Math Problem: Tenter

MATH PROBLEM: TENTER

The windmill uses a “tentering gear” to lift the “runner stone” and adjusts the spacing between the “runner stone” and the “bed stone.” This spacing helps grain to move between the stones as it is ground into flour. The head miller has to adjust the spacing as the wind changes to keep the stones turning.

PROBLEMS:  What is the force on each of the three connectors of the tentering gear?  Using the tentering gear, how much force does the miller use to lift the millstone?

HINT:  The tentering gear is a series of levers and work similar to “teeter-totters.”  Levers trade distance for force.

1 2 1 2 GIVENS:  The “Runner Stone” weighs 2500 pounds.  The “Bridge Tree” has a “fulcrum” or “pin” at the end. The distance from the pin to the shaft supporting the Bed Stone is 68 cm. The distance from the pin to the “Cross Bridge” connecting rod is 165 cm.  The “Cross Bridge” has a “fulcrum” or “pin” at the end. The distance from the pin to the “Bridge Tree” connecting rod is 15 cm. The distance from the pin to the “Lift Tenter” connecting rod is 113 cm.  The “Lift Tenter” has a fulcrum in the middle. The distance from the fulcrum to the “Cross Bridge” connecting rod is 36 cm. The distance from the fulcrum to the block and tackle is 109 cm.  The block and tackle has a 2-to-1 lift ratio.

SOLUTION:  First, determine the force on the “Cross Bridge” connecting rod. 2500 lbs x (68 cm/165 cm) = 1030 lbs  Next, determine the force on the “Lift Tenter” connecting rod. 1030 lbs x (15 cm/113 cm) = 137 lbs  Next, calculate the force on rope connecting the Lift Tenter and the block and tackle. 137 lbs x (36 cm/109 cm) = 45 lbs  Finally, calculate the force on block and tackle rope. 45 lbs/2 = 23 lbs 36 cm 109 cm

Hurst Frame

Wallower 45 LBS Lift TenterTentering (3-to-1 ratio) Gear (A LessonBlock and in Levers) Tackle 23 (2-to-1 ratio) LBS

113 cm 15 cm Runner Stone Cross Bridge (7.5-to-1 ratio) 136 1023 2500 LBS LBS LBS Bridge Tree (2.4-to-1 ratio)

68 cm 165 cm

Cross Bridge, Lift Tenter and the Block and Tackle.

Bridge Tree under the millstone. The windmill uses a series of four gears Brake Wheel to convert wind power into mechanical energy to turn the millstones. 55 cogs Based on the information shown, how 15 revolutions per Wind Connected fast is the runner stone turning (turns minute Shaft to per minute)? Sails

GIVENS: Wallower 31  The sails turn the wind shaft at cogs 15 revolutions per minute  The brake wheel contains 55 cogs Cap Floor  The wallower contains 31 cogs Sack Hoist Floor  The spur wheel contains 101 cogs  Each stone nut contains 25 staves Main Spindle

SOLUTION: Stone Nut  First, determine how many times the main spindle turns for each turn of 101 cogs 25 staves the brake wheel. Great Spur Wheel o Each time the brake wheel turns once, the wallower turns by 1.77 Stone times. Spindle 1 x (55/31) = 1.77 sack hoist Floor  Next determine how many times the stone nut turns for each turn of the stone Floor spur wheel. o Each time the spur wheel turns once, the stone nut turns by Runner Stone 4.04 times. Bed Stone 1 x (101/25) = 4.04

 Finally, the rotation of the runner stone is the product of rotation of the sails/brake wheel and the proportions calculated above. 15 x (1.77 x 4.04) = 15 x 7.15 = 107 REVOLUTIONS/MINUTE