Problem 4. (Grinding) (SI units) Wheel diameter = 160 mm, and infeed = 0.03 mm in a surface grinding operation. Wheel speed = 1500 m/min, work speed = 0.25 m/s, and crossfeed = 4 mm. The number of active grits per area of wheel surface = 35 grits/cm². When the wheel is engaged in the work, determine: a. average length per chip, b. metal removal rate, and C. number of chips formed per unit time for the portion of the operation Equations used V = TDN R MR lc rg = √ Dd = U = vwwd nc = vwC w' t GR Fev vwwd rgvw d F'. = K₁ (TW) 0.5 (1) 0.25 vC D Ts = K₂d0.75 = V fr = TD,N, sin I w Vg 0.5 20.75 ( TO CU) OD D rg Cv บ D0.25 ▶

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### Problem 4. (Grinding)

In a surface grinding operation using SI units, the parameters are as follows:
- **Wheel Diameter**: 160 mm
- **Infeed**: 0.03 mm
- **Wheel Speed**: 1500 m/min
- **Work Speed**: 0.25 m/s
- **Crossfeed**: 4 mm
- **Number of Active Grits per Area of Wheel Surface**: 35 grits/cm²

When the wheel is engaged in the work, determine:

a. The average length per chip,  
b. The metal removal rate, and  
c. The number of chips formed per unit time for this portion of the operation.

### Equations Used

1. **Peripheral Wheel Speed**  
   \[
   v = \pi D N
   \]

2. **Metal Removal Rate**  
   \[
   R_{MR} = v_w w d
   \]

3. **Force on the Wheel**  
   \[
   f_r = \pi D_r N_r \sin I
   \]

4. **Chip Length**  
   \[
   l_c = \sqrt{D d}
   \]

5. **Grinding Ratio**  
   \[
   r_g = \frac{w'}{t}
   \]

6. **Number of Chips**  
   \[
   n_c = v_w C
   \]

7. **Energy per Unit Volume**  
   \[
   U = \frac{F_c v}{v_w w d}
   \]

8. **Cutting Force**  
   \[
   F'_c = K_1 \left( \frac{r_g v_w}{v C} \right)^{0.5} \left( \frac{d}{D} \right)^{0.25}
   \]

9. **Specific Energy**  
   \[
   T_s = K_2 d^{0.75} \left( \frac{r_g C v}{v_w} \right)^{0.5} D^{0.25}
   \]

10. **Grinding Ratio (alternate expression)**  
    \[
    GR = \frac{V_w}{V_g}
    \]

These equations are used to analyze the grinding process, calculate chip formation, and evaluate the efficiency of metal removal.
Transcribed Image Text:### Problem 4. (Grinding) In a surface grinding operation using SI units, the parameters are as follows: - **Wheel Diameter**: 160 mm - **Infeed**: 0.03 mm - **Wheel Speed**: 1500 m/min - **Work Speed**: 0.25 m/s - **Crossfeed**: 4 mm - **Number of Active Grits per Area of Wheel Surface**: 35 grits/cm² When the wheel is engaged in the work, determine: a. The average length per chip, b. The metal removal rate, and c. The number of chips formed per unit time for this portion of the operation. ### Equations Used 1. **Peripheral Wheel Speed** \[ v = \pi D N \] 2. **Metal Removal Rate** \[ R_{MR} = v_w w d \] 3. **Force on the Wheel** \[ f_r = \pi D_r N_r \sin I \] 4. **Chip Length** \[ l_c = \sqrt{D d} \] 5. **Grinding Ratio** \[ r_g = \frac{w'}{t} \] 6. **Number of Chips** \[ n_c = v_w C \] 7. **Energy per Unit Volume** \[ U = \frac{F_c v}{v_w w d} \] 8. **Cutting Force** \[ F'_c = K_1 \left( \frac{r_g v_w}{v C} \right)^{0.5} \left( \frac{d}{D} \right)^{0.25} \] 9. **Specific Energy** \[ T_s = K_2 d^{0.75} \left( \frac{r_g C v}{v_w} \right)^{0.5} D^{0.25} \] 10. **Grinding Ratio (alternate expression)** \[ GR = \frac{V_w}{V_g} \] These equations are used to analyze the grinding process, calculate chip formation, and evaluate the efficiency of metal removal.
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