Boring Bar Deflection
Boring Bar Deflection, Cutting Forces, and Horsepower Requirement
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Boring Bar Deflection:
Calculating boring bar deflection, provides a means for analyzing a boring bar¡¯s performance characteristics, prior to machining a part. Deflection can affect the surface finish or in extreme circumstances the part¡¯s dimensional tolerances. To minimize deflection select a boring bar that offers the most rigidity with the shortest overhang.? ? ? ? ? ?
Boring Bar Deflection (y) Formula:
y = FL33EI
F = Cutting force [lbf or N]
Cutting force = unit of power constant x d x f x Kp x C
unit of power constant = 396,000 (Imperial) or 60,000 (Metric)?
d = DOC [inch or mm]
f = feed rate [inch per minute or mm per minute]
Kp = power constant [hp/inch3/minute or kW/mm3/minute]?
C = feed rate factor for the power constant adjustment? ??
L = Unsupported length (overhang) of the boring bar [inch or mm]
E = Modulus of elasticity (in tension) for the boring bar material [psi or N/mm?]
Steel Modulus of elasticity = 30,000,000 psi
Steel Modulus of elasticity = 206,843 N/mm2
Heavy Metal (Tungsten alloy) modulus of elasticity = 48,000,000 psi
Heavy Metal (Tungsten alloy) modulus of elasticity = 330,948 N/mm2?
Carbide Modulus of elasticity = 80,000,000 psi
Carbide Modulus of elasticity = 551,581 N/mm2??
Note: The stated values are specific to JDBµç×Ó boring bars.
I = Moment of inertia for the boring bar cross-sectional area
Moment of Inertia for a solid cylindrical bar = ¦Ð ¡Á DOD4 ¡Â 64
Moment of Inertia for a hollow cylindrical bar = ¦Ð ¡Á (DOD4 - DID4) ¡Â 64
To use the boring bar deflection formula you must calculate the required cutting force (F), measure the boring bar¡¯s overhang (L), select the correct modulus of elasticity for the boring bar (E), and calculate the moment of inertia for the boring bar¡¯s cross-sectional area (I). Once those items are input into the formula the resulting outcome will be the amount of deflection (given as a distance).?
If the resulting deflection is unacceptable; recalculate using a boring bar with a greater modulus of elasticity or a boring bar with a larger moment of inertia.?
Deflection should be minimized but balanced against what is possible, based on the intended boring operation (depth and width).?