Inertia compensating dancer roll for web feed

A method of designing a floating roller in a tensioning system adapted to one of supply and receive a web of material to or from one of a web supply and a processing machine, said method comprising:

• inputting an external radius of said floating roller, a measure of elasticity of said material, a thickness of said material, a width of said material, and angles at which said material contacts said floating roller;
• and
• adjusting a mass of said floating roller and a rotational inertia of said floating roller such that said floating roller maintains a constant tension on said web of material as said material is passing through said tensioning system based on the following equation:
• M
• 2
• ≈
• (
• 1
• -
• T
• _
• a
• ⁢
• ⁢
• 3
• Ebw
• )
• ⁢
• sin
• 2
• ⁡
• (
• α
• /
• 2
• )
• ⁢
• J
• 2
• R
• 2
• 2
• wherein M2 is said mass of said floating roller, J2 is said rotational inertia of said floating roller, R2 is said external radius of said floating roller, E is a Young's modulus of said web of material, b is said thickness of said web of material, w is said width of said web of material, Ta3 is said tension force on said material and α is an angle at which said web of material contacts said floating roller.

An apparatus comprising:

• a receiver roller adapted to one of supply and receive a web of material to or from a web supply;
• an output roller adapted to output said web of material to a processing machine;
• and
• a floating roller between said receiver roller and said output roller adapted to pass said material from said receiver roller to said output roller,
• a controller adjusting a mass of said floating roller and a rotational inertia of said floating roller based on an external radius of said floating roller, a measure of elasticity of said material, thickness of said material, width of said material, and an angle at which said material contacts said floating roller such that said floating roller maintains a constant tension on said web of material as said material is passing.

An apparatus comprising:

• a receiver roller adapted to receive a web of material from a web supply;
• an output roller adapted to output said web of material to a processing machine;
• and
• a floating roller between said receiver roller and said output roller adapted to pass said material from said receiver roller to said output roller,
• a controller that adjusts a mass of said floating roller and a rotational inertia of said floating roller such that said floating roller maintains a constant tension on said web of material as said material is passing based on the following equation:
• M
• 2
• ≈
• (
• 1
• -
• T
• _
• a
• ⁢
• ⁢
• 3
• Ebw
• )
• ⁢
• sin
• 2
• ⁡
• (
• α
• /
• 2
• )
• ⁢
• J
• 2
• R
• 2
• 2
• wherein M2 is said mass of said floating roller, J2 is said rotational inertia of said floating roller, R2 is an external radius of said floating roller, E is a Young's modulus of said web of material, b is a thickness of said web of material, w is a width of said web of material, Ta3 is said tension force on said material and α is an angle at which said web of material contacts said floating roller.

A computer program product comprising:

• a computer-usable data carrier storing instructions that, when executed by a computer, cause said computer to perform a method of designing a floating roller in a tensioning system adapted to one of supply and receive a web of material to or from one of a web supply and a processing machine, said method comprising:
• inputting an external radius of said floating roller, a measure of elasticity of said material, a thickness of said material, a width of said material, and angles at which said material contacts said floating roller;
• and
• adjusting a mass of said floating roller and a rotational inertia of said floating roller based on said external radius of said floating roller, said measure of elasticity of said material, said thickness of said material, said width of said material, and said angles at which said material contacts said floating roller such that said floating roller maintains a constant tension on said web of material as said material is passing through said tensioning system.