Basic calculation formula of steel
The conversion formula among Rockwell hardness, Brinell hardness, Vickers hardness and Knoop hardness
Knoop hardness→Vickers hardness
The maximum relative conversion error of the formula is 0.75% verified by actual data, which has high reference value.
Rockwell hardness → Vickers hardness
The formula is converted by the standard hardness data of ferrous metals published in China, and the error of HRC is basically less than 0 ± In the range of 0.4 HRC, the maximum error is only 0.5% ± 9 HRC, the maximum error of HV is 0 ± 15HV.
According to the stress of different indenters σ HRC= σ Through the analysis of the relationship between Rockwell hardness and Vickers hardness indentation depth, the formula is obtained:
This formula is compared with the national standard experimental conversion value, and the error between the calculation result of the conversion formula and the standard experimental value is ± 0.1HRC.
Rockwell hardness → Brinell hardness
The relationship between the depth of Brinell indentation and Rockwell indentation is analyzed σ HRC= σ HB obtains the conversion formula:
The calculated results are compared with the national standard experimental values, and the error between the calculated results and the standard experimental values is 0 ± 0.1HRC.
Brinell hardness → Vickers hardness
The relationship between Brinell hardness and Vickers hardness is also based on“ σ HB= σ HV “to get the formula:
The conversion result of this formula is compared with the national standard conversion value, and the conversion error is ± 2HV.
Knoop hardness → Rockwell hardness
Because the corresponding curve of Knoop hardness and Rockwell hardness is similar to parabola, the approximate conversion formula obtained from the curve is:
This formula is more accurate and can be used as a reference.
Common calculation formula of continuous casting
Pouring capacity: the amount of molten steel poured by the caster per minute 

Q=nFVr 

Q 
Casting capacity of continuous caster (T / min). 
n 
Stream number 
F 
Sectional area of continuous casting slab (M2).^{} 
V 
Drawing speed (M/min). 
r 
Proportion of continuous casting billet. 
Billet yield of molten steel 
C_{1}=（Quantity of casting billet / quantity of liquid steel casting) × 100% Generally 9698% 
Pass rate of continuous casting slab 
C_{2}=(qualified billet quantity / casting billet quantity) × 100% Generally 9699% 
Daily effective operation rate of continuous casting slab 
C_{3}=(daily actual casting time of continuous caster / 24) × 100% 
Daily output of continuous caster 

Q_{day}=24×60×Q×C1×C2×C3 

Q 
Pouring capacity (T / min) 
Yield of molten steel 
C_{4}=(qualified billet quantity / molten steel pouring quantity) × 100% 
Flow number of continuous caster 

n=G/(F×V×r×T) 

n 
Flow number of continuous caster. 
G 
Capacity of steel drum (T). 
F 
Sectional area of slab (m^{2}). 
V 
Billet drawing speed (M / min). 
r 
Proportion of continuous casting billet(t/m^{3})(carbon killed steel 7.6, rimmed steel 7.4). 
T 
Allowable pouring time of molten steel in ladle (min). 
The maximum allowable pouring time of liquid steel in the ladle 

T_{max}=[(lgG0.2)/0.3]×f 

T_{max} 
Maximum allowable pouring time of molten steel in ladle (min). 
G 
Capacity of steel bucket (ton). 
f 
The mass coefficient depends on the allowable temperature loss of the ladle. The required steel grade is 10, and the required low steel grade is 12. 
Drawing speed 

V=K×L/F 

V 
Drawing speed (M / min). 
L 
Billet section perimeter (mm). 
F 
Sectional area of slab(mm^{2}). 
K 
velocity coefficient(m×mm/) Square billet 4575, slab 4560, round billet 3545. 
Minimum capacity of tundish 

G_{middlesized and small}=1.3FVrTn 

G_{middlesized and small} 
Minimum capacity of tundish (T). 
F 
Sectional area of slab (m^{2}). 
V 
Drawing speed(m/min). 
r 
Specific gravity of liquid steel(t/m^{3}) Generally 7.0. 
T 
Time required to replace steel barrel (T). 
n 
Stream number 
Mould reverse taper 

εs=（S_{下}S_{上}）/S_{下}×100% 

εs 
Mould reverse taper（%）. 
S_{lower} 
Area of mould bottom opening(mm^{2}). 
S_{upper} 
Mold top area(mm^{2).} 
For rectangular billet and slab caster, the shrinkage of slab in width and thickness direction is different. 

