### 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/cm²When 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 Used1. **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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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 ▶

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 ▶

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.

Question

### 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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The following data is given for slab milling of a 300 mm long 50 mm wide mild steel block: Cutter of diameter= 60 mm; Numbers of teeth =12; Cutter speed = 120 rev/min; Depth of cut = 3.2 mm; Feed is 0.25 mm/tooth.Determine (i) Table feed in mm/min, (ii) MRR (iii) Power (iv) Torque and (v) Total machining time. Assumesuitable approach and over-run and specific energy of mild steel as 5 Ws/mm3.
PLEASE SUMMARIZE IT IN YOUR WORDS!
(Grinding Operations and Grinding Machines) (USCS units) In a centerless grinding operation, the grinding wheel diameter = 8 in, and the regulating wheel diameter = 5.0 in. The grinding wheel rotates at 1500 rev/min, and the regulating wheel rotates at 180 rev/min. The inclination angle of the regulating wheel = 2.3°º. Determine the production rate of cylindrical work parts whose diameter = 0.5 in and length = 5.0 in.
Problem 2. (Determining Cutting Speeds in Machining Economics) A turning operation is performed with HSS tooling on mild steel, with Taylor tool life parameters n = 0.12, C = 60 m/min. Work part length = 450 mm and diameter = 80 mm. Feed = 0.20 mm/rev. Handling time per piece = 4.0 min, and tool change time = 1.5 min. Cost of machine and operator = $27/hr, and tooling cost = $2 per cutting edge. Find the a. cutting speed for maximum production rate and b. cutting speed for minimum cost Problem 3. (Production Rate and Cost in Machining Economics) For the two cutting speeds computed in problem 2, determine: the hourly production rate and a. b. the cost per piece.