200 nanoSeries Design  

It is important  when  discussing  the relative  merits  of these various  encoding  techniques  to make a  distinction  between ‘wide  angle errors’  and ‘narrow angle  errors’,  since  they arise  from different sources.  

Wide  Angle Error is a term used to encompass  all of the low spatial  frequency  errors  that arise  as a result  of  optical  pattern  align ment to the axis of rotation,  i.e., perpendicularity  and concentricity, and the  repeatable  and non- repeatable runout  of the spindle bearings.  From  a kinematic point of view,  wide angle errors  are  those that result  from translation  of the code pattern relative to the readhead rather  than pure rotation. None  of the methods  discussed  above  address  these  geomet ry- induced errors.  Over  the years,  the primary   method of  mitigation for these  wide angle errors  has been  the use of multiple  read stations. Clearly  the use  of multiple  read stations  can cancel  the most damaging harmonics  of the error  at the expense of increasing  other  less harmf ul error components.  In extreme cases,  some  larger  encoders  have had 8, 12,  or 16  readheads  which d ramatically  reduce the effects of  these geometr ic errors.  As a specific  example,  cons ider  an encoder  with a Total  Indicated  Runout  (TIR)  of 2.54 micrometers  (μm). For a code  disk with a radius of    50 mm , the peak once- per-turn error component due to spindle runout would be:  

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑡𝑡𝑡𝑡𝑡𝑡−1�𝑇𝑇𝑇𝑇𝑇𝑇2� 𝑇𝑇𝑇𝑇𝑇𝑇𝑝𝑝𝑇𝑇𝑝𝑝�= 𝑡𝑡𝑡𝑡𝑡𝑡−1�2.54∙10−6 2� 50∙10−3�=25.4 𝜇𝜇𝐸𝐸𝑡𝑡𝜇𝜇   Adding  a second read station  located at π radians  relative to the first station, properly calibrated, will reduce  the error resulting from  this particular harmonic to less than 1.3 μrad (95% reduction typically).  However,   mechanical ball  bearing errors  are rarely  purely  sinusoid al. They usually  contain  many  harmonics  of the  fundamental. In this example, if the twice- per-turn error is  10% of the fundamental  (i.e., 2.5  μrad),  the  addition of two readheads  can actually  double that particular  component  of the error  to 5.0 μrad,  as well as  doubling every other  even  harmonic  of the error.  Adding  still more pairs  of readheads  will reduce other   harmonics,  at the expense of increasing the  higher  order  residual  errors.  Clearly  this solution to wide angle   error  is a diminishing  returns game,  as well as being a distinct cost adder,  since  each new readhead adds   associated circuitry.    In recent  times,  with the advent  of digital signal  processors  to encoders,  it has been  found that even without   multiple  read heads  it is possible to remove  many  of these geometry -induced  errors algorithmically. This   can be accomplished by  adding optical  features  which  make  it possible  to discriminate which  errors  arise   from wide angle  causes  and which  from narrow  angle causes.  Since wide  angle errors  result  from translations   of the code pattern instead of the expected pure rotation, this  change in approach allows  mechanical   repeatabili ty to be ‘finessed’  into accuracy.  However, it  should be apparent  that any  sort of algorithmic   correction can only be as repeatable as the hardware.  

The multiple  read station approach,  although expensive in terms  of hardware,  is very fast and can usually   remove 95+%  of the wide angle errors  for a high quality  spindle.  A software  approach takes addit ional  processing time, and generally  removes  somewhat  less of the wide angle  error.  However, there  is a large  cost  advantage  to using the software approach.  Moreover,  as technology  advances, the correction algorithms   have become more capabl e, processing hardware  is faster, and the disadvantages  of the software   approach are dimin ishing.  In addition,  the software approach  does not  prefer  any harmonic  relative  to  another.  In the traditional multiple  read head  approach the harmoni c doubling  described  abov e has  sometime s resulted  in exciting mechanis m resonances  with servo systems.  That sort of problem is v ery  unlikely with the software correction method.    As can be seen  in Figure 1, the nanoSeries correct ion scheme reduces the large once- per-turn harmonic   more than 99% while  still not doubling the 2 nd harmonic, and reducing higher order  errors. The same raw  curve  compared to a typical  two-head reduction scheme would have indeed reduced the once- per-turn, but  the 2nd harmonic would have doubled.  In this specific case,  that would  have  doubled  the residual error!