Cranksets are mounted with bottom brackets and also contain their own nut bolts, if all the chin rings of the crankset are moving side by side and the chain is not moving from higher to lower and lower to higher cogs, then it is the problem of the nut bolts of the crankset, you have to tighten the bolts so that that chain ring does not move when you shift gears between them. but if all the chain ring is wobbling and moving side by side then the problem is at the mounting place with the bottom bracket, you can check the bottom bracket where the chain ring is installed and mounted and tighten the bolts to avoid its wobbling and moving.
The crankset has two crank legs which are attached to the chainring by two bolts and these bolts are opposite in direction from each other, the direction of one bolt is at 9 o clock and the other bolt is at 3 o clock, you have to tighten these bolts because loosely attached crank arms are also responsible for the wobbling and moving of the crankset side by side. if a single crank leg became loose, then it comes in the outer and opposite direction from the bottom bracket, before tightening gives an exact position to the crank leg and brings it near the bottom bracket and frame, so that it would not slide and unmount from the bottom bracket, then tight the bolt of the crank leg.
Crank legs also contain top caps, when these become loose or fell down on the trails then chain rings and crank legs would start becoming loose, you have to install another top cap and then tight it with the hex key, but never apply a greater torque force because it will disposition and dislocate the internal bearings of the bottom bracket and the crank legs. after every ride always check the bolts and top cap of the crank legs, if these are loosely attached, further tight them because it is important, loosely attached bolts would result in damage to the splines, and when you tighten the bolts, you will always find that bolts are not going to tight very hardly and the crank legs are a little bit wobbling and moving, then you have to replace the top cap and bolts to minimize the play and wobbling with the crank legs. The recommended torque force on the bolts of the crank legs is 11 to 13Nm.
Old traditional bottom brackets contain bearings on both driver and non-drive sides. and sometimes these bearings are ruined and rubbed bad and totally becomes non-responsive, you have to replace and change the bearings with the new bearings and lube them properly, install them within the bottom bracket, your BB will work fine without any issues, bearings would also increase the lifespan of the bottom bracket.
Spacers And Wavy Washers:
There are small 2 to 3-mm spacers are installed on both the drive and non-drive sides of the cranksets, these spacers would play a major role in the BB and the chainrings, you have to look and inspect the drive and non-drive sides, install spacers which will minimize the wobbling and side by side moving of the crankset.
Seals:
The bottom bracket also contains seals on both left and right sides of the frame, sometimes these seals will damage and do not work properly, and you have to change or replace the seals with a new one for better working and maintaining the wobbling and play of the bottom bracket.
Length of The Spindles:
Spindle lengths are also much more important for the bottom bracket and chainrings, smaller or greater lengths of spindles would work abnormally and it feels like there is an issue or problem within the bottom bracket, spindle lengths are recommended for the diameter of the bottom brackets, if the spindle lengths and bottom bracket are non-compatible with each other, the setup will not work.
If the length of both of the spindles is the same then check the smoothness and straightening of the spindles, many times it happens, the spindles are flexed and bent in their shapes which will affect the crankset and it feels like the chainrings or crankset is moving side by side.
Bent Crankset:
If the crankset is bent, then the chainrings would also respond not better, and it feels like the chainrings are also flexing when these are rotating, if the crankset is of aluminum and steel, then remove the crankset and hit it with a hammer to bring it in its original non-flexing state. after that install the chainrings and also check the chainrings, check the smoothness of the chainrings before installing.
Hollow Space Of Bottom Bracket Frame:
Most f the time the width and diameter of the hollow space of the frame where the BB is inserted are not exactly matched with the width of the bottom bracket, due to which when you push the pedals you will note that the bottom bracket is also freely moving with the chainrings and crank arms, you have to check the internal space of the frame, most of the time it is damaged ad ruined and it is not capable of holding h bottom bracket, it is not a small issue, you have to bring your bike on the mechanic shop for repairing bike frame.
Cracked Frame Tubes:
Frame tube includes the chain stay tube and the bottom seat tube, if these are fractured or cracked, then it will also affect the chain ring ad crankset, bike loses its tension, grip, and control, you have to weld your frame tube by bringing your bike on welding shops. if the rear side of the bike frame and wheel is cracked or damaged, it will also put a negative effect on the crankset, chainrings, and crank legs.
Checking And Inspecting Of Chain:
Most of the chain happens due to the lining of the chain, you can check the chain and if the chin links are bent and deformed t any place, it will also raise these kinds of problems and issues. straight the chain or remove the chain links, and if you have any extra spare chain, install it in your crankset and check the lining, because the time chains are damaged and ruined thoroughly which will also affect the chainrings and cranksets.