Abrasive Formulas
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Approximate specific Energy Requirements for Surface Grinding. Work piece Material Aluminum Cast iron (class 40) Low carbon steel(1020) Titanium Tool steel(TIS)
Hardness 150 HB 215 HB 110 HB
Specific Energy w.s/mm3 hp.min/in3 7-27 2.5-10 12-60 4.5-22 14-68 5-25
300 HB 67 HRC
16-55 18-82
6-20 6.5-30
Example: Calculation of forces in surface grinding Assume that you are performing a surface grinding operation on a low-carbon steel with a wheel of diameter D =10 in. and rotating at N=4000rpm and a width of cut w=1in. depth of cut d=0.002 in. and the feed rate v of the work piece is 60 in. /min. Calculate the running force (force tangential to the wheel) Fc and the thrust force Fn (normal to the work piece surface) Solution: We first determine the MRR, as follows: MRR=dwv= (0.0020(1)(60)=0.12 in3 /min The Power assumed is given by Power = u (MRR) For the low-carbon steel, let us estimate it to be 15hp.min/in3. Hence, Power= (15)(0.12)= 1.8 hp By noting that 1 hp=33000 ft.lb/min=39600 in. lb/min, we obtain Power = (1.8)(396000)= 712 800 in.lb/min Since power is defined as Power = Tw ; where T is the torque and is equal to T=(Fc)(D/2) and w is the rotational speed of the wheel in radians per minute, hence w=2 . 712800= Fc (10/2)(2)( )(4000) and therefore, Fc=57 lb The thrust force Fn can be calculated by noting from experimental data in the technical literature that it is about 30% higher than the cutting force Fc , consequently
Fn= (1.3)(57)=74 lb
Surface Grinding Undeformed chip length l
l=
;
where D= diameter d= depth (wheel depth of cut)
Undeforned chip thickness t
t=
where
;
V= tangential velocity v= velocity C= number of cutting points (per unit area) r= ratio of chip width to average undeformed thickness
Grain Force (Tangential force on the wheel)
Grain Force
(
) strength of the material
Forces in the Surface Grinding MRR= dwv ; where w=width d= depth of cut v= feed rate of workpiece Power= u (MRR); where u=specific energy
Power = Tw ; where T= (Fc)(D/2) w=2 Surface Temperature Temperature rise
Grinding Ratio G=
D1/4 d3/4 ( )1/2
Hardness 150 HB 215 HB 110 HB
Specific Energy w.s/mm3 hp.min/in3 7-27 2.5-10 12-60 4.5-22 14-68 5-25
300 HB 67 HRC
16-55 18-82
6-20 6.5-30
Example: Calculation of forces in surface grinding Assume that you are performing a surface grinding operation on a low-carbon steel with a wheel of diameter D =10 in. and rotating at N=4000rpm and a width of cut w=1in. depth of cut d=0.002 in. and the feed rate v of the work piece is 60 in. /min. Calculate the running force (force tangential to the wheel) Fc and the thrust force Fn (normal to the work piece surface) Solution: We first determine the MRR, as follows: MRR=dwv= (0.0020(1)(60)=0.12 in3 /min The Power assumed is given by Power = u (MRR) For the low-carbon steel, let us estimate it to be 15hp.min/in3. Hence, Power= (15)(0.12)= 1.8 hp By noting that 1 hp=33000 ft.lb/min=39600 in. lb/min, we obtain Power = (1.8)(396000)= 712 800 in.lb/min Since power is defined as Power = Tw ; where T is the torque and is equal to T=(Fc)(D/2) and w is the rotational speed of the wheel in radians per minute, hence w=2 . 712800= Fc (10/2)(2)( )(4000) and therefore, Fc=57 lb The thrust force Fn can be calculated by noting from experimental data in the technical literature that it is about 30% higher than the cutting force Fc , consequently
Fn= (1.3)(57)=74 lb
Surface Grinding Undeformed chip length l
l=
;
where D= diameter d= depth (wheel depth of cut)
Undeforned chip thickness t
t=
where
;
V= tangential velocity v= velocity C= number of cutting points (per unit area) r= ratio of chip width to average undeformed thickness
Grain Force (Tangential force on the wheel)
Grain Force
(
) strength of the material
Forces in the Surface Grinding MRR= dwv ; where w=width d= depth of cut v= feed rate of workpiece Power= u (MRR); where u=specific energy
Power = Tw ; where T= (Fc)(D/2) w=2 Surface Temperature Temperature rise
Grinding Ratio G=
D1/4 d3/4 ( )1/2
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