THE TWO TORTOITU US MUUTUUD 20180094946A1 TOOTMINE 

( 19 ) United States 

( 12 ) Patent Application Publication ( 10 ) Pub . No . : US 2018 / 0094946 A1 

Vog ] ( 43 ) Pub . Date : Apr . 5 , 2018 

( 54 ) INERTIAL MEASUREMENT UNIT AND 

DIAGNOSTIC SYSTEM ( 52 ) U . S . CI . CPC . . . . . . . . . . . . . G01C 23 / 00 ( 2013 . 01 ) ; GOIP 15 / 18 

( 2013 . 01 ) ; GOIC 19 / 5712 ( 2013 . 01 ) ( 71 ) Applicant : Government of the United States of 

America , as Represented by the 

Secretary of Commerce , Gaithersburg , MD ( US ) ( 57 ) ABSTRACT 

( 72 ) Inventor : Gregory Vogl , Gaithersburg , MD ( US ) 

( 21 ) Appl . No . : 15 / 692 , 262 

( 22 ) Filed : Aug . 31 , 2017 

Related U . S . Application Data 

( 60 ) Provisional application No . 62 / 403 , 416 , filed on Oct . 3 , 2016 . 

A an inertial measurement unit determines performance degradation of a linear axis and includes : an accelerometer 

that , when disposed on a motion member of the linear axis 

including the motion member and a base member : measures 

acceleration of the motion member ; and provides a displace 

ment of the motion member in response to movement of the 

motion member ; and a rate gyroscope that : measures an 

angular rate of movement of the motion member ; and 

provides a yield angle for the motion member in response to 

movement of the motion member , wherein the displacement 

and yield angle determine performance degradation of the 

linear axis based on an error in linear movement of the 

motion member along the base member . 

Publication Classification 

( 51 ) Int . Ci .GOIC 23 / 00 ( 2006 . 01 ) 

G01C 19 / 5712 ( 2006 . 01 ) 

G01P 15 / 18 ( 2006 . 01 ) 

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Patent Application Publication Apr . 5 , 2018 Sheet 1 of 29 US 2018 / 0094946 A1 

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Patent Application Publication Apr . 5 , 2018 Sheet 2 of 29 US 2018 / 0094946 A1 

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Patent Application Publication Apr . 5 , 2018 Sheet 3 of 29 US 2018 / 0094946 A1 

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Patent Application Publication Apr . 5 , 2018 Sheet 4 of 29 US 2018 / 0094946 A1 

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Patent Application Publication Apr . 5 , 2018 Sheet 7 of 29 US 2018 / 0094946 A1 

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US 2018 / 0094946 A1 
US 2018 / 0094946 A1 Apr . 5 , 2018 

INERTIAL MEASUREMENT UNIT AND 

DIAGNOSTIC SYSTEM 

CROSS REFERENCE TO RELATED 

APPLICATIONS 

[ 0001 ] This application claims the benefit of U . S . Provi sional Patent Application Ser . No . 62 / 403 , 416 , filed Oct . 3 , 2016 , the disclosure of which is incorporated herein by 

reference in its entirety . 

rate data by measuring the angular rate of the motion 

member by the rate gyroscope of the inertial measurement 

unit ; integrating the acceleration data to produce the trans 

lational displacement data for the movement of the motion 

member ; filtering the translational displacement data to 

produce filtered translational displacement data versus a 

travel length of the motion member ; integrating the angular 

rate data to produce angular displacement data for the 

movement of the motion member ; and filtering the angular displacement data to produce filtered angular displacement 

data to diagnose the geometric performance of a linear axis . STATEMENT REGARDING FEDERALLY 

SPONSORED RESEARCH 

[ 0002 ] This invention was made with United States Gov 

ernment support from the National Institute of Standards and 

Technology ( NIST ) , an agency of the United States Depart 

ment of Commerce . The Government has certain rights in 

the invention . Licensing inquiries may be directed to the 

Technology Partnerships Office , NIST , Gaithersburg , Md . , 20899 ; voice ( 301 ) 301 - 975 - 2573 ; email tpo @ nist . gov ; ref 

erence NIST Docket Number 16 - 039US1 . 

BRIEF DESCRIPTION 

[ 0003 ] Disclosed is an inertial measurement unit to deter mine a performance degradation of a linear axis , the inertial 

measurement unit comprising : an accelerometer that , when 

disposed on a motion member of the linear axis comprising 

the motion member and a base member : measures accelera 

tion of the motion member , and provides a displacement of 

the motion member in response to movement of the motion 

member ; and a rate gyroscope that : measures an angular rate 

of movement of the motion member ; and provides a yield 

angle for the motion member in response to movement of the 

motion member , wherein the displacement and yield angle 

determine performance degradation of the linear axis based 

on an error in linear movement of the motion member along 

the base member . [ 0004 ] Also disclosed is a diagnostic apparatus to deter 

mine a performance degradation of a linear axis , the diag nostic apparatus comprising : a linear axis comprising : a base 

member ; a motion member disposed on the base member , the motion member having substantially linear movement 

with respect to a first direction along the base member prior 

to performance degradation of the linear axis with respect to 

movement along the first direction ; and an inertial measure 

ment unit disposed on the motion member such that the 

inertial measurement unit moves with the motion member 

and comprises : an accelerometer that : measures acceleration 

of the motion member ; and provides a displacement of the 

motion member in response to movement of the motion 

member ; and a rate gyroscope that : measures an angular rate 

of movement of the motion member , and provides a yield angle for the motion member in response to movement of the 

motion member , wherein the displacement and yield angle determine performance degradation of the linear axis based 

on an error in linear movement of the motion member along 

the base member . [ 0005 ] Further disclosed is a process for diagnosing a 

geometric performance of a linear axis , the process com 

prising : providing the diagnostic apparatus ; moving the 

motion member at a first speed in the first direction , the first 

speed being constant ; producing acceleration data by mea 

suring acceleration of the motion member by the acceler 

ometer of the inertial measurement unit ; producing angular 

BRIEF DESCRIPTION OF THE DRAWINGS 

[ 0006 ] The following descriptions should not be consid 

ered limiting in any way . With reference to the accompa 

nying drawings , like elements are numbered alike . 100071 FIG . 1 shows an inertial measurement unit ( IMU ) ; 

[ 0008 ] FIG . 2 shows an IMU ; 

[ 0009 ] FIG . 3 shows an IMU ; 

[ 0010 ] FIG . 4 shows an IMU ; 

[ 0011 ] FIG . 5 shows a diagnostic apparatus ; 

[ 0012 ] FIG . 6 shows a diagnostic apparatus ; 

[ 0013 ] FIG . 7 shows a plurality of configurations and 

motions of a linear axis in machine tools ; 

[ 0014 ] . FIG . 8 shows a graph of velocity versus time ; 

[ 0015 ] FIG . 9 shows graphs of velocity versus time and 

acceleration versus time ; 

[ 0016 ] FIG . 10 shows a graph of displacement in panel A 

and a graph of error versus position in panel B ; 

[ 0017 ) FIG . 11 shows a process for determining error ; 

[ 0018 ] FIG . 12 shows an isometric view of IMU in panel 

A and a top view of the IMU without its lid in panel B ; 

[ 0019 ] . FIG . 13 shows an experimental setup of an IMU 

disposed on a machine tool and a commanded machine tool 

motion ( Z versus X ) in an inset ; 

[ 0020 FIG . 14 shows a comparison of ( a ) commanded 

and ( b ) estimated high - pass filtered error motions with their 

( c ) metric values as a function of degradation amplitude ; 

[ 0021 ] FIG . 15 shows an experimental setup of an IMU 

disposed on a machine tool worktable in which IMU is 

disposed at ( a ) Location A , ( b ) Location B , and ( c ) Location 

C , wherein ( d ) shows a schematic of three IMU locations 

relative to center point P of worktable , such that angular 

errors ( e ) Ear ( f ) Eby , and ( g ) Ecr are based on data 

collected at the three locations ( Locations A , B , and C ) with 

the IMU and a reference system ; the reference data has 

shaded areas representing measurement expanded uncertain 

ties ( k = 2 ) at 95 % confidence based on five runs ; 

[ 0022 ] FIG . 16 shows a process for diagnosing perfor 

mance degradation of a machine tool with an IMU ; 

10023 ] FIG . 17 shows ( a ) linear axis testbed for an IMU 

and ( b ) top view of the IMU without its lid ; 

10024 ] FIG . 18 shows displacement and angular errors of 

a motion member commanded to move along a ( nominal ) 

straight - line trajectory parallel to the X - axis ; 

[ 0025 ] . FIG . 19 shows convergence of ( a ) an estimated 

straightness error motion ( via accelerometer data ) and ( b ) an 

estimated angular error motion ( via rate gyroscope data ) 

with increasing number of runs for averaging ( from 5 to 50 ) ; 

[ 0026 ] FIG . 20 shows converged ( a ) linear positioning 

error motion , ( b ) straightness error motion , and ( c ) angular 

error motion for various sensing methods with an IMU ; 

[ 0027 ] FIG . 21 shows ( a ) an experimental setup to repre sent low - frequency degradations of a guideway rail of a base 
US 2018 / 0094946 A1 Apr . 5 , 2018 

member , resulting in changes in straightness error motion 

( Eyx ) observed by ( b ) a laser - based reference system and ( c ) 

an IMU ; 

[ 0028 ] FIG . 22 shows ( a ) yaw error motion ( Ecx ) sepa rated into low - and high - pass components , and ( b ) the 

high - pass component of Ecy for various number of runs for 

averaging ( from 5 to 50 ) ; 

[ 0029 ] FIG . 23 shows simulated uncertainty for straight 

ness error motions due to data fusion with accelerometer 

noise and data acquisition noise from an IMU ; 

( 0030 ] FIG . 24 shows data fusion for angular motions via 

use of an IMU that provides ( a ) rate gyroscope data or ( b ) 

accelerometer and rate gyroscope data , wherein filter cutoff 

frequencies are shown in parentheses ; 

[ 0031 ] FIG . 25 shows data fusion for displacemental motions via use an IMU that provides accelerometer data , wherein filter cutoff frequencies are shown in parentheses ; 

[ 0032 ] FIG . 26 shows convergence of ( a ) an estimated 

straightness error motion ( via accelerometer data ) and ( b ) an 

estimated angular error motion ( via rate gyroscope data ) 

with increasing number of runs for averaging ; [ 0033 ] FIG . 27 shows converged ( a ) linear positioning 

error motion , ( b ) straightness error motion , and ( c ) angular 

error motion for various sensing processes with an IMU ; 

[ 0034 ] FIG . 28 shows ( a ) an experimental setup to repre 

sent low - frequency degradations of a guideway rail of a base 

member , resulting in ( b ) changes in pitch error motion ( EBx ) 

observed by an IMU ( data averaged for 50 runs ) ; and 

[ 0035 ] FIG . 29 shows data for high - frequency degrada tions due to defects of bearing balls in which ( a ) 32 balls of 

a truck were degraded via the abrasive removal of material , resulting in ( b ) changes in pitch error motion ( EBx ) observed 

by an IMU ( data averaged for 50 runs ) . 

account for yearly economic losses of tens of billions of US 

dollars such that practice of embodiments herein provide 

economic incentives . 

