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Rockwell hardness number of work material from Lindsay semiempirical analysis Formula

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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). Check FAQs

N hardness = {(\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 Λ t})}^{\frac{100}{142}}

N_hardness - Rockwell Hardness Number?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?d_g - Grain Diameter of The Grinding wheel?Λ_t - Wheel Removal Parameter?

Rockwell hardness number of work material from Lindsay semiempirical analysis Example

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Here is how the Rockwell hardness number of work material from Lindsay semiempirical analysis equation looks like with Values.

Here is how the Rockwell hardness number of work material from Lindsay semiempirical analysis equation looks like with Units.

Here is how the Rockwell hardness number of work material from Lindsay semiempirical analysis equation looks like.

20 = {(\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 7^{0.13} \cdot 2.4})}^{\frac{100}{142}}

20 = {(\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 {7mm}^{0.13} \cdot 2.4})}^{\frac{100}{142}}

20 = {(\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 7^{0.13} \cdot 2.4})}^{\frac{100}{142}}

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Rockwell hardness number of work material from Lindsay semiempirical analysis Solution

Follow our step by step solution on how to calculate Rockwell hardness number of work material from Lindsay semiempirical analysis?

FIRST Step Consider the formula

N hardness = {(\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 Λ t})}^{\frac{100}{142}}

Next Step Substitute values of Variables

∴

N hardness = {(\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 {7mm}^{0.13} \cdot 2.4})}^{\frac{100}{142}}

Next Step Convert Units

∴

N hardness = {(\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 {0.007m}^{0.13} \cdot 2.4})}^{\frac{100}{142}}

Next Step Prepare to Evaluate

∴

N hardness = {(\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 {0.007}^{0.13} \cdot 2.4})}^{\frac{100}{142}}

LAST Step Evaluate

∴

N hardness = 20

Rockwell hardness number of work material from Lindsay semiempirical analysis Formula Elements

Variables

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

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