Code:
  [additional comments]
Adding Retsch to the list of known shaker manufacturers now 3 known companies:
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                               Shaking speed (rpm)    Taps per minute    Website
AdvanTech Duratap                    250                  160         [URL=http://www.advantechmfg.com/]Advance Tech[/URL] 
WS Tyler (or Haver-Boecker)          278 +/- 10           150 +/- 5   [URL=http://www.wstyler.com/rotap_test_sieve_shakers.html]WS Tyler RoTap[/URL] 
Retsch                               280                  150         [URL=http://www.retsch.com/377897.0.html?&L=7]Retsch[/URL] 
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The comment on the Retsch website also gives some insight in on what basis the shaking and tapping speed have been determined: 
"This combination of sieving motions simulates hand sieving." Combined with the comment in the ASTM D1214 this gives the impression 
that the shaking and tapping speed requirements in the SAE J444 and ASTM B214 may be based on the simulation of hand sieving. 
However still this does not give any information why exactly these tapping and shaking speed requirements are specified in the J444. 
I can only assume that somebody at some point in time must have done some research to determine this.