[ 0039 ] Machine tools should be maintained and available 

for cost - effective production . Embodiments provide accu 

rate detection of degradation performance of the linear axes 

in contrast to conventional manual procedures that can be 

time consuming and cost - prohibitive . Indeed , manufacturers 

typically do not know the condition of the linear axes of their 

machine tools , and instead react to problems as they occur . Hence , manufacturers need automated and efficient methods 

for periodic ( e . g . , daily or weekly ) diagnosis of a condition 

of machine tool linear axes with minimal disruption to 

production . Uniquely , embodiments provide for periodically 

measuring linear axis health in a short period , e . g . , about 5 

minutes . [ 0040 ] In an embodiment , a process for condition moni 

toring of a linear axis include combining data collected from 

an inertial measurement unit disposed on a linear axis and 

estimating the linear axes errors due to degradation . Data is 

collected by the IMU during motion of the linear axis at a 

plurality ( e . g . , three ) different speeds . Data collection for a 

linear axis may take as little as 5 minutes . When the IMU 

moves with a linear axis , performance degradation of the 

linear axis is determined . Beneficially , determination of 

performance degradation of the linear axis is used for 

diagnostics and prognostics to optimize maintenance of the 

linear axis , e . g . , in a machine tool . 

[ 0041 ] Conventional condition monitoring is based on 

sensing temporal changes in vibrations metrics of acceler 

ometer signals . These methods do not yield linear axis 

errors , the result of degradation that affects the quality of 

production parts . On the other hand , conventional methods 

for measuring linear axis errors are based on laser - , capaci tive - , or probe - based metrology equipment but are time - and 

cost - prohibitive for maintenance of a fleet of production 

machines . Embodiments of the processes and articles 

described herein overcome these issues and uniquely acquire 

sensor data at various speeds , process such data , and com 

bine the data to estimate the linear axis errors . 

[ 0042 ] In an embodiment , with reference to FIG . 1 , iner 

tial measurement unit 24 determines a performance degra 

dation of a linear axis and includes accelerometer 28 that , when disposed on a motion member of the linear axis ( that 

includes the motion member disposed on a base member ) 

measures acceleration of the motion member and provides a 

displacement of the motion member in response to move 

ment of the motion member . Accelerometer 28 produces 

acceleration data 32 that can be communicated from accel 

erometer 28 . Inertial measurement unit 24 also includes rate 

gyroscope 26 that measures an angular rate of movement of 

the motion member and provides a yield angle for the 

motion member in response to movement of the motion 

member . Here , rate gyroscope 26 produces angular rate data 

30 that can be communicated from rate gyroscope 26 . The 

displacement and yield angle determine performance deg 

radation of the linear axis based on an error in linear 

movement of the motion member along the base member . 

100431 .With reference to FIG . 2 , inertial measurement unit 

24 can include a plurality of accelerometers 28 ( e . g . , one , two , . . . , 10 , or more accelerometers ) , the plurality of rate 

gyroscopes 26 ( e . g . , one , two , . . . , 10 , or more rate 

gyroscopes ) . In an embodiment , inertial measurement unit 

24 includes x - direction gyroscope 28A , y - direction gyro 

DETAILED DESCRIPTION 

[ 0036 ] A detailed description of one or more embodiments 

is presented herein by way of exemplification and not 

limitation . [ 0037 ] Advantageously and unexpectedly , it has been dis 

covered that an inertial measurement unit ( IMU ) herein 

provides determination of error in translational and angular 

geometric errors of a linear axis . A linear axis can be a 

subsystem of a machine used , e . g . , in manufacturing . Linear 

axes can degrade during a production run , and knowledge of 

degradation is not acquired or known until a fault or failure 

occurs that halt production . Beneficially , a process and 

article includes the IMU and quickly estimates performance degradation of a linear axis without a disruption to produc 

tion . The process and article combine data collected from the 

IMU when a motion member of the linear axis is subjected 

to movement at various axis speeds and determine changes 

in translational and angular geometric errors of the linear 

axis due to axis degradation . Moreover , maintenance of a 

machine tool can include determining axis degradation with 

the article and process herein . 

[ 0038 ] As a machine tool , e . g . , a computer numerical 

control ( CNC ) tool such as a lathe or mill , produces machined parts , faults can emerge that lead to performance degradation of the machine tool . The performance degrada tion lowers control precision and accuracy of the linear axis 

of the machine tool . Eventually , the linear axis of CNC 

machines may undergo wear , failure , or loss of production 

quality . A fault or failure can be common in automation and production during manufacturing . Machine tool faults 
US 2018 / 0094946 A1 Apr . 5 , 2018 

scope 28B , and z - direction gyroscope 28C that provide acceleration data ( 32A , 32B , 32C ) . In an embodiment , inertial measurement unit 24 includes x - direction rate gyro 

scope 26A , y - direction rate gyroscope 26B , and z - direction 

rate gyroscope 26C that provide angular rate data ( 30A , 30B , 30C ) . [ 0044 ] According to an embodiment , rate gyroscope 26 

can be a monolithic device such as a triaxial rate gyroscope that provides X - , y - , and z - direction angular rate data . In 

some embodiments , rate gyroscope 26 is a micro - electro 

mechanical system ( MEMS ) device that provides angular 

rate data 30 at a spatial frequency from 0 Hz ( also referred 

to as a DC response ) to a high frequency such as 200 Hz . [ 0045 ] According to an embodiment , accelerometer 28 

can be a monolithic device such as a triaxial accelerometer 

that provides X - , y - , and z - direction acceleration data . In 

some embodiments , accelerometer 28 is a MEMS device 

that provides acceleration data 32 at a spatial frequency from 

0 Hz ( also referred to as a DC response ) to a high frequency such as 500 Hz . [ 0046 ] Alternatively , accelerometers 28 or rate gyroscopes 26 can be configured differently . For example , an alternate 

configuration may use two rate gyroscopes and one accel 

erometer . In some applications , a level detector such as an 

inclinometer can be used to measure a local level of inertial 

measurement unit 24 as shown in FIG . 3 and FIG . 4 . 10047 ] In an embodiment , with reference to FIG . 5 , diag nostic apparatus 100 determines a performance degradation 

of linear axis 40 . Here , diagnostic apparatus includes linear 

axis 40 and inertial measurement unit 24 disposed on linear 

axis 40 . Linear axis 40 includes base member 20 and motion 

member 22 disposed on base member 20 . Motion member 

22 has substantially linear movement with respect to a first 

direction ( e . g . , the x - direction ) along base member 20 prior 

to performance degradation of linear axis 40 with respect to 

movement along the first direction . Inertial measurement 

unit 24 is disposed on motion member 22 such that inertial 

measurement unit 24 moves with motion member 22 . Iner 

tial measurement unit 24 includes accelerometer 28 that 

measures acceleration of motion member 22 and provides a 

displacement of motion member 22 in response to move 

ment of motion member 22 , and rate gyroscope 26 that 

measures an angular rate of movement of motion member 22 

and provides a yield angle for motion member 22 in 

response to movement of motion member 22 . The displace 

ment and yield angle acquired by inertial measurement unit 

24 determines performance degradation of linear axis 40 

based on an error in linear movement of motion member 22 

along base member 20 . [ 0048 ] With reference to FIG . 6 , it is contemplated that in 

diagnostic apparatus 100 , accelerometer 28 produces accel 

eration data 32 for motion member 22 , and rate gyroscope 26 produces angular rate data 30 for motion member 22 . Also , inertial measurement unit 24 produces inertial data 

that includes acceleration data 32 and angular rate data 30 . Moreover , diagnostic apparatus 100 further can include 

analyzer 34 that receives inertial data , i . e . , acceleration data 

32 from accelerometer 28 and angular rate data 30 from rate 

gyroscope 26 , produces straightness error 38 based on 

acceleration data 32 , and produces angular error 36 based on 

angular rate data 30 . [ 0049 ] Further , diagnostic apparatus 100 can include 

movement controller 44 in communication ( e . g . , in electrical 

communication , in mechanical communication , or a com 

bination thereof ) with motion member 22 . Movement con 

troller 44 controls movement of motion member 22 in the 

first direction via control signal 42 communicated from 

movement controller 44 to motion member 22 . Analyzer 34 

can also receive control signal 42 from movement controller 

44 so that inertial data ( 30 , 32 ) from inertial measurement 

unit 24 can be simulated or compared to movement of 

motion member 22 . It should be appreciated that inertia data 

is produced by inertial measurement unit 24 independently 

of control of movement of motion member 22 in the first 

direction by movement controller 44 . [ 0050 ] In an embodiment , diagnostic apparatus 100 

includes a machine tool that includes linear axis 40 , wherein 

motion member 22 and base member 20 in combination 

provide movement of a cutting tool ( e . g . , an end mill , a fly 

cutter , and the like ) or a workpiece disposed on motion 

member 22 . Here , movement controller 44 controls move 

ment of the machine tool and motion member 22 in the first 

direction such that inertia data is produced by inertial 

measurement unit 24 independently of control of movement 

of motion member 22 in the first direction by movement 

controller 44 . It is contemplated that movement controller 

44 controls movement of motion member 22 at a fast speed 

and a slow speed such that : accelerometer 28 provides a low 

spatial frequency of translational motion of motion member 

22 at the fast speed , and accelerometer 28 provides a high spatial frequency of translation motion of motion member 

22 at the low speed . Also , rate gyroscope 26 provides a low 

spatial frequency of angular motion of motion member 22 at 

the fast speed , and rate gyroscope 26 provides a high spatial 

frequency of angular motion of motion member 22 at the 

low speed . 

[ 0051 ] With reference to FIG . 7 , inertial measurement unit 

24 can be disposed on a linear axis or another part of a 

machine tool such as a cutting tool . Here , the cutting tool 

and workpiece can be on different stacked ( or unstacked ) linear axes , or even not on a linear axis . In this manner , IMU 

24 ( or a plurality of IMUS 24 ) can be used to measure the 

motion of the cutting tool or workpiece . It should be 

appreciated that IMU 24 can be disposed on any of the linear 

axes , cutting tool , or any combination thereof . Accordingly , a plurality of IMUS 24 can be disposed on these various 

components 

[ 0052 ] In an embodiment , a process for making inertial 

measurement unit 24 includes attaching of accelerometers 

28 and rate gyroscopes 26 to a housing or enclosure , wherein 

such attaching can occur via a temporary or permanent 

bonding material such as a screw , thread locker , adhesive 

( e . g . , an epoxy ) , and the like . A housing for inertial mea 

surement unit 24 can be rigid and provide fixed locations of 

sensors ( 28 , 26 , and the like ) with respect to motion member 

22 . An aluminum - based alloy or a material with sufficiently high stiffness - to - weight ratio be the material for the housing . Also , the housing can be as monolithic as possible to 

maximize its rigidity . In an embodiment , the housing con 

tains holes for screws to fasten motion member 22 to the 

housing . 

