Rolling a wheel over a threshold

[Anic]

Does anyone know the math for estimating if a four wheel cart with certain mass, wheel diameter, and speed will cross over a 20mm threshold? This is for ISO 60601-1, 9.4.2.4.3 safety test.

In fact, I already have the cart. I need to solve for minimum wheel diameter.

Andy

[MichaelH]

Andy Nicoll wrote:

Does anyone know the math for estimating if a four wheel cart with certain mass, wheel diameter, and speed will cross over a 20mm threshold? This is for ISO 60601-1, 9.4.2.4.3 safety test.

As far as I can tell from a quick search on the internet, the ISO standard deals with the safety and stability of crossing noted threshold (a risk assessment), not whether or not the cart can physically cross it.

Any wheel diameter greater than 4 cm should technically be able to go over the 20 mm threshold if (1/2)v^2 > g*h, where v is the speed of the cart, h = 20 mm, and g is 9.8 m/sec^2.

I think there are other criteria you are missing for your ISO question.

[Anic]

That's where I started, too Michael.

According to the spec, the test set up is a speed of 0.4m/s. Given your constraint, that kinetic energy must be greater than (or equal to)potential energy, (1/2)V^2 > g*h, and re-arranging we find an impossible situation, (1/(2*h)v^2 >g --> 4 (m/s^2) > 9.8(m/s^2).

Looking at the problem again, the obstruction, 20mm high x 80mm wide, only has to lift one end of the cart at a time. The total mass isn't involved in the potential energy term. That modifies the equation to (1/2)V^2 > (b/c)g*h where b is the distance from the wheels on the opposite end of the cart to the center of mass (gravity) and c is the distance from the front wheels to the back wheels.

Solving for b/c, b/c < (v^2)/(2g*h) --> b/c < ~0.41 (unitless). That implies that the distance from the front wheels to the center of gravity must be greater than ~0.59 * distance-between-the-wheels and !!the center of mass can't be in the middle of the cart!!(??).

As for wheel radius, when the wheel hits the obstruction, it does so at an angle. Not all of the force is vertical. This is the tricky bit I'm having trouble with. It has to help or wheels would be useless. Any clues?

You're right about the current regulation (version 2) discussing things in terms of causing hazards. However, version 3 takes effect in July 2013 and is very specific about hazards caused by tipping (overbalancing), speed, and thresholds including test setup and pass/fail conditions. For example, a cart is launched at the thrshold obsticle at 0.4m/s. If it tips over, fails to cross, or causes a hazard in any other way, it fails the test.

Andy

[Fred_Kohlhepp]

Maybe this will be a place to start!

[Anic]

Thanks Fred,

I just found the references to this approach in various places on the WEB and have been downloading PDF's. You saved me at least a day (and who knows how long debugging) posting it in MC15. Thank you very much.

("Don't forget the second wheel.") Right. For now I'm using a 2-dimensioal, two wheel model (like a side view of the cart).

Perhaps I'm nieve, but since 60601-1 ver3 has been in effect in Europe and Canada for a number of years (released in 2005), I expected to find nomographs to help folks consider minimum wheel sizes in early design stages. If I manufactured wheels for the medical industry, I'd sure have it on MY WEB site!

Andy

[Anic]

Hi Fred,

It's still not working out. I think it's a UNITS issue with MC15 (same result in Prime).

I put a sheet together with the basics and attached a PDF version and the Prime 2.0 sheet.

Hmm...How do I attach these files? That's surprisingly confontive. There is no Help button either. My day is going from bad to worse.

Andy

[mzeftel]

Hi Andy,

To attach files, click on the Use Advanced Editor link in the upper right corner.

Mona

[VladimirN]

See:

[Anic]

Okay, HERE are the attachments.

Thanks Mona and Vladimir

[Fred_Kohlhepp]

Your energy balance is correct.

But there's another way to look at it. See attached shorthand.

[Anic]

I just couldn't get over the fact that the energy of the cart moving horizontal was less than the energy required to lift one end of the cart up onto the obstruction, Fred. It doesn't matter what size the wheels are for those equations. The mass cancels out, too.

So I started asking safety testers and searching the WEB. Finally I ran across an article saying that the IEC had just approved (September 28, 2012) and amendment to the 60601-1 that increases the speed x2 (increasing the energy x4) and decreases the obstacle height x1/2. All the problems go away. PHYSICS RULES!!!

Thanks for your help.

Andy