I am "feeling" a new vibration. I first noticed it while driving, but it is definitely noticeable when I put my hand on the valve cover with the motor running. It is sort of a low frequency, (not audible and not quite a knock), very subtle vibration at this point. It seems to me that there are three possibilities: external on the front end, (water pump or fan/pully?), external on the rear, (clutch or flywheel), or internal, (rod bearing?)
Any hints on trying to narrow this down?

Was it rebuilt recently?
Maybe check for
Loose flywheel
Possible bad cam bearing in middle of cam

These use little to none for a balancer, what does yours have?

These engines vibrate but you say this one is new. I'd first check the easy stuff starting with timing. Then the crank flange and everything driven from it pulleys, fan, water pump.......Next I'd go to the other end and check the flywheel and everything on that. You might be able to access some of it if it has an inspection cover on the bottom of the bell housing. You can try listening to the bearings with a stick or stethoscope held at different places on the engine while it is running. That can be difficult on these little guys because there is so much in a small space.

It may help to know what it is in, how it is used, how many miles are on it, if the vibration increases, decreases, or goes away with rpm changes.

Block casting tells me that this 153 came out of a '68 Chevy II. It appears to have been put into this '47 CJ2a about 1971 judging by the rebuild tag on the transfer case. I see no evidence that it has been rebuilt since. I don't have a clue as to the milage. I rebuilt the tranny and transfer case this winter, and they both really needed it, so there's either 20,000 or so on there somewhere, or a total lack of maintenance. But they must have been low speed miles as the driveshafts were cobbled together, (cut an inch out of the rear and weld an inch into the front with no attempt to balance them), and the alignment was toed out, rear hubs bent, original 9" brakes, and on and on. I think this was someones around town "parade jeep" that never saw 30mph. Whats different is that I tuned it up, fixed the issues, put on disc brakes and have been using it for a daily driver +/- 60 mph on the tar, (it has a warn overdrive), for two summers for the 6 miles round trip to town and maybe 40 miles round trip once a month to the local USPSA match. In August my wife and I put a couple of 100 mile days on it. A mix of bad paved roads, (+/- 55 mph) and worse dirt roads, (10 to 40 mph). It was during the second of those trips that I thought I noticed the vibration. I stopped and checked the lug nuts and adjusted the front wheel bearings when we got home, but the odd vibe is still there, even at idle in the garage. I had my hands on this motor many times through rebuilding and adjusting the old carb and setting the timing, and I'm certain this is something new. Not dangerous yet, but it lit the "check engine light" in my head. So miles at higher rpm and a lot of very bumpy road, ( not airborne, but make sure your dentures are in well). Runs smooth and drives well, but that nagging worry is there.
I am open to any and all thoughts on diagnosing this as I have a CJ5 in line for a total rebuild that I was hoping to complete before this CJ2a gets the frame off that it deserves. I'd though I was at the point where I could drive it two years at the least.

It does have an early corvette bellhousing with the removable bottom inspection cover, so I can get in there, but I don't know that I can torque the flywheel bolts without pulling the tranny and clutch.

I have no more ideas. If you could check for movement of the flywheel maybe using a pry bar and a dial indicator ? What could have loosened on your trips? Anything in the valve train? lifter, sticky valve, bent push rod.....? Crank shaft end play?

On the 270 in my pickup I chased a slight knock that I thought was a main bearing for a couple of years. It never got worse. During an exhaust change I went from tube headers to cast headers and the knock disappeared. So did some rpm. I know you haven't made a change but just be open to the unexpected. If nothing outside works drop the pan and measure the rod & main bering clearance.

I had a problem with a distributor on an engine that went out of round on the shaft, but the problem was intermittent, it was a difficult problem to troubleshoot.

What about putting your hand on the distributor while the engine is running/reving? Maybe you can narrow it down if the distributor may be the source of that vibration.

I'm going to try and isolate this over the holiday weekend. I'll post back with any info. I think I should be able to get a dial indicator on both the flywheel and the balancer. I do see that the fan has a little wobble, but that has always been there and it is not loose. This vibration seems "heavier" than a fan, if that impression makes any sense.

How is the engine mounted? If it's mounted on conventional engine mounts, there is a possibility that a mount has collapsed to the point that the normal vibration of the engine is transferring to the frame and on into the passenger compartment.

Does the vibration change when the clutch is disengaged? Have you run the engine with the fan belts removed? Does the vibration change frequency with RPM? With load?

Like Beater said, these little guys naturally vibrate. I decreased the felt vibration in mine by changing to a six cylinder balancer from the original front pulley. It made a significant difference!

I used the jeep for firewood hauling yesterday so I didn't get much chance to look in to this. However, I did put my hand on the valve cover after a cold start in the morning and did not feel this vibration, however it was very evident on the fenders, so maybe Blackwater is onto something and I'll get lucky with the motor mounts. Rain in the forecast for today so I'm hoping to get to the bottom of it.

