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Grain diameter from Lindsay's semiempirical analysis Formula

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Grain Diameter of The Grinding wheel is defined as the actual diameter of the grain of the grinding wheel used in grinding operation. Check FAQs

d g = {(\frac{7.93 \cdot 100000 \cdot {(\frac{v w}{v t})}^{0.158} \cdot (1 + (4 \cdot \frac{a d}{3 \cdot f})) \cdot f^{0.58} \cdot v t}{{d e}^{0.14} \cdot {V b}^{0.47} \cdot Λ t \cdot {N hardness}^{1.42}})}^{\frac{100}{13}}

d_g - Grain Diameter of The Grinding wheel?v_w - Surface Speed of Workpiece?v_t - Surface Speed of Wheel?a_d - Depth of Dress?f - Feed?d_e - Equivalent Wheel Diameter?V_b - Percentage Volume of Bond Material in Grinding?Λ_t - Wheel Removal Parameter?N_hardness - Rockwell Hardness Number?

Grain diameter from Lindsay's semiempirical analysis Example

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Here is how the Grain diameter from Lindsay's semiempirical analysis equation looks like with Values.

Here is how the Grain diameter from Lindsay's semiempirical analysis equation looks like with Units.

Here is how the Grain diameter from Lindsay's semiempirical analysis equation looks like.

7 = {(\frac{7.93 \cdot 100000 \cdot {(\frac{100}{4.8})}^{0.158} \cdot (1 + (4 \cdot \frac{0.6577}{3 \cdot 0.9})) \cdot {0.9}^{0.58} \cdot 4.8}{40^{0.14} \cdot 16^{0.47} \cdot 2.4 \cdot 20^{1.42}})}^{\frac{100}{13}}

7mm = {(\frac{7.93 \cdot 100000 \cdot {(\frac{100mm/s}{4.8mm/s})}^{0.158} \cdot (1 + (4 \cdot \frac{0.6577mm}{3 \cdot 0.9mm})) \cdot {0.9mm}^{0.58} \cdot 4.8mm/s}{{40mm}^{0.14} \cdot 16^{0.47} \cdot 2.4 \cdot 20^{1.42}})}^{\frac{100}{13}}

7 = {(\frac{7.93 \cdot 100000 \cdot {(\frac{100}{4.8})}^{0.158} \cdot (1 + (4 \cdot \frac{0.6577}{3 \cdot 0.9})) \cdot {0.9}^{0.58} \cdot 4.8}{40^{0.14} \cdot 16^{0.47} \cdot 2.4 \cdot 20^{1.42}})}^{\frac{100}{13}}

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Grain diameter from Lindsay's semiempirical analysis Solution

Follow our step by step solution on how to calculate Grain diameter from Lindsay's semiempirical analysis?

FIRST Step Consider the formula

d g = {(\frac{7.93 \cdot 100000 \cdot {(\frac{v w}{v t})}^{0.158} \cdot (1 + (4 \cdot \frac{a d}{3 \cdot f})) \cdot f^{0.58} \cdot v t}{{d e}^{0.14} \cdot {V b}^{0.47} \cdot Λ t \cdot {N hardness}^{1.42}})}^{\frac{100}{13}}

Next Step Substitute values of Variables

∴

d g = {(\frac{7.93 \cdot 100000 \cdot {(\frac{100mm/s}{4.8mm/s})}^{0.158} \cdot (1 + (4 \cdot \frac{0.6577mm}{3 \cdot 0.9mm})) \cdot {0.9mm}^{0.58} \cdot 4.8mm/s}{{40mm}^{0.14} \cdot 16^{0.47} \cdot 2.4 \cdot 20^{1.42}})}^{\frac{100}{13}}

Next Step Convert Units

∴

d g = {(\frac{7.93 \cdot 100000 \cdot {(\frac{0.1m/s}{0.0048m/s})}^{0.158} \cdot (1 + (4 \cdot \frac{0.0007m}{3 \cdot 0.0009m})) \cdot {0.0009m}^{0.58} \cdot 0.0048m/s}{{0.04m}^{0.14} \cdot 16^{0.47} \cdot 2.4 \cdot 20^{1.42}})}^{\frac{100}{13}}

Next Step Prepare to Evaluate

∴

d g = {(\frac{7.93 \cdot 100000 \cdot {(\frac{0.1}{0.0048})}^{0.158} \cdot (1 + (4 \cdot \frac{0.0007}{3 \cdot 0.0009})) \cdot {0.0009}^{0.58} \cdot 0.0048}{{0.04}^{0.14} \cdot 16^{0.47} \cdot 2.4 \cdot 20^{1.42}})}^{\frac{100}{13}}

Next Step Evaluate

∴

d g = 0.007m

LAST Step Convert to Output's Unit

∴

d g = 7mm

Grain diameter from Lindsay's semiempirical analysis Formula Elements

Variables

Grain Diameter of The Grinding wheel

Grain Diameter of The Grinding wheel is defined as the actual diameter of the grain of the grinding wheel used in grinding operation.

