I've had quite a few cheeky hamsters over the years who have taken to bar chewing. Here are a few of the tricks I've used to try and address this (illustrated by some of the cheeky hamsters who wanted to be in the photos!)
Training (human training the hamster, not the other way round)
Firstly I try not to reward bar chewing with cuddles. No matter how annoying it is or how sweetly they beg.
Pretty please? by
vectishams, on Flickr
My first female Syrian Bella trained me very well to get her out each time she chewed! I've had other hamsters who have only chewed their bars when I was in the hamster room and not paying them attention as they'd learned it got a response.
Wheels
Some of my hams have started bar chewing if their wheels have stopped working or they have outgrown them. I always check the wheel of a bar chewer as fixing/replacing the wheel can be an easy solution to a chewer.
Cages
I've found bar chewers are often the cheekiest hamsters so I make sure their cages are well secured. I recommend padlocking or clipping barred cage doors shut:
Cage security by
vectishams, on Flickr
A narrow barred cage can help reduce bar chewing and associated bar rub.
It's important to check the cages for signs of damage regularly and block off any potential chew points. Places that hamsters can smell the outside world through a tank are prime areas for chewing of cages to start:
L1040604 by
vectishams, on Flickr
Bolts and washers are useful for blocking holes, whether the holes are planned by the manufacturer or custom made by the hamster!
L1040462 by
vectishams, on Flickr
I wouldn't choose a plastic tank type cage or a wooden cage for a known bar chewer. Instead I use glass tanks with 6mm mesh lids, secured so they can't be pushed up by a determined ham. If you use a perfecto tank, the mesh lid can be pushed forwards enough from inside for a ham to escape so slip a bolt or padlock through the hook at the back.
lympy's new cage by
vectishams, on Flickr
Enrichment
Putting something in the area most favoured by chewers can provide distraction.
Wheel by
vectishams, on Flickr
Some wooden chews can be bought, such as the bolt-on one that Tania is standing on or the little wooden one in the peg. I also use wooden clothes pegs on their own clipped to the bars. Attaching a large wooden toy is another option - I prefer to use wire to do this rather than cable ties.
I make sure there's plenty of enrichment in the cage and other chewing opportunities such as:
wooden playsticks/fiddlesticks
Dog chews
antlers, e.g. StagBar
Swinging bridges (these are loved by my hams)
Metal kebab toys (which I fill with barley rings as a healthy treat)
Wooden logs stuffed with paper and treats hanging from the roof
Toys for cheeky girls by
vectishams, on Flickr
kebab treats by
vectishams, on Flickr
Cheeky hamsters often like new activities to keep them from misbehaving. I find cardboard toys the easiest to improvise and change around. I always ask fast food shops for an extra drinks holder. With a little rope it makes a fun hanging swinging bridge for Atlanta.
Cardboard toys by
vectishams, on Flickr
Putting the hamster's dinner ration in a small cardboard box or eggbox and then sealing it makes the ham work to get their food, and keeps them occupied. You can see this in one of the photos in the 'cage' section above - the box had been attached to the roof to make it harder! Another way of hiding the food is to use a small section of toilet/kitchen roll tube wrapped in plain paper to form a cracker.
crackers copy by
vectishams, on Flickr
Scatter feeding can also keep chewers occupied, but if using a food bowl I recommend a ceramic not a plastic one.
I found my Cadie rather soggy one morning having chewed a big hole in her plastic bottle:
oops by
vectishams, on Flickr
Some very naughty hams may need a metal and glass water bottle not a plastic one!
Cadie-resistant bottle by
vectishams, on Flickr
I hope this may keep your cheeky chewers occupied - for a minute or two!