Machinery's Handbook, 31st Edition
1182 CUTTING FLUIDS IN MICROMACHINING Example 12, Contact Angle Measurement: Set volume V = 0.25 m L on a micropipette and then dispense several droplets of CL2100EP on a clean titanium plate. The average size of the droplets, measured on a toolmaker’s microscope, is P = 2.520 mm. To find wetting capability of this coolant on titanium, it is necessary to calculate its contact angle. Graphical Solution: Using 1 m L= 10 –6 L = 1 mm 3 , the normalized diameter is
. 2520
mm 3
P
. 40
=
=
1 ⁄ 3
1 ⁄ 3
V
mm
. 025
h
^
Starting at point A = 4.0 on the vertical Normalized Diameter ( P / V 1⁄3 ) axis of Fig. 22b, draw a horizontal line until it intersects with the curve at B. Draw a vertical line from point B until it intersects with the Contact Angle axis at C. Read the contact angle ~9° for this oil and titanium. Table Look-up Solution: Locate drop volume of 0.25 m L on the first row of Table 8. Locate projected drop size of 2.52 mm on the first column. Since 2.52 mm is not available, choose the closest number, 2.50 mm. Read the contact angle from the intersection of row and column as 9.3° Example 13, Contact Angle Measurement (continued from Example 11 ): In Example 11, droplets of CL2100EP were collected on a glass plate, the average projected drop size P = 2 m m was measured, and the average drop volume was calculated to be V = 0.49 m m 3 . The information obtained can be used to calculate contact angle. a) The normalized diameter is . . V P 049 2 253 m m 3 µ µ = ^ h 1 ⁄ 3 1 ⁄ 3 = b) Use Fig. 22b with normalized diameter of 2.53, and read the contact angle of ~18°. The same cutting fluid Cl2100EP forms different contact angles of 18° on glass and 9° on titanium. This is due to the different surface energies of glass and titanium. Dynamics of Microdroplets.— Several models are derived to study the dynamics of a microdroplet when it approaches a fast rotating tool. To effectively wet and lubricate a rotating tool, a microdroplet must (i) have enough momentum to penetrate the boundary layer around a fast rotating tool to reach the tool surface, and then (ii) adhere and wet the tool surface despite centrifugal force acting on the microdroplet.
z
σ S σ SL
x
σ L
Micromist nozzle
F c
Air
F a
Micromill
Micromill
Fig. 24a. Propelling of Microdroplets Toward a Rotating Tool. Fig. 24b. Force Balancing of a Microdroplet on the Rotating Tool. Propelling Microdroplets Toward a Rotating Tool: The coordinates of a microdroplet after leaving a nozzle and moving toward a rotating tool can be expressed as
α
cos
V e 1 − h^
h t ⁄ m
x V t m V pn f 0 = + ^
(16) (17)
α −
β
−
f
e 1
sin y m V pn
h t ⁄ m
^
α −
0 = α β −
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