[ 0053 ] According to an embodiment , a process for diag nosing a geometric performance of linear axis 40 includes : 

providing diagnostic apparatus 100 ; moving motion member 

22 at a first speed in the first direction , the first speed being 

constant ; producing acceleration data 32 by measuring 

acceleration of motion member 22 by accelerometer 28 of 

inertial measurement unit 24 ; producing angular rate data 30 
US 2018 / 0094946 A1 Apr . 5 , 2018 

by measuring the angular rate of motion member 22 by rate 

gyroscope 26 of inertial measurement unit 24 ; integrating 

acceleration data 32 to produce the translational displace 

ment data for the movement of motion member 22 ; filtering the translational displacement data to produce filtered trans 

lational displacement data versus a travel length of motion 

member 22 ; integrating angular rate data 30 to produce angular displacement data for the movement of motion 

member 22 , and filtering the angular displacement data to 

produce filtered angular displacement data to diagnose the 

geometric performance of linear axis 40 . [ 0054 ] The process for diagnosing the geometric perfor 

mance , further can include moving motion member 22 at a 

second speed in the first direction , wherein the second speed is constant , and the second speed is different than the first 

speed . Here , with respect to moving motion member 22 at 

the second speed , the process can include : producing second 

acceleration data 28B by measuring acceleration of motion 

member 22 by accelerometer 28 of inertial measurement 

unit 24 ; producing second angular rate data 30B by mea 

suring the angular rate of motion member 22 by rate 

gyroscope 26 of inertial measurement unit 24 ; integrating 

second acceleration data 32B to produce second transla 

tional displacement data for the movement of motion mem 

ber 22 ; filtering the second translational displacement data to 

produce second filtered translational displacement data ver 

sus a travel length of motion member 22 ; integrating second 

angular rate data 30B to produce second angular displace 

ment data for the movement of motion member 22 , and 

filtering the second angular displacement data to produce 

second filtered angular displacement data ; summing the 

second filtered translational displacement data with the 

second filtered translational displacement data to produce a 

plurality of straightness errors ; and summing the second 

filtered angular displacement data with the second filtered 

angular displacement data to produce a plurality of angular 

errors . 

[ 0055 ] In the process , moving motion member 22 at a first 

speed in the first direction includes accelerating the motion 

member 22 from rest at one end of its travel , maintaining 

motion of the motion member 22 at the first speed , and 

decelerating the motion member 22 to rest at its other end of 

travel . The machine tool performs these steps according to 

its control system . 

[ 0056 ] Producing acceleration data 32 by measuring 

acceleration of motion member 22 by accelerometer 28 of 

inertial measurement unit 24 includes measurements within five subsequent phases of motion described in the prior paragraph such as before motion , during acceleration , during motion at first speed , during deceleration , after motion . The 

measurements can be collected by a data acquisition unit at 

a sufficiently high sampling rate and timestamped to a 

system clock used for all measurements of the inertial 

measurement unit 24 . [ 00571 Producing angular rate data 30 by measuring the 

angular rate of motion member 22 by rate gyroscope 26 of 

inertial measurement unit 24 includes measurements within 

five subsequent phases of motion such as before motion , during acceleration , during motion at first speed , during 

deceleration , after motion . The measurements can be col 

lected by a data acquisition unit at a sufficiently high sampling rate and timestamped to a system clock used for all 

measurements of the inertial measurement unit 24 . 

[ 0058 ] Integrating acceleration data 32 to produce the 

translational displacement data for the movement of motion 

member 22 includes removal of sensor data offsets , drift , or 

inclination - related terms , and double integration of the 

resulting time - based function to produce a time - based trans 

lational displacement data function . [ 0059 ] Filtering the translational displacement data to pro duce filtered translational displacement data versus a travel 

length of motion member 22 includes filtering the transla 

tional displacement data function with a phase - preserving 

bandpass filter , and relating the translational displacements 

to position of the motion member 22 via use of a position 

versus time function . Position versus time may be known 

either through data collected from the controller of the linear 

axis 40 or approximated via use of acceleration data 32 in 

the direction of motion . 10060 ] Integrating angular rate data 30 to produce angular 

displacement data for the movement of motion member 22 

includes removal of sensor data offsets and drift and single integration of the resulting time - based function to produce a 

time - based angular displacement data function . 10061 ] Filtering the angular displacement data to produce 

filtered angular displacement data to diagnose the geometric 

performance of linear axis 40 includes filtering the angular displacement data function with a phase - preserving band 

pass filter , and relating the angular displacements to position 

of the motion member 22 via use of a position versus time 

function . Position versus time may be known either through 

data collected from the controller of the linear axis 40 or 

approximated via use of acceleration data 32 in the direction 

of motion . 

[ 0062 ] Moving motion member 22 at a second speed in the 

first direction includes accelerating the motion member 22 

from rest at one end of its travel , maintaining motion of the 

motion member 22 at the second speed , and decelerating the 

motion member 22 to rest at its other end of travel . The 

machine tool performs these steps according to its control 

system . 

[ 0063 ] Producing second acceleration data 28B by mea 

suring acceleration of motion member 22 by accelerometer 

28 of inertial measurement unit 24 includes measurements 

within five subsequent phases of motion including before 

motion , during acceleration , during motion at second speed , during deceleration , after motion . The measurements should 

be collected by a data acquisition unit at a sufficiently high 

sampling rate and timestamped to a system clock used for all 

measurements of the inertial measurement unit 24 . [ 0064 ] Producing second angular rate data 30B by mea 

suring the angular rate of motion member 22 by rate 

gyroscope 26 of inertial measurement unit 24 includes 

measurements within five subsequent phases of motion 

including before motion , during acceleration , during motion 

at second speed , during deceleration , after motion . The 

measurements should be collected by a data acquisition unit 

at a sufficiently high sampling rate and timestamped to a 

system clock used for all measurements of the inertial 

measurement unit 24 . 100651 Integrating second acceleration data 32B to pro 

duce second translational displacement data for the move 

ment of motion member 22 includes removal of sensor data 

offsets , drift , or inclination - related terms , and double inte 

gration of the resulting time - based function to produce a 

time - based translational displacement data function 
US 2018 / 0094946 A1 Apr . 5 , 2018 

[ 0066 ] Filtering the second translational displacement data 

to produce second filtered translational displacement data 

versus a travel length of motion member 22 includes filter 

ing the translational displacement data function with a 

phase - preserving bandpass filter , and relating the transla 

tional displacements to position of the motion member 22 

via use of a position versus time function . Position versus 

time may be known either through data collected from the 

controller of the linear axis 40 or approximated via use of 

acceleration data 32 in the direction of motion . [ 0067 ] Integrating second angular rate data 30B to pro duce second angular displacement data for the movement of 

motion member 22 includes removal of sensor data offsets 

and drift , and single integration of the resulting time - based 

function to produce a time - based angular displacement data 

function 

10068 ] Filtering the second angular displacement data to 

produce second filtered angular displacement data includes 

filtering the angular displacement data function with a 

phase - preserving bandpass filter , and relating the angular displacements to position of the motion member 22 via use 

of a position versus time function . Position versus time may 

be known either through data collected from the controller 

of the linear axis 40 or approximated via use of acceleration 

data 32 in the direction of motion . [ 0069 ] Summing the second filtered translational displace 

ment data with the second filtered translational displacement data to produce a plurality of straightness errors includes 

summing the results of [ 0059 ] and [ 0066 ] , yielding a trans 

lational error as a function of position of the motion member 

a dashed vertical line shows when the linear axis has become 

out of tolerance . Being out of tolerance is a flag for main 

tenance of the linear axis . [ 0072 ] FIG . 11 shows a graphical summary of data col 

lection and processing of acceleration data 32 from accel 

erometer 28 to provide an error in straightness of movement 

of motion member 22 of linear axis 40 . 10073 ] Inertial measurement unit 24 , diagnostic apparatus 100 , and processes herein have numerous advantageous and 

beneficial properties . Advantageously , inertial measurement 

unit 24 and diagnostic apparatus 100 is potentially signifi 

cantly cheaper than ballbar - based or laser - based systems for 

measuring error motions within machine tools . Also , inertial 

measurement unit 24 and diagnostic apparatus 100 provides 

error motion data without requiring a setup change on the 

linear axis 40 , in contrast to ballbar - based or laser - based 

systems . Moreover , inertial measurement unit 24 , diagnostic 

apparatus 100 , and processes provide 6 degree - of - freedom 

error motions , in contrast to ballbar - based systems . Further , inertial measurement unit 24 can be integrated within a 

linear axis 40 , in contrast to ballbar - based or laser - based 

systems . Fourth also , because the invention described herein 

can be integrated within linear axis 40 and allows for data 

collection with setup change of the linear axis 40 , the 

invention described herein can allow for periodic measure 

ments of linear axis 40 for error motion tracking and health 

management of linear axis 40 . [ 0074 ] The articles and processes herein are illustrated 

further by the following Examples , which are non - limiting . 

