Notes, Questions and Replies on Assignment Three
latest update 11:00am 23 Jan2014 - We'll add more as FAQ come in.
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The spreadsheet for the gear example done in class is uploaded onto Coursework under Week2 notes (GearExample.zip). The point of the spreadsheet is to give people a point of reference for making their own spreadsheet or Matlab program. It is not meant to be a comprehensive gear design tool. You cannot just use it for the homework or any real design problems.
- The spreadsheet assumes a 2 stage transmission and same face width everywhere (which is NOT correct in the present case).
- Some items, like computing the outer diameter of the gears for the contact ratio check, need to be modified if using a different pitch. There is a more general formula using gears with N+2 teeth that you might like to use (see notes). Note also that base radius, r_b, is pitch radius r_p * cos(phi) -- see Announcement that Maura sent out with attached drawing for clarification.
- As usually happens when using all gears of the same pitch, the "worst case" gear is the pinion for the second stage. This may or may not be relevant in your case.
- Also the spreadsheet just looks at infinite life and not for allowable finite life stresses of various gears...
FYI: For an "industrial strength" version of a spreadsheet (worthwhile if you have a job where you are designing lots of gear trains) there is the AGMA gear design manual.
Note that the gear selections for both problems are taken from actual catalogs. Problem 1 is from the Boston Gear Catalog; problem 2 is from the PIC gear catalog. For example, click on "Gears" in the left frame and look for the page with "spur gears" that have a pitch of 48, Face Width of 1/8inch and Pressure Angle of 20 degrees.
New for 2014:
- Boston Gear Catalog: Spur Gears
- Engineering Manual for Boston Gears
- Boston Gear Theory with links to downloads
- PIC gear catalog and links to manuals -- these are more typically of the size used in ME112 projects, small robotics, etc.
1) What is a cycle?
A cycle is a fatigue cycle -- for a gear it corresponds to one rotation of the gear. So if the gear rotates 1000 times, each tooth gets bent 1000 times and undergoes 1000 cycles. (The exception to this rule is an "idler" gear which nestles between two adjacent gears, so its teeth are loaded twice per cycle. Also, the teeth on an idler have reversed bending stresses, so Kms is different from the normal case.)
Due to the various gear ratios in a multi-gear transmission, the gears undergo different numbers of cycles. If the input gear does a million cycles, the other gears do less, by varying amounts. This means that they can actually handle somewhat larger allowable lifetime stresses, because they have fewer cycles.
Q: Do we need to write up all of the calculations or would turning in a spreadsheet be fine?
For Problem 2 of this and all future assignments: You need to write up and explain your calculations. Attach your spreadsheet or Matlab printout for backup. The problem with any spreadsheet is that unless you go through painstakingly and examine each cell formula you can't tell what is really going on. Even Matlab/Python, which is better about making formulas visible in the printouts, needs lots of comment statements to be self-explanatory.
Q: Could we use same basic layout as in problem 1?
Sure. Please be prepared to explain why you like it.
The trend is the same for normal & stainless steels and pretty much all steels (but not for Aluminum :-) The actual value of Su for 303 stainless is a little lower than for carbon steel, but it still holds true that Sn' = 0.9 Su at 1000 cycles and 0.5 Su at a million cycles.
Do we need to estimate the contact stresses? If so, what is the procedure for stainless steel?
You do not need contact stresses in Problem 2 -- bending only. We're assuming that in this application, having chosen 303 stainless instead of aluminum, that we don't need to worry much about the contact stresses.
For the second problem, it asks us to minimize the size of the gearbox. I'm wondering what dimensions are important.
You can establish your own criterion for minimizing size. It is an open-ended problem. Pick something reasonable and Explain your rationale. Diagrams are most helpful -- for example, you could show a bounding box around your set of gears.