I find that the 1/2" lathe bits do little for me. There is 10x as much grinding to achieve the tool shape that I want and my 10 x 22 lathe really can't take advantage of the increased rigidity. For the grooving tool you need, I would probably use a 1/8" bit. My usual choice for HSS lathe bits is 1/4" or 3/8". Looking at my stash of bits, I made a .030" grooving tool by grinding down the side of a parting tool.
I haven't bought lathe bits from CME but have had good luck with other purchases.
SQUARE LENGTH HSS PART NO HSS PRICE COBALT PART NO. 10% COBALT COBALT PRICE 1/4” 5/16” 3/8” 1/2” 5/8” 3/4” 2-1/2” 2-1/2” 3” 4” 4-1/2” 5” HS-2BT-14 HS-2BT-516 HS-2BT-38 HS-2BT-12 HS-2BT-58 HS-2BT-34 $0.85 $1.00 $1.60 $2.95 $5.00 $6.50 HS-CO2B-14 HS-CO2B-516 HS-CO2B-38 HS-CO2B-12 HS-CO2B-58...
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