22 EXAMPLES 

[ 0070 ] Summing the second filtered angular displacement data with the second filtered angular displacement data to 

produce a plurality of angular errors includes summing the 

results of [ 0061 ] and [ 0068 ] , yielding an angular error as a 

function of position of the motion member 22 . [ 0071 ] In the process that includes the first speed and 

second speed , it should be appreciated that a plurality of 

speeds can be incorporated in the process as illustrated in 

FIG . 8 that shows a graph of velocity of motion member 22 

versus time . Here , motion member 22 is subjected to : a slow 

speed from time T2 to time T3 in the first direction ( e . g . , the 

+ x - direction ) , the slow speed in the opposite direction 

( - x - direction ) of the first direction from time T6 time 17 , a 

medium speed from time T10 to time T11 in the first 

direction , the medium speed in the opposite direction from 

time T14 time T15 , and a fast speed from time T18 to time 

T19 in the first direction , the fast speed in the second 

direction from time T22 time T23 . During these periods , accelerometer 28 and rate gyroscope 26 monitor motion 

member 22 and produce acceleration data 32 and angular 

rate data 30 . As shown in FIG . 9 , acceleration data 32A in 

the x - direction of motion member 22 and velocity in the 

x - direction are graphed versus time in the upper graph . The 

lower graph shows acceleration data 32B in a second 

direction ( orthogonal to the first direction ; e . g . , in the 

y - direction or z - direction of motion member 22 and veloc 

ity versus time . Moreover , a graph of filtered response 

versus position ( e . g . , a travel length L ) is shown in the upper 

panel of FIG . 10 for the fast speed , medium speed , and slow 

speed of motion member 22 for exemplary data . The lower 

panel of FIG . 10 shows a graph of error versus position for 

motion member 22 for a summation of filtered response data 

with a tolerance limit shown as a dashed for the online , and 

Example 1 . Identification of Machine Tool 

Geometric Performance Using On - Machine Inertial 

Measurements 

[ 0075 ] Machine tools degrade during operations , yet accu 

rately detecting degradation of machine components such as 

linear axes is typically a manual and time - consuming pro 

cess . Thus , manufacturers need automated and efficient 

methods to diagnose the condition of their machine tool 

linear axes with minimal disruptions to production . Towards 

this goal , a method was developed to use accelerometer and 

rate gyroscope data from an inertial measurement unit 

( IMU ) for identification of changes in the translational and 

angular errors due to axis degradation . An IMU was created 

for application of the method on a machine tool . As a proof 

of concept for detection of translational error motions , IMU 

data was collected on a machine tool with experimentally simulated degradation ; as the worktable moved along its 

nominal path , a cross - axis moved along a swept sinusoidal 

pattern with micrometer - level amplitudes . In another experi 

ment , data was collected at three different locations on a 

worktable for the same axis motion . These experiments 

showed that the IMU detected micrometer - level and micro 

radian - level degradation of linear axes , revealing that the 

IMU - based method is plausible for use in smart machine 

tools . [ 0076 ] Over a machine tool ' s lifetime , various faults lead 

to performance degradation , lowering accuracy and repeat 

ability . Typical sources of errors within linear axes are due 

to pitting , wear , corrosion , and cracks of the system com 

ponents such as guideways and recirculating balls . A typical machine tool has multiple linear axes , and their accuracies directly impact the quality of manufactured parts . As deg 
US 2018 / 0094946 A1 Apr . 5 , 2018 

radation increases , tool - to - workpiece errors increase that 

eventually may result in a loss of production quality or a 

failure . Yet knowledge of degradation is elusive ; proper 

assessment of axis degradation is often a manual , time 

consuming , and potentially cost - prohibitive process . [ 0077 ] . An online condition monitoring system for linear 

axes is needed to help reduce machine downtime , increase productivity and product quality , and improve knowledge 

about manufacturing processes . Previous attempts at condi 

tion monitoring of linear axes had limited success , partly 

because of the lack of robustness and defined relationships of signals to axis degradation composed of a wide range of 

spatial frequencies . Consequently , efficient quantitative 

measures are needed to monitor the degradation of linear 

axes . [ 0078 ] . For online monitoring of linear axis degradation , an inertial measurement unit ( IMU ) processes accelerometer 

and rate gyroscope data to detect changes in the translational 

and angular error motions due to axis degradation . For 

industrial application , the IMU can be physically small and 

economical while satisfying measurement needs . As seen in 

FIG . 12 , an industrial IMU was created that is about 9 cm 

long and contains a triaxial accelerometer and a triaxial rate 

gyroscope . The bandwidths and noise properties of these 

sensors are shown in Table 1 . An IMU was made to satisfy design constraints such as cost , size , and accuracy . 

TABLE 1 

Accelerometer 0 Hz to 500 Hz 20 

( um / s ) / VHz 

35 

( urad / s ) / V / Hz 

Rate 0 Hz to 200 Hz 

Gyroscope 

[ 0081 ] IMU data ( i . e . , inertial data including acceleration 

data and angular rate data ) was collected and processed for 

each of the five values of A , the parameter representing 

translational error motion in the Z - direction due to ' degra dation ' . The results of each set of 50 runs were averaged to 

yield the estimated straightness error motion Ezy for each 

value of A . FIG . 14 ( a ) and FIG . 14 ( b ) compare the com 

manded and estimated values for hp ( Ezy ) , the high - pass filtered values of Ezx The error motions are high - pass filtered because the specific accelerometer was determined 

post facto to have noise during testing that exceeded the 

noise specification listed in Table 1 . Hence , convergence of 

Ezy did not occur to sufficient levels for spatial frequencies 

below 1 . 25 m - , so those terms were filtered out via the use 

of zero - phase forward and reverse digital infinite impulse 

response ( IIR ) Butterworth filters . [ 0082 ] FIG . 14 ( b ) shows how the mechanically - simulated 

degradation is detected by the IMU - based method . As the 

commanded degradation amplitude A increases to 20 um , as 

seen in FIG . 14 ( a ) , the estimated degradation amplitude also 

increases , as shown in FIG . 14 ( b ) . Error motions due to the 

sensor noise and mechanical elements of the machine tool 

are present in the curves of FIG . 14 ( b ) , but the degradation 

terms are still clearly visible . The estimated degradation amplitudes seen in FIG . 14 ( b ) are roughly similar to the 

commanded ones seen in FIG . 14 ( a ) , but the estimated 

amplitudes increase as the spatial frequency of the swept sine decreases . When the spatial frequency is at its highest 

around X = 0 . 2 m , the required accelerations for the com 

manded motions within FIG . 14 ( a ) for A = 20 um are as high 

as 1 . 75 m / s for the fast speed ( 0 . 1667 m / s ) , which is far 

greater than the maximum allowable acceleration for the 

machine tool during feed motion . Hence , the high - frequency motions for A = 20 um near X = 0 . 2 m are not detectable 

because they did not occur with amplitudes near 20 um , but 

rather with much smaller amplitudes . Unfortunately , a laser 

based device , such as a laser tracker , was not available to 

measure the actual amplitudes during motion for verification 

and validation of the acceleration - limiting motion . [ 0083 ] The high - passed motions , shown in FIG . 14 for 

various amplitudes A , can be processed with a single metric 

value for comparison and tracking of ' degradation ' . FIG . 14 ( c ) shows the scaled root mean square ( rms ) of each of the 

curves seen in FIG . 14 ( a ) and FIG . 14 ( b ) . The metric for the 

commanded motion increases linearly from Oum ( the small 

est value for A ) to 20 um ( the largest value for A ) as A 

increases , while the metric for the estimated motion 

increases fairly linearly from about 5 um to about 16 um . The estimated - motion metric value reaches 5 um , instead of 

O um , at A = 0 um because even with no commanded cross 

axis motion ( A = 0 um ) , the Z - axis still exhibits an error 

motion as the X - axis moves . At the other end , the estimated 

motion metric value reaches 16 um , instead of 20 um , at 

A = 20 um because of the machine tool ' s acceleration limit 

that inhibits the Z - axis motion , as evidenced in FIG . 14 ( b ) . Nonetheless , FIG . 14 ( c ) reveals how even a simple metric , based on results from the IMU - based method , can track 

linear axis degradation in a quantitative manner . [ 0084 ] Detection of Angular Error Motion . 10085 ] Another experiment was conducted to test the 

capability of the IMU for on - machine detection of error 

motions . However , before experimentation , the IMU was 

improved via replacement of the triaxial accelerometer with 

a different model that had relatively stable low - frequency 

frequencies correspond to half - power points , also known as 3 dB points 

[ 0079 ] Detection of Translational Degradation . 10080 ] Repeated testing of the IMU on a machine tool is 

performed for acceptance testing . FIG . 13 shows an experi 

mental setup of the IMU on a horizontal milling machine . The IMU is attached to the worktable , which can translate in 

two directions since the X - axis is stacked on the Z - axis . Of 

course , unwanted translational errors exist and can worsen 

due to degradation as the machine tool produces parts . For 

example , the error motion Ezy is the translational error , as a 

function of X , in the Z - direction for X - axis motion . Because 

the X - and Z - axes are stacked for the machine tool , we can 

simulate Ezy via two - axis commanded motion . The boxed 

inset of FIG . 13 shows the points used for machine path 

generation . As the X - axis moves from 0 mm to 1250 mm , the Z - axis experiences a swept - sine - like form of degradation with magnitude A . The path is independent of feed rate , which can be as large as 10 m / min ( 0 . 1667 m / s ) . Hence , data 

was collected for 50 runs for each of three speeds for use 

within the method : 0 . 1667 m / s ( Fast speed ) , 0 . 1 m / s ( Mod 

erate speed ) , and 0 . 02 m / s ( Slow speed ) . The fast speed of 

0 . 1667 m / s was the machine limit , but preferably a speed of 

0 . 5 m / s would have been used otherwise . Furthermore , the 

magnitude A was changed to represent different levels of 

degradation . Data was collected for five values of A : O um 

( representing no degradation ) , 5 um , 10 um , 15 um , and 20 

um ( representing significant degradation ) . Consequently , the 

swept - sine - like motion is a " mechanically - simulated degra 

dation ” that will test the ability of the industrial IMU to 

measure micrometer - level degradation for various spatial frequencies . 
US 2018 / 0094946 A1 Apr . 5 , 2018 

noise , but higher overall noise ( 69 ( um / s ) / VHz ) compared 

to the accelerometer used in the first experiment ( see Table 

enable the prediction of future machine performance and 

part quality based upon current and projected equipment 

1 ) . health . [ 0086 ] FIG . 15 ( a - d ) shows an experimental setup of the 

IMU on a vertical milling machine at the National Institute 

of Standards and Technology ( NIST ) . For each dataset , the 

IMU is attached to the worktable at one of three different 

locations ( A , B , or C ) and the Y - axis travels between Y = 0 m 

and Y = 0 . 5 m . Hence , IMU data was collected for 50 runs 

sequentially at each location with motion back and forth 

along the Y axis for use within the method . The three speeds 

for data collection are 0 . 5 m / s ( fast speed ) , 0 . 1 m / s ( mod 

erate speed ) , and 0 . 02 m / s ( slow speed ) . The IMU data was 

then used to estimate the three angular error motions at each 

of the three worktable locations ( A , B , and C ) . The accel 

erometer and rate gyroscope data were processed to estimate 

two angular error motions ( Eay and Eby ) , while the rate 

gyroscope data only was used to estimate the third angular 

error motion ( Ecy ) . If the worktable is rigid , then the 

estimated angular error motions should be identical among 

each location . 

