How to Calculate and Solve for Young’s Modulus | Fracture Mechanics

The image above represents young’s modulus.

To compute for young’s modulus, two essential parameters are needed and these parameters are Stress and Strain.

The formula for calculating young’s modulus:

Young’s Modulus = Stress / Strain

Let’s solve an example;
Given that the stress is 12 and the strain is 6. Find the Young’s modulus?

This implies that;

Stress = 12
Strain = 6

Young’s Modulus = Stress / Strain
Young’s Modulus = 12 / 6
Young’s Modulus = 2

Therefore, the young’s modulus is 2.

Calculating the Stress when the Young’s Modulus and the Strain is Given.

stress = young’s modulus x strain

Let’s solve an example;
Find the stress when the young’s modulus is 32 and the strain is 10.

This implies that;

Young’s Modulus = 32
Strain = 10

stress = young’s modulus x strain
stress = 32 x 10
stress = 320

Therefore, the stress is 320.

Continue reading How to Calculate and Solve for Young’s Modulus | Fracture Mechanics

How to Calculate and Solve for Probability of Glass Fracturing | Weibull Statistics | Glass Making Technology

The image above represents probability of glass fracturing.

To compute for probability of glass fracturing, three essential parameters are needed and these parameters are Scaling Factor (σo), Fracture Strength of Glass (σ) and Weibull Distribution Modulus (m).

The formula for calculating probability of glass fracturing:

P = 1 – exp[-(σ / σo)m]

Where:

P = Probability of Glass Fracturing
σo = Scaling Factor
σ = Fracture Strength of Glass
m = Weibull Distribution Modulus

Let’s solve an example;
Find the probability of glass fracturing when the scaling factor is 24, the fracture strength of glass is 10 and the weibull distribution modulus is 8.

This implies that;

σo = Scaling Factor = 24
σ = Fracture Strength of Glass = 10
m = Weibull Distribution Modulus = 8

P = 1 – exp[-(σ / σo)m]
P = 1 – exp [-(10 / 24)8]
P = 1 – exp [-(0.416)8]
P = 1 – exp [-0.0009]
P = 1 – 0.999
P = 0.0009

Therefore, the probability of glass fracturing is 0.0009.

Continue reading How to Calculate and Solve for Probability of Glass Fracturing | Weibull Statistics | Glass Making Technology

How to Calculate and Solve for Batch Calculation Factor | Glass Making Technology

The image above represents batch calculation factor.

To compute for batch calculation factor, two essential parameters are needed and these parameters are Molecular Weight of Raw Material (Mwand Oxide Factor (OF).

The formula for calculating batch calculation factor:

F = Mw / OF

Where:

F = Batch Calculation Factor
Mw = Molecular Weight of Raw Material
OF = Oxide Factor

Let’s solve an example;
Find the batch calculation factor when the molecular weight of raw material is 30 and the oxide factor is 15.

This implies that;

Mw = Molecular Weight of Raw Material = 30
OF = Oxide Factor = 15

F = Mw / OF
F = 30 / 15
F = 2

Therefore, the batch calculation factor is 2.

Calculating the Molecular Weight of Raw Material when the Batch Calculation Factor and the Oxide Factor is Given.

Mw = F x OF

Where;

Mw = Molecular Weight of Raw Material
F = Batch Calculation Factor
OF = Oxide Factor

Let’s solve an example;
Find the molecular weight of raw material when the batch calculation factor is 14 and the oxide factor is 10.

This implies that;

F = Batch Calculation Factor = 14
OF = Oxide Factor = 10

Mw = F x OF
Mw = 14 x 10
Mw = 140

Therefore, the molecular weight of raw material is 140.

Continue reading How to Calculate and Solve for Batch Calculation Factor | Glass Making Technology

How to Calculate and Solve for Metal Removal Rate (for Cylinderical Workpieceturning in a Lathe) | Metal Forming processes

The image above represents metal removal rate.

To compute for metal removal rate, two essential parameters are needed and these parameters are Initial Diameter (D1), Final Diameter (D2), Cutting Force (Normal) (N) and Cutting Force (F).

The formula for calculating metal removal rate:

MRR = π / 4 (D12 – D22)F.N

Where:

MRR = Metal Removal Rate (for Cylinderical Workpiece turning in a Lathe)
D1 = Initial Diameter
D2 = Final Diameter
F = Cutting Force
N = Cutting Force (Normal)

Let’s solve an example;
With an initial diameter of 22, a final diameter of 18, a cutting force of 32 and a cutting force of 12. Find the metal removal rate?

