Despite West Germany's plans to sign an accord this week covering industrial cooperation in President Reagan's Strategic Defense Initiative, a political battle over the nature and impact of Bonn's involvement in the program is still raging within the country's ruling center-right coalition.

While members of Chancellor Helmut Kohl's ruling Christian Democratic Union have urged enthusiastic support for SDI's military and political goals, the junior coaltion partners from the liberal Free Democratic Party have increased their criticism of the space-based missile defense research program with the approach of a final agreement.

Economics Minister Martin Bangemann flew to Washington today hoping to seal a pact that would make West Germany the second European ally, after Britain, to join the administration's SDI program.

Before leaving, Bangemann acknowledged that there were "a few important questions" to be resolved, but he said he still expected to be able to conclude the deal by the end of the week.

Kohl's sudden declaration last Wednesday, after a meeting with Defense Secretary Caspar Weinberger, that basic agreement had been reached between their two countries on SDI aroused resentment among Kohl's coalition partners that he was too eager to cut a deal.

Kohl insisted today that SDI is "politically necessary because the Soviet Union is conducting similar research." He said that "our agreement with the United States should make it possible for German industry and science to cooperate as fair partners in the program, if they so wish."

Nonetheless, members of Bangemann's Free Democratic Party have continued to express skepticism about the wisdom of joining a project that they say could unleash a new arms race in space, undermine the strategic balance of nuclear forces and damage Bonn's relations with East Bloc countries.

Those concerns have been cited repeatedly by Foreign Minister Hans-Dietrich Genscher, who guided the Free Democrats' successful policy fight to thwart a direct government role and to restrict SDI involvement to private companies.

By stressing commercial links and playing down Bonn's endorsement of SDI's controversial political aims, Genscher and other Free Democrats hope to deflect criticism from the Soviet Union and East Germany, which have warned that Bonn's role in SDI could harm relations with them.

If Bangemann can work out the last details, the United States will sign two agreements this week. One will set forth the terms for West German firms engaged in SDI contracts, and the other will elaborate on the broader principles involved in the transfer of technology.

Many Free Democrats also have voiced concern about the strict secrecy clauses and tight controls on the sharing of research findings demanded by the United States.

According to officials involved in the negotiations, the United States has insisted on limiting any technology spinoffs to be exploited by West German firms to strictly military projects that would aid the western alliance. Washington has rejected West Germans' appeals for commercial applications of SDI research by their firms, the officials added.

The search for a quick deal with the United States, according to political commentators here, reflects Kohl's hope that the SDI issue will dissipate as a campaign theme before West German national elections are held next January.

West German conservatives have contended that the country's scientists and engineers must be allowed to participate in the SDI program if only to stay abreast of advanced technologies.

They say West Germany's traditional strength in the fields of optics and lasers should yield a bountiful harvest of lucrative contracts.