 36 includes a time and date stamp in some examples. Thus, future analysis of data includes meaningful data points.

[0088] Returning to the model / regimes executed in FIG.9 by the monitoring system 20, the operation is based on following assumptions: a) capacitance of film thickness can be modeled as a parallel plate capacitor; b) using a deep groove ball bearing under axial load, so the load on each ball is considered equally distributed; c) using a polymer cage to simplify the electronic network; d) neglecting the effect of surface asperities on resistance measurement; and neglecting the temperature gradient through the inlet region, the contact region and the outlet region. In other examples, less than all the listed assumptions are relied upon.

[0089] The arrangement of FIG.9 is a computer program or algorithm(s) stored in a non- transitory computer-readable storage medium, such as memory 32, 36 for execution by anAttorney Docket No.023644-0009-WO01 electronic processor 28 of the computing device 24. The electronic processor 28 is configured to: obtain background impedance and / or background admittance; obtain both static and dynamic impedance and / or both static and dynamic admittance; determine electrical contact resistance for a rolling element; and when the electrical contact resistance is zero, assume that a bearing device is in a fully flooded regime and operate to: calculate inner capacitance and outer capacitance from the impedance or the admittance; calculate central film thickness (hc) in the contact region; calculate inlet distance (m) and dimensionless meniscus distance (m*); and determine whether the inlet distance (m) is less than the dimensionless meniscus distance (m*). When the inlet distance (m) is not less than the dimensionless meniscus distance (m*), the electronic processor 28 stores the central film thickness in memory 32, 36. When the inlet distance is less than the dimensionless meniscus distance, the electronic processor 28 recalculates the central film thickness in the contact region using a starved regime. When the electrical contact resistance is not zero, the bearing device 80, 90 is in a mixed regime and the electronic processor 28 is configured to: calculate inner capacitance and outer capacitance from the impedance or the admittance; determine the central film thickness for the bearing device in the mixed regime; and store the central film thickness in memory 32, 36.

[0090] While FIG.9 shows the electrical contact resistance Rccompared with a high resistance value of 10 megaohms (MΩ), other high resistance values are contemplated. For instance, the high resistance value may be any value between 1 MΩ and 100 MΩ in some examples. In other examples, the high resistance value for comparison with the electrical contact resistance Rc may values from 1KΩ to 999KΩ. The high resistance value is dependent on many factors of the bearing device 80, 90.

[0091] In some instances, the communication bus 44 shown in FIG.1 is a controller area network (CAN) bus. In some instances, the communication bus 44 is an Ethernet, a FlexRay™ communications bus, or another suitable bus. In alternative instances, some or all of the components may be communicatively coupled using suitable wireless modalities (for example, Bluetooth™ or near field communication connections).

[0092] The electronic processor 28 shown in FIG.1 is configured to retrieve from the memory 32, 36 and execute, among other things, software including an algorithm for performingAttorney Docket No.023644-0009-WO01 methods as described herein. It should be understood that the monitoring system 20 may include additional components than those illustrated in FIG.1 and in various configurations. For example, in some examples, the monitoring system 20 includes multiple electronic processors 28, multiple memories 32, 36, multiple input / output interfaces 40, or a combination thereof.

[0093] In other arrangements, the electronic processor 28 receives information from a cloud- based memory (not shown).

[0094] The benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential features or elements of any or all the claims. The arrangement is defined solely by the appended claims including any amendments made during the pendency of this application and all equivalents of those claims as issued.

[0095] The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it may be seen that various features are grouped together in various examples for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed examples require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed example. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter.

[0096] In addition, unless the context of their usage unambiguously indicates otherwise, the articles “a” and “an” should not be interpreted as meaning “one” or “only one.” Rather these articles should be interpreted as meaning “at least one” or “one or more.”

[0097] In the above equations, εair is a dielectric constant in air or atmosphere.

[0098] Although certain arrangements, examples, features, and aspects have been described and illustrated, variations and modifications exist within the scope and spirit of the subject matter explained and shown.

