Density of abrasive particles Calculator

✖Brinell Hardness uses a hard, spherical indenter which is forced into the surface of the metal to be tested.ⓘ Brinell Hardness [h_b]			+10% -10%
✖Metal Removal Rate(MRR) is the amount of material removed per time unit (usually per minute) when performing machining operations such as using a lathe or milling machine.ⓘ Metal Removal Rate [Z_w]			+10% -10%
✖The Empirical constant is a self determined constant whose value is accessible from table of such constants. This constant is used to calculate the intrinsic carrier concentration.ⓘ Empirical Constant [A₀]			+10% -10%
✖Abrasive Particles Number Impacting Per Unit Time is defined as the average number of particles impacting work surface to cut it during Abrasive Jet Machining.ⓘ Abrasive Particles Number Impacting Per Unit Time [N]			+10% -10%
✖Mean diameter of Abrasive Particles is the mean calculated from sampling method.ⓘ Mean Diameter of Abrasive Particles [d_mean]			+10% -10%
✖Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.ⓘ Velocity [V]			+10% -10%

✖The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.ⓘ Density of abrasive particles [ρ]

⎘ Copy

👎

Formula

✖

Density of abrasive particles

Formula

`"ρ" = 12*"h"_{"b"}*("Z"_{"w"}/("A"_{"0"}*"N"*"d"_{"mean"}^3*"V"^(3/2)))^(4/3)`

Example

`"997kg/m³"=12*"200kgf/mm²"*("0.16m³/s"/("100"*"5"*("4mm")^3*("1420686.92120444m/s")^(3/2)))^(4/3)`

Calculator

LaTeX

Reset

👍

Download Production Engineering Formula PDF PDF Image

Density of abrasive particles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density = 12*Brinell Hardness*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3)
ρ = 12*h_b*(Z_w/(A₀*N*d_mean^3*V^(3/2)))^(4/3)
This formula uses 7 Variables

Variables Used

Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.
Brinell Hardness - (Measured in Pascal) - Brinell Hardness uses a hard, spherical indenter which is forced into the surface of the metal to be tested.
Metal Removal Rate - (Measured in Cubic Meter per Second) - Metal Removal Rate(MRR) is the amount of material removed per time unit (usually per minute) when performing machining operations such as using a lathe or milling machine.
Empirical Constant - The Empirical constant is a self determined constant whose value is accessible from table of such constants. This constant is used to calculate the intrinsic carrier concentration.
Abrasive Particles Number Impacting Per Unit Time - Abrasive Particles Number Impacting Per Unit Time is defined as the average number of particles impacting work surface to cut it during Abrasive Jet Machining.
Mean Diameter of Abrasive Particles - (Measured in Meter) - Mean diameter of Abrasive Particles is the mean calculated from sampling method.
Velocity - (Measured in Meter per Second) - Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.

STEP 1: Convert Input(s) to Base Unit

Brinell Hardness: 200 Kilogram-Force per Square Millimeter --> 1961329999.99986 Pascal (Check conversion here)
Metal Removal Rate: 0.16 Cubic Meter per Second --> 0.16 Cubic Meter per Second No Conversion Required
Empirical Constant: 100 --> No Conversion Required
Abrasive Particles Number Impacting Per Unit Time: 5 --> No Conversion Required
Mean Diameter of Abrasive Particles: 4 Millimeter --> 0.004 Meter (Check conversion here)
Velocity: 1420686.92120444 Meter per Second --> 1420686.92120444 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ = 12*h_b*(Z_w/(A₀*N*d_mean^3*V^(3/2)))^(4/3) --> 12*1961329999.99986*(0.16/(100*5*0.004^3*1420686.92120444^(3/2)))^(4/3)

Evaluating ... ...

ρ = 996.999999999997

STEP 3: Convert Result to Output's Unit

996.999999999997 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

996.999999999997 ≈ 997 Kilogram per Cubic Meter <-- Density

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Production Engineering » Unconventional machining processes » Abrasive Jet Machining (AJM) » Density of abrasive particles

Credits

Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

Rajat Vishwakarma has created this Calculator and 400+ more calculators!

