the present invention comprises an insulating wear liner with a sensor that is positioned either within the liner or placed on the non - wearing surface of the liner . the sensor is comprised of a conductive electrode and one or more pads for interrogating the electrical properties of the sensor . the liner is situated between the race and the moving part . by way of example but not limitation , a sensor may be positioned inside of the wear liner of a sleeve bearing , and the capacitance between the wear liner and the shaft can be calculated in the new condition of the shaft and wear liner , and after wear by a shaft . looking now at fig1 a , fig1 illustrates a new sleeve bearing with a sensor inserted into the wear liner according to this invention . the new , unused sleeve bearing is assembled with a shaft which has radius r shaft . the shaft is centered in the bearing , concentric with the race , which has a radius r race . the sensor conductive electrode is positioned inside the liner , having radius r sensor , such that all three are concentric and r race & gt ; r sensor & gt ; r shaft . we assume the liner has a uniform dielectric constant of ∈. the new bearing , with no wear , will have a capacitance c new between the sensor and the shaft , which is given by : table 1 shows a calculation of capacitance for a new shaft bearing . there will also be capacitance between the sensor electrode and the outer race , but this value should be constant over the life of the bearing . between the sensor electrode and the moving shaft , there will be wear . accordingly , the thickness of the wear liner will decrease , and the shaft will exhibit more play . one aspect of this invention is the effect of concentricity on the measured capacitance of a sensor embedded in a wear lining . we recognize two wear modes that could occur , concentric uniform or non - concentric non - uniform . to illustrate uniform wear , we consider a bearing that is worn with perfect symmetry so that some of the wear liner is removed from its entire circumference . next , we position the shaft in perfect concentricity with the race and sensor electrode . fig1 b illustrates a symmetrically worn sleeve bearing with a sensor inserted into the wear liner according to the present invention . in this arrangement , there are two capacitors in series , one made of air c air , and another made from the remaining liner c liner . the air gap , having thickness w , will have a capacitance based on the radial gap , r liner = r shaft + w . the capacitance of that gap will follow : likewise , the wear liner will have a capacitance based on its thickness , equal to r sensor − r liner , or r sensor −( r shaft + w ): the total capacitance , c t , will follow that of two capacitors in series ; c t =( c air × c liner )/( c air + c liner ). table 2 shows the result of this calculation . the resulting capacitance is lower than the value calculated in table 1 for the new bearing . we note that this is the case only if the shaft is held at the center . if loaded , the shaft will be non - concentric and the following example will apply . next , to illustrate the non - concentric , non - uniform case , we consider a bearing that has been loaded and worn preferentially on one side . the result is that the shaft is no longer concentric with the sensor . fig1 c illustrates a non - concentrically worn sleeve bearing with a sensor inserted into the wear liner according to the present invention . the capacitance of two cylinders eccentrically located one inside the other with radii ( r shaft ) and ( r sensor ), respectively , but with the centers of the two cylinders having a distance ( w ) apart , will be larger than in the concentric case . ignoring the replacement of the worn - away dielectric with air , the capacitance would be : the capacitance is calculated for an eccentrically worn sleeve bearing in table 3 . in table 3 , we see that the capacitance is significantly higher for the non - concentric worn bearing than for the new bearing . a notable aspect of this invention is that the capacitance between a metallic shaft and a sensor placed inside or behind the wear liner will increase with concentric or non - concentric wear , as long as the shaft is loaded . the capacitance is an inverse function of the liner thickness . accordingly , the capacitance increases rapidly as the liner thickness approaches zero . between the two previous examples , we expect to find the non - uniform , non - concentric case to be prevalent , as the loading and wear of bearings is rarely uniform . as such , we can relate the wear of a bearing to a measurable increase in capacitance between the shaft and the sensor . the capacitance measurement can be made at different frequencies . a standard frequency for capacitance measurement