In an unusual gesture of friendship, West German Chancellor Helmut Schmidt came to the Bonn-Cologne airport last night to greet president Carter as Carter began a five-day visit that will include an economic summit conference.

Schmidt's unexpected appearance at the airport, a departure from the normal West German practice of officially greeting visiting heads of state the day after their arrival, was viewed here as a significant sign of Schmidt's determination to improve his relations with the president and pave the way for a smoothly functioning summit conference.

Nevertheless some of the underlying differences that are bound to come up at the summit were underscored by American officials traveling with the president as they insisted that the United States will not accept anywhere near the full blame for the economic and energy problems that plague the industrialized democracies.

"It suits us fine to be reminded of what we have to do on energy," one senior White House official said aboard Air Force One. "It does not suit us fine to have our problems on energy used as an excuse by everybody else not to do anything on other problems."

The official also gave the strongest indication to date that Carter does not intend to make any specific commitments on imposing higher oil import fees or quotas when he meets here Sunday and Monday with Schmidt and the leaders of France, Britain, Italy, Canada and Japan.

Led by Schmidt, the other leaders, concerned over the adverse impact on the value of the dollar from the continued high level of U.S. oil imports, reportedly are prepared to pressure the President to make suh a pledge should Congress fall to enact the administration's natural energy legislation.

"He (Carter) would discuss what needs to be done but would be disinclined to talk in detail about specific steps or timing to get the job done," the White House official said.

Reacting to the continued suggestions by European leaders that the United States must cut its oil imports for the sake of the world economy, he added:

"There is some concern about attempts in some quarters to place the blame for the economic problems of the entire Western world and the developing countries on the shoulders of the United States. While . . . we do share a large part of the responsibility . . . we don't consider it healthy of the industrial democracies to allow that sort of idea to take hold."

Of all the leaders the president will meet here, Schmidt has been the most skeptical of Carter's leadership abilities and there reportedly has been some strain in their personal relationship. Whether the chancellor's airport gesture would smooth that over and ease the underlying tensions at the summit remained uncertain, but it clearly was meant as a start in that direction.

Except for Schmidt's unexpected appearance, last night's arrival was low-keyed and routine, with neither leader making public remarks.The president, accompanied by his wife, Rosalynn, daughter Amy and a large contingent of administration officials, walked between an honor guard of gray-clad West German troops to be greeted by Schmidt and a delegation of West German officials.

In his own gesture, Carter gave Schmidt a ride from the airport in the presidential limousine that was flown here from Washington.

The Carter visit to West Germany, his first here since taking office, is meant to re-emphasize the bonds linking the U.S. and its most economically and militarily most importantally in the Atlantic alliance. It is meant also to improve the sometimes strained political relations between the two governments and personal relations between the two leaders, something that both Carter and Schmidt seem to have concluded is worth doing.

In a statement issued here yesterday in advance of the president's arrival, Schmidt spoke of the "incontestable ties of friendship" between the people of both countries. He described West German-American relations as "as good as ever before," an assessment meant to overshadow problems between the two countries on economic, nuclear, export and trade policies but also reflecting the effort to smooth things out.

The president has jammed visits to three cities, to troops in the field and a town hall meeting in West Berlin into a whirlwind 33-hour state visit before the seven-nation economic summit meeting opens here sunday.

One thing which apparently has caused some hurt feelings in Schmidt's chancellory, however, is a white House turn-down of an invitation by Schmidt for the president to dine in Schmidt's Hamburg home tomorrow night after the Berlin visit.

Although White House officials explained that the schedule was too tight and the summit began the next morning, sources close to Schmidt say the decision was viewed as "insensitive" if the president truly does want friendlier personal relations with Schmidt.

Soviet President Leonid Brezhnev, French President Giscard D'Estaing and a handful of other world leaders have been invited to Hamburg and have accepted.