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A paper machine processes rolls of paper having a density of 984 kg/m3. The paper roll is ...

A paper machine processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50-m outside dia (OD) X 0.22-m inside dia (ID) X 3.23 m long and is on a simply supported, hollow, steel shaft with Sut = 400 MPa. Design a 2.5:1 reduction helical gearset to drive this roll shaft to obtain a minimum dynamic safety factor of 2 for a 10-year life if the shaft OD is 0.22 m and the roll turns at 50 rpm with 1.2 hp absorbed.
A 2-start wormset has d = 50 mm, px = 10 mm, mG = 22:1. Find the lead, lead angle, worm-gear diameter, and center distance. Will it self-lock? The input speed is 2 200 rpm.

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Helical Gearset Design (2.5:1 reduction)

Given:

Paper roll density: 984 kg/m³
Paper roll dimensions:
- OD (Outside diameter) = 1.5 m
- ID (Inside diameter) = 0.22 m
- Length = 3.23 m
Shaft outer diameter (OD) = 0.22 m
Shaft material tensile strength (Sut) = 400 MPa
Roll turns at 50 rpm
Power absorbed = 1.2 hp
Dynamic safety factor = 2 for a 10-year life

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