Adopted high-order power function and short modification as the profile modification mode of spur gears used in astronomical telescopes

it can meet the necessity of the contact ratio and improve the static transmission error

and avoid stress concentration by eliminating addendum edge contacting with scraping.The pre-designed manufacturing transmission error curve is defined as profile modification parameter

the modified teeth faces are established based on virtual manufacturing process.The manufacture transmission error curve

the deformation error curve and the static transmission error curve are calculated by tooth contact analysis theory and finite element method

and the function of profile modification considering pitch errors is also derived under a certain torque.The static transmission errors and stress of pinion addendum are contrasted between ordinary spur gear and modified one in the simulation example.The simulated results verify that the effect of modification is obvious.