Calculation of mould reverse taper


ε=(L_{lower}L_{upper})/L_{lower}×100% 

ε

Reverse taper of mould side length calculation(%). 
L_{lower} 
The length of the wide or narrow side of the mold bottom opening(mm). 
L_{upper} 
Length of wide or narrow side of mould top(mm). 
Cooling intensity of mould


Q=0.0036Fv 

Q 
Cooling water quantity of mould(m^{3}/h). 
F 
Total area of mould water gap(mm^{2}) Where f = b × D. 
B 
Perimeter of water gap in mould(mm). 
D 
The width of mould water gap section is 45mm. 
v 
The flow rate of cooling water in the water seam, the square billet is taken as 612m/s, and the slab is 3.55m/s. 
Water consumption of secondary cooling section 

Q=W×G 

Q 
Water consumption of secondary cooling zone(m3/h). 
W 
Secondary cooling intensity (L / kg steel) (also known as specific cooling water: the ratio of the cooling water consumed to the mass of the slab passing through the secondary cooling zone.) The specific water content of low carbon steel is 1.01.2 L / kg steel; The specific water content of medium high carbon steel and low alloy steel is 0.71.0 L / kg; Stainless steel, crack sensitive steel, specific water content 0.40.6 L / kg steel; The specific water content of high speed steel is 0.10.3 L / kg steel. 
G 
Theoretical hourly output of continuous caster (t/h). 
Pouring platform temperature (measured temperature of liquid steel in the ladle at the beginning of pouring) 

T_{flat}=T_{tundish}+△T_{1}+△T_{2}+βt 

T_{flat} 
Pouring platform temperature（℃）. 
T_{tundish} 
Theoretical pouring temperature of molten steel in Tundish（℃）. 
△T_{1} 
Initial temperature drop (℃) of molten steel in tundish (related to tundish preheating state, generally 1015 ℃). 
△T_{2} 
Temperature drop of molten steel from ladle to tundish (℃). 
β 
Natural cooling rate in ladle (℃ / min).

t 
Maximum allowable pouring time of molten steel in ladle (min). 
Casting temperature of continuous casting (molten steel temperature in tundish) 

T_{tundish}=T_{melt}+a 

T_{tundish} 
Theoretical pouring temperature of molten steel in tundish (℃). 
T_{melt} 
Melting point of liquid steel (℃). 
T_{melt}=1538℃[88C%+8Si%+5Mn%+30P%+25S%+5Ca%+4Ni%+2Mo%+2V%+1.5Cr%] 

a 
Superheat of liquid steel (℃).

Empirical formula for heat treatment process design of steel
Heat treatment of steel
Normalizing heating time
t=KD 

t 
Heating time 
D 
Effective thickness of workpiece(mm) 
K 
Heating time coefficient(s/mm) 
Empirical data of K value 

Heating equipment 
Heating temperature (℃) 
Carbon steel K/(S/mm) 
Alloy steel K(S/mm) 
Box furnace 
800~950 
50~60 
60~70 
Salt bath furnace 
800~950 
12~25 
20~30 
The normalizing temperature is selected according to the critical point of phase transformation 

Mild steel 
T=Ac3+(100~150℃) 
Medium carbon steel 
T=Ac3+(50~100℃) 
High carbon steel 
T=Ac3+(30~50℃) 
Hypoeutectoid rigidity 
T=Ac3+(30~80℃) 
Eutectoid and hypereutectoid steels 
T=Acm+(30~50℃) 
Quenching heating time
t=a×K×D（Without preheating） 

t=(a+b)×K×D（After one preheating） 

t=(a+b+c)×K×D（After twice preheating） 

t 
Heating time(min) 
a 
Heating coefficient up to quenching temperature(min/mm) 
b 
Heating coefficient reaching preheating temperature(min/mm) 
c 
Heating coefficient reaching the secondary preheating temperature(min/mm) 
K 
Charging correction factor 
D 
Effective thickness of workpiece(mm) 
Under the general heating conditions, when box furnace is used for heating, carbon steel and alloy steel a are mostly 11.5min/mm; B is 1.52min/mm (a = 0.50.3 for high speed steel and alloy steel at one time preheating); b=2.5～3.6； The second preheating a = 0.50.3; b=1.5～2.5； When the furnace temperature is 100 ~ 150 ℃ higher than the quenching temperature, the coefficient a is about 1.5 ~ 20s / mm, and the coefficient B need not be added. If the salt bath is used for heating, the heating time should be 1 / 5 (preheated) to 1 / 3 (not preheated) less than that in the box furnace.
Workpiece charging correction factor K 