Verified by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

Nishan Poojary has verified this Calculator and 400+ more calculators!

< 7 Abrasive Jet Machining (AJM) Calculators

Mean diameter of abrasive particles

Go Mean Diameter of Abrasive Particles = (Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)))^(1/3)

Velocity of abrasive particles

Go Velocity = (Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*(Density/(12*Brinell Hardness))^(3/4)))^(2/3)

Number of abrasive particles impacting per unit time

Go Abrasive Particles Number Impacting Per Unit Time = Metal Removal Rate/(Empirical Constant*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4))

Empirical constant for AJM

Go Empirical Constant = Metal Removal Rate/(Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4))

Hardness of work material

Go Brinell Hardness = Density/(12*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3))

Density of abrasive particles

Go Density = 12*Brinell Hardness*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3)

Material removal rate

Go Metal Removal Rate = Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)*(Density/(12*Brinell Hardness))^(3/4)

Density of abrasive particles Formula

What is Abrasive Jet Machining ?

Abrasive Jet Machining is a process that uses a very high speed (supersonic about 2.5 Mach number) water jet mixed with abrasives to cut any type of material without, in any way, affecting the work material or the environment.
The AJM machines aim a highly focused, supersonic stream of water at the material such that it can cut composites smoothly by eroding them without generating any heat. Thus the AJM process eliminates all the thermal and mechanical distortion caused by conventional cutting methods. Also the water jet nozzle can be directed at any angle to the material thereby allowing for angled cuts. For cutting soft materials such as textiles and food stuffs, pure water without any abrasives is used.

How to Calculate Density of abrasive particles?

Density of abrasive particles calculator uses Density = 12*Brinell Hardness*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3) to calculate the Density, The Density of abrasive particles formula is defined as the ratio of mass per unit volume of the abrasive particles material used in AJM. Density is denoted by ρ symbol.

How to calculate Density of abrasive particles using this online calculator? To use this online calculator for Density of abrasive particles, enter Brinell Hardness (h_b), Metal Removal Rate (Z_w), Empirical Constant (A₀), Abrasive Particles Number Impacting Per Unit Time (N), Mean Diameter of Abrasive Particles (d_mean) & Velocity (V) and hit the calculate button. Here is how the Density of abrasive particles calculation can be explained with given input values -> 997 = 12*1961329999.99986*(0.16/(100*5*0.004^3*1420686.92120444^(3/2)))^(4/3).

FAQ

What is Density of abrasive particles?

The Density of abrasive particles formula is defined as the ratio of mass per unit volume of the abrasive particles material used in AJM and is represented as ρ = 12*h_b*(Z_w/(A₀*N*d_mean^3*V^(3/2)))^(4/3) or Density = 12*Brinell Hardness*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3). Brinell Hardness uses a hard, spherical indenter which is forced into the surface of the metal to be tested, Metal Removal Rate(MRR) is the amount of material removed per time unit (usually per minute) when performing machining operations such as using a lathe or milling machine, The Empirical constant is a self determined constant whose value is accessible from table of such constants. This constant is used to calculate the intrinsic carrier concentration, Abrasive Particles Number Impacting Per Unit Time is defined as the average number of particles impacting work surface to cut it during Abrasive Jet Machining, Mean diameter of Abrasive Particles is the mean calculated from sampling method & Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.

How to calculate Density of abrasive particles?

The Density of abrasive particles formula is defined as the ratio of mass per unit volume of the abrasive particles material used in AJM is calculated using Density = 12*Brinell Hardness*(Metal Removal Rate/(Empirical Constant*Abrasive Particles Number Impacting Per Unit Time*Mean Diameter of Abrasive Particles^3*Velocity^(3/2)))^(4/3). To calculate Density of abrasive particles, you need Brinell Hardness (h_b), Metal Removal Rate (Z_w), Empirical Constant (A₀), Abrasive Particles Number Impacting Per Unit Time (N), Mean Diameter of Abrasive Particles (d_mean) & Velocity (V). With our tool, you need to enter the respective value for Brinell Hardness, Metal Removal Rate, Empirical Constant, Abrasive Particles Number Impacting Per Unit Time, Mean Diameter of Abrasive Particles & Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search