is 10 khz . measurements taken at a higher frequency improve the sensitivity of the measurement , but also increase the error due to interference . the optimal frequency for accuracy will depend on the electromagnetic interference in the environment surrounding the bearing . the measurement of q factor , which can be calculated from the active and inductive current components in the sensor , provides information about the status of the liner . if at any point the gap between the sensor and the ball approaches zero , q will drop rapidly toward zero . it will also be electrically shorted at this point . a q under 5 indicates that the bearing needs immediate replacement , and a q above 20 indicates a bearing with good health . the electrical shorting of the sensor and ball can also be used as an indicator that the wear liner has failed in at least one spot , and therefore needs replacement . turning again to fig1 , fig1 a illustrates a new sleeve bearing ( without wear ) 200 , comprising an outer race 201 , a movable shaft 203 , a wear liner 206 and a sensor 205 inserted into wear liner 206 . fig1 b illustrates the sleeve bearing 200 of fig1 a after symmetric wear of wear liner 206 . the symmetric wear of wear liner 206 results in a worn sleeve bearing 200 having an equal air gap 222 between wear liner 206 and movable shaft 203 , with erosion of all wear on sleeve bearing 200 lining up to sensor 205 . fig1 c illustrates an asymmetrically , a non - concentrically worn sleeve bearing 200 with a sensor 205 , where shaft 203 is closer to sensor 205 in one location than in another location . an air gap 222 is created by the removed material . looking now at fig2 a , fig2 a illustrates a sensor 205 for a sleeve bearing 200 , comprising a race 201 , a shaft 203 , a sensor 205 and a wear liner 206 . sensor 205 comprises a conductive trace 208 sandwiched between a lower and upper layer of insulating substrate 209 which may be of differing thicknesses ( fig2 b ). when sensor 205 is laid flat ( fig2 c ), conductive trace 208 can be seen in detail , along with tabs 210 that extend from sleeve bearing 200 . slots 215 formed on sensor 205 assist in the flow of adhesive between layers . electrode pads 213 are positioned on the surface of tabs 210 which can be probed with a capacitance meter to measure the capacitance between one electrode pad and shaft 203 ( fig2 d ). looking now at fig3 a , fig3 a illustrates a sensor 205 for a sleeve bearing 200 , comprising a race 201 , a shaft 203 , a sensor 205 and a wear liner 206 . sensor 205 comprises a conductive trace 208 sandwiched between a lower layer of insulating substrate 209 and an upper layer of insulating substrate 214 ( fig3 b ). when sensor 205 is laid flat ( fig3 c ), conductive trace 208 can be seen in detail , along with tabs 210 that extend from sleeve bearing 200 . slots 215 formed on sensor 205 assist in the conformation of the sensor to surface variations , and to flow of adhesive between layers . electrode pads 213 are positioned on the surface of tabs 210 which can be taken together as a connection point 220 for an antenna 221 . fig4 a illustrates a spherical bearing 200 comprising a race 201 , a ball 202 , a shaft 203 , a sensor 205 , a wear liner 206 and an insulator 207 . sensor 205 comprises a conductive trace 208 sandwiched between two layers of insulating substrate 209 ( fig4 b ). when sensor 205 is laid flat ( fig4 c ), conductive trace 208 can be seen in detail , along with tabs 210 that extend from sleeve bearing 200 . holes 211 formed on sensor 205 assist in the flow of adhesive between layers . strain relief cuts 212 formed on sensor 205 enable sensor 205 to deform into a more conformal shape . electrode pads 213 are positioned on the surface of tabs 210 for the interrogation of sensor 205 ( fig4 d ). viewed end on , after installation , electrode pads 213 may be touched with one probe of a capacitance meter . looking now at fig5 a and 5b , fig5 a and 5b , illustrate a method of interrogating sensor 205 . as shown in fig5 a , a probe 225 of a precision capacitance meter 230 makes contact with an electrode pad 213 on the circumference of spherical bearing 200 . assuming that race 201 and shaft 203 are both conductive and electrically connected elsewhere , the capacitance measured by the precision capacitance meter shall be comprised of the capacitance between ball 202 and sensor 205 , which is electrically in series with the capacitance between sensor 205 and race 201 . fig6 a illustrates a spherical bearing 200 comprising a race 201 , a ball 202 , a shaft 203 , a sensor 205 , a wear liner 206 and an insulator 207 . sensor 205 comprises a conductive trace 208 sandwiched between two layers of insulating substrate 209 ( fig6 b ). when sensor 205 is laid flat ( fig6 c ), conductive trace 208 can be