Transcript Tool Cutting Force Estimates - The Web Page for Roger Cortesi

Tool Stiffness & Displacement
Calculations
By: Roger Cortesi
[email protected]
http://pergatory.mit.edu/rcortesi/
Precision Engineering Research Group
Massachusetts Institute of Technology, Mechanical Engineering Department
Room 3-470
77 Massachusetts Ave.
Cambridge, MA 02139
Phone: (617) 253-1953
Fax: (617) 258-6427
http://pergatory.mit.edu/
Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.
Tool Cutting Force Estimates
P   2 20 0W
R at ed Spindle Power
 power  0 .05
Perc ent of Tot al Spindle Power on Final Pass
   4 50 00RP M
Spindle Speed
Fcut( D)    power
2 P
D 
W here D is the Tool D iam et er
Fcut( 4mm)  1 1.7N
For Example a 4mm Tool has a c ut ting f orc e of
Fcut( 4mm)  2 .6l bf
Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.
Cutting Force Calculations
Too l D iamet er vs. Cu tt in g Fo rce
100
Cutting Force (Newtons )
80
60
40
20
0
0.002
0.004
0.006
Tool Diameter (m)
0.008
For P, , and  listed on the previous slide
Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.
Tool Deflection Calculation
Given These Cutti ng Forces wh at wil l be the Tool Tip D eflection and Tool Si ffness?
Etool   3 00G P a Y oungs Modulus of a C arbide Tool
4
Icyl( D)  
D
C ross Sect ional Momm ent of Inert ia of a Solid Cy linder t hat is the tool diameter
64
 inertia   0 .66
Perc ent inertia of a t ool compaired t o a solid c y linder of t he same diameter
L( D)   4 D
As sume that the tool is protruding 4 Diamet ers f rom the t ool holder
tool( D)  
Fcut( D)  L( D)
3
3 Etool  inertia Icyl( D)
This allows us t o writ e an ex pres sion f or the def lect ion
of t he t ool as a f unc tion it s diameter.
 ( 4mm)  2 0.1m
For Example the 4 mm tool in a spindle wit h t he tool
abov e propert ies would hav e a def lect ion of :
4
tool( 4mm)  7 .9  1 0 i n
Fcut( D)
The s tif f nes s of t he Ktool( D)  
tool( D)
t ool is giv en by
Ktool( 4mm)  0 .6
N
m
l bf
Ktool( 4mm)  3 31 2.3
in
Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.
Tool Tip Deflection (m)
Tool Deflection Plot
2 1 0
4
1.751 0
4
1.5 1 0
4
1.251 0
4
1 1 0
4
7.5 1 0
5
5 1 0
5
2.5 1 0
5
0
0.002
0.004
0.006
Tool Diameter (m)
0.008
Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.
A FEA Check of the Inertia Estimate
This FEA indicates that the tool has about 33% the cross
sectional inertia of a solid rod the same diameter
Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.