Answered: The wear resistance of a steel gear is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The wear resistance of a steel gear is to be improved by hardening its surface. This is to
be accomplished by increasing the carbon content within an outer surface layer as a result of
carbon diffusion into the steel; the carbon is to be supplied from an external carbon-rich gaseous
atmosphere at an elevated and constant temperature. The initial carbon content of the steel is
0.20 wt%, whereas the surface concentration is to be maintained at 1.00 wt%. For this treatment
to be effective, a carbon content of 0.60 wt% must be established at a position 0.75 mm below
the surface.
Specify an appropriate heat treatment in terms of temperature and time for temperatures
between 900 0C and 1050 0C (you may select any 3 temperatures). For the diffusion of carbon
in steel, D0 = 2.3 x 10-5 m2

/s, Q = 148 kJ/mol. (The error function values are given below)

Q13. The wear resistance of a steel gear is to be improved by hardening its surface. This is to
be accomplished by increasing the carbon content within an outer surface layer as a result of
carbon diffusion into the steel; the carbon is to be supplied from an external carbon-rich gaseous
atmosphere at an elevated and constant temperature. The initial carbon content of the steel is
0.20 wt%, whereas the surface concentration is to be maintained at 1.00 wt%. For this treatment
to be effective, a carbon content of 0.60 wt% must be established at a position 0.75 mm below
the surface.
Specify an appropriate heat treatment in terms of temperature and time for temperatures
between 900 °C and 1050 °C (you may select any 3 temperatures). For the diffusion of carbon
in steel, Do = 2.3 x 10$ m²/s, Q = 148 kJ/mol. (The error function values are given below)
erf(z)
erf(z)
erf(z)
0.55
0.5633
1.3
0.9340
0.025
0.0282
0.60
0.6039
1.4
0.9523
0.05
0.0564
0.65
0.6420
1.5
0.9661
0.10
0.1125
0.70
0.6778
1.6
0.9763
0.15
0.7112
0.7421
0.1680
0.75
1.7
0.9838
0.20
0.2227
0.80
1.8
0.9891
0.25
0.2763
0.85
0.7707
1.9
0.9928
0.30
0.3286
0.90
0.7970
2.0
0.9953
0.35
0.3794
0.95
0.8209
2.2
0.9981
0.40
0.4284
1.0
0.8427
2.4
0.9993
0.8802
0.9103
0.45
0.4755
1.1
2.6
0.9998
0.50
0.5205
1.2
2.8
0.9999

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