Symbol: d_g

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Grain Diameter of The Grinding wheel

Surface Speed of Workpiece

Surface Speed of Workpiece is the speed of the surface rotating with respect to grinding tool.

Symbol: v_w

Measurement: SpeedUnit: mm/s

Note: Value should be greater than 0.

Formulas to find Surface Speed of Workpiece

Surface Speed of Wheel

Surface speed of wheel is defined as the speed of the surface of the wheel which is used for grinding.

Symbol: v_t

Measurement: SpeedUnit: mm/s

Note: Value should be greater than 0.

Formulas to find Surface Speed of Wheel

Depth of Dress

Depth of Dress in the dressing process is defined as the amount displacement of the dressing tool towards the workpiece.

Symbol: a_d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Dress

Feed

The Feed is the distance from the cutting tool advances along the length of the work for every revolution of the spindle.

Symbol: f

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Feed

Equivalent Wheel Diameter

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.

Symbol: d_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Equivalent Wheel Diameter

Percentage Volume of Bond Material in Grinding

The Percentage Volume of Bond Material in Grinding refers to the proportion of the total volume of the grinding wheel that is occupied by the bond material.

Symbol: V_b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Percentage Volume of Bond Material in Grinding

Wheel Removal Parameter

The Wheel Removal Parameter is the ratio of the volume of wheel removed per unit time per unit thrust force.

Symbol: Λ_t

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wheel Removal Parameter

Rockwell Hardness Number

The Rockwell Hardness Number is directly related to the indentation hardness of the plastic material (i.e., the higher the reading of Rockwell Hardness Number ,the harder the material is).

Symbol: N_hardness

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Rockwell Hardness Number

Other formulas in Lindsay Semiempirical Analysis category

Go Wheel removal parameter from Lindsay's semiempirical analysis

Λ t = \frac{7.93 \cdot 100000 \cdot {(\frac{v w}{v t})}^{0.158} \cdot (1 + (4 \cdot \frac{a d}{3 \cdot f})) \cdot f^{0.58} \cdot v t}{{d e}^{0.14} \cdot {V b}^{0.47} \cdot {d g}^{0.13} \cdot {N hardness}^{1.42}}

Go Equivalent wheel diameter from Lindsay's semiempirical analysis

d e = {(\frac{7.93 \cdot 100000 \cdot ({(\frac{v w}{v t})}^{0.158}) \cdot (1 + (4 \cdot \frac{a d}{3 \cdot f})) \cdot f^{0.58} \cdot v t}{Λ t \cdot {V b}^{0.47} \cdot {d g}^{0.13} \cdot {N hardness}^{1.42}})}^{\frac{100}{14}}

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

Grain diameter from Lindsay's semiempirical analysis evaluator 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 evaluate the Grain Diameter of The Grinding wheel, Grain diameter from Lindsay's semiempirical analysis, commonly used in the study of grinding processes, provides a formula for estimating the diameter of abrasive grains in a grinding wheel. This formula takes into account various factors including the grinding force, the material removal rate, and the specific energy of the process. Grain Diameter of The Grinding wheel is denoted by d_g symbol.

How to evaluate Grain diameter from Lindsay's semiempirical analysis using this online evaluator? To use this online evaluator 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), Equivalent Wheel Diameter (d_e), Percentage Volume of Bond Material in Grinding (V_b), Wheel Removal Parameter (Λ_t) & Rockwell Hardness Number (N_hardness) and hit the calculate button.

FAQs on Grain diameter from Lindsay's semiempirical analysis

What is the formula to find Grain diameter from Lindsay's semiempirical analysis?

The formula of Grain diameter from Lindsay's semiempirical analysis is expressed as 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). Here is an example- 7000 = ((7.93*100000*(0.1/0.0048)^0.158*(1+(4*0.000657680918744346/(3*0.0009)))*0.0009^0.58*0.0048)/(0.04^0.14*16^0.47*2.4*20^1.42))^(100/13).

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

With Surface Speed of Workpiece (v_w), Surface Speed of Wheel (v_t), Depth of Dress (a_d), Feed (f), Equivalent Wheel Diameter (d_e), Percentage Volume of Bond Material in Grinding (V_b), Wheel Removal Parameter (Λ_t) & Rockwell Hardness Number (N_hardness) we can find Grain diameter from Lindsay's semiempirical analysis using the formula - 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).

Can the Grain diameter from Lindsay's semiempirical analysis be negative?

No, the Grain diameter from Lindsay's semiempirical analysis, measured in Length cannot be negative.

Which unit is used to measure Grain diameter from Lindsay's semiempirical analysis?

Grain diameter from Lindsay's semiempirical analysis is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Grain diameter from Lindsay's semiempirical analysis can be measured.

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Grain diameter from Lindsay's semiempirical analysis Formula

Grain diameter from Lindsay's semiempirical analysis Example

Grain diameter from Lindsay's semiempirical analysis Solution

Grain diameter from Lindsay's semiempirical analysis Formula Elements

Other formulas in Lindsay Semiempirical Analysis category

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

FAQs on Grain diameter from Lindsay's semiempirical analysis

Variable Name