Grain diameter from Lindsay's semiempirical analysis Calculator

✖Surface Speed of Workpiece is the speed of the surface rotating with respect to grinding tool.ⓘ Surface Speed of Workpiece [v_w]			+10% -10%
✖Surface speed of wheel is defined as the speed of the surface of the wheel which is used for grinding.ⓘ Surface Speed of Wheel [v_t]			+10% -10%
✖Depth of dress in the dressing process is defined as the amount displacement of the dressing tool towards the workpiece.ⓘ Depth of Dress [a_d]			+10% -10%
✖The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.ⓘ Feed [f_in]			+10% -10%
✖Equivalent Wheel Diameter is the diameter of the grinding wheel used in plunge surface that would give the same length of work wheel contact for the same feed speed.ⓘ Equivalent Wheel Diameter [d_e]			+10% -10%
✖The Percentage volume of bond material in grinding is the percentage of the volume of bond material in the grinding wheel.ⓘ Percentage Volume of Bond Material in Grinding [V_b]			+10% -10%
✖The wheel removal parameter is the ratio of the volume of wheel removed per unit time per unit thrust force.ⓘ Wheel Removal Parameter [Λ_t]			+10% -10%
✖The Rockwell hardness number is directly related to the indentation hardness of the plastic material (i.e., the higher the reading, the harder the material).ⓘ Rockwell Hardness number [R_kc]			+10% -10%

✖Grain diameter of the grinding wheel is defined as the actual diameter of the grain of the grinding wheel used in grinding operation.ⓘ Grain diameter from Lindsay's semiempirical analysis [d_g]

⎘ Copy

👎

Formula

✖

Grain diameter from Lindsay's semiempirical analysis

Formula

`"d"_{"g"} = ((7.93*100000*(("v"_{"w"}/"v"_{"t"})^0.158)*(1+(4*"a"_{"d"}/(3*"f"_{"in"})))*"f"_{"in"}^0.58*"v"_{"t"})/("d"_{"e"}^0.14*"V"_{"b"}^0.47*"Λ"_{"t"}*"R"_{"kc"}^1.42))^(100/13)`

Example

`"1.2E^8mm"=((7.93*100000*(("100mm/s"/"4.8mm/s")^0.158)*(1+(4*"11mm"/(3*"0.9mm")))*("0.9mm")^0.58*"4.8mm/s")/(("40mm")^0.14*("16")^0.47*"2.4"*("20")^1.42))^(100/13)`

Calculator

LaTeX

Reset

👍

Download Production Engineering Formula PDF

Grain diameter from Lindsay's semiempirical analysis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Grain diameter of the grinding wheel = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Wheel Removal Parameter*Rockwell Hardness number^1.42))^(100/13)
d_g = ((7.93*100000*((v_w/v_t)^0.158)*(1+(4*a_d/(3*f_in)))*f_in^0.58*v_t)/(d_e^0.14*V_b^0.47*Λ_t*R_kc^1.42))^(100/13)
This formula uses 9 Variables

Variables Used

Grain diameter of the grinding wheel - (Measured in Meter) - Grain diameter of the grinding wheel is defined as the actual diameter of the grain of the grinding wheel used in grinding operation.
Surface Speed of Workpiece - (Measured in Meter per Second) - Surface Speed of Workpiece is the speed of the surface rotating with respect to grinding tool.
Surface Speed of Wheel - (Measured in Meter per Second) - Surface speed of wheel is defined as the speed of the surface of the wheel which is used for grinding.
Depth of Dress - (Measured in Meter) - Depth of dress in the dressing process is defined as the amount displacement of the dressing tool towards the workpiece.
Feed - (Measured in Meter) - The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle.
Equivalent Wheel Diameter - (Measured in Meter) - Equivalent Wheel Diameter is the diameter of the grinding wheel used in plunge surface that would give the same length of work wheel contact for the same feed speed.
Percentage Volume of Bond Material in Grinding - The Percentage volume of bond material in grinding is the percentage of the volume of bond material in the grinding wheel.
Wheel Removal Parameter - The wheel removal parameter is the ratio of the volume of wheel removed per unit time per unit thrust force.
Rockwell Hardness number - The Rockwell hardness number is directly related to the indentation hardness of the plastic material (i.e., the higher the reading, the harder the material).

