Physics of the Lathe

Physics of the Lathe

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"How much wood could a woodchuck chuck if a wood chuck could chuck wood?" An age old tongue twister that has never been answered. In this rhyme, the common assumption is that the woodchuck is a small furry groundhog like creature, but there is another kind of wood chuck that is not as common but could chuck wood. Here we will explore this path of answering this age old riddle.

In the production of many wood products a common manufacturing tool known as a lathe is used, and to hold the wood in the lathe a chuck is used. In order to calculate the amount of wood a wood chuck can chuck we must first define how the wood will be chucked. When wood chucking the chuck will be spinning around the spindle and an attachment will be used that will act as a catcher that will be on the outer radius of the chuck. We will also be able to calculate the velocity of the wood leaving the chuck and the kinetic energy.

Lathes & Chucks

A LATHE is "a machine tool designed primarily to do turning, facing, and boring. Their versatility permits multiple operations to be done with a single setup of the workpiece. Consequently, the lathe is the most common machine tool." The lathe used to theoretically calculate the amount of wood that can be chucked is the TECHNO CNC WOOD LATHE. This lathe has a spindle speed rate from 500 to 2000 RPM, which will be used to calculate the amount of wood chucked.

The Chuck is an attachment that is the most commonly used way to hold a workpiece on the lathe. It attaches to the spindle on the lathe and is spun by it at speeds up to 4000 RPM depending on the lathe. The chuck that will be used for our calculations will have an approximate mass of 4 kilograms and a diameter of 6 inches.

Wood Chucking

To calculate the amount of wood that is chucked, and the other properties of wood chucking, using the TECHNO CNC WOOD LATHE the following values and assumptions will be used:

* The spindle speed of the lathe has a range of 500-2000 RPM
* The diameter of the chuck is 6 in. approximately 15 cm.
* A one kilogram block of wood made out of American Spruce with a density of .

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541 grams per cubic centimeter has approximate dimensions of 12x12x12 cm.
* An attachment is used to feed wood blocks at a rate equal to the rate of the chuck spinning (1 Block Per Revolution).
* The lathe is run for 1 minute.

At 500 revolutions per minute:

500 RPM x 1 Block Per Revolution x 1 minute = 500 Blocks
* 500 RPM / 60 seconds = 8.33 Revolutions per second = 8.33 Blocks per second

At 2000 revolutions per minute:

2000 RPM x 1 Block Per Revolution x 1 minute = 2000 Blocks
* 2000 RPM / 60 seconds = 33.3 Revolutions per second = 33.3 Blocks per second

Other Properties

In addition to the amount of wood calculated to be chucked, we can predict the velocity of the wood leaving the chuck and the kinetic energy of the wood.


@ 500 RPM the angular velocity at the Block Center of Mass is calculated by:
1 rev = 2(3.14)(13.625) = 85.6 cm
.856 m / 1 min * 1 min / 60 sec = .01427 m/s
500 * .01427 m/s = 7.135 m/s

the linear velocity at the Block Center of Mass is calculated by:
v = rw
v = (.13625)(7.135)
v = .79365 m/s

@2000 RPM the velocity at the Block Center of Mass is calculated by:
1 rev = 2(3.14)(13.625) = 85.6 cm
.856 m / 1 min * 1 min / 60 sec = .01427 m/s
2000 * .01427 m/s = 28.54 m/s

the linear velocity at the Block Center of Mass is calculated by:
v = rw
v = (.13625)(28.54)
v = 3.1746 m/s

Kinetic Energy:

Angular @ 500 RPM: KE = 1/2 Iw^2
I = SUM(mass * (radius)^2)
I = (4.0)(.075)^2 + (1.0)(13.625)^2
I = .041064
KE = ½(.041064)(5.825)^2
KE = 0.696665

Angular @ 2000 RPM: KE = 1/2 Iw^2
I = SUM(mass * (radius)^2)
I = (4.0)(.075)^2 + (1.0)(13.625)^2
I = .041064
KE = ½(.041064)( 23.3)^2
KE = 11.14663

Linear @ 500 RPM: KE = 1/2v^2
KE = ½( 0.793656)^2

Linear @ 2000 RPM: KE = 1/2v^2
KE = ½( 3.174625)^2

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