Claims

Attorney Docket No.023644-0009-WO01 CLAIMS What is claimed is:

1. A method for detecting an oil film state according to a lubricant in a bearing device including an inner race, an outer race, and rolling elements, the method comprising: obtaining background impedance and / or background admittance; obtaining both static and dynamic impedance and / or both static and dynamic admittance; determining electrical contact resistance for a rolling element; when the electrical contact resistance is greater than a high resistance value, assume that the bearing device is in a fully flooded regime and operate to: calculate inner capacitance and outer capacitance from the impedance or the admittance; calculate central film thickness (hc) in the contact region; calculate inlet distance (m) and dimensionless meniscus distance (m*); determine whether the inlet distance (m) is less than the dimensionless meniscus distance (m*): when the inlet distance (m) is not less than the dimensionless meniscus distance (m*), store the central film thickness; when the inlet distance is less than the dimensionless meniscus distance, recalculate the central film thickness in the contact region using a starved regime; when the electrical contact resistance is not greater than the high resistance value, the bearing device is in a mixed regime and operates to: calculate inner capacitance and outer capacitance from the impedance or the admittance; determine the central film thickness for the bearing device in the mixed regime; and store the central film thickness.Attorney Docket No.023644-0009-WO01 2. The method according to claim 1, wherein the calculating of the central film thickness (hc) is performed in the fully flooded regime by an electronic processor processing an equation: hinlet= hc- b2 / 2R + x2 / 2R, wherein hinlet has a geometric boundary of 51hc and represents a height of an inlet region, b represents half of a length of a Hertzian contact region, R represents a contact radius, and x represents a length of the inlet region and half of the length of the Hertzian contact region.

3. The method according to claim 2, wherein calculating the inner capacitance is performed by the electronic processor processing an equation: a-b1 Cinlet= ε0εoil∫ ∫ -----------------------dxdy -a -10√(hcR) hc – b2 / 2Rc + x2 / 2R wherein ε0is the dielectric constant in a vacuum and εoil is the dielectric constant of oil.

4. The method according to claim 3, the method including determining a breakdown ratio for the rolling elements when the bearing device is in the mixed regime by an electronic processor processing an equation: α = (breakdown area) / (Hertzian contact area).

5. The method according to claim 1, the method including determining a breakdown ratio α for the rolling elements when the bearing device is in the mixed regime by an electronic processor processing an equation: α = (breakdown area) / (Hertzian contact area).

6. The method according to claim 1, wherein the recalculating of the central film thickness in the contact region using a starved regime is performed by an electronic processor processing an equation: Hc= Hff((m-1) / (m*-1))0.29wherein Hffis fully flooded film thickness.Attorney Docket No.023644-0009-WO01 7. The method according to claim 1, wherein an electronic processor receives a temperature from a temperature sensor disposed near the bearing device, and wherein the high resistance value is 10 MΩ.

8. A monitoring system for detecting an oil film state according to a lubricant in a bearing device including an inner race, an outer race, and rolling elements, the monitoring system comprising: an electronic processor; a memory; and a sensing arrangement including an impedance / admittance sensor; wherein the electronic processor is configured to: obtain background impedance and / or background admittance; obtain both static and dynamic impedance and / or both static and dynamic admittance; determine electrical contact resistance for a rolling element; and when the electrical contact resistance is greater than a high resistance value, assume that the bearing device is in a fully flooded regime and: calculate inner capacitance and outer capacitance from the impedance or the admittance; calculate central film thickness (hc) in the contact region; calculate inlet distance (m) and dimensionless meniscus distance (m*); determine whether the inlet distance (m) is less than the dimensionless meniscus distance (m*): when the inlet distance (m) is not less than the dimensionless meniscus distance (m*), store the central film thickness; when the inlet distance is less than the dimensionless meniscus distance, recalculate the central film thickness in the contact region using a starved regime; and when the electrical contact resistance is not greater than the high resistance value, the bearing device is in a mixed regime and the electronic processor is configured to: calculate inner capacitance and outer capacitance from the impedance or the admittance;Attorney Docket No.023644-0009-WO01 determine the central film thickness for the bearing device in the mixed regime; and store the central film thickness.

9. The monitoring system according to claim 8, wherein the calculating of the central film thickness (hc) is performed in the fully flooded regime by an electronic processor processing an equation: hinlet = hc - b2 / 2R + x2 / 2R, wherein hinlethas a geometric boundary of 51hcand represents a height of an inlet region, b represents half of a length of a Hertzian contact region, R represents a contact radius, and x represents a length of the inlet region and half of the length of the Hertzian contact region.

