Rotation speed control of axial roll.

The driving force that rotates the ring in the ring mill is generated by the main roll and the axial roll.
Of these two rotational speeds, the rotational speed of the main roll is used as a reference, and the axial roll is controlled according to the rotational speed of the main roll.  Normally, the rotation speed of the main roll is fixed and the rotation speed of the axial roll is controlled according to the position of the ring.
In the previous, we have understood the concept of linear velocity(What is linear velocity) and studied how to obtain the linear velocity of the main roll(The linear velocity of main roll) and the linear velocity of the axial roll(The linear velocity of axial roll).
The linear velocity of the main roll(Vm) is fixed and constant and we control the rpm of axial roll to match the linear velocity of the axial roll(Va) with that of the main roll.
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The linear velocity of the main roll(Vm) is,
Vm = Rm x ωm
The linear velocity of the axial roll(Va) is,
Va = Ra x ωa = TR x sin(θ/2) x ωa
The rotation speed(rpm) of the axial roll(ωa) is,
Va = Vm
TR x sin(θ/2) x ωa = Rm x ωm
ωa = Rm x ωm / (TR x sin(θ/2)) (eq.1)
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The radius of the main roll(Rm), the rotation speed of the main roll(ωm) and the angle of the axial roll(θ) in the equation 1 are constant.  But TR varies according to the position of the ring.  So we have encoder to measure the distance from the edge of the axial roll cone to the out surface of the ring in the ring mill(The encoders in the ring mill).

Let's use the actual example to calculate the rotational speed of the axial roll.
* main roll diameter : 1,000 mm
* main roll rotation speed : 1,200 rpm
* reducer ratio of the main gear box : 1/40
* reducer ratio of the axial roll gear box : 1/10
* angle of the axial roll : 40˚
* TR encoder value measuring the ring postion : 600 mm
The rotation speed of the axial roll that we need to control is,
ωa = Rm x ωm / (TR x sin(θ/2))
ωa = (1,000 / 2) x (1,200/40 ) / (600 x sin(40/2)) x 10
= 731 rpm
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If the ring is at the position of TR 300, the rotation speed of the axial roll is 1,462 rpm
This means that the smaller the ring, the faster the rotation speed of the axial roll.
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We calculate the rotation speed of the axial motor in the ring mill program and control it in real time.
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This is the rotation speed of the axial motor.(when main motor rpm is 1,200, axial roll angle is 40 degree, main roll diameter is 1,000 mm, main gear box reducer ratio is 1/40 and axial gear box reducer ratio is 1/10)
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