The Army's new high-speed and high-cost M1 tank has had its share of problems, and now comes a new one.

Its transmission is so delicate that it cannot do what previous tanks have traditionally done and dig itself in when it arrives where it wants to be.

So the Army has come up with a companion vehicle, called ACE, which will travel along with the M1. ACE stands for Armored Combat Earthmover. It's what a civilian might call a high-speed bulldozer.

M1s cost more than $2.5 million apiece. The Army wants more than 7,000 of them, or about $19 billion worth.

The ACEs cost about $1.1 million apiece. The Army is said to want more than 600 of them. That is at least another $600 million.

And then there is the fuel problem. The M1s not only have delicate transmissions, they are gas guzzlers.

To keep each battalion of M1s supplied with fuel, the Army says it will need 26 additional fuel trucks and tanks. These will cost $632,000 per battalion. The number of planned battalions is classified, but experts say it is almost sure to be more than 100. That is $63 million more.

The M1 and its trail-along vehicles are an example of a problem now plaguing the Army. Many of its proposed new weapons systems are running beyond their original cost estimates. Even defenders acknowledge that the Army is thus likely to be one of the main targets for defense budget cutters on the Hill this year.

The ACE is programmed to travel 30 miles an hour on the battlefield. Army officers say that it is needed and that it will be able to do the job much better than the old D7 military bulldozer, which has to be carried by a tractor-trailer and on its own can go no faster than five or six miles an hour.

Tanks normally dig in on the battlefield either to fire or to protect themselves from the enemy. Older tanks can have a blade attached to do the digging themselves. Or they wait for the slower bulldozers to arrive, carried by tractor-trailers.

At a congressional hearing last year, Army Chief of Staff Gen. Edward C. Meyer said that in order to install a blade on the M1 "you would have to use a different engine, different transmission, suspension, and make other significant modifications to be able to do the kinds of earth-moving tasks required."

That is why, for years, the Pacific Car and Foundry Co. of Renton, Wash., and the Army have been trying to sell Congress on the speedy, versatile armed bulldozer.

Not until last year did Congress approve $40.7 million for the Army to buy the first 36 of the earth-moving machines. Now there are plans to produce up to 100 a year for more than six years.

For the first three years that the Army sought the vehicle, the House Appropriations subcommittee on defense turned it down. During those years, congressional sources said yesterday, the Army had not appeared to be very enthusiastic about the bulldozer, which in those days was called the Universal Engineering Tractor or UET.

Then, last year, things seemed to change. The system was given its new name and jazzier acronym, ACE. It also was more actively supported than before by subcommittee member Norman D. Dicks (D-Wash.), in whose state the ACE is built.

The Army, sources said, buoyed by an increasing Reagan defense budget, "got its act together and decided what missions the ACE was to perform."

Dicks got the Army to report on a test that showed the ACE during maneuvers resulting in "significant increases in task force combat effectiveness, evident in increases over 22 percent in the ratio of enemy to U.S. weapons systems losses."

The Army, with new enthusiasm, described ACE as "not only affordable, but in terms of weapons system survivability, absolutely necessary." As a clincher, it was linked to the Rapid Deployment Force because, unlike the traditional bulldozer, it was "both air-transportable and air-droppable . . . ."

Congress bought the argument and the ACE started to roll, but at some cost.

When the new bulldozer was first proposed in fiscal 1978, its cost was put at $200,000 per unit. By 1979, the price was $660,000, and by April last year, when the Army testified about it before the House subcommittee, it had risen to $1.1 million.

The new version of the old Army bulldozer, including the tractor-trailer to carry it around, would cost only $300,000, according to Army officials.