TEMPERATURES IN METAL CUTTING Chapter 3 TEMPERATURES IN METAL CUTTING Prof. Dr. S. Engin KILIÇ

Heat sources in metal cutting Primary shear zone (A-B) plastic deformation Secondary shear zone (C-B) friction Between tool and workpiece (D-B) plowing force (negligible)

High temperatures during cutting - shortens tool life - causes thermal distortion - causes dimensional changes in the workpiece, making control of dimensional accuracy difficult

Heat generation in metal cutting Energy consumption (or heat generated) during machining Pm : Pm = Fc v Fc : cutting force V : cutting speed Pm = Ps + Pf Ps : heat generated in primary shear zone Pf : heat generated in secondary shear zone Pf = Ff v0 Ff : friction force V0 : velocity of chip flow METU / ME535 / CH-3 / SPRING’01

Heat transfer in a moving material Element ABCD has unit thickness through which material flows in x direction Point A (x,y) has an inst. temp θ Heat transferred accross boundaries AB and CD by conduction (temp. gradient in x) and by transportation (flow of heated body across boundaries) Heat transfer accross BC and AD only by conduction (no material flow) Net heat flow into element is nill (no heating within element)

Heat transfer in a moving material Heat transfer across AB Heat transfer across CD Heat transfer across AD Heat transfer across BC

QAB + QAD = QCD + QBC Heat transfer in a moving material R : thermal number= v : cutting speed, m/s : undeformed chip thickness, m r : density of work material, kg/m3 k : thermal conductivity, J/smK c : specific heat capacity, J/kgK Therefore; (in metal cutting)

Heat transfer in a moving material x X=0 -x θ=θs v Heat source P Unit thickness Temperature distribution Temperature distribution in a fast-moving material for a one-dimensional case, where

Temperature distribution in metal cutting Temperature distribution in workpiece and tool during orthogonal cutting (V=2.5m/s , HSS tool)

Pm = Qc + Qw + Qt Temperature distribution in metal cutting Heat generated during cutting is distributed among chip, workpiece and tool Pm = Qc + Qw + Qt Pm : total rate of heat generation Qc : rate of heat transportation by the chip Qw : rate of heat conduction into the workpiece Qt : rate of heat conduction into the tool

Temperature distribution in metal cutting Qt has usually very small proportion in Pm . Except for very low cutting speeds, it may be neglected. The maximum temperature in the tool/chip interface area is almost in the middle of the tool/chip contact length. Particular temperature distribution depends on specific heat and thermal conductivity of tool - work pair materials, cutting conditions such as cutting speed, feed, depth of cut and type of cutting fluid.

Temperatures in the primary shear zone energy generated energy carried away volume flow

Temperatures in the primary shear zone Or, where Ps : heat generation in primary shear zone Γ : portion of Ps which is conducted to the workpiece, so, this portion will not cause temperature increase in chip θs : average temperature rise in primary shear zone c : specific heat ρ : density v : cutting speed ac : undeformed chip thickness aw : depth of cut METU / ME535 / CH-3 / SPRING’01

Temperatures in the primary shear zone The idealized model of the cutting process defined by Weiner and Rapier: Assumptions: Primary deformation zone is a plane heat source of uniform strength No heat loss from free surfaces of workpiece and chip Thermal properties of work material are constant and independent of temperature No heat is conducted in the material in the direction of its motion METU / ME535 / CH-3 / SPRING’01

Temperatures in the primary shear zone Simplified heat transfer equation became: The following figure shows the theoretical solution of Weiner and experimental work of Nakayama for expressing the relationship between Γ and RtanΦ. R, thermal number= It can be seen that the theory has slightly underestimated Γ at high values of Rtanφ (i.e., at high speeds and high feeds) due to the plane heat source assumption which ignored the fact that the resulting heat source extends some distance into the chip due to severe deformation of the chip material. METU / ME535 / CH-3 / SPRING’01

R tanf METU / ME535 / CH-3 / SPRING’01

Temperatures in the secondary shear zone (friction zone) The maximum temperature in the chip occurs where the material leaves the secondary deformation zone (point C in the figure of slide 14 and is given by θmax=θm+ θs + θ0 where θm= temperature rise of the material passing through the secondary shear zone θs= temperature rise of the material passing through the primary shear zone θ0= initial workpiece temperature Rapier assumed that the heat zone resulting from friction between chip and tool is a plane heat source of uniform strength when solving the Equation METU / ME535 / CH-3 / SPRING’01

Temperatures in the secondary shear zone After solving the equation for the given boundary conditions, the following expression was obtained: where θf : average temperature rise in chip due to frictional heating θm : maximum temperature rise in chip due to frictional heating l0 : length of heat source divided by the chip thickness (lf/a0) This result does not agree with the experimental observations. This equation overestimates θm. The reason is that the heat generation does not take place in a plane . The figure in the next slide indicates the effect of variations in the width of the uniformly distributed heat source.

