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.
Finite Element Analysis of Contact and Bending Stresses in Helical Gear Pair
In gear design, excessive tooth contact stresses and bending stresses are one of the prime gear failure factors; therefore, its analysis is very important in order to shorten the possibility of gear tooth failure. In the present work, the tooth bending stresses and contact stresses in a helical gear pair is calculated using AGMA theory and finite element analysis (FEA). The modelling of helical gear pair is carried out in CREO and ANSYS is used for FEA. It is observed that the bending stresses and contact stresses, both decreases with an increase in the helix angle if pressure angle remains constant. However, the error in the calculation by AGMA and FEA is higher for the bending stresses than the contact stresses and bending stresses.
Decidability of some intuitionistic predicate theories
Suppose T is a first order intuitionistic theory (more precisely, a theory of Heyting's predicate calculus, e.g., abelian groups, one unary function, dense linear order, etc.) presented to us by a set of axioms (denoted also by) T. Question. Is T decidable? One knows that if the classical counterpart of T (i.e., take the same axioms but with the classical predicate calculus as the underlying logic) is not decidable, then T cannot be decidable. The problem remains for theories whose classical counterpart is decidable. In [8], sufficient conditions for undecidability were given, and several intuitionistic theories such as abelian groups and unary functions (both with decidable equality) were shown to be undecidable. In this note we show decidability results (see Theorems 1 and 2 below), and compare these results with the undecidability results previously obtained. The method we use is the reduction-method, described fully in [12] and widely applied in [3], which is applied here roughly as follows: Let T be a given theory of Heyting's predicate calculus. We know that Heyting's predicate calculus is complete for the Kripke-model type of semantics. We choose a class M of Kripke models for which T is complete, i.e., all axioms of T are valid in any model of the class and whenever φ is not a theorem of T, φ is false in some model of M.