STEP 1: Convert Input(s) to Base Unit

Surface Speed of Workpiece: 100 Millimeter per Second --> 0.1 Meter per Second (Check conversion here)
Surface Speed of Wheel: 4.8 Millimeter per Second --> 0.0048 Meter per Second (Check conversion here)
Depth of Dress: 11 Millimeter --> 0.011 Meter (Check conversion here)
Feed: 0.9 Millimeter --> 0.0009 Meter (Check conversion here)
Equivalent Wheel Diameter: 40 Millimeter --> 0.04 Meter (Check conversion here)
Percentage Volume of Bond Material in Grinding: 16 --> No Conversion Required
Wheel Removal Parameter: 2.4 --> No Conversion Required
Rockwell Hardness number: 20 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_g = ((7.93*100000*((v_w/v_t)^0.158)*(1+(4*a_d/(3*f_in)))*f_in^0.58*v_t)/(d_e^0.14*V_b^0.47*Λ_t*R_kc^1.42))^(100/13) --> ((7.93*100000*((0.1/0.0048)^0.158)*(1+(4*0.011/(3*0.0009)))*0.0009^0.58*0.0048)/(0.04^0.14*16^0.47*2.4*20^1.42))^(100/13)

Evaluating ... ...

d_g = 124547.286004932

STEP 3: Convert Result to Output's Unit

124547.286004932 Meter -->124547286.004932 Millimeter (Check conversion here)

FINAL ANSWER

124547286.004932 ≈ 1.2E+8 Millimeter <-- Grain diameter of the grinding wheel

(Calculation completed in 00.009 seconds)

You are here -

Home » Engineering » Production Engineering » Metal Machining » Machine Tools and Operations » Grinding Operation » Analysis of Grinding Process » Lindsay Semiempirical Analysis » Grain diameter from Lindsay's semiempirical analysis

Credits

Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

Parul Keshav has created this Calculator and 300+ more calculators!

Verified by Kumar Siddhant

Indian Institute of Information Technology, Design and Manufacturing (IIITDM), Jabalpur

Kumar Siddhant has verified this Calculator and 100+ more calculators!

< 8 Lindsay Semiempirical Analysis Calculators

Workpiece surface speed from Lindsay's semiempirical analysis

Go Surface Speed of Workpiece = ((Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Grain diameter of the grinding wheel^0.13*Rockwell Hardness number^1.42*Wheel Removal Parameter)/(7.93*100000*((1/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel))^(1000/158)

Rockwell hardness number of work material from Lindsay semiempirical analysis

Go Rockwell Hardness number = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Grain diameter of the grinding wheel^0.13*Wheel Removal Parameter))^(100/142)

Percentage Volume of Bond material from Lindsay's semiempirical analysis

Go Percentage Volume of Bond Material in Grinding = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Wheel Removal Parameter*Grain diameter of the grinding wheel^0.13*Rockwell Hardness number^1.42))^(100/47)

Equivalent wheel diameter from Lindsay's semiempirical analysis

Go Equivalent Wheel Diameter = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Wheel Removal Parameter*Percentage Volume of Bond Material in Grinding^0.47*Grain diameter of the grinding wheel^0.13*Rockwell Hardness number^1.42))^(100/14)

Grain diameter from Lindsay's semiempirical analysis

Go Grain diameter of the grinding wheel = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Wheel Removal Parameter*Rockwell Hardness number^1.42))^(100/13)

Wheel removal parameter from Lindsay's semiempirical analysis

Go Wheel Removal Parameter = (7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Grain diameter of the grinding wheel^0.13*Rockwell Hardness number^1.42)

Depth of dress from Lindsay semiempirical analysis

Go Depth of Dress = (((Wheel Removal Parameter*Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Grain diameter of the grinding wheel^0.13*Rockwell Hardness number^1.42)/(7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*Feed^0.58*Surface Speed of Wheel))-1)*3*Feed/4

Wheel surface speed from Lindsay's semiempirical analysis

Go Surface Speed of Wheel = ((Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Grain diameter of the grinding wheel^0.13*Rockwell Hardness number^1.42*Wheel Removal Parameter)/(7.93*100000*((Surface Speed of Workpiece)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58))^(1/(1-0.158))

Grain diameter from Lindsay's semiempirical analysis Formula

Why dressing of wheel is necessary for grinding?

