Unit 2: Hydraulic Actuators and Control Components

Overview of Hydraulic Actuators and Energy Conversion

Definition of Actuators: An actuator is a device at the output end of a hydraulic system that converts fluid power back into mechanical power. While pumps and electric motors serve as the input, actuators are the "real working elements" that perform the final physical task.
Energy Conversion Process: * Input End: Electric Motor ( $T, \omega$ ) $\rightarrow$ Hydraulic Pump/Pneumatic Compressor $\rightarrow$ Pressurized Fluid (Liquid or Gas) at Pressure ( $P$ ) and Flow ( $Q$ ). * Internal Energy State: Pressurized liquids/gases represent Fluid Energy. * Output End (Actuators): Fluid Energy $\rightarrow$ Mechanical Energy in the form of Torque ( $T$ ) and Angular Velocity ( $\omega$ ) or Force ( $F$ ) and Velocity ( $V$ ). * Losses: Undesirable losses ( $q$ ) occur during these conversions.
Types of Motion and Actuator Selection: * Rotary Actuators (Motors): Deliver continuous rotational motion or deliver torque ( $T$ ) and speed ( $N$ ). * Rotary Oscillators (Limited Rotary Motors): Produce back-and-forth rotation through a limited arc, usually less than one full revolution ( $360^{\circ}$ ). * Linear Actuators (Cylinders): Produce straight-line motion, delivering a "push" or "pull." These are the most commonly used actuators and can be converted to limited rotary motion via levers, racks, and pinions.

Hydraulic Cylinders (Linear Actuators)

General Components: Consists of a cylinder bore containing a movable element, a piston, and a piston rod.
Classification of Cylinders: 1. Single Acting Cylinder: Applies force in only one direction. Retraction occurs via gravity or an internal compression spring at the rod end. These are compact and simple but unsuitable for large stroke lengths when using spring returns. 2. Double Acting Cylinder: Delivers force in both directions. The piston (often made of ductile iron) uses U-cup packing for sealing. * Extension: Fluid enters Port 1, piston moves forward, fluid returns to reservoir from Port 2. * Retraction: Fluid enters Port 2, piston moves back, fluid returns to reservoir from Port 1. 3. Special Design: Double Rod Cylinder: Features a single piston with a rod extending from both ends, allowing work to be performed at either side. This is ideal when extension and retraction speeds must be equal. 4. Special Design: Tandem Cylinder: Two cylinders mounted in line with a common piston rod. Provides increased output force when bore size is limited. Disadvantages include increased length and the requirement for a higher flow rate ( $Q$ ) to maintain speed. 5. Special Design: Telescoping Cylinder: Used for long work strokes with reduced overall retracted length. Multiple nested rams (e.g., Ram A, B, and C) extend sequentially. Ram A (largest) provides the highest initial force; subsequent rams (B and then C) provide smaller forces to complete the lift.

Cylinder Performance and Cushioning

Cylinder Cushioning: At high speeds, inertia can cause the piston to hit the cylinder head, potentially causing damage. Designers provide a cushioning arrangement to retard the piston during the last portion of the stroke.
Piston Speed Limits: * Un-cushioned Cylinder: Maximum restricted to $8\,m/min$ . * Cushioned Cylinder: Permissible up to $12\,m/min$ . * High-Speed Cylinders: Permissible up to $45\,m/min$ .
Mathematical Modeling (Double Acting Cylinder): * Piston Area (Blank End): $A = \frac{\pi D^2}{4}$ * Piston Rod Area: $a = \frac{\pi d^2}{4}$ * Rod End Area: $(A - a) = \frac{\pi (D^2 - d^2)}{4}$ * Extension Velocity ( $V_E$ ): $V_E = \frac{Q}{A}$ * Retraction Velocity ( $V_R$ ): $V_R = \frac{Q}{A - a}$ * Flow Rate Considerations: During extension, flow leaving the rod end ( $q_E$ ) is less than input flow ( $Q$ ). During retraction, flow leaving the blank end ( $q_R$ ) is greater than input flow ( $Q$ ).

Hydraulic Motors (Rotary Actuators)

Principle: Exactly the reverse of rotary pumps. Pressurized fluid pushes rotating elements (vanes, gears, or pistons) to generate torque ( $T$ ). They are rated by torque capacity or differential pressure.
Continuous Rotary Motors: * External Gear Motors: A pair of matched gears in a housing. One is the driver (connected to the output shaft), the other is the idler. Advantages include simple design, low cost, and bidirectionality. Limitations include high internal leakage and high bearing loads due to pressure imbalance. Typical limits: $137.8951\,bar$ ( $2000\,psi$ ) and $2400\,rpm$ . * Internal Gear Motors: Includes Gerotor and Crescent seal types. These can handle higher pressures and speeds with greater displacement. * Vane Motors: Use rectangular vanes in a slotted rotor within a cam ring. Springs or hydraulic pressure hold vanes against the ring. * Unbalanced: Side loading occurs on the shaft due to pressure differences between inlet and outlet. * Balanced: Features two inlets and two outlets $180^{\circ}$ apart to cancel side loads, increasing bearing life and operating pressure ( $172.3689\,bar$ or $2500\,psi$ at $4000\,rpm$ ).
Piston Motors: Most efficient type, capable of highest speed and torque. * Axial Piston: Pistons parallel to the shaft. