CUTTING FLUIDS IN MICROMACHINING Machinery's Handbook, 31st Edition
1183
where x pn , y pn = coordinates of a microdroplet from the nozzle α = 3 m D D, m = diameter and mass of a droplet t = time V f = velocity of boundary air layer
V 0 = velocity of a microdroplet when leaving the mist nozzle m = viscosity b = angle between microdroplet velocity and the x-axis
The distance y pn away from a nozzle will reach a steady state value ( a / m ) V 0 sin b after a long time ( t → ∞ ). This means if a tool and nozzle distance is closer than this steady state value, then the microdroplets will reach the tool surface. Force Balancing of Microdroplets on a Rotating Tool: After reaching the tool surface, a microdroplet on a rotating tool is subject to adhesion force along lubricant/solid interface and centrifugal force. The work of adhesion is given by Young-Dupre equation: (18a) where σ L = surface tension of lubricant/air σ S = surface tension of solid/air σ SL = surface tension of solid/lubricant W a = work of adhesion between solid/lubricant q = contact angle If the adhesion force from surface tension is greater than centrifugal force, then the microdroplet will adhere and spread on the tool surface. Otherwise, the droplet will be separated from the rotating tool due to a higher centrifugal force. The condition for a microdroplet to adhere to the rotating cutting tool is given in Equation (18b) and plotted with tool surface speed and microdroplet size as two independent variables. (18b) where σ L = surface tension of lubricant/air (N/m) θ = contact angle (º) m = mass of microdroplet (kg) V c = cutting tool surface speed (m/s) P = projected drop size (m) D t = tool diameter (m) The plot in Fig. 25 is for CL2210EP lubricant and uncoated carbide tool with Ø1 mm flute diameter. The curve divides the plot into two regions: the upper region where adhe sion is dominating, and the lower region where centrifugal force is stronger, i.e., a micro droplet is propelled radially away and does not wet the tool. With the droplet size of 1–10 m m for all lubricants in this study, the adhesion force is dominating and a micro droplet should adhere to the rotating tool at any rotating speed of the tested machine (0–50,000 rpm or 0–150 m/min for a Ø1 mm tool). Wetting of CL2210EP microdroplets on carbide tools was also experimentally verified. cos D mV P 2 1 t c L 2 # i + σ ^ h cos W 1 a S L SL = + − = + ^ σ σ σ L σ h i
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online