Workpiece charging mode 
Correction factor 
t030111.1 
1.0 
t030111.3 
2.0 
t030111.5 
1.3 
t030111.7 
1.0 
Quenching temperature
Quenching temperature of hypoeutectoid steel 
Ac3+(30~50℃) 
Eutectoid and hypereutectoid steels 
Ac1+(30~50℃) 
Quenching heating temperature of alloy steel 
Ac1（or Ac3）+(50~100℃) 
For the workpiece tempered at medium or high temperature, tempering time refers to the time for uniform through burning: t=aD+b 

t 
Tempering holding time(min) 
D 
Effective size of workpiece(mm) 
a 
Heating coefficient(min/mm) 
b 
Additional time, usually10~20min 
The heating coefficient of salt bath is 0.5 ~ 0.8 min / mm;

Tempering heating temperature
T=200+k(60x) 

x 
Hardness value after tempering(HRC) 
k 
Undetermined coefficient, for 45 steel, x > 30, k = 11 
A large number of tests show that when the tempering parameter p of steel is constant, the technological effect of tempering hardness or mechanical properties are the same. Therefore, according to the traditional empirical formula, the tempering parameters can only be used in the standard state (tempering for 1 h), and the actual production application is limited.
In order to solve the above problems, the related factors are expressed quantitatively.
(1) In the range of 200 ~ 400 ℃: HV=640(T20)×1.05+(lgt1.28)×366+(T200)(lgt1.28)×0.036 

(2) In the range of 400 ~ 600 ℃: HV=17.2×10^{3}/T(lgt1.28)×29.4(T400)(lgt1.28)×0.023 

T 
Tempering temperature (℃) 
t 
Tempering time min 
It can be seen from the comparison that the main factors affecting the tempering effect are that T and t can better reflect the influence of actual process parameters, and quantitatively express the variation characteristics of tempering hardness in different temperature ranges.
Calculation of quenching cooling time of steel
Air precooling time of steel during precooling and quenching ty(s) 

ty=12+(3~4)D 

D 
Dangerous section thickness of quenched workpiece (mm) 
Step cooling time of steel at MS point tf(s) 

tf=30+5D 
Calculation of quenching hardness of steel
The hardness of each point in the range of 4 ~ 40mm from the top of the sample is H4 ~ 40 (HRC) during the steel terminal quenching test. 

H_{4~40}=88C^{1/2}0.0135E^{2}C^{1/2}+19Cr^{1/2}+6.3Ni^{1/2}+16Mn^{1/2}+35Mo^{1/2}+5Si^{1/2}0.82G20E^{1/2}+2.11E2 

E 
Distance to top (mm) 
G 
Austenite grain size 
The highest quench hardness of steel, that is, the hardness HH (HRC) of quenched steel when 90% martensite is obtained. 

Hh=30+50C 

The critical quenching hardness of steel is the hardness H1 (HRC) when 50% martensite is obtained. 

H1=24+40C 

Hardness HVM of steel with martensite as quenched structure. 

HVM=127+949C+27Si+11Mn+8Ni+16Cr+21logvM 

Hardness HVB of steel with Bainite as quenched structure. 

HVB=323+185C+330Si+153Mn+65Ni+144Cr+191Mo+logv B(89+54C55Si22Mn10Ni20Cr33Mo) 

The quenched microstructure of steel is pearlite ferrite hardness HVPF. 

HVPF=42+223C+53Si+30Mn+13Ni+7Cr+19Mo+logv PF(1019Si+4Ni+8Cr+130V) 
Calculation of hardness of tempered steel
Tempering hardness HVM of steel with martensite as quenched structure 

HVM=74434C368Si+15Mn+37Ni+17Cr335Mo2235V+(10^{3}/PB)(260+616C+321Si21Mn35Ni11Cr+352Mo2345V) 

PB 
Tempering parameters (tempering temperature) × The heating time here is 1 h. 
Tempering hardness HVB when the steel is bainite. 

HVB=262+162C349Si64Mn6Ni186Cr485Mo857+(10^{3}/PB)(149+43C+336Si+79Mn+16Ni+196Cr+498Mo+1094V) 

Regression equation of hardness of tempered steel. 

HRC=75.50.094T+0.66CM 

T 
Tempering temperature (℃) 
CM 
Carbon content or carbon equivalent of steel (%) 
CM=C+Mn/6+(Cr+Mo+V)/5+(Ni+Cu)/15 

Regression equation of hardness of 45 steel after tempering. 