seen in detail , along with tabs 210 that extend from sleeve bearing 200 . holes 211 formed on sensor 205 assist in the flow of adhesive between layers . strain relief cuts 212 formed on sensor 205 enable sensor 205 to deform into a more conformal shape . electrode pads 213 are positioned on the surface of tabs 210 for the interrogation of the sensor ( fig4 d ). viewed end on , after installation , tabs 210 and electrode pads 213 are connected at a point 220 to an antenna 221 , which may be mounted on the face of race 201 . looking now at fig7 a and 7b , fig7 a and 7b illustrate a method of interrogating sensor 205 wirelessly . a signal produced by a tracking generator 235 is coupled through a matching network 240 to a loop antenna 245 , which interacts with sensor antenna 221 , for measuring bearing wear remotely . the output frequency of tracking generator 235 is varied over time , and at one moment will match the frequency of the lc circuit created by the sensor &# 39 ; s capacitance and the antenna &# 39 ; s inductance . at that moment , a spectrum analyzer 250 will detect the resonance frequency . the shift in resonant frequency shift from the change in sensor capacitance will correspond to the reduction in the wear liner thickness . preferably , sensor antenna 221 may be placed in a detent , which is a circumferential groove in bearing race 201 . fig8 a illustrates a new square telescoping bearing with a sensor inserted into the wear liner in accordance with the present invention . fig8 b illustrates a worn square telescoping bearing with a sensor inserted into the wear liner in accordance with the present invention . one illustrative procedure for producing a device according to the present invention is shown in fig9 a - 9c . in fig9 a , there is shown an insulating substrate 209 with a metallic coating 208 . in fig9 b , a second layer of insulator 214 is applied to sandwich the electrode , which may be patterned . in fig9 c , at least one hole or a pattern is cut out , producing a sensor that can be inserted into a bearing . holes in the sheet are expected to improve the bonding with the substrate . turning back to fig8 a , fig8 a is an end - view of a new , un - worn telescoping structure comprising an outer sleeve 201 , an inner shaft 203 and a wear lining 206 , which has been instrumented with a sensor 205 part - way through wear lining 206 . in fig8 b , wear liner 206 has been worn , leaving an air gap 222 and a reduced lining thickness on one side . the capacitance of this system can be modeled as the sum of the four parallel plate capacitors . capacitance in this system is equal to the product of the permittivity of free space ∈ 0 , the dielectric constant ∈ and the area a divided by the distance d : c =∈∈ 0 a / d . comparing fig8 a to fig8 b , the lining thickness on the sides is unchanged , but in fig8 b the upper and lower distances are changed . at the bottom , the thickness of wear lining 206 has been reduced by wear , and a corresponding air gap 222 has opened up above shaft 203 at the top . the upper capacitor will have a lower value than before as the distance between shaft 203 and sensor 205 is increased by air gap 222 . the lower capacitor will have a much higher value than before , as it has a distance between shaft 203 and sensor 205 that is reduced by the same distance as air gap 222 . the increase in capacitance for the lower capacitor will more than make up for the decrease in capacitance for the upper capacitor . this is clear because the function 1 / d is nonlinear . it approaches infinity as the quantity ‘ d ’ gets small , and it approaches zero as ‘ d ’ gets large . we note that a similar type of measurement could be made if the wear liner material was conductive , and the resistance was measured as a function of wear . there are two methods to measure the capacitance of the sensor . the first is to measure the value directly with a probe and a capacitance meter . the other alternative is to measure the resonant frequency of the combination of the sensor &# 39 ; s capacitance and the attached antenna &# 39 ; s inductance . a similar measurement could be implemented using an inductive sensor and a distributed capacitor to create the resonant circuit . the preceding examples should be construed as non - limiting , as other methods of implementing the sensor are possible . also , other methods can be used to measure the wear in addition to capacitance , including inductance and resistance . it should be understood that many additional changes in the details , materials , steps and arrangements of parts , which have been herein described and illustrated in order to explain the nature of the present invention , may be made by those skilled in the art while still remaining within the principles and scope of the invention .