1. **Problem Statement:** Design and analyze a 5 kW, 220 V, 1500 rpm DC shunt machine meeting electromagnetic and performance constraints including efficiency ≥ 85%, safe commutation, and temperature rise ≤ 55°C. 2. **Output Equation & Main Dimensions:** The output power $P = 5\,000$ W, voltage $V = 220$ V, speed $N = 1500$ rpm. The output power equation for a DC machine is: $$P = \frac{\pi^2}{60} \times D^2 \times L \times n \times B_{av} \times a_c \times 10^{-3}$$ where $D$ is armature diameter (m), $L$ is core length (m), $n$ is speed (rpm), $B_{av}$ is average flux density (T), and $a_c$ is specific electric loading (A/m). Given $B_{av} \approx 0.8$ T (typical), and electric loading $a_c$ (ampere conductors per meter) to be assumed or calculated. 3. **Calculate Main Dimensions:** Assuming ratio $\frac{L}{D} = 0.8$ (within 0.6–1.0 for cooling and magnetic design), solve for $D$ and $L$ using the output power equation. 4. **Magnetic Design:** - Pole pitch $\tau = \frac{\pi D}{P}$ where $P=4$ poles. - Pole arc $= 0.7 \times \tau$ (typical). - Calculate flux per pole $\phi = \frac{B_{av} \times \pi D L}{P}$. - Number of turns per field coil $N_f = \frac{\phi}{\mu_0 \times H_c}$ (using magnetomotive force and magnetic circuit relations). 5. **Electrical Design:** - Choose armature winding type (lap or wave) based on voltage and current. - Calculate number of conductors $Z$ from $Z = \frac{I_a}{J} \times \text{cross-sectional area}$ where $J$ is current density. - Current per path $I_p = \frac{I_a}{\text{number of parallel paths}}$. - Commutator segments equal to number of coils. 6. **Losses & Efficiency:** - Armature copper loss $P_{cu,a} = I_a^2 R_a$. - Field copper loss $P_{cu,f} = I_f^2 R_f$. - Brush contact loss and iron loss estimated from standard tables or empirical formulas. - Calculate efficiency $\eta = \frac{P_{out}}{P_{out} + \text{losses}}$. 7. **Voltage Regulation & Performance:** - Generated emf $E = V + I_a R_a + \text{voltage drop due to armature reaction}$. - Voltage regulation $= \frac{E - V}{V} \times 100\%$. - Field current adjustment compensates voltage drop by controlling flux. 8. **Design Refinement:** - Vary $B_{av}$ and $a_c$ within ±10% to optimize efficiency and size. 9. **Visualization:** - Model 2D section and simulate flux distribution to verify $B_{av} \approx 0.8$ T. **Final Answer:** The design process involves calculating armature diameter $D$ and core length $L$ from the output power equation, selecting magnetic and electrical parameters to meet performance criteria, estimating losses to ensure efficiency ≥ 85%, and verifying voltage regulation and commutation safety. The detailed calculations depend on assumed or given magnetic and electric loading values, which must be chosen based on standard machine design data.