[ 0087 ] FIG . 15 ( e - g ) shows the estimated angular errors 

based on the IMU data . Error motion data was also collected 

at each location with a laser - based commercial reference 

system ( with standard uncertainties of 0 . 7 um and 3 . 0 urad ) , and the data from the reference system is shown in the 

figures ( as thinner lines ) for comparison purposes . At each 

worktable location , reference data was collected for five 

runs , which were averaged to produce the curves seen in 

FIG . 15 ( e - g ) . The standard deviations of each set of five runs 

was also used to produce the shaded 95 % - confidence zones 

in FIG . 15 ( e - g ) . Thus , the shaded zones represent a contri 

bution towards , but not the total of , the measurement uncer 

tainty . As seen in FIG . 15 ( e - g ) , the estimated angular errors 

from the IMU data match each other respectively to within 

about 5 grad for the three worktable locations ( A , B , and C ) . Also , the estimated error motions from the IMU match those 

from the reference system to within about 8 grad . The 

differences may be due to differences in error type ( inertial 

for IMU , while relative for the reference system ) as well as 

to sources of uncertainty . [ 0088 ] The IMU was developed to test the effectiveness of 

a new IMU - based method for on - machine application . The 

industrial IMU includes a triaxial accelerometer and a 

triaxial rate gyroscope , both with noise levels shown to be 

sufficiently low for convergence via averaging . One experi 

ment was conducted in which two stacked axes were moved 

simultaneously to simulate translational degradation up to 

20 um in amplitude . The IMU data showed that the mechani 

cally - simulated degradation is detected by the IMU - based 

method . In a second experiment , data was collected from an 

improved IMU at three different locations on a worktable for 

the same axis motion . The IMU results were within about 8 

urad of those from a laser - based reference system . Both 

experiments show that the IMU - based method detects 

micrometer - level and microradian - level degradation of lin 

ear axes . When coupled with existing data exchange and 

formatting standards , verified and validated data from an 

' industrial IMU ' provides manufacturers and machine tool 

operators with near - real - time equipment health , diagnostic , and prognostic intelligence to significantly enhance asset 

availability and minimize unscheduled maintenance . This 

information can be coupled with equipment performance metrics and quality data ( resultant from part inspection ) to 

Example 2 . Inertial Measurement Unit for 

On - Machine Diagnostics of Machine Tool Linear 

Axes 

[ 0089 ] An IMU was created for application of an IMU 

based method on a machine tool for detection of linear axis 

error motions . Data collection and analysis are integrated 

within a machine controller , and the process is streamlined 

for the optimization of maintenance activities and schedul 

ing , supporting more intelligent decision - making by manu 

facturing personnel and the development of self - diagnosing 

smart machine tools . [ 0090 ] Machine tool linear axes move the cutting tool and 

workpiece to their desired positions for parts production . A 

typical machine tool has multiple linear axes , and their 

accuracies directly impact the quality of manufactured parts . However , over a machine tool ' s lifetime , various faults lead 

to performance degradation , lowering accuracy and repeat ability . Typical sources of errors within linear axes are due 

to pitting , wear , corrosion , and cracks of the system com 

ponents such as guideways and recirculating balls . As deg 

radation increases , tool - to - workpiece errors increase that 

eventually may result in a failure and / or a loss of production 

quality . Yet knowledge of degradation is illusive ; proper 

assessment of axis degradation is often a manual , time consuming , and potentially cost - prohibitive process . [ 0091 ] An online condition monitoring system for linear 

axes is needed to help reduce machine downtime , increase 

productivity and product quality , and improve knowledge 

about manufacturing processes . Consequently , efficient 

quantitative measures are needed to monitor the degradation 

of linear axes . An inertial measurement unit herein is attrac 

tive for on - machine condition monitoring . 

[ 0092 ] Online monitoring of linear axis degradation was 

implemented with an IMU . As seen in the schematic of FIG . 16 , an IMU is mounted to a moving machine tool compo 

nent . To diagnose axis degradation , the axis is moved back 

and forth at various speeds to capture data for different 

frequency bandwidths . This data is then integrated , filtered , and ‘ fused to estimate the changes in the 6 - degree - of 

freedom WoO geometric errors of the axis . Because the 

linear axes are stacked , coordinate transformations may be 

used with all 6 - DOF errors to estimate the errors at the 

functional point . Data can be collected periodically to track 

axis degradation with minimal disruptions to production . With robust diagnostics and prognostics algorithms , incipi 

ent faults may be detected and future failures may be 

avoided . In essence , IMU data can be used to help optimize maintenance , production planning , flexibility , and ultimately part quality . [ 0093 ] IMU and Error Motions for Diagnostics . [ 0094 ] A testbed was designed for evaluation of the IMU 

based method . As seen in FIG . 17 ( a ) , the testbed includes a 

translation stage , the IMU , a commercial laser - based system for measuring the geometric errors of the axis , and a direct 

current ( DC ) motor with encoder for motion control . While 

the metrology system measures the motion of the carriage 

with respect to the base of the linear axis , the carriage 

mounted IMU measures the changes in the inertial motion of 

the carriage . The commercial metrology system measures 

straightness and angular error motions over the travel length 
US 2018 / 0094946 A1 Apr . 5 , 2018 

of 0 . 32 m with standard uncertainties of 0 . 7 um and 3 . 0 grad , respectively . The laser - based system is used for verification 

and validation ( V & V ) of the IMU - based results . [ 0095 ] For the detection of both translational and rota 

tional motions , the IMU contains three accelerometers and 

one triaxial rate gyroscope , as seen in FIG . 17 ( b ) . Table 2 

outlines key specifications of the IMU sensors . Individual 

sensors were used to obtain sufficiently low noise , despite the larger sensor volume compared to a single 6 - DOF IC sensor . 

TABLE 2 

Accelerometer0 Hz to 1800 Hz 4 . 0 

( um / s ) / VHz 

from 0 Hz 

to 100 Hz 

35 

( urad / s ) / / Hz 

Rate 0 Hz to 200 Hz 

Gyroscope 

afrequencies correspond to half - power points , also known as 3 dB points 

[ 0096 ] Consequently , these sensors enable the estimation 

of 6 - DOF motion . A typical machine tool has three linear 

axes , which means that a total of 18 ( = 6x3 ) translational and 

angular motion errors exist . These errors are major contribu 

tors to the position - dependent tool - to - workpiece errors . FIG . 18 shows these six errors that change with axis degradation . As the carriage is positioned along the X axis , it experiences 

three translational errors from its nominal path : one linear displacement error ( Ex ) in the X - axis direction and two 

straightness errors ( Eyx and Ezy ) in the Y - and Z - axis 

directions . The carriage also experiences three angular errors 

( Eax , Eby , and Ecx ) about the X - , Y - , and Z - axes . [ 0097 ] Small levels of degradation of linear axes are 

expected and allowed , but there are limits specified for axis 

errors . ISO 10791 - 2 ( International Organization for Stan 

dardization , 2001 ) specifies the tolerances for linear axis 

errors of vertical machining centers . As shown in Table 3 , the acceptable straightness error is limited to 20 um and the 

acceptable angular error is limited to 60 urad . A test uncer 

tainty ratio ( TUR ) of at least 4 : 1 is deemed to be acceptable , which means that straightness and angular error measure 

ment uncertainties of 5 um and 15 urad , respectively , are 

acceptable based on the tolerances outlined in Table 3 . 

excitations , especially resulting from the initial and final 

accelerations during the Fast speed cycle . [ 0100 ] FIG . 19 shows the typical convergence of an esti 

mated straightness error motion and an estimated angular 

error motion with increasing number of runs for averaging . As seen in FIG . 19 , 10 runs is usually sufficient for conver 

gence within 5 um or 15 urad , which means the IMU - based 

method has the potential to estimate geometric motion errors 

with a test uncertainty ratio ( TUR ) of at least 4 : 1 . FIG . 20 

compares the laser - based measurement and IMU - based 

results ; the standard deviations of the differences are 11 um , 2 . 3 um , and 13 urad for the linear positioning , straightness , and angular error motions , respectively . [ 0101 ] Testbed Experimentation . [ 0102 ] FIG . 21 ( a ) shows how a linear axis rail was 

deformed with shims to simulate low spatial frequency 

degradations of a machine tool axis . The entire rail was 

raised with shims so that the center shims could be changed 

without loosening more than one screw ( the center rail 

screw ) . Measurements for each case were taken with the 

reference - and IMU - based systems , resulting in the Y - axis 

straightness error motions seen in FIG . 21 ( b ) and FIG . 21 ( c ) , respectively . The IMU - based method is able to detect the 

approximately 5 um change in straightness from Case 0 to 

Case 4 , as verified by the reference measurements . [ 0103 ] One approach for investigating degradation of lin 

ear axes is to use filtering to focus on certain sources of 

errors , such as surface pitting of the rails Specifically , low - frequency components can be neglected through high 

pass filtering . Towards this end , FIG . 22 ( a ) shows data 

smoothed via use of a linear Savitzky - Golay smoothing filter . The frame size for the Savitzky - Golay filter was 

chosen to be 2 cm , which is large compared to millimeter 

sized defects . Thus , the high - pass filtered data is represen 

tative of many defects caused by wear . In FIG . 22 ( a ) , the 

error motion ( ' No filter ' ) is filtered via the Savitzky - Golay filter to produce low - pass filtered data ( Low - pass ) , and the 

high - pass filtered data ( High - pass ' ) is the complement of the 

low - pass filtered data ; the low - pass and high - pass filtered 

data sum to yield the unfiltered error motion . [ 0104 ] This filtering process can be applied to any linear 

axis error motion . FIG . 22 ( b ) shows typical high - pass fil 

tered data for Ecx for various numbers of runs for averaging ( from 5 to 50 ) , where hp ( Ecx ) is the high - pass filtered data 

of Ecr . As seen in FIG . 22 ( b ) , convergence for hp ( Ecx ) is 

achieved to within 5 um ( TUR = 4 ) in less than 10 runs for 

averaging . Furthermore , the high - pass filtered error motion 

reveals influences from the ball bearings in the trucks . Each 

ball has a diameter of about 4 mm , which means that each 

ball rolls on its rail with a ball - passing distance of 12 . 5 mm 

( the ball circumference ) . FIG . 22 ( b ) shows how the com 

bined influence of these balls creates a net error motion with 

significant components dependent upon the ball - passing 

distance . 10105 ] IMU for Industrial Application . [ 0106 ] The IMU seen in FIG . 17 was created for testing of 

the method within the linear axis testbed . For industrial 

application , the IMU can be physically smaller and more 

economical while still satisfying the measurement needs . 

