Parametric investigation of the combined effect of Gear parameters on Tangential Force and Dynamic Tooth Load of 40 Ni2 Cr1 Mo 28 Steel Helical Gear
Global competitive business market had brought increasing awareness to optimize the gear design. Gears have the advantage over friction and belt drives in that they are positive drive, a feature which most of the machine tools require, since exact speed ratios are essential. The design and manufacture of precision cut gears, made from materials of high strength, have made it possible to produce gears which are capable of transmitting extremely large loads at extremely high circumferential speeds with very little noise, vibration and other undesirable aspects of gear drives. The present work is to focus on investigating the combined effect of gear parameters on tangential force and dynamic tooth load of helical gear.
Deformation overlap in the design of spur and helical gear pair
The elastic deflection of gear teeth is analyzed to investigate the deformation overlap. The deformation overlap, which is a numerically calculated quantity through displacement analysis at the initial contact, is defined as the piled region of a contact tooth pair due to the elastic deformation. The deformation overlap is suggested for an effective indicator to represent the whole deformation of a meshing gear pair. The elastic contact theory and finite element method are used to compute the contact force and teeth deflection. The contact problem is defined as a QP problem, and the contact forces between teeth are calculated from the transmitted torque. Then the deformation overlap is calculated with the contact forces as boundary conditions. For a spur gear pair, the calculated deformation overlap is used for the basis of the tooth tip relief, analysis of deformation characteristics for a profile shifted gear pair, and the selection of profile shift coefficient considering teeth deflection. Deformation overlap is extended to a three-dimensional problem, and implemented to a helical gear pair.
UNIVERSAL LOCALLY COMPACT SCATTERED SPACES
If δ is an ordinal, we denote by C(δ) the class of all cardinal sequences of length δ of locally compact scattered (in short: LCS) spaces. If λ is an infinite cardinal, we write Cλ(δ) = {s ∈ C(δ) : s(0) = λ = min[s(ζ) : ζ < δ]}. An LCS space X is called Cλ(δ)-universal if SEQ(X) ∈ Cλ(δ), and for each sequence s ∈ Cλ(δ) there is an open subspace Y of X with SEQ(Y ) = s. We show that • there is a Cω(ω1)-universal LCS space, • under CH there is a Cω(δ)-universal LCS space for every ordinal δ < ω2, • under GCH for every infinite cardinal λ and every ordinal δ < ω2, there is a Cλ(δ)-universal LCS space, • there may exist a Cω(ω2)-universal LCS space. As a consequence, we obtain that it is consistent that 2 = ω2 and Cω(ω2) is large as possible, i.e. Cω(ω2) = {s ∈ 2{ω, ω1, ω2} : s(0) = ω}. 2000 Mathematics Subject Classification. 54A25, 06E05, 54G12, 03E35.