Just a note. Resistive heating elements can trip GFCI outlets and have nothing wrong with them. The ground to the smoker chassis should be sufficient as long as you are not tripping circuit breakers.
Why would you want to run your smoker on a GFCI outlet any way? A standard three prong grounded outlet should be all you need for that.
Current NEC requires all outdoor outlets as well as all outlets in garages to be GFCI protected. Thus, anyone with a deck or garage that is wired to meet current code will likely be plugging their smoker into a GFCI protected outlet. And most folks won't want to rewire an outlet to eliminate the GFCI.
There should be no reason for a good resistive heating element to trip a GFCI outlet. In fact, resistive loads are the least likely loads to create nuisance trips of GFCIs (unlike motor or other inductive loads, which can create arcing at switch contacts as their magnetic fields collapse when the switch interrupts the current during parts of the cycle other than zero-crossing of the current (not voltage) waveform).
If a resistive heating element trips a GFCI, that means that there is leakage current above the threshold for that GFCI flowing. And there's no reason for that to happen unless the insulation in the element (the mineral packing between the actual heating element at the outer sheath) is compromised OR there is a buildup of gunk or moisture at the uninsulated area where the heating element is exposed just where it enters into the mineral insulation in the ends of the sheath tube of the element.
The reason code requires GFCI outlets for outdoor or garage outlets is because of the high likelihood that tools or appliances will be used and touched by people whose feet may be in contact with soil, damp concrete, or other grounded surfaces, thus providing a potentially deadly path for current to flow from the tool or appliance through the person on its way to ground. That path through the person can end up being particularly lethal because it can be through the heart where even relatively small currents can disrupt the heart rhythm by interfering with the very tiny electrical impulses that ordinarily control the heart muscles.
This is the same logic that code observes when requiring GFCIs for any wet location or kitchens, bathrooms, etc., these days. The potential for the victim to be in contact with a ground makes it important to protect against "ground faults" (current taking a path to ground other than through the neutral conductor).
Of course, if the appliance is properly grounded, then the leakage in (or at the terminal area of) the heating element
should find its path to ground through the grounding conductor of the appliance cord, and the case of the appliance would then not be driven to a dangerous voltage. Thus, you would never be in danger, nor would you even realize that this leakage was taking place.
The code requirement for the GFCI outlets in these areas protects potential victims even if the appliance becomes ungrounded for whatever reason AND it alerts the user to an internal fault in the appliance even if the unit
is grounded.
And this is what disturbs me about the OP's situation. Clearly, his heating element has a short inside of it. (Perhaps a high-resistance short, but a short, nonetheless) between the element and the sheath (and mounting bracket) of the element. His test where the element trips the GFCI when the mounting plate is grounded proves this. So we know his heating element is defective.
Yet with the element mounted in his supposedly grounded smoker, the GFCI doesn't trip. That means that either the mounting bracket of the heating element is NOT tied to the chassis of his smoker OR his smoker is not grounded. Both of those are potentially deadly situations. So he needs to figure out what's going on.
Older GFCIs were more prone to nuisance tripping than newer ones. I do understand how GFCIs can be a pain, especially for appliances with motors that may create transients as their motors are switched-off mid cycle, though. I even have a freezer in my garage that specifically says on one of its labels to NOT connect it to a GFCI protected outlet. Presumably it is known to generate transients when its compressor switches off, and they don't want you to end up with a freezer full of spoiled food when it trips your GFCI.
Technically, there's no legal and safe way for me to use that freezer in my garage.
So I wired an outlet just for it that is NOT GFCI-protected, and which is behind the freezer, so nobody can plug in a tool or extension cord to that particular non-protected outlet. However, this would not pass an electrical inspection these days.
Newer fridges and freezers as well as other appliances are designed to not generate transients that trip GFCIs. And newer GFCIs are designed to not trip from motor transients.
But I understand your point!
Still, I'd want to know if there was leakage current from hot to ground in any smoker or other similar gadget of mine. And if it did trip the GFCI, I'd want to find the location where the leakage was happening and fix the problem before it got bad enough to cause a more serious issue, even if the appliance was safely grounded.
This is one of those things where you can see both sides of the argument! :)
But what has me really concerned for the OP is the fact that his GFCI test of the element alone proved that it's defective and leaking. Yet his smoker with that element installed is NOT tripping the GFCI. Either the smoker isn't really grounded OR the element is not grounded to the smoker's case. Both are potentially lethal situations.
And keep in mind that this is a DIY build that we can't test and troubleshoot for him,.