Temperatures in the secondary Deformation zone (friction zone) METU / ME535 / CH-3 / SPRING’01

w0

heat generated in friction zone heat carried away from friction zone Finally, the maximum temperature in chip can be obtained by: θmax = θm + θs + θ0 where θm : maximum temperature rise in chip due to frictional heating θs : average temperature rise in primary shear zone θ0 : initial temperature of the workpiece METU / ME535 / CH-3 / SPRING’01

Example: Find the maximum temperature along the tool face for the following conditions during the orthogonal cutting of mild steel: Normal rake angle gn = 00 Cutting force Fc= 890 N Thrust force Ft= 667 N Cutting speed v = 2m/s Undeformed chip thickness ac= 0.25 mm Width of cut aw= 2.50 mm Cutting ratio rc = 0.3 Contact length between chip and tool lf = 0.75mm METU / ME535 / CH-3 / SPRING’01

gn= 0  Ff= Ft Example (cont.’d): The total heat generation rate: Pm = Fc v = 890x2=1780 J/s The rate of heat generated by friction between the chip and the tool: Pf = Ff v0 = Ff vrc gn= 0  Ff= Ft Hence, Pf = 667x2x0.3=400J/s Ps= Pm- Pf =1780-400=1380J/s It is first needed to find Rtanf in order to estimate the temperature rise from the graph in slide 16. METU / ME535 / CH-3 / SPRING’01

R= rcvac/k = 7200x502x0.00025/43.6=41.5 gn= 0  tanf = rc Example (cont.’d): Assuming that for mild steel: r = 7200 kg/m3 k = 43.6 J/smK c =502 J/kgK R= rcvac/k = 7200x502x0.00025/43.6=41.5 gn= 0  tanf = rc Hence, Rtanf = 41.5x0.3=12.45 G= 0.1 (from the graph in slide 16) METU / ME535 / CH-3 / SPRING’01

Substituting the appropriate values in the following equation: Example (cont.’d): Substituting the appropriate values in the following equation: s = (1-0.1)(1380)/(7200x502x2x0.00025x0.0025) s = 275 K  f = (400)/(7200x502x2x0.00025x0.0025) f = 88.5 oC METU / ME535 / CH-3 / SPRING’01

m /f=4.2 (from the graph in slide 20)  m= 4.2x88.5 =372 oC Example (cont.’d): To obtain the ratio m /f , hence m from the graph in slide 20, it is necessary to estimate the values of w0 and R/l0 . w0 is assumed to be 0.2 for mild steel under unlubricated cutting conditions and; Let lf = 0.75mm a0= ac/rc =0.25/0.3  l0= lf /a0 = 0.9 R/ l0=41.5/0.9=46.1 m /f=4.2 (from the graph in slide 20)  m= 4.2x88.5 =372 oC max = m+ s+ 0 =372+275+22=669 oC 0 = 22 oC (assumed room temperature) METU / ME535 / CH-3 / SPRING’01

Effect of cutting speed on temperature If cutting speed increases, heat generation increases. Increase in heat generation causes temperature increase only where the heat transfer does not increase by higher speed, i.e., at tool face. Maximum tool-face temperature s+m T (C) Mean shear-zone temperature s V (m/s)

Measurement of cutting temperature 1. Work Tool Thermocouple Most widely used - Limited since it can not give the temperature distribution on chip-tool interface Calibration is needed for each tool/workpiece combination - Calibration of stationary tool may not give the same values during cutting

Measurement of cutting temperature Work Tool Thermocouple measurement technique

Measurement of cutting temperature 2. Direct Thermocouple Measurements i. Nakayama technique (see figure below) ii. Thermocouple inserted on tool shank to measure insert temperature Nakayama cutting temperature measurement technique

Measurement of cutting temperature 3. Infrared Radiation Suitable for determining of temperature distribution in the cutting zone i. Radiation pyrometer method ii. Infrared photograph of cutting operation iii. Thermal imaging camera, an improved method for infrared radiation 4. Others i. Calorimetric techniques ii. Temperature-sensitive chemicals