[ 0107 ] For application on machine tools , an ' industrial 

IMU ' was created that is about 73 % smaller than the ' testbed 

IMU ' . As seen in FIG . 6 , the industrial IMU is about 9 cm 

long and contains a triaxial accelerometer and a triaxial rate 

gyroscope . The bandwidths and noise properties of these 

TABLE 3 

Straightness 

Angular ( Pitch , Yaw , or 

Roll ) 

20 um 

60 urad 

* for axes capable of 1 meter of travel , according to ISO 10791 - 2 

[ 0098 ] IMU - Based Method and General Results . 10099 ] As outlined in FIG . 16 , the IMU - based method 

relies on fusion of data collected at three programmed speeds of the carriage : Fast speed ( v2 = 0 . 5 m / s ) , Moderate 

speed ( V2 = 0 . 1 m / s ) , and Slow speed ( Vz = 0 . 02 m / s ) . The different speeds allow for sensing of repeatable error 

motions , composed of low to high spatial frequencies , 

within different temporal bandwidths . Such a process takes 

advantage of the enhanced signal - to - noise and lower sensor 

drift at faster speeds , while taking advantage of the detection 

of higher spatial frequencies at slower speeds without vio 

lating sensor bandwidths . As seen in FIG . 16 , matching the 

spatial cutoff frequencies enables the data fusion , while 

filtering allows for the attenuation of significant modal 
US 2018 / 0094946 A1 Apr . 5 , 2018 

sensors are seen in Table 4 . The rate gyroscope in the 

industrial IMU is identical to the one used in the testbed 

IMU . In contrast , the three uniaxial accelerometers seen in 

FIG . 17 ( b ) have been replaced with a triaxial accelerometer 

seen in FIG . 6 ( b ) . This change had many advantages : the 

reduction of space required for acceleration sensors , the 

elimination of the L - bracket for accelerometer mounting , and a significant reduction of sensor cost . However , the 

change also had some disadvantages , specifically the reduc 

tion of accelerometer bandwidth from 1800 Hz to 500 Hz 

and the 5 - fold increase of accelerometer noise from 4 . 0 

( um / s ) / VHz to 20 ( um / s ) / Hz . 

TABLE 4 

Accelerometer 0 Hz to 500 Hz 20 

( um / s ) / VHz 

35 

( urad / s ) / / Hz 

Rate 0 Hz to 200 Hz 

Gyroscope 

ofrequencies correspond to half - power points , also known as 3 dB points 

[ 0108 ] According to simulations of the data fusion pro 

cess , the accelerometer used in the industrial IMU will result in approximately twice as much uncertainty in straightness 

errors as that for the testbed IMU . As seen in FIG . 23 , the 

5 - fold increase of accelerometer noise from 4 . 0 ( um / s ) / Hz 

( for the testbed IMU ) to 20 ( um / s2 ) / VHz ( for the industrial 

IMU ) should result in an approximate 2 - fold increase in 

straightness uncertainty . FIG . 23 shows that as the acceler 

ometer noise decreases , the uncertainty decreases to a limit 

caused by noise of the data acquisition ( DAQ ) equipment . Experimental data can be collected to confirm the slower 

rate of convergence for the industrial IMU . [ 0109 ] Manufacturers need efficient and robust methods 

for diagnosis of machine tool linear axes with minimal 

disruptions to production . Towards this end , a new IMU 

based method was developed for linear axis diagnostics . Measurements from accelerometers and rate gyroscopes are 

used to identify changes in translational and angular error 

motions due to axis degradation . Data is fused in the spatial 

frequency domain via filtering in order to include both low 

and high - frequency error motions while excluding signifi 

cant modal excitations . A linear testbed was used to verify and validate the IMU - based method through use of a laser 

based system for measurement of the geometric axis per formance . The IMU - based results typically converge within 

5 um or 15 urad when using 10 runs for averaging , needed 

for the estimation of changes in geometric motion errors 

with test uncertainty ratios of at least 4 : 1 . [ 0110 ] Data collection and analysis can be integrated 

within a machine controller , and the process can be stream 

lined for the optimization of maintenance , supporting the 

development of self - diagnosing smart machine tools . When 

coupled with existing data exchange and formatting stan 

dards , verified and validated data from an “ industrial IMU ' 

provides manufacturers and machine tool operators with 

near - real - time equipment health , diagnostic , and prognostic intelligence to significantly enhance asset availability and 

minimize unscheduled maintenance . 

component . To diagnose axis degradation , the axis is moved 

back and forth at various speeds to capture data for different 

bandwidths . This data is then ' fused ' to estimate the changes in the 6 - degree - of - freedom ( DOF ) geometric errors of the 

axis . Because the linear axes are stacked , coordinate trans 

formations may be used with all 6 - DOF errors to estimate 

the errors at the functional point . Data can be collected 

periodically to track axis degradation with minimal disrup tions to production . With robust diagnostics and prognostics algorithms , incipient faults may be detected and future 

failures may be avoided . In essence , IMU data can be used 

to help optimize maintenance , production planning , and 

ultimately part quality . [ 0112 ] This Example describes an IMU - based method for 

diagnostics of machine tool linear axes . A linear axis testbed 

was designed to physically implement the custom IMU and 

the IMU - based method . Various degradation patterns were experimentally simulated by adjustments of a guideway rail 

or defects imparted on bearing balls . This paper outlines the 

major findings of these experiments , revealing the potential 

of the novel IMU - based approach for diagnostics and prog nostics of machine tools . [ 0113 ] Testbed Setup . [ 0114 ] A testbed was designed for evaluation of the IMU 

based method . As seen in FIG . 17 ( a ) , the testbed includes a 

linear axis , the IMU , a commercial laser - based system for 

measuring the geometric errors of the axis , and a direct 

current ( DC ) motor with encoder for motion control . While 

the metrology system measures the motion of the carriage 

with respect to the base of the linear axis , the carriage 

mounted IMU measures the changes in the inertial motion of 

the carriage . The commercial metrology system is able to 

measure straightness and angular error motions over the 

travel length of 0 . 32 m with standard uncertainties of 0 . 7 um 

and 3 . 0 urad . The laser - based system is used for verification 

and validation ( V & V ) of the IMU - based results . 10115 ] . For the detection of both translational and rota 

tional motions , the IMU contains three accelerometers and 

one triaxial rate gyroscope , as seen in FIG . 17 ( b ) . Table 5 

outlines key specifications of the IMU sensors . Each sensi 

tive direction is nominally aligned with either the X - , Y - , or 

Z - axis of the testbed coordinate system . Consequently , these 

sensors enable the estimation of 6 - DOF motion . 

TABLE 5 

Sensor Bandwidth Noise 

Accelerometer 0 Hz to 1800 Hz 4 . 0 

( um / s ) / Hz 

from 0 Hz to 

100 Hz 

35 

( urad / s ) / VHz 

Rate 0 Hz to 200 Hz 

Gyroscope 

frequencies correspond to half - power points , also known as 3 dB points 

Example 3 . Diagnostics for Geometric Performance 

of Machine Tool Linear Axes 

[ 0116 ] IMU - Based Method . [ 0117 ] As shown in FIG . 16 , the IMU - based method relies 

on sensor data collected during a fixed - cycle test , in which 

an axis is programmed to move unloaded at three constant 

speeds : Fast speed ( v , = 0 . 5 m / s ) , Moderate speed ( V2 = 0 . 1 

m / s ) , and Slow speed ( V3 = 0 . 02 m / s ) . Constant speeds allow 

for simple correlation of error motions with axis position 

while minimizing transient dynamic effects . The different 

speeds allow for sensing of repeatable error motions , com 

posed of low to high spatial frequencies , within different 

[ 0111 ] For online monitoring of linear axis degradation of 

an inertial measurement unit was constructed . As seen in 

FIG . 16 , an IMU is mounted to a moving machine tool 
US 2018 / 0094946 A1 Apr . 5 , 2018 

( 3a ) visw ) vaVizcay ) = [ 1 – 63 Jas ( 2 ) 

v2 ( 126 ) – vsViz3 ( ) = [ 1 - 603 ) Januac ) ( 3b ) 

temporal bandwidths . Such a process takes advantage of the 

enhanced signal - to - noise and lower sensor drift at faster 

speeds , while taking advantage of the detection of higher spatial frequencies at slower speeds without violating sensor 

bandwidths . As seen in FIG . 16 , matching the spatial cutoff 

frequencies enables the data fusion , while filtering allows 

for the attenuation of significant modal excitations , espe cially resulting from the initial and final accelerations during the Fast speed cycle . [ 0118 ] For the linear axis testbed , data is collected while 

the carriage moves back and forth sequentially at each of 

three speeds for 50 runs . Data collection for multiple runs 

allows averaging for convergence purposes . Once data is 

collected , data fusion follows . [ 0119 ] Angular Motions . [ 0120 ] Data fusion for estimation of angular motions is 

represented in FIG . 24 . Rate gyroscope data for three speeds is integrated once , low - or band - pass filtered , processed , and 

summed to yield the total angular motions following the 

scheme in FIG . 24 ( a ) . [ 0121 ] In contrast , the scheme in FIG . 24 ( 6 ) may also be 

used to estimate the angular motions about the X - and 

Y - directions . Measuring down to 0 Hz ( see Table 5 ) , the 

three accelerometer signals ( Ax , Ay , and Az ) for the X - , Y - , and Z - directions relate to the inclination angles ( Oy and Oy ) 

as approximately 

Ay = ax - goy ( la ) 

Ay = ay + gox ( 1b ) 

( 1c ) Az = az – 5 : 00 + ) 

where g is the magnitude of acceleration due to gravity . Thus , Eqs . ( 1a ) and ( 1b ) yield the respective inclinations , Oy and Oy , when the accelerations ( ay , and ay ) are negligible . However , the data fusion scheme in FIG . 24 ( b ) may not be 

applied for the Z - axis , for which no ' inclinometer ' exists . 

[ 0122 ] Translational Motions . [ 0123 ) Data fusion for estimation of translational error 

motions is represented in FIG . 25 . The accelerometer data is 

integrated twice , low - or band - pass filtered , processed , and 

summed to yield the net translational motions . Similar to the 

schemes in FIG . 24 , the scheme in FIG . 25 relies upon the 

matching of spatial cutoff frequencies and the exclusion of 

significant modal excitations . [ 0124 ] An element of the processing utilized for the 

scheme in FIG . 25 involves accounting for corruptive effects 

due to inclinations as described by Eqs . ( 1a ) and ( 1b ) . For 

the ith accelerometer , three signals are collected ( A1 , 1 , A1 , 2 , and A1 ,3 ) per run , one for each speed . Each signal may be 

represented as 

Ain - fi ( x ) + ai , ( t ) ( 2 ) 

where f / ( x ) is the common inclination - related component as 

a function of position , x , not of time , t . Equation ( 2 ) is 

integrated in time and related to position as Vi , 1 ( x ) , Vi , 2 ( x ) , or V ; 3 ( x ) . Equation ( 2 ) is then applied for two speeds ( Fast 

and Moderate , or Moderate and Slow ) to isolate the accel 

eration , a ; n ( x ) , due to common geometric error motions , resulting in Eqs . ( 3a ) and ( 3b ) . 