HV=640(T200)1.05(logt1.28)36.6+(T200)(logt1.28)0.0036 20≤T≤400 

HV=17.2×10^{4}/T(logt1.28)29.4(T400)(logt1.28)0.014 400≤T≤600 

t 
Tempering time (min) 
Estimation of tempering temperature of steel (for carbon steel)
T=200+k(60x) 

x 
Hardness value after tempering (HRC) 
k 
For 45 steel, x > 30, k = 11; x≤30,k=12 
Estimating mechanical properties from chemical composition of steel
Yield ratio (yield limit) σ S/ tensile strength σ b）
Quenching and tempering of oil σs/ σb(%) 
σs/σb=55+3Si+4Mn+8Cr+10Mo+3Ni+20V Si≤1.8%,Mn≤1.1%,Cr≤1.8%,Mo≤0.5%,Ni≤5%,V≤0.25% The applicable diameter of the material is φ 150~200mm. 
Air quenched and tempered steel σs/σb(%). 
σs/σb=48+3Si+4Mn+8Cr+10Mn+3Ni+20V 
Seeking tensile strength σb(9.8 × MPa)
Quenched and tempered steel 

σb=100C100(C0.40)/3+100Si/10+100Mo/4+30Mn+6Ni+2W+60V Apply C≤0.9%,Si≤1.8%,Mn≤1.1%,Cr≤1.8%,Ni≤5%,V≤2% 

Normal and annealed steel 

σb =20+100C_{M} 

Hot rolled steel 

σb=27+56C_{M} 

Forged steel 

σb=27+50C_{M} 

Cast iron 

σb=27+48C_{M} 

C_{M} 
Carbon equivalent of steel 
C_{M}=[1+0.5(C0.20)]C+0.15Si+[0.125+0.25(C+0.20)Mn]+[1.250.5(C0.20)]P+0.20Cr+0.10Ni 
Angle bar = side length * side thickness * 0.015 
Welded pipe / seamless steel pipe = (outer diameter wall thickness) × wall thickness × 0.02466 
Square tube = side length × four × 00785 = perimeter / 3.14 
Rectangular tube = (L + W) × two × wall thickness×0.00785 
Flat bar = width * wall thickness*0.00785 
Galvanized flat steel = width × wall thickness×0.00785×1.06 
Sheet = length × width × thickness×0.00785 
Pattern plate = [thickness] × 0.0785+0.3] × Length * width 
Hexagon = opposite side × Opposite distance×0.0065 
Octagonal steel = opposite side × Opposite distance×0.0065 
Stainless steel plate = length × width × thickness×7.93 
Round bar weight (kg) = 0.00617 × diameter × diameter × length 
Square bar weight (kg) = 0.00785 × Side width × Side width × length 
Weight of hexagonal angle bar (kg) = 0.0068 × Opposite side width × Opposite side width × length 
Octagonal bar weight (kg) = 0.0065 × Opposite side width × Opposite side width × length 
Rebar weight (kg) = 0.00617 × Calculated diameter × Calculated diameter × length 
Weight of angle bar (kg) = 0.00785 ×（ Edge width + edge width – edge thickness) × Edge thickness × length 
Weight of flat bar (kg) = 0.00785 × thickness × Side width × length 
Steel pipe weight (kg) = 0.02466 × wall thickness ×（ Outer diameter – wall thickness) × length 
Calculation of volume of hexahedron
Formula s20.866 × H/m/k is opposite side × Opposite side × zero point eight six six × Height or thickness
Weight conversion formula of various steel pipes (materials)
Weight of steel pipe = 0.25 ×π×( Outer diameter square – inner diameter Square) × L × Proportion of steel.
Among them: π = 14, l = length of steel pipe, specific gravity of steel is 7.8.
So, the weight of the steel pipe is 0.25 × three point one four ×( Outer diameter square – inner diameter. Square) × L × seven point eight.
*If the dimension unit is meter (m), the weight result is kilogram (kg).
Density of steel: 7.85g/cm3 (Note: unit conversion).
The unit of measurement for calculating the theoretical weight of steel is kilogram (kg).
The basic formula is as follows:
 W (weight, kg) = f (sectional area, mm2) × L (length, m) ×ρ( Density, g / cm3) × 1/1000.
Common data 

1 meter (m) = 3.281 feet 
1 inch = 25.4 mm 
1 lb = 0.4536 kg 
1 oz = 28.3 G 
1kg force = 9.81n 
1 LBF = 4.45 n 
1 MPa = 145.161 lb / in 
Specific gravity (density) of steel: 7.8g/cm 
Specific gravity (density) of stainless steel: 7.78g/cm 
Zinc specific gravity (density): 7.05g/cm 
Specific gravity (density) of aluminum: 2.7g/cm 
Source: China Flange Manufacturer – Yaang Pipe Industry (www.steeljrv.com)
(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)
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