Machinery's Handbook, 31st Edition
2180
Thread Cutting
lead of thread
lead of thread
tan
tan
φ
=
φ
′
=
K
D
π
π
a a a a ′
e = + = − e
φ φ
′
2 1
tan tan cos tan tan cos tan tan b a b a n a 2 2 1 ′ ′ = = = −
ω
2 1
ω
tan tan
a
′
ω
where θ = helix angle of thread at minor diameter θ ′ = helix angle of thread at major diameter
K = minor diameter of thread D = major diameter of thread
a = side relief angle parallel to thread axis at leading edge of tool a ′ = side relief angle parallel to thread axis at trailing edge of tool a e = effective relief angle b = side relief angle perpendicular to leading edge of tool b ′ = side relief angle perpendicular to trailing edge of tool ω = included angle of thread cutting tool n = nose angle resulting from intersection of flank surfaces
Example: Calculate the relief angles and the nose angle n for a single-point thread cutting tool that is to be used to cut a 1-inch diameter, 5-threads-per-inch, double Acme thread. The lead of this thread is 2 × 0.200 = 0.400 inch. The included angle ω of this thread is 29 degrees, the minor diameter K is 0.780 inch, and the effective relief angle a e below all cutting edges is to be 10 degrees.
. 927 9 16 K lead of thread D lead of thread ° ° ′ ^ π π h
. 0400
tan
= =
=
φ
. 0780
π
×
φ
. 0400
tan
=
=
φ φ
′ ′
. 1000
π
×
. 726 7 15 ° ° ′ = = + = + ′ = − = − φ φ ^ h
. 10 927 1927 10 726 274 . . . ° ° ° ° ° = =
a a a a b ′
°
e e
2 1
. 1927 145 . cos
tan tan cos a =
tan
=
ω
. 1870 18 42 2 1 ω
b
h
° ° ′ ^
=
. tan cos
. 274 145
tan tan cos b a ′ ′ =
=
. 265 2 39 2 2 1 tan tan tan a ω − ° ° ′ ^
b
h
= =
′
. 1927
. 274
tan
tan
a
−
′
tan
n
=
. 2 145 tan
. 3026 30 16 ° ° ′ ^
n
h
=
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