Melted torroid

[soundguy]

PRR-

thanks for another great post, that was really easy to understand. like so many of the things in electronics I have trouble understanding, when it clicks, its so painfully obvious, it hurts. lesson learned.

dave

 

[PRR]

> The resistance to current flow could be as low as 0.001Ω.

I wondered what the real value was.

The bolt is fat. The sheetmetal is thin but wide. Seems to me the bottleneck is where the bolt meets the sheetmetal.

Say 1/4" bolt in 1/16" panel. Say it makes perfect contact all around the circumference. (That won't happen in DIY hole-drilling, but partial contact under the wider head will give a similar result.) Circumference of the bolt is 0.25"*pi= 0.8". Panel is 0.0625" thick. 0.8*0.0625"= 0.050 square inches.

The total length of the path through the panel may average 10 inches. But it will also be ~10" wide. Right at the bolt, the circumference expands from 0.8" at the bolt to 2.4" at 1/4" away (3/4" diameter), to 4" at another 1/4" (5/4" diameter), etc. Most of the resistance is in about the first bolt-diameter. If we wanna avoid radial math and integration, we can pretend we have a conductor with cross-section 0.25"*0.0625", and 0.25" long.

The 0.25"*0.0625"= 0.050 sq.in. cross-section turns out to be the same as a US #2 wire (0.258" diameter, car-battery cable). Say the panel is Aluminum. I don't have an Al wire table handy, but Al is about twice copper the same size. #2 Copper is 0.159Ω per 1,000 feet. So Al would be 0.32Ω per 1.000 feet. We want to know the ohms of 0.0208 feet (0.25") of #2 Al wire. 0.02/1,000= 0.000,02, and 0.000,02 times 0.32Ω/1,000' = 0.000,0067Ω.

The bolt has two ends, double that number.

Whoops: I didn't notice that the cross-section of the panel is around the same as the bolt. Most of the panel resistance is in the first fraction of an inch, but the bolt is 1.75" long. A brass bolt is better than aluminum, a steel bolt is worse. Oy, round up to 4 inches of 1/4" diameter copper. (0.16Ω/1000')/3,000= 0.000,05Ω.

Assuming the transformer wants to run at 0.1 Volts per turn, 0.1V/0.000,05Ω= 1,875 Amps.

If that could actually happen: at 150 Amps, #2 Al wire runs as hot as common insulation can stand. So 1,800 Amps would be far-far-far too hot for any nearby insulation. (I suspect the bolt would glow and melt.)

But at 120V primary, 0.1 volts per turn, we have a 1,200:1 step-down ratio from line primary to the bolt+case shorted turn. So the primary current, neglecting primary resistance, is 1,875/1200 or about 1.5 Amps. Not enough to burn the house, not enough to pop a 2 Amp fuse.

The accidental shorted turn appears at the 120V side as 120V/1.5A= 80 ohms. We already estimated that a 120V 25VA 20% reg transformer has about 144 ohms effective resistance. I neglected to note that half of that is primary, half is reflected secondary, and the normal secondary is overwhelmed by the accidental bolt+case secondary. So the line sees 72 ohms primary loss, 80 ohms load in bolt+case. Current is about 120/(72+80)= 0.79 Amps. Power is 120V*0.79A= 95 Watts. This is divided between primary copper and bolt+case in 72:80 proportion.

About 45 Watts of heat appears in the primary, about 50 Watts of heat appears in bolt and case. The 25VA 20% transformer is sized for about 5 or 6 Watts of internal dissipation. Now it has 45 Watts of heat inside it, and another 50 Watts of heat in its bolt and the case near it. It cooks. Yet the 95 Watts of power sucked from the wall is no problem for house-fuse, house wiring, or even a 1A line-fuse.

 

[bcarso]

Bravo PRR. That sounds about right. It reminds me (by analogy) of the really dangerous currents through the human body---not the mere unpleasant jolts nor the clamp-the-heart serious cooking ones, but the ones that are right in the middle (10-100mA or so) that disrupt but don't blow the figurative fuses/breakers. And from which the system doesn't recover readily, without heroic intervention.

Someday I will tell of my worst career crisis, involving the most seemingly innocent of components. Fortunately, no one died.

 

[maxwall]

Question for Dave or anyone reading this,

When you first built that box did you ever take notice to any heat buildup in the transformer . Example , I sometimes put my hand on the power xformer to detect any abnormal heat being caused by a AC ground loop kind of a short circuit in a way. The tranformer becomes a big power resistor. then burns up.

I caught one of my projects in this way and determined that when I disconected the screen wire of this power xformer that was attached to the chassis , the heat went away almost instantly. I think the screen was in conflict in some way with chassis ground or these was something wrong with the transformer or screen winding. Additionally, from experience have learned that power transformers don't usually build up heat unless their VA's are not adequate for the amp draw in the circuit. Or the box has poor ventilation and is left on for hours in the middle of summer or something like that.

 

[adrianh]

Roger;
Make that electric motor rewinding shops.

 

[soundguy]

[quote author="maxwall"]Question for Dave or anyone reading this,

When you first built that box did you ever take notice to any heat buildup in the transformer . [/quote]

no, it was totally fine. What happened was I placed a unit loose in the rack which depressed the top of the lid enough for it to short against the mounting bolt I had installed, the bolt I used was way to long and only had maybe 1/4" inch clearance or less to the top of the chasis.

dave

 

[PRR]

> power transformers don't usually build up heat unless their VA's are not adequate

Over-generalization, but true in most audio work.

A transformer power rating goes roughly by its volume or weight. So a transformer that is twice as tall/wide/deep gives 8 times the power. Cube of linear dimension. But the heat escapes through the surface, which increases only as the square of linear dimension. Twice as tall gives 4 times the surface area to transfer heat out of the transformer.

So under 100VA, transformers usually have ample surface area to run cool in the open, just-warm in a box. But the small volume "needed" (and the low value/price of small transformers) means you can't put in as much copper as you would like: they have large voltage drop. OTOO 20% no-load to full-load.

Over 1,000VA, there is room for enough copper, and the economics of big loads force buyers to look hard at efficiency. 5%, even 2% regulation (loss) is possible and common. But even with such low self-heat, the surface area has not kept up with power and volume. A 1,000VA tranny runs hot at full load. A 10,000VA transformer may be oil-cooled: fairly small core in a big can of oil. At 100,000VA you want fins outside the case.

Most of us will never see 100KVA in audio. We have 1,000VA in big speaker amps, but they idle at 50 Watts and peak to 100 Watts less than 10% of the time, 1000 Watts less than 1% of the time. Class AB audio is pretty inefficient at 10%-50% of max power, so a disco-amp will get pretty warm, even hot if the maker used high-temperature varnish to allow a smaller design. And much DIY is down in the <100VA range. Down there, trannies only run hot at full load if the designer pushed every corner of the design down to lowest possible size and price.