Engineering College

the decision has been made to use ϕn = 20°, pt = 6 teeth/in, and ψ = 30° for a 2:1 reduction. choose the smallest acceptable full-depth pinion and gear tooth count to avoid interference

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Answer 1

The smallest acceptable full-depth pinion and gear tooth count to avoid interference is Np = 9 and Ng = 18, respectively.

Given:ϕn = 20°pt = 6 teeth/inψ = 30°r = 2:1 reduction Formula Used:1. Tooth Depth formula: h t = 2.2/PN+2PTNcosϕ2. Circular pitch (p) formula: P = πd/N where, h t = Tooth depth PT = Transverse pressure angle N = Number of teethϕ = Pressure angle P = Circular pitch d = Pitch circle diameter Procedure: First, calculate the value of N using the relation for a 2:1 reduction: R = r = 2:1For this, Let the pinion tooth count be Np and the gear tooth count be Ng.

We will use the formulas of tooth depth and circular pitch to 1. Tooth depth: ht = 2.2/PN+2PTNcosϕIf there is no interference, h t should be smaller than the minimum allowable clearance cmin. This minimum allowable clearance can be taken as c min = 0.1575P + 0.01575 inch for involute gears.ht for pinion and gear teeth must be equal, so we get:2.2/Pp+2PTpcosϕ = 2.2/Pg+2PTgcosϕWe are given: PT = 6 teeth/inϕ = 20°ψ = 30°Np = (1/2)Ng Ng = smallest full-depth gear tooth count.

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