Study Notes: Inclined Plane Boat Elevator Engineering Analysis

Overview and System Description of the Inclined Plane Boat Elevator

• Definition and Purpose: A boat elevator is a mechanical device designed to transport boats between two canals (watercourses) located at different altitudes (upstream and downstream). This infrastructure facilitates river navigation for both commercial traffic and recreational boating.

• System Components:

  • Bac (Tank): A water-filled container that holds the boat during transport. It is guided by an inclined rail system.

  • Counterweights: Two units used to compensate for the total mass of the water-filled tank and the boat.

  • Cables and Drums: Steel cables connect the counterweights to the tank via two drums (tambours).

  • Propulsion: A motor-brake ensures the ascent and descent of the tank. A second redundant motor-brake is installed for emergency backup.

  • Transmission: Three cascaded reducers adapt the high speed of the motor to the slow speed required for the tank's movement.

  • Vertical Sliding Doors: Four doors in total: one for the upstream canal, one for the downstream canal, and two at the ends of the tank. These facilitate water exchange and boat entry/exit.

  • Sensors and Control:

    • Inductive Speed Sensor: Monitors the displacement speed of the tank.

    • Position Sensors: Controlling the tank's specific locations.

    • Control Unit: An Industrial Programmable Logic Controller (A.P.I - Automate Programmable Industriel).

Functional Analysis (SEV 1)

• Analytical Tools:

  • Bête à cornes (Horned Beast):

    • To whom does it provide service? To the Navigators/Boats.

    • On what does it act? On the boat.

    • In what goal? To move a boat from one canal to another.

  • Service Functions (FS):

    • FP (Principal Function): Move a boat from one canal to another.

    • FC1: Adapt to different boat dimensions.

    • FC2: Integrate harmoniously into the environment.

    • FC3: Adapt to the available energy source.

    • FC4: Be easy to manipulate.

    • FC5: Ensure stable boat displacement.

    • FC6: Conform to safety standards.

Power Transmission and Mechanical Systems

• Transmission Chain Characteristics:

  • Moteur-frein (Motor-Brake): $P_m = 90\,kW$, $N_m = 1475\,tr/min$, $C_m$ (motor torque).

  • Reducer $R_1$: Reduction ratio $r_1 = 0.18$, efficiency $\eta_1 = 0.94$.

  • Reducer $R_2$: Reduction ratio $r_2 = 0.15$, efficiency $\eta_2 = 0.94$.

  • Reducer $R_3$: $Z_{pignon} = 38$, $Z_{roue} = 475$, efficiency $\eta_3 = 0.92$.

  • Drum ($Tambour$) + Cables: Diameter $D_t = 3.62\,m$, efficiency $\eta_4 = 0.90$.

• Calculations and Formulas:

  • Reduction Ratio of $R_3$:         $r_3 = \frac{Z_{pignon}}{Z_{roue}} = \frac{38}{475} = 0.08$

  • Global Reduction Ratio ($r_g$):         $r_g = r_1 \times r_2 \times r_3 = 0.18 \times 0.15 \times 0.08 = 0.00216$

  • Drum Rotation Speed ($N_t$):         $N_t = N_m \times r_g = 1475 \times 0.00216 = 3.186\,tr/min$

  • Tank Displacement Speed ($V_b$):         $V_b = \frac{\pi \times D_t \times N_t}{60} \approx \frac{3.14 \times 3.62 \times 3.2}{60} \approx 0.606\,m/s$

  • Power at Reducer Output ($P_1$):         $P_1 = P_m \times \eta_1 = 90 \times 0.94 = 84.6\,kW$

  • Final Output Power ($P_s$):         $P_s = P_m \times (\eta_1 \times \eta_2 \times \eta_3 \times \eta_4) = 90 \times (0.94 \times 0.94 \times 0.92 \times 0.90) = 90 \times 0.7317 \approx 65.85\,kW$

  • Drive Effort ($F_t$):         $F_t = \frac{P_s}{V_b}$

• Brake Study (Disque-based Mechanism):

  • Operating Description: When powered on, the coil (5) attracts the mobile disk (6), compressing the springs (7) and releasing the motor shaft (2). When powered off, the coil releases the disk (6), and springs push the brake disk (3) against the fixed plate (15).

  • Brake Characteristics:

    • Pressing force of springs: $F_p = 1500\,N$

    • Friction coefficient: $f = 0.85$

    • Mean radius of linings: $R_{moy} = 306\,mm = 0.306\,m$

  • Brake Torque ($C_f$): For a disk brake with $n$ friction surfaces (typically $n=2$ for such systems):         $C_f = n \times f \times F_p \times R_{moy}$

Energy Chain Study (SEV 2)

• Power Distribution Structure:

  • The machine room is fed by an HTA (High Voltage A) network.

  • Network Structure: It follows a "Coupure d'artère" (Ring Main System) or "Double dérivation" structure based on the DRES 03 diagram.