The objective of dressing the wheel is to: True the wheel by knocking abrasive particles from the wheel's surface and making the wheel concentric. This minimizes vibration and improves surface finish, eliminating the vibration of the out-of-balance wheel across the workpiece's surface.

How to Calculate Grain diameter from Lindsay's semiempirical analysis?

Grain diameter from Lindsay's semiempirical analysis calculator uses Grain diameter of the grinding wheel = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Wheel Removal Parameter*Rockwell Hardness number^1.42))^(100/13) to calculate the Grain diameter of the grinding wheel, The Grain diameter from Lindsay's semiempirical analysis formula is defined as the actual diameter of the grain of the grinding wheel used in the grinding operation. Grain diameter of the grinding wheel is denoted by d_g symbol.

How to calculate Grain diameter from Lindsay's semiempirical analysis using this online calculator? To use this online calculator for Grain diameter from Lindsay's semiempirical analysis, enter Surface Speed of Workpiece (v_w), Surface Speed of Wheel (v_t), Depth of Dress (a_d), Feed (f_in), Equivalent Wheel Diameter (d_e), Percentage Volume of Bond Material in Grinding (V_b), Wheel Removal Parameter (Λ_t) & Rockwell Hardness number (R_kc) and hit the calculate button. Here is how the Grain diameter from Lindsay's semiempirical analysis calculation can be explained with given input values -> 1.2E+11 = ((7.93*100000*((0.1/0.0048)^0.158)*(1+(4*0.011/(3*0.0009)))*0.0009^0.58*0.0048)/(0.04^0.14*16^0.47*2.4*20^1.42))^(100/13).

FAQ

What is Grain diameter from Lindsay's semiempirical analysis?

The Grain diameter from Lindsay's semiempirical analysis formula is defined as the actual diameter of the grain of the grinding wheel used in the grinding operation and is represented as d_g = ((7.93*100000*((v_w/v_t)^0.158)*(1+(4*a_d/(3*f_in)))*f_in^0.58*v_t)/(d_e^0.14*V_b^0.47*Λ_t*R_kc^1.42))^(100/13) or Grain diameter of the grinding wheel = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Wheel Removal Parameter*Rockwell Hardness number^1.42))^(100/13). Surface Speed of Workpiece is the speed of the surface rotating with respect to grinding tool, Surface speed of wheel is defined as the speed of the surface of the wheel which is used for grinding, Depth of dress in the dressing process is defined as the amount displacement of the dressing tool towards the workpiece, The Feed is the distance the cutting tool advances along the length of the work for every revolution of the spindle, Equivalent Wheel Diameter is the diameter of the grinding wheel used in plunge surface that would give the same length of work wheel contact for the same feed speed, The Percentage volume of bond material in grinding is the percentage of the volume of bond material in the grinding wheel, The wheel removal parameter is the ratio of the volume of wheel removed per unit time per unit thrust force & The Rockwell hardness number is directly related to the indentation hardness of the plastic material (i.e., the higher the reading, the harder the material).

How to calculate Grain diameter from Lindsay's semiempirical analysis?

The Grain diameter from Lindsay's semiempirical analysis formula is defined as the actual diameter of the grain of the grinding wheel used in the grinding operation is calculated using Grain diameter of the grinding wheel = ((7.93*100000*((Surface Speed of Workpiece/Surface Speed of Wheel)^0.158)*(1+(4*Depth of Dress/(3*Feed)))*Feed^0.58*Surface Speed of Wheel)/(Equivalent Wheel Diameter^0.14*Percentage Volume of Bond Material in Grinding^0.47*Wheel Removal Parameter*Rockwell Hardness number^1.42))^(100/13). To calculate Grain diameter from Lindsay's semiempirical analysis, you need Surface Speed of Workpiece (v_w), Surface Speed of Wheel (v_t), Depth of Dress (a_d), Feed (f_in), Equivalent Wheel Diameter (d_e), Percentage Volume of Bond Material in Grinding (V_b), Wheel Removal Parameter (Λ_t) & Rockwell Hardness number (R_kc). With our tool, you need to enter the respective value for Surface Speed of Workpiece, Surface Speed of Wheel, Depth of Dress, Feed, Equivalent Wheel Diameter, Percentage Volume of Bond Material in Grinding, Wheel Removal Parameter & Rockwell Hardness number 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