10. The monitoring system according to claim 9, wherein calculating the inner capacitance is performed by the electronic processor processing an equation: a -b 1 Cinlet= ε0εoil∫ ∫ -----------------------dxdy -a -10√(hcR) hc– b2 / 2R + x2 / 2R wherein ε0is the dielectric constant in a vacuum and εoilis the dielectric constant of oil.

11. The monitoring system according to claim 10, wherein the electronic processor is configured to determine a breakdown ratio for the rolling elements when the bearing device is in the mixed regime by an electronic processor processing an equation: α = (breakdown area) / (Hertzian contact area).Attorney Docket No.023644-0009-WO01 12. The monitoring system according to claim 8, wherein the electronic processor is configured to obtain background impedance and / or background admittance by determining the background impedance and / or background admittance, and wherein the high resistance value is 10 MΩ.

13. The monitoring system according to claim 8, wherein the recalculating of the central film thickness in the contact region using a starved regime is performed by an electronic processor processing an equation: Hc = Hff((m-1) / (m*-1))0.29lly flooded film thickness.

14. A non-transitory computer-readable storage medium for storing a computer program for execution by an electronic processor configured to: obtain background impedance and / or background admittance; obtain both static and dynamic impedance and / or both static and dynamic admittance; determine electrical contact resistance for a rolling element; and when the electrical contact resistance is greater than a high resistance value, assume that a bearing device is in a fully flooded regime and operate to: calculate inner capacitance and outer capacitance from the impedance or the admittance; calculate central film thickness (hc) in the contact region; calculate inlet distance (m) and dimensionless meniscus distance (m*); and determine whether the inlet distance (m) is less than the dimensionless meniscus distance (m*): when the inlet distance (m) is not less than the dimensionless meniscus distance (m*), store the central film thickness; and when the inlet distance is less than the dimensionless meniscus distance, recalculate the central film thickness in the contact region using a starved regime; andAttorney Docket No.023644-0009-WO01 when the electrical contact resistance is not greater than the high resistance value, the bearing device is in a mixed regime and the electronic processor is configured to: calculate inner capacitance and outer capacitance from the impedance or the admittance; determine the central film thickness for the bearing device in the mixed regime; and store the central film thickness.

15. The non-transitory computer-readable storage medium according to claim 14, wherein the calculating of the central film thickness (hc) is performed in the fully flooded regime by an electronic processor processing an equation: hinlet= hc- b2 / 2R + x2 / 2R, wherein hinlet has a geometric boundary of 51hc and represents a height of an inlet region, b represents half of a length of a Hertzian contact region, R represents a contact radius, and x represents a length of the inlet region and half of the length of the Hertzian contact region.

16. The non-transitory computer-readable storage medium according to claim 15, wherein calculating the inner capacitance is performed by the electronic processor processing an equation: a -b 1 Cinlet = ε0 εoil ∫ ∫ -----------------------dxdy -a -10√(hcR) hc– b2 / 2R + x2 / 2Rwherein ε0 constant in a vacuum and εoil is the dielectric constant of oil.

17. The non-transitory computer-readable storage medium according to claim 16, including determining a breakdown ratio for the rolling elements when the bearing device is in the mixed regime by an electronic processor processing an equation: α = (breakdown area) / (Hertzian contact area).Attorney Docket No.023644-0009-WO01 18. The non-transitory computer-readable storage medium according to claim 14, including determining a breakdown ratio α for the rolling elements when the bearing device is in the mixed regime by an electronic processor processing an equation: α = (breakdown area) / (Hertzian contact area).

19. The non-transitory computer-readable storage medium according to claim 14, wherein the recalculating of the central film thickness in the contact region using a starved regime is performed by an electronic processor processing an equation: Hc= Hff((m-1) / (m*-1))0.29wherein Hffis fully flooded film thickness.

20. The non-transitory computer-readable storage medium according to claim 14, wherein the electronic processor receives a temperature from a temperature sensor disposed near a bearing device, and wherein the high resistance value is 10 MΩ.

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