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CurlyBen1-Visitor
1-Visitor
March 9, 2014
Question

Units issue

  • March 9, 2014
  • 5 replies
  • 10881 views

Hi all

Apologies if this is covered elsewhere, I've done some searching but not found anything that quite covers what I'm looking at. I'm brand new to Mathcad, I started using it on Friday (v14 at work, trial copy of Prime 3 at home) and I'm trying to enter a fairly simple equation into it. The equation gives the output torque of a hydraulic motor:

T=(displacement * change in pressure)/ 20 * pi

Displacement is in cc, deltaP in bar and torque in Nm. If I just enter the numbers, all is fine. However, if I add units the result is divided by 10, and I can't figure out why. I realise Mathcad must think the units are inconsistent if left at face value, but they're not. Is there any way I can correct this behaviour, or at the very least be notified of it? I'm reluctant simply to leave out units, and I don't want to modify the equation as if somebody came along later and checked my numbers with a calculator it would appear I'd made an error.

Cheers

Ben

5 replies

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Werner_E25-Diamond I
25-Diamond I
March 9, 2014

Please post your worksheet so we see what you have done and also state which result (including units) you had expected as opposed to the result Mathcad gave you.

A
AlanStevens19-Tanzanite
19-Tanzanite
March 9, 2014

CC = 10^-6 m^3 and bar = 10^5 N/m^2

Mathcad works in the underlying units so you should probably only divide by 2 for consistency!

Alan

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CurlyBen1-VisitorAuthor
1-Visitor
March 9, 2014

Thanks for the replies. I have attached a worksheet with the equation in - once with units and once without. The equation without units gives the correct answer (the motor in question exists and is used on a winch - if the equation with units in was correct it would only be able to lift about a quarter of a ton, and I've seen it lift over two tons!).

Alan that makes sense, but the factor 10 is included in the equation and I would like to leave it that way so if somebody comes along and looks at it later it doesn't appear as a mistake - if I print it out and hand it to someone and they check it with their calculator they should get the same numbers. With Mathcad adding it's own unit conversion factor in that's not the case. I hate to say it but if I can't produce calculations which clearly show assumptions and working with units then the units functionality is worse than useless to me.

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Werner_E25-Diamond I
25-Diamond I
March 9, 2014

As displacement actally is cm^3 per revolution it also makes sense to divide by 2*pi (and not 20*pi). I did a quick search in the net and only find 2*pi, e.g. here: http://www.engineershandbook.com/Tables/fluidpowerformulas.htm

It i scorrect that the formula you were given results the value in Nm, but ONLY if you use it without any units and you must put in the measured values of exactly the units given. Its kind of an epirical formula which were used for convenience before we had such tools as Mathcad 😉

A similar example for better understanding: Someone tells you that A = x * y /1000 is the formula for the area of a rectangle - x must be in cm, y must be in dm and you get the result in m^2. This is true and it works.

2 cm * 3 dm IS 6*10^-3 m^2, but if you use the very same formula with units you would get the wrong 6*10^-6 m^2 of course.

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CurlyBen1-VisitorAuthor
1-Visitor
March 9, 2014

Thanks for all the replies, it's much appreciated. I'll have to have a think about how best to approach this - the reason for carrying out these calculations is as a design verification process, to show that we comply with the relevant standards. This particular equation isn't likely to be put under much scrutiny, but others I'm going to be working through soon potentially are more significant. For that reason I'm a bit reluctant to deviate from the published equations, in this case from Sauer Danfoss (for example on page 12 of this PDF http://powersolutions.danfoss.com/stellent/groups/publications/documents/product_literature/520l0926.pdf ), particularly as it may well be viewed in hard copy and its origin in Mathcad may not be apparent. I'm already varying a little bit, as the spec sheet for the particular motor I am using (still Sauer) doesn't quote 20*pi but approximates it as 62.8 I may well use Richard Jackson's approach, so thanks for that. I suppose the ideal solution from my point of view would be to use units and have Mathcad insert a (visible) correction factor at the end of the equation - this could then dynamically update dependant on the input units, but maintain the transparency of the calculation. I don't suppose this is possible?

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dschenken1-Visitor
1-Visitor
March 10, 2014

You just need to comment the calculation and note the reason it's differentfrom the Danfoss example with units enabled. Note that in the Sauer Danfoss calc for English units it is simply 2pi because the pressure and volume calcs both use inches; however if the result was to be lbf-ft instead of lbf-in, then it would be 24pi. Sigh.

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Fred_Kohlhepp23-Emerald I
23-Emerald I
March 10, 2014

Are you sure the 20 isn't 2.0?

see attached

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CurlyBen1-VisitorAuthor
1-Visitor
March 10, 2014

Thanks for the effort - however the displacement term is really displacement per revolution, so that's where the 2*pi comes from. The displacement per revolution can be measured or calculated fairly easily (and dependent on the type of motor may not even be constant!) and is very different from the volume of the housing. The factor 10 is simply required because 1 bar is 10^5 Pascals (approximately atmospheric pressure). I'm clear on all this now. The remaining problem for me is how to handle Mathcad's internal units conversion. I'd really like to use units and just have Mathcad display the correction factor it applies, but I haven't found a way to do this. It might be that I'm terrible at maths (for an engineer at least) but I like each step to be laid out in a clear and logical way - which so far (in my very limited experience) Mathcad does very well, other than this units issue. Having 'hidden' steps, such as this unit conversion, was one of the reasons I was trying to get away from Excel. I'll have to have a think as to how I'm going to handle it.

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Fred_Kohlhepp23-Emerald I
23-Emerald I
March 10, 2014

multiply the LHS of your equation by (mL bar)/(N m), leave the 20, it'll come out right.

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