The national Transportation Safety Board recommended yesterday an intensified program of inspections for axles on railroad locomatives after discovering that an axle, faulty from the date of its manufacture, caused a major" Auto-Train derailment.

Twenty-four of 503 passengers were injured last Feb. 24 when the locomotive and 19 cars of the northbound train derailed in the early morning hours at Florence, S.C. Total damage from the accident was estimated at $775,0000.

One of the locomotive axles failed, the board said, despite the fact it had a flaw and that the flaw had escaped detection during normal safety tests.

The fracture in the axle, the board said, "originated in an undetected void (hole) that developed during the manufacture of the arle. . . ." The axle, manufactured by the Bethlehem Steel Corporation in 1972, was installed on a General Electric Company locomotive in 1976. It had traveled 298,000 miles at the time of the accident.

The manufacturer's ultra-sonic inspection failed to detect internal defects, and routine testing during maintenance periods also missed the flaw.

The board, which has no regulatory powers, recommended that the Federal Railway Administration:

Establish regulatory specifications for manufacturing and testing of locomotive axles "to insure the discovery of internal defects;"

Require tests of in-service axles that will dettct flaws, and remove faluty axles;

Develop a method for automatic trackside detection of such flaws.

FRA specialists had no comment yesterday because they had not seen the board's detailed report. There are about 27,000 locomotives in the nation. Most of them have four axles; some of them have six.

A spokesman for Auto-Train sakd that "we will immediately test all of our axles" for possible flaws.