@Eli Grobin: Yaskawa is here defining "pitch" as rev/inch, instead of the (much more common) inch/rev or mm/rev. With this definition, a higher "pitch" does give you a finer thread ball screw. Their definition of pitch was confusing for me also. At 2:28, I was expecting to see the pitch term P in the numerator.
It is possible that he is referring to ball screw lead instead of pitch. The friction torque units appear correct in LBFF-in. Here is more information on lead versus pitch. hwww.thomsonlinear.com/en/support/tips/what-is-the-difference-between-pitch-and-lead-when-referring-to-a-screw#:~:text=for%20e%2Dcommerce.-,What%20is%20the%20difference%20between%20pitch%20and%20lead%20when%20referring,ball%20screws%20are%20typically%20specified.
The tm is the time required to complete the motion profile, excluding the dwell time. In the example from the catalog, it is labeled as feeding time. Here is a link from our Yaskawa Solution Center: solutioncenter.yaskawa.com/selfservice/viewdocument.do?noCount=true&externalId=DMSD-MotionProductEngineering-YEA-KAEPS80000042-YEA-KAEPS80000042Kpdf&sliceId=pdfPage_393&noCount=true&isLoadPublishedVer=&docType=kc&docTypeID=DT_MARKETINGDOCUMENTS_1&stateId=2830&cmd=displayKC&dialogID=147806&ViewedDocsListHelper=com.kanisa.apps.common.BaseViewedDocsListHelperImpl&openedFromSearchResults=true
It is all about unit conversion. US Customary Units are implied in this case. Gravitational acceleration is included at 6:30 to convert weight to mass. At 8:17, to be consistent, the assumed units are also weight per cubic volume (for example lb/ft^3). We might have made this more clear by expressing the term as ρ/g. Hope this helps.
When you reference the change in pitch around 6:50, what are the units of pitch? Your example references a larger pitch but then shows a finer thread ball screw, and this confuses me. I would think going from pitch of 1.5 mm to pitch of 1.0 mm would decrease the effect of the linear components inertia on the total inertia.
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