So I had an hour or so yesterday and a couple hours today to investigate this. I pulled the underarmour so I could get at things. The vibration dampens a bit with the clutch pushed in , but doesn't go away. It is worse when warmed up than when cold. It diminishes about 30% or so with the fan belt off, but it also diminishes when I lean on the fender on one side while my wife leans on the other side. When cold I feel it much more in the fenders than on the valve cover. The motor mounts are really poorly fabbed and the rubbers are old and cracked, but I cannot feel a difference between the engine side of the mount and the frame side of the mount on either side. I pulled the lower bell housing cover and pried on the bell housing a bit with a flat bar. No indication that it was loose and the pressure plate bolts are tight and appear undisturbed for a long time. I put a dial indicator to the flywheel as best I could. Wild readings while turning it with the starter, so I held a piece of sandpaper to it and then turned it by hand to read the face that the pressure plate bolts to. Not much room there, maybe a 1/4" between the ring gear and the flange of the pressure plate. (+/- 3 thou = 6 thousandths between the highest and lowest indication. And the high and low readings were only about 40 degrees apart. If it was loose I'd expect the variation would be widest 180 degrees apart? I have no idea what is considered acceptable here?
So at this point the thing that seems the most out of wack is the water pump pulley. Maybe I've shook enough of the old girl loose that the pulley and fan wobble are transmitting to the fenders and body work and that's what I'm feeling? It's a new water pump, (a year ago), that I bought because the old one wobbled. I also replaced the pulley, but its a used one from a mercruiser. I suppose I could buy a new pulley and fan. Is there a brand more likely to be true? Is the pulley something that I could have trued up or balanced?

Sounds like you're on the right track. If it were me, I'd replace the engine mounts, (upgrading if possible) and replace the pulley and fan. Also!! Check the bearings in the water pump! If that pulley has been wobbling, it has likely damaged the water pump.

Operating the clutch changes the vibration. That indicates to me that it may be shifting the engine on its mounts, it's moving the crankshaft in the engine forward, which could mean internal engine issues,or you COULD have an issue in the transmission! Does the vibration change much from the lower gears to high gear?

The vibration seems to track rpm, whether in gear or not. I just rebuilt the transmission last winter, While I didn't replace all of the gears, I did use all new bearings and a new second gear, (which has a bronze internal sleeve).

I'm going with Blackwater on the mounts. They might seem solid but still be transmitting the vibration to the frame & body. The fenders are just the outermost part of the signal.

Did you put a pilot bushing in the crankshaft?

I did not replace the pilot bushing, and in fact I did not even pull the clutch when I rebuilt the tranny and transfer case for two reasons:
1. The clutch seemed very good and would easily stall the engine against the brakes, the 10-1/2" clutch seems like significant overkill for this 90 hp 153.
2. this is getting a transmission upgrade in the near future. The T-90 has some real limitations and I have an SM465 to go in it.
I did put my hand on the distributor and it seems very solid, no vibration.

Any opinions on what is an acceptable tolerance for the flywheel? I show =/- 3 thou reading the face, (.006 between highest and lowest readings, and high and low are about 40 deg apart. If this seems within the range for "normal", I am planning to put the cover back on and re-install the under armor to day so I can concentrate on the motor mounts

I don't see how that could her changed if everything it tight. Turn to 180 and bump it with a hammer and see if it changes.

Bummer, I did as Beater suggested and my flywheel does move. I put the dial indicator on it and I can tap it back and forth .008
I suppose I'm lucky that I got to the bottom of this before it went too far.

With the "open on the bottom" bellhousing, I don't suppose this is something I could accomplish without removing the bellhousingf?

Man, I really don't now how bad this is? .008" in a 12" diameter? A piece of dirt or rust? Where is the best pace to go from here?

So, I pulled the transmission and transfer case, pulled the clutch and took a close look at the flywheel. All bolts are tight and torqued to a minimum of 70 ft/lb. So I fiddled around until I could get the dial indicator on the end of the crankshaft and tried tapping the flywheel again. As it turns out the .008" is not flywheel wobble, it's the over all crank end play. So I'm a couple hours into it, and no closer to the solution. It's a 13-1/2" heavy flywheel and a 10" clutch. Flywheel, clutch and pressure plate look fine, very little wear, but the throwout bearing has a notch worn into it from the clutch fork so I did order a new one. The good news is that the bottom cover on the bell housing allows easy access to all of the clutch components without removing the bell housing.
I also ordered a new fan and dropped the water pump pulley off at a machine shop to be checked. We'll see where we land after that.

The problem with these issues is all the time necessary to eliminate a possible cause. You can only progress through the possibilities and check them out. Or you could buy a new Jeep and have it fall apart the day after the warranty expires.

I don't have a warm and fuzzy feeling toward "new" jeeps. 1971 ia about as new as I go. Its a learning experience for sure.

We have owned several since the 80s. My wife has a 2014 Grand Cherokee for which we bought a lifetime warranty. They don't offer those anymore. Even if we get her something in the future we'll keep this one until we ring the last out of this one. They are getting a lot more picky about fixing things as time goes on, especially the same thing several times.

Just to circle back and close this out. I installed the new throwout bearing and fan, tightened all the fender bolts, put it all back together and made sure the exhaust system was all back together snug. The vibration is gone now, but I am still entirely clueless as to what was the source in the first place.
You win some, you lose some and I guess the rest get rained out.

It was probably one or more if those things. Chalk it up in the win column.

I would bet on the fan! I feel like the vibration would be more pronounced from a bad fan blade.

Glad you got it fixed!!