Equations ( 3a ) and ( 3b ) are used to isolate accelerations for 

the ‘ Fast ' and ` Moderate ' regimes . [ 0125 ] Convergence and General Results . [ 0126 ] The data fusion method is not very useful without 

convergence . FIG . 26 shows the typical convergence of an 

estimated straightness error motion and an estimated angular 

error motion with increasing number of runs for averaging . The errors are labelled per the convention in ISO 10791 - 1 . As seen in FIG . 26 , 10 runs are usually sufficient for 

convergence within 5 um or 15 urad , which means the 

IMU - based method has the potential to estimate geometric motion errors with a test uncertainty ratio ( TUR ) of at least 

4 : 1 per ISO 10791 - 1 

( 0127 ] In addition to convergence , the estimated error 

motions should match those of the laser - based commercial 

system . FIG . 27 compares the laser - based and IMU - based 

results ; the standard deviations of the differences are 11 um , 2 . 3 um , and 13 urad for the linear positioning , straightness , and angular error motions , respectively . Lower - frequency deviations are partly due to thermal drift , since the reference 

and IMU data were not collected simultaneously . Higher 

frequency deviations are partially due to the fact that IMU 

based results are averaged for multiple runs , while laser 

based results are not ; differences include non - repeatable 

error motions . ( 0128 ] . However , due to the quadratic terms in Eq . ( lc ) , the 

data fusion method is not robust for straightness error 

motions in the Z - axis direction . The quadratic nonlinearity implies that high - frequency angular vibrations cause low 

frequency sensor offsets , which cannot be eliminated via Eq . ( 3a ) . One possible solution is to modify the IMU via rotation 

of the X - and Z - axis accelerometers about the Y - axis ( see 

FIG . 12 ) , such that accelerometer signals depend linearly on 

angular motions as in Eqs . ( la ) and ( 1b ) . ( 0129 ] Experiments were performed to investigate the 

ability of the IMU - based method to resolve low - and high 

frequency components of error motions . In the first experi 

ment outlined in FIG . 28 ( a ) , a linear axis rail was deformed 

with shims to simulate low spatial frequency degradations of 

a machine tool axis . The entire rail was raised with shims so 

that the center shims could be changed without loosening 

more than one screw ( the center rail screw ) . The systematic change in center height to 38 um is evidenced in the change of the angle about the Y - axis , as seen in FIG . 28 ( b ) . Low 

spatial frequency changes over 200 urad dominate the 

response with insignificant differences in high - frequency 

components among the curves of FIG . 28 ( b ) . [ 0130 ] In a second experiment outlined in FIG . 29 , bearing balls within a truck were degraded to simulate high spatial 

frequency degradations of a machine tool linear axis . Thirty 

two balls of a truck were degraded via the abrasive removal 

of material , one ball at a time , resulting in defects in the form 

of flattened rougher surfaces as shown in FIG . 29 ( a ) . Case 

O in FIG . 29 is the nominal case of Grade 25 chrome steel 

balls with no defects ( nominal diameter = 3 . 981 mm ) . For 

each subsequent case , one extra defect was created on each 

ball at a random location , and the additional defect was of 
US 2018 / 0094946 A1 Apr . 5 , 2018 

a sto 

a greater nominal size . Defects ranged in depth from 3 um 

to 10 um . Consequently , differences are dominated by high frequency terms among the curves of FIG . 29 ( b ) once DC 

shifts ( due to loosening / tightening of testbed screws 

between cases ) are neglected . [ 0131 ] Manufacturers need efficient and automated meth 

ods for diagnosis of machine tool linear axes with minimal 

disruptions to production . Towards this end , an inertial 

measurement unit and associated data fusion method were 

developed for machine tool application . The IMU - based 

method uses data from both accelerometers and rate gyro 

scopes to identify changes in translational and angular error 

motions due to axis degradation . Data is fused in the spatial 

frequency domain via filtering in order to include both low 

and high - frequency error motions while excluding signifi 

cant modal excitations . [ 0132 ] The IMU - based method was verified and validated 

via a testbed containing a linear axis and a laser - based 

system for measurement of the geometric axis performance . The IMU - based results typically converge within 5 um or 15 

urad when using 10 runs for averaging , needed for the 

estimation of changes in geometric motion errors with test 

uncertainty ratios of at least 4 : 1 . Several experiments showed that the IMU - based method is capable of resolving both low - and high - frequency error motion components . Measurement results are prone to variations in system noise , but the method incorporates averaging along with conver 

gence testing to accommodate increased noise . [ 0133 ] Because the method is robust for the detection of defects , appropriate diagnostic metrics based on this method 

can be defined to facilitate industrial applications . Such 

metrics would use the IMU - based data to quantify machine 

tool linear axis degradation , and to inform the user of the 

magnitude and location of wear and any violations of 

performance tolerances . Further tests may show the value of 

additional metrics for prognostic purposes to estimate the 

remaining useful life of linear axes performance . Finally , if 

the data collection and analysis are integrated within a 

machine controller , the process may be streamlined for the 

optimization of maintenance , supporting the development of 

self - diagnosing smart machine tools . [ 0134 ] Embodiments of the subject matter and the opera tions described in this specification can be implemented in 

digital electronic circuitry , in tangibly - embodied computer 

software or firmware , in computer hardware , including the 

structures disclosed in this specification and their structural 

equivalents , or in combinations of one or more of them . Embodiments of the subject matter described in this speci fication can be implemented as one or more computer 

programs , i . e . , one or more modules of computer program instructions , encoded on a computer storage medium for 

execution by , or to control the operation of , data processing 

apparatus . Alternatively , or in addition , the program instruc 

tions can be encoded on an artificially - generated propagated signal , e . g . , a machine - generated electrical , optical , or elec 

tromagnetic signal , that is generated to encode information 

for transmission to suitable receiver apparatus for execution 

by a data processing apparatus . A computer storage medium 

can be , or be included in , a computer - readable storage 

device , a computer - readable storage substrate , a random or 

serial access memory array or device , or a combination of 

one or more of them . Moreover , while a computer storage medium is not a propagated signal , a computer storage 

medium can be a source or destination of computer program 

instructions encoded in an artificially - generated propagated 

signal . The computer storage medium can also be , or be 

included in , one or more separate physical components or 

media ( e . g . , multiple CDs , disks , or other storage devices ) . [ 0135 ] The operations described in this specification can 

be implemented as operations performed by a data process 

ing apparatus on data stored on one or more computer 

readable storage devices or received from other sources . 

[ 0136 ] The term “ data processing apparatus ” encompasses all kinds of apparatus , devices , and machines for processing data , including by way of example a programmable proces 

sor , a computer , a system on a chip , or multiple ones , or 

combinations , of the foregoing . The apparatus can include 

special purpose logic circuitry , e . g . , an FPGA ( field pro grammable gate array ) or an ASIC ( application - specific integrated circuit ) . The apparatus can also include , in addi 

tion to hardware , code that creates an execution environment 

for the computer program in question , e . g . , code that con 

stitutes processor firmware , a protocol stack , a database 

management system , an operating system , a cross - platform 

runtime environment , a virtual machine , or a combination of 

one or more of them . The apparatus and execution environ 

ment can realize various different computing model infra 

structures , such as web services , distributed computing and 

grid computing infrastructures . [ 0137 ] A computer program ( also known as a program , software , software application , script , or code ) can be writ 

ten in any form of programming language , including com 

piled or interpreted languages , declarative or procedural languages , and it can be deployed in any form , including as 

a stand - alone program or as a module , component , subrou 

tine , object , or other unit suitable for use in a computing environment . A computer program may , but need not , cor 

respond to a file in a file system . A program can be stored in 

a portion of a file that holds other programs or data ( e . g . , one 

or more scripts stored in a markup language document ) , in 

a single file dedicated to the program in question , or in 

multiple coordinated files ( e . g . , files that store one or more 

modules , sub - programs , or portions of code ) . A computer 

program can be deployed to be executed on one computer or 

on multiple computers that are located at one site or dis 

tributed across multiple sites and interconnected by a com 

munication network . [ 0138 ] The processes and logic flows described in this 

specification can be performed by one or more computers executing one or more computer programs to perform 

actions by operating on input data and generating output . The processes and logic flows can also be performed by , and 

apparatus can also be implemented as , special purpose logic circuitry , e . g . , an FPGA ( field programmable gate array ) or 

an ASIC ( application - specific integrated circuit ) . [ 0139 ] Computers suitable for the execution of a computer 

program include , by way of example , can be based on 

general or special purpose microprocessors or both , work 

stations , or any other kind of central processing unit . Gen 

erally , a central processing unit will receive instructions and 

data from a read - only memory or a random access memory 

or both . The essential elements of a computer are a central 

processing unit for performing or executing instructions and 

one or more memory devices for storing instructions and 

data . Generally , a computer will also include , or be opera 

tively coupled to receive data from or transfer data to , or 

both , one or more mass storage devices for storing data , e . g . , magnetic ; magneto - optical disks , optical disks , USB drives , 
US 2018 / 0094946 A1 Apr . 5 , 2018 

[ 0143 ] While this specification contains many specific implementation details , these should not be construed as 

limitations on the scope of the invention or of what may be 

claimed , but rather as descriptions of features specific to 

particular embodiments of the invention . Certain features 

that are described in this specification in the context of 

separate embodiments can also be implemented in combi 

nation in a single embodiment . Conversely , various features 

that are described in the context of a single embodiment can 

also be implemented in multiple embodiments separately or 

in any suitable subcombination . Moreover , although features 

may be described above as acting in certain combinations 

and even initially claimed as such , one or more features from 

a claimed combination can in some cases be excised from 

the combination , and the claimed combination may be 

directed to a subcombination or variation of a subcombina 

tion . 

and so on . However , a computer need not have such devices . Moreover , a computer can be embedded in another device , e . g . , a mobile telephone , a personal digital assistant ( PDA ) , a microwave oven , mobile audio or video player , a game console , a Global Positioning System ( GPS ) receiver , or a 

portable storage device ( e . g . , a universal serial bus ( USB ) 

flash drive ) , to name just a few . Devices suitable for storing 

computer program instructions and data include all forms of 

non - volatile memory , media and memory devices , including by way of example semiconductor memory devices , e . g . , EPROM , EEPROM , and flash memory devices ; magnetic disks , e . g . , internal hard disks or removable disks ; magneto optical disks ; and CD - ROM and DVD - ROM disks . The 

central processing unit and the memory can be supple mented by , or incorporated in , special purpose logic cir 

cuitry . 

