I typically use my Weber Kettle for my smoking chore, and with charcoal, and chunks of wood, it does a great job. I did have an electric smoker though, and it also did a great hob. The wood was fine chips, or even sawdust of the smoking wood, and the chip/sawdust tray was laced directly on the heating element. It produce lots of smoke, but required a fireproof wrap below 65; F. outside temp.
I find that as was mentioned above, that the wood must be dry. Once it is smoldering, then needs to be sufficient air-flow to keep it smoldering, without flaming. That;s where your vents come in.air flow to the wood is critical.
My suggestion, use small, dry chips, or sawdust in the chip tray, and make sure the chip tray is close enough to the heat source to get the wood smoldering. Make sure the vents are letting in enough air to keep the wood going.
I am fortunate enough to have done a lot of camping in my youth, in wet, rainy fall weather, in snow, on hot beaches, and during summertime camping. I've had to use green wood, punky wood, wet wood, hardwoods, and soft woods to make an sustain fires for warmth, and cooking. Once you understand fire, you will have more success in getting the smoke you want. Remember, fire requires three things, heat, oxygen, and fuel. Remove any one of those three things, and the fire goes out.
Seeeeeeya; Chief Longwind of the Norh