The linear velocity of the axial roll in ring rolling.

I posted on this blog about the linear velocity of the main roll.(The linear velocity of the main roll in ring rolling)
The formula for calculating the linear velocity of an axial roll is a bit more complicated than that of the main roll because the axial roll is a cone shape.
As you know, the linear velocity is the product of the rotation radius and the rotation speed.
V = R x ω
(V : linear velocity, R : rotation radius, ω : rotation speed)



1. The rotation radius of the axial roll

The rotation radius of the main roll(Rm) is constant, but the rotation radius of the axial roll(Ra) varies with the position of the ring.
image

The rotation radius of the axial roll(Ra) is,
Ra  = TR x sin(θ/2)
(TR : the encoder value of the Tracer Roll, θ : the cone angle of the axial roll)
I explained in the previous post about the TR encoder(The encoders of the ring mill).
image

2. The linear velocity of the axial roll

The linear velocity of the axial roll is,
Va = Ra x ωa
image
Va = TR x sin(θ/2) x ωa
Let's take the linear velocity of the axial roll as an example.
Suppose that the cone angle of the axial roll is 40 degrees and the rotation speed of the axial roll is 100 rpm.
If the ring is located at TR position 500, the linear velocity of the axial roll is:
Va = 500mm x sin(40/2) x 100 rev/min = 1.789 m/s
If the ring is located at TR position 300, the linear velocity of the axial roll is:
Va = 300mm x sin(40/2) x 100 rev/min = 1.073 m/s

#RingRolling, #Forging, #Metal, #Forge

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