But when the pinions are shrouded, that is, have flanges at each end, the teeth are strengthened; and since the wear will continue greater than in wheels having more teeth in contact, the shrouding may be regarded as a provision against breakage in consequence of the reduction of tooth thickness resulting from wear.
In the following table is given the thickness of the tooth for a given stress at the pitch circle, calculated from Tredgold's rule for teeth supposed to have contact when new at one corner only.
+-------------------+--------------------+---------------------+ | Stress in lbs. at | Thickness of tooth | Actual pitches to | | pitch circle. | in inches. | which wheels may be | | | | made. | +-------------------+--------------------+---------------------+ | 400 | .52 | 1-1/8 to 1-1/4 | | 800 | .75 | 1-1/2 " 1-5/8 | | 1,200 | .90 | 1-7/8 " 2 | | 1,600 | 1.03 | 2 " 2-1/8 | | 2,000 | 1.15 | 2-1/4 " 2-3/8 | | 2,400 | 1.26 | 2-1/2 " 2-5/8 | | 2,800 | 1.36 | 2-5/8 " 2-3/4 | | 3,200 | 1.43 | 2-7/8 " 3 | | 3,600 | 1.56 | 3-1/8 " 3-1/4 | | 4,000 | 1.63 | 3-1/4 " 3-3/8 | | 4,400 | 1.70 | 3-3/8 " 3-1/2 | | 4,800 | 1.78 | 3-1/2 " 3-5/8 | | 5,200 | 1.86 | 3-5/8 " 3-3/4 | | 5,600 | 1.93 | 3-3/4 " 4 | | 6,000 | 2.00 | 4 " 4-1/4 | +-------------------+--------------------+---------------------+
In wheels that have their teeth cut to form in a gear-cutting machine the thickness of tooth at any point in the depth is equal at any point across the breadth; hence, supposing the wheels to be properly keyed to their shafts so that the pitch line across the breadth of the wheel stands parallel to the axis of the shaft, the contact of tooth upon tooth occurs across the full breadth of the tooth.
As the practical result of these conditions we have three important advantages: first, that the stress being exerted along the full breadth of the tooth instead of on one corner only, the tooth is stronger (with a given breadth and thickness) in proportion to the duty; second, that with a given pitch, the thickness and therefore the margin for safety and allowance for wear are increased, because the tooth may be increased in thickness at the expense of the clearance, which need be merely sufficient to prevent contact on both sides of the spaces so as to prevent the teeth from locking in the spaces; and thirdly, because the teeth will not be subject to sudden impacts or shocks of tooth upon tooth by reason of back lash.