10140 ] To provide for interaction with a user , embodi 

ments of the subject matter described in this specification 

can be implemented on a computer having a display device , e . g . , a CRT ( cathode ray tube ) or LCD ( liquid crystal display ) monitor , for displaying information to the user and 

a keyboard and a pointing device , e . g . , a mouse or a 

trackball , by which the user can provide input to the com 

puter . Other kinds of devices can be used to provide for 

interaction with a user as well ; for example , feedback 

provided to the user can be any form of sensory feedback , 

e . g . , visual feedback , auditory feedback , or tactile feedback ; 

and input from the user can be received in any form , including acoustic , speech , or tactile input . In addition , a 

computer can interact with a user by sending documents to 

and receiving documents from a device that is used by the 

user ; for example , by sending web pages to a web browser 

on a user ' s client device in response to requests received 

from the web browser . [ 0141 ] Embodiments of the subject matter described in this specification can be implemented in a computing system 

that includes a back - end component , e . g . , as a data server , or 

that includes a middleware component , e . g . , an application 

server , or that includes a front - end component , e . g . , a client 

computer having a graphical user interface or a Web browser 

through which a user can interact with an implementation of 

the subject matter described in this specification , or any combination of one or more such back - end , middleware , or 

front - end components . The components of the system can be 

interconnected by any form or medium of digital data 

communication , e . g . , a communication network . Examples 

of communication networks include a local area network 

( “ ' LAN " ) and a wide area network ( “ WAN ' ) , an inter 

network ( e . g . , the Internet ) , and peer - to - peer networks ( e . g . , ad hoc peer - to - peer networks ) . Such interconnects may involve electrical cabling , fiber optics , or be wireless con 

nections . [ 0142 ] The computing system can include clients and 

servers . A client and server are generally remote from each 

other and typically interact through a communication net 

work . The relationship of client and server arises by virtue 

of computer programs running on the respective computers 

and having a client - server relationship to each other . In some 

embodiments , a server transmits data ( e . g . , an HTML page ) 

to a client device ( e . g . , for purposes of displaying data to and 

receiving user input from a user interacting with the client 

device ) . Data generated at the client device ( e . g . , a result of 

the user interaction ) can be received from the client device 

at the server . 

[ 0144 ) Similarly , while operations are depicted in the 

drawings in a particular order , this should not be understood 

as requiring that such operations be performed in the par ticular order shown or in sequential order , or that all illus 

trated operations be performed , to achieve desirable results . In certain circumstances , multitasking and parallel process ing may be advantageous . Moreover , the separation of 

various system components in the embodiments described 

above should not be understood as requiring such separation 

in all embodiments , and it should be understood that the 

described program components and systems can generally be integrated together in a single software product or pack aged into multiple software products . [ 0145 ] Thus , particular embodiments of the invention 

have been described . Other embodiments are within the 

scope of the following claims . In some cases , the actions 

recited in the claims can be performed in a different order 

and still achieve desirable results . In addition , the processes depicted in the accompanying figures do not necessarily 

require the particular order shown , or sequential order , to 

achieve desirable results . In certain implementations , mul titasking and parallel processing may be advantageous . 0146 ] While one or more embodiments have been shown 

and described , modifications and substitutions may be made 

thereto without departing from the spirit and scope of the 

invention . Accordingly , it is to be understood that the present invention has been described by way of illustrations and not 

limitation . Embodiments herein can be used independently 

or can be combined . [ 0147 ] Reference throughout this specification to “ one 

embodiment , ” “ particular embodiment , " " certain embodi 

ment , ” “ an embodiment , ” or the like means that a particular feature , structure , or characteristic described in connection 

with the embodiment is included in at least one embodiment . Thus , appearances of these phrases ( e . g . , " in one embodi 

ment ” or “ in an embodiment ” ) throughout this specification 

are not necessarily all referring to the same embodiment , but 

may . Furthermore , particular features , structures , or charac 

teristics may be combined in any suitable manner , as would 

be apparent to one of ordinary skill in the art from this 

disclosure , in one or more embodiments . [ 0148 ] All ranges disclosed herein are inclusive of the 

endpoints , and the endpoints are independently combinable 

with each other . The ranges are continuous and thus contain 

every value and subset thereof in the range . Unless other 

wise stated or contextually inapplicable , all percentages , when expressing a quantity , are weight percentages . The 
US 2018 / 0094946 A1 Apr . 5 , 2018 

suffix “ ( s ) ” as used herein is intended to include both the 

singular and the plural of the term that it modifies , thereby 

including at least one of that term ( e . g . , the colorant ( s ) 

includes at least one colorants ) . “ Optional ” or “ optionally ” 

means that the subsequently described event or circumstance 

can or cannot occur , and that the description includes 

instances where the event occurs and instances where it does 

not . As used herein , “ combination ” is inclusive of blends , mixtures , alloys , reaction products , and the like . [ 01491 As used herein , “ a combination thereof ” refers to a 

combination comprising at least one of the named constitu 

ents , components , compounds , or elements , optionally 

together with one or more of the same class of constituents , components , compounds , or elements . 

[ 0150 ] All references are incorporated herein by reference . 0151 ] The use of the terms " a " and " an ” and “ the ” and 

similar referents in the context of describing the invention 

( especially in the context of the following claims ) are to be 

construed to cover both the singular and the plural , unless 

otherwise indicated herein or clearly contradicted by con 

text . “ Or ” means " and / or . ” Further , the conjunction " or ” is 

used to link objects of a list or alternatives and is not 

disjunctive ; rather the elements can be used separately or 

can be combined together under appropriate circumstances . 

It should further be noted that the terms “ first , " " second , " 

" primary , " " secondary , ” and the like herein do not denote 

any order , quantity , or importance , but rather are used to 

distinguish one element from another . The modifier “ about ” 

used in connection with a quantity is inclusive of the stated 

value and has the meaning dictated by the context ( e . g . , it 

includes the degree of error associated with measurement of 

the particular quantity ) . What is claimed is : 

1 . An inertial measurement unit to determine a perfor 

mance degradation of a linear axis , the inertial measurement 

unit comprising : 

an accelerometer that , when disposed on a motion mem 

ber of the linear axis comprising the motion member 

and a base member : 

measures acceleration of the motion member ; and 

provides a displacement of the motion member in 

response to movement of the motion member , and 

a rate gyroscope that : 

measures an angular rate of movement of the motion 

member ; and 

provides a yield angle for the motion member in 

response to movement of the motion member , 

wherein the displacement and yield angle determine per formance degradation of the linear axis based on an 

error in linear movement of the motion member along the base member . 2 . The inertial measurement unit of claim 1 , wherein the 

accelerometer comprises a triaxial accelerometer . 3 . The inertial measurement unit of claim 2 , wherein the 

triaxial accelerometer is a micro - electro - mechanical system ( MEMS ) that provides the acceleration at a spatial frequency 

at 0 Hz . 

4 . The inertial measurement unit of claim 1 , wherein the 

rate gyroscope comprises a triaxial rate gyroscope . 5 . The inertial measurement unit of claim 4 , wherein the 

triaxial rate gyroscope is a micro - electro - mechanical system ( MEMS ) that provides the angular rate at a spatial frequency 

at 0 Hz . 

6 . A diagnostic apparatus to determine a performance degradation of a linear axis , the diagnostic apparatus com 

prising : 

a linear axis comprising : 

a base member ; 

a motion member disposed on the base member , the 

motion member having substantially linear move 

ment with respect to a first direction along the base 

member prior to performance degradation of the 

linear axis with respect to movement along the first 

direction ; and 

an inertial measurement unit disposed on the motion 

member such that the inertial measurement unit moves 

with the motion member and comprises : 

an accelerometer that : 

measures acceleration of the motion member , and 

provides a displacement of the motion member in 

response to movement of the motion member ; and 

a rate gyroscope that : 

measures an angular rate of movement of the motion 

member ; and 

provides a yield angle for the motion member in 

response to movement of the motion member , wherein the displacement and yield angle determine per 

formance degradation of the linear axis based on an 

error in linear movement of the motion member along 

the base member . 7 . The diagnostic apparatus of claim 6 , wherein the 

accelerometer comprises a triaxial accelerometer , and 

the rate gyroscope comprises a triaxial rate gyroscope . 8 . The diagnostic apparatus of claim 7 , wherein : 

the accelerometer produces acceleration data of the 

motion member , and the rate gyroscope produces angular rate data of the 

motion member , the inertial measurement unit produces inertial data com 

prising the acceleration data and the angular rate data . 9 . The diagnostic apparatus of claim 8 , further compris ing : 

an analyzer that : 

receives the acceleration data from the accelerometer 

and the angular rate data from the rate gyroscope ; 

produces a straightness error based on the acceleration 

data ; and 

produces an angular error based on the angular rate 

data . 10 . The diagnostic apparatus of claim 9 , further compris ing : 

a movement controller in communication with the motion 

member and that controls movement of the motion 

member in the first direction . 11 . The diagnostic apparatus of claim 10 , wherein the 

inertia data is produced by the inertial measurement unit 

independently of control of movement of the motion mem 

ber in the first direction by the movement controller . 12 . The diagnostic apparatus of claim 11 , the movement 

controller controlling movement of the motion member at a 

fast speed and a slow speed such that : 

the accelerometer provides a low spatial frequency of 

translational motion of the motion member at the fast speed , and 

the accelerometer provides a high spatial frequency of 

translation motion of the motion member at the low 

speed . 
US 2018 / 0094946 A1 Apr . 5 , 2018 

14 

13 . The diagnostic apparatus of claim 12 , wherein 

the rate gyroscope provides a low spatial frequency of 

angular motion of the motion member at the fast speed , and 

the rate gyroscope provides a high spatial frequency of 

angular motion of the motion member at the low speed . 14 . The diagnostic apparatus of claim 9 , further compris ing : 

a machine tool that comprises the linear axis , wherein the motion member and base member in combi 

nation provide movement of a cutting tool disposed on 

the motion member . 15 . A process for diagnosing a geometric performance of 

a linear axis , the process comprising : 

providing the diagnostic apparatus of claim 6 ; 

moving the motion member at a first speed in the first 

direction , the first speed being constant ; 

producing acceleration data by measuring acceleration of 

the motion member by the accelerometer of the inertial 

measurement unit ; 

producing angular rate data by measuring the angular rate 

of the motion member by the rate gyroscope of the 

inertial measurement unit ; 

integrating the acceleration data to produce the transla 

tional displacement data for the movement of the 

motion member ; filtering the translational displacement data to produce 

filtered translational displacement data versus a travel 

length of the motion member ; 

integrating the angular rate data to produce angular dis 

placement data for the movement of the motion mem 

ber ; and 

filtering the angular displacement data to produce filtered 

angular displacement data to diagnose the geometric performance of a linear axis . 16 . The process of claim 15 , further comprising : 

moving the motion member at a second speed in the first 

direction , wherein the second speed is constant , and 

the second speed is different than the first speed . 17 . The process of claim 15 , further comprising , with 

respect to moving the motion member at the second speed : producing second acceleration data by measuring accel 

eration of the motion member by the accelerometer of 

the inertial measurement unit ; producing second angular rate data by measuring the 

angular rate of the motion member by the rate gyro 

scope of the inertial measurement unit ; 

integrating the second acceleration data to produce second 

translational displacement data for the movement of the 

motion member ; 

filtering the second translational displacement data to 

produce second filtered translational displacement data 

versus a travel length of the motion member ; 

integrating the second angular rate data to produce second 

angular displacement data for the movement of the 

motion member ; and filtering the second angular displacement data to produce second filtered angular displacement data ; 

summing the first filtered translational displacement data 

with the second filtered translational displacement data 

to produce a plurality of straightness errors ; and 

summing the second filtered angular displacement data 

with the second filtered angular displacement data to 

produce a plurality of angular errors . 

* * * * *