Number of abrasive particles impacting per unit time Calculator

✖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%
✖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 [ρ]			+10% -10%
✖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%

✖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.ⓘ Number of abrasive particles impacting per unit time [N]

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Formula

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Number of abrasive particles impacting per unit time

Formula

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

Example

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

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Number of abrasive particles impacting per unit time Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
N = Z_w/(A₀*d_mean^3*V^(3/2)*(ρ/(12*h_b))^(3/4))
This formula uses 7 Variables

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Metal Removal Rate: 0.16 Cubic Meter per Second --> 0.16 Cubic Meter per Second No Conversion Required
Empirical Constant: 100 --> 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
Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Brinell Hardness: 200 Kilogram-Force per Square Millimeter --> 1961329999.99986 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = Z_w/(A₀*d_mean^3*V^(3/2)*(ρ/(12*h_b))^(3/4)) --> 0.16/(100*0.004^3*1420686.92120444^(3/2)*(997/(12*1961329999.99986))^(3/4))

Evaluating ... ...

N = 4.99999999999999

STEP 3: Convert Result to Output's Unit

4.99999999999999 --> No Conversion Required

FINAL ANSWER

4.99999999999999 ≈ 5 <-- Abrasive Particles Number Impacting Per Unit Time

(Calculation completed in 00.004 seconds)

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Created by Rajat Vishwakarma

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

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

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< 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)

Number of abrasive particles impacting per unit time 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 Number of abrasive particles impacting per unit time?

Number of abrasive particles impacting per unit time calculator uses 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)) to calculate the Abrasive Particles Number Impacting Per Unit Time, The Number of abrasive particles impacting per unit time formula is defined as the average no. of particles impacting work surface to cut it during AJM. Abrasive Particles Number Impacting Per Unit Time is denoted by N symbol.

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

FAQ

What is Number of abrasive particles impacting per unit time?

The Number of abrasive particles impacting per unit time formula is defined as the average no. of particles impacting work surface to cut it during AJM and is represented as N = Z_w/(A₀*d_mean^3*V^(3/2)*(ρ/(12*h_b))^(3/4)) or 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)). 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, 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, 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 uses a hard, spherical indenter which is forced into the surface of the metal to be tested.

How to calculate Number of abrasive particles impacting per unit time?

The Number of abrasive particles impacting per unit time formula is defined as the average no. of particles impacting work surface to cut it during AJM is calculated using 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)). To calculate Number of abrasive particles impacting per unit time, you need Metal Removal Rate (Z_w), Empirical Constant (A₀), Mean Diameter of Abrasive Particles (d_mean), Velocity (V), Density (ρ) & Brinell Hardness (h_b). With our tool, you need to enter the respective value for Metal Removal Rate, Empirical Constant, Mean Diameter of Abrasive Particles, Velocity, Density & Brinell Hardness and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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