Cardiff Crown Court was told that 30 of Nordam Europe's employees were exposed to risk of "significant" harm.
An investigation by the Health and Safety Executive (HSE) found that workers at the company's site in Gwent, South Wales, used various hand-held vibrating tools, including orbital sanders, rivet guns, grinders and drills.
It said Nordam Europe "should have carried out a suitable assessment of work activities which exposed employees to vibration and should have implemented additional controls to reduce exposure so far as was reasonably practicable".
The HSE also found the company had failed to implement a safe system of work to control exposure to vibration and there was no suitable health surveillance to identify symptoms at an early stage of the disease. "This would have prevented it from progressing to a disabling condition", it said.
Nordam Europe, which is a joint venture between Oklahoma, US-headquartered aerospace firm Nordam and GE Aircraft Engine Services, pleaded guilty to breaching s 2(1) of the Health and Safety at Work Act. It was fined and ordered to pay costs of £39,620.
HSE inspector Janet Hensey said: "This was a case of the company completely failing to grasp the importance of HAVS health surveillance.
"If they had understood why health surveillance was necessary, it would have ensured that it had the right systems in place to monitor workers' health and employees' condition would not have been allowed to develop to a severe and life-altering stage."