• Transformer $T_1$ (HTA/BT):

  • Nominal Specs: $S_N = 1000\,kVA$, $U_{1N} = 20\,kV$, $U_{2N} = 400\,V$.

  • Coupling: High-voltage side (Primary) is Delta ($\Delta$); Low-voltage side (Secondary) is Star ($Y$) with neutral ($n$).

  • Nominal Secondary Current ($I_{2N}$):         $I_{2N} = \frac{S_N}{U_{2N} \sqrt{3}} = \frac{10^6}{400 \times 1.732} \approx 1443.4\,A$

  • Transformation Ratios:         $m = \frac{N_2}{N_1}$         $M = \frac{U_{ab}}{U_{AB}} = \frac{400}{20000} = 0.02$

• Parallel Operation (Adding $T_2$):

  • Conditions for Parallelism:

    1. Identical transformation ratios ($M$).

    2. Identical primary supply network.

    3. Compatible clock indices (indice horaire).

    4. Power ratio between transformers should not exceed 2:1.

    5. Short-circuit voltages ($U_{cc}$) equal within a 10% margin.

• Asynchronous Traction Motor:

  • Tech Specs: 4 poles, $50\,Hz$, $90\,kW$, $230V/400V$.

  • Coupling: For a $400\,V$ network, the motor phases must be in Star ($Y$) configuration because each winding is rated for $230\,V$.

  • Synchronous Speed ($n_s$):         $n_s = \frac{60 \times f}{p} = \frac{60 \times 50}{2} = 1500\,tr/min$

  • Actual Speed ($n$): With slip $g = 2\% = 0.02$:         $n = n_s \times (1 - g) = 1500 \times 0.98 = 1470\,tr/min$

  • Absorbed Current ($I$):         $P_a = P_u \text{ (neglecting losses)} = 90\,kW$         $I = \frac{90000}{400 \times \sqrt{3} \times 0.85} \approx 152.8\,A$

Information Chain and Signal Conditioning (SEV 3)

• Inductive Speed Sensor:

  • Works by modulating magnetic flux via a gear wheel ($Z = 20$ teeth).

  • Frequency Equation:         $f = \frac{n}{60} \times Z$

  • At nominal speed ($n = 1475\,tr/min$):         $f = \frac{1475 \times 20}{60} \approx 491.67\,Hz$

• Conditioning Circuitry:

  • Step 1: Mise en forme (Wave Shaping): Uses a non-inverting Schmitt Trigger (comparator with hysteresis).

    • Input potential at positive terminal: $V^{+} = \frac{U \times R_2 + U_1 \times R_1}{R_1 + R_2}$

    • Threshold relationship at switching: $U = \frac{R_1 + R_2}{R_1} V_{ref} - \frac{R_2}{R_1} U_1$

  • Step 2: Monostable: Generates calibrated pulses of height $E = 5\,V$ and width $T_0 = 1\,ms$.

    • Average voltage output: $U_{2moy} = E \times T_0 \times f$

  • Step 3: Low-pass Filter (Filtre moyenneur):

    • Extracts the DC component (average value) representing speed.

    • Transfer Function:             $A_v = \frac{U_s}{U_2} = \frac{2}{1 + jRC\omega}$

    • Maximum Amplification: $A_0 = 2$

    • Cut-off Frequency ($f_0$):             $f_0 = \frac{1}{2 \pi RC}$

    • For $R = 2\,k\Omega$ and $C = 15\,\mu F$:             $f_0 = \frac{1}{2 \times 3.14 \times 2000 \times 15 \times 10^{-6}} \approx 5.3\,Hz$

  • Output Voltage ($U_s$): At $n = 1475\,tr/min$ ($f = 492\,Hz$):         $U_s = A_0 \times U_{2moy} = 2 \times (5 \times 0.001 \times 492) = 4.92\,V$

Automation and Control Logic (Grafcet)

• Cycle of Operation (Descent):

  1. Step 1: Initial state.

  2. Step 2: Open upstream doors (Order $OPM$) when boat detected and manual order received.

  3. Step 3: Close upstream doors (Order $FPM$).

  4. Step 4: Descent Translation (Start $DGV$).

  5. Step 5: Slow down descent (Start $DPV$) when slowing position sensor ($b$) is hit.

  6. Step 6: Stop at bottom; open downstream doors ($OPV$).

  7. Step 7: Close downstream doors ($FPV$) after boat exit.

• PLC I/O Mapping:

  • Inputs: $I_1$ (Descent), $I_2$ (Open Upstream), $I_6$ (Doors open status), $I_7$ (Doors closed status), $IA$ (Slowing point), $IB$ (Bottom limit), $IC$ (Top limit).

  • Outputs: $Q_1$ (Open Upstream), $Q_2$ (Close Upstream), $Q_5$ (Translate Down), $Q_6$ (Slow Down), $Q_3$ (Open Downstream).