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Gear Noise and Vibration Episode 1 Part 5

Tham khảo tài liệu 'gear noise and vibration episode 1 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Marcel Dekker Inc. Madison Avenue New York New York 10016 Copyright Marcel Dekker Inc. All rights reserved. 5 Prediction of Dynamic Effects 5.1. Modelling of gears in 2-D Static determination of T.E. under load is sufficient for most drives where the loading is relatively heavy and the inertias are low so that there is little danger of the length of line of contact varying greatly or of the teeth losing contact. The T.E. is then the input vibration and as the system remains reasonably linear in its behaviour it can be modelled using a conventional matrix approach in the frequency domain. Drives which are lightly loaded or which drive high inertias such as printing rolls may lose contact with rather dramatic results. It is then possible for the teeth to be in contact for less than 10 of the time with rather large impulsive forces while they are in contact. The simple assumption of a linear system with an input displacement of the quasi-static T.E. is then no longer realistic and a more detailed model is required see section 5.2 and Chapter 11 . Even when the teeth do not come fully out of contact the simple assumption of a linear system can be wildly unrealistic. This is due to the large variations in the true length of the contact line partly due to the gear flank shapes and partly due to the vibration. If the nominal mean elastic deflection in the mesh is of the order of 10 pm then a vibration of 2 pm can easily alter the contact stiffness by a factor of 2 by changing the length of the line of contact during the vibration. A simple assumption that stiffness is proportional to nominal length of line of contact is near the truth for well-aligned spur gears but not true for misaligned gears especially helicals. The simplest realistic model of a pair of gears is shown in Fig. 5.1. Axial movements are negligible or ignored although the gears are taken to be helical. There is considerable simplification if we take the linear axis along the line of thrust and ignore any