This implies that;

D1 = Initial Diameter = 22
D2 = Final Diameter = 18
F = Cutting Force = 32
N = Cutting Force (Normal) = 12

MRR = π / 4 (D12 – D22)F.N
MRR = π / 4 (222 – 182) x 12 x 32
MRR = 0.78 x (484 – 324) x 384
MRR = 0.78 x 160 x 384
MRR = 48254.8

Therefore, the metal removal rate is 48254.8.

Continue reading How to Calculate and Solve for Metal Removal Rate (for Cylinderical Workpieceturning in a Lathe) | Metal Forming processes

How to Calculate and Solve for Metal Removal Rate (for Single Point tools) | Metal Forming processes

The image above represents metal removal rate.

To compute for metal removal rate, two essential parameters are needed and these parameters are Cross – Sectional Area of Uncut Chip (Acand Cutting Velocity (v).

The formula for calculating metal removal rate:

MRR = 1000 x Ac x v

Where:

MRR = Metal Removal Rate (for Single Point tools)
Ac = Cross – Sectional Area of Uncut Chip
v = Cutting Velocity

Let’s solve an example;
Find the metal removal rate when the cross-sectional area of uncut chip is 20 and the cutting velocity is 10.

This implies that;

Ac = Cross – Sectional Area of Uncut Chip = 20
v = Cutting Velocity = 10

MRR = 1000 x Ac x v
MRR = 1000 x 20 x 10
MRR = 200000

Therefore, the metal removal rate is 200000.

Calculating the Cross-Sectional Area of Uncut Chip when the Metal Removal Rate and the Cutting Velocity is Given.

Ac = MRR / 1000 x v

Where;

Ac = Cross – Sectional Area of Uncut Chip
MRR = Metal Removal Rate (for Single Point tools)
v = Cutting Velocity

Let’s solve an example;
Find the cross-sectional area of uncut chip when the metal removal rate is 400 and the cutting velocity is 2.

This implies that;

MRR = Metal Removal Rate (for Single Point tools) = 400
v = Cutting Velocity = 2

Ac = MRR / 1000 x v
Ac = 400 / 1000 x 2
Ac = 400 / 2000
Ac = 0.2

Therefore, the cross-sectional area of uncut chip is 0.2.

Continue reading How to Calculate and Solve for Metal Removal Rate (for Single Point tools) | Metal Forming processes

How to Calculate and Solve for Cutting Force | Metal Forming processes

The image above represents cutting force.

To compute for cutting force, seven essential parameters are needed and these parameters are Depth of Cut (d), Feed (f), Cutting Velocity (v), Dependent Value on the Work Piece Material (C), Dependent Value on the Work Piece Material (x), Dependent Value on the Work Piece Material (y) and Dependent Value on the Work Piece Material (n).

The formula for calculating cutting force:

Fc = C.dx.fy.vn

Where:

Fc = Cutting Force
d = Depth of Cut
f = Feed
v = Cutting Velocity
C = Dependent Value on the Work Piece Material
x = Dependent Value on the Work Piece Material
y = Dependent Value on the Work Piece Material
n = Dependent Value on the Work Piece Material

Let’s solve an example;
Find the cutting force when the depth of cut is 12, the feed is 15, the cutting velocity is 18, the dependent value on the work piece material is 10, the dependent value on the work piece material is 6, the dependent value on the work piece material is 3 and the dependent value on the work piece material is 21.

This implies that;

d = Depth of Cut = 12
f = Feed = 15
v = Cutting Velocity = 18
C = Dependent Value on the Work Piece Material = 10
x = Dependent Value on the Work Piece Material = 6
y = Dependent Value on the Work Piece Material = 3
n = Dependent Value on the Work Piece Material = 21

Fc = C.dx.fy.vn
Fc = 10 x 126 x 153 x 1821
Fc = 10 x 2985984 x 3375 x 2.29e+26
Fc = 2.31

Therefore, the cutting force is 2.31e+37 N.

Continue reading How to Calculate and Solve for Cutting Force | Metal Forming processes

How to Calculate and Solve for Power Consumed during Metal Cutting | Metal Forming processes

The image above represents power consumed during metal cutting.

To compute for power consumed during metal cutting, two essential parameters are needed and these parameters are Cutting Force (Fcand Work Piece Velocity (v).

The formula for calculating power consumed during metal cutting:

Pc = Fc.v / 1000

Where:

Pc = Power Consumed during Metal Cutting
Fc = Cutting Force
v = Work Piece Velocity

Let’s solve an example;
Find the power consumed during metal cutting when the cutting force is 32 and the work piece velocity is 12.

This implies that;

Fc = Cutting Force = 32
v = Work Piece Velocity = 12

Pc = Fc.v / 1000
Pc = 32 x 12 / 1000
Pc = 384 / 1000
Pc = 0.384

Therefore, the power consumed during metal cutting is 0.384 KW.

Calculating the Cutting Force when the Power Consumed During Metal Cutting and the Work Piece Velocity is Given.

Fc = Pc x 1000 / v

Where;

Fc = Cutting Force
Pc = Power Consumed during Metal Cutting
v = Work Piece Velocity

Let’s solve an example;
Find the cutting force when the power consumed during metal cutting is 20 and the work piece velocity is 16.

This implies that;

Pc = Power Consumed during Metal Cutting = 20
v = Work Piece Velocity = 16

Fc = Pc x 1000 / v
Fc = 20 x 1000 / 10
Fc = 20000 / 10
Fc = 2000

Therefore, the cutting force is 2000.

Continue reading How to Calculate and Solve for Power Consumed during Metal Cutting | Metal Forming processes

How to Calculate and Solve for Work Piece Velocity | Metal Forming processes

The image above represents work piece velocity.

To compute for work piece velocity, two essential parameters are needed and these parameters are Diameter of Job or Tool (D) and Velocity of Job or Tool (N).

The formula for calculating work piece velocity:

v = πDN / 1000 x 60

Where:

v = Work Piece Velocity
D = Diameter of Job or Tool
N = Velocity of Job or Tool

Let’s solve an example;
Find the work piece velocity when the diameter of job or tool is 21 and the velocity of job or tool is 7.

This implies that;

D = Diameter of Job or Tool = 21
N = Velocity of Job or Tool = 7

v = πDN / 1000 x 60
v = π x 21 x 7 / 1000 x 60
v = 461.814 / 60000
v = 0.0076

Therefore, the work piece velocity is 0.0076 m/s.

Calculating the Diameter of Job or Tool when the Work Piece Velocity and the Velocity of Job or Tool is Given.

D = v (1000 x 60) / πN

Where;

D = Diameter of Job or Tool
v = Work Piece Velocity
N = Velocity of Job or Tool

Let’s solve an example;
Find the diameter of job or tool when the work piece velocity is 20 and the velocity of job or tool is 15.

This implies that;

v = Work Piece Velocity = 20
N = Velocity of Job or Tool = 15

D = v (1000 x 60) / πN
D = 20 (1000 x 60) / π x 15
D = 1200000 / 47.12
D = 25466.8

Therefore, the diameter of job or tool is 25466.8.

Continue reading How to Calculate and Solve for Work Piece Velocity | Metal Forming processes

How to Calculate and Solve for Energy Required for Metal Cutting | Metal Forming processes

The image above represents energy required for metal cutting.

To compute for energy required for metal cutting, two essential parameters are needed and these parameters are Cutting Force (Fcand Work Piece Velocity (v).

The formula for calculating energy required for metal cutting:

E = Fc.v

Where:

E = Energy Required for Metal Cutting
Fc = Cutting Force
v = Work Piece Velocity

Let’s solve an example;
Find the energy required for metal cutting when the cutting force is 44 and the work piece velocity is 20.

This implies that;

Fc = Cutting Force = 44
v = Work Piece Velocity = 20

E = Fc.v
E = 44 x 20
E = 880

Therefore, the energy required for metal cutting is 880 J.

Calculating for the Cutting Force when the Energy Required for Metal Cutting and the Work Piece Velocity is Given.

Fc = E / v

Where;

Fc = Cutting Force
E = Energy Required for Metal Cutting
v = Work Piece Velocity

Let’s solve an example;
Find the cutting force when the energy required for metal cutting is 38 and the work piece velocity is 14.

This implies that;

E = Energy Required for Metal Cutting = 38
v = Work Piece Velocity = 14

Fc = E / v
Fc = 38 / 14
Fc = 2.71

Therefore, the cutting force is 2.71.

Continue reading How to Calculate and Solve for Energy Required for Metal Cutting | Metal Forming processes

How to Calculate and Solve for Shear Angle | Merchant Force Circle

The image above represents shear angle.

To compute for shear angle, two essential parameters are needed and these parameters are Rake Angle (in Degrees) (α) and Angle of Friction (in Degrees) (β).

The formula for calculating shear angle:

φ = 45° + α / 2β / 2

Where:

φ = Shear Angle (φ)
α = Rake Angle
β = Angle of Friction

Let’s solve an example;
Find the shear angle when the rake angle is 34 and the angle of friction is 28.

This implies that;

α = Rake Angle = 34
β = Angle of Friction = 28

φ = 45° + α / 2β / 2
φ = 45° + 34° / 228° / 2
φ = 45° + 17° – 14°
φ = 48°

Therefore, the shear angle is 48°.

Continue reading How to Calculate and Solve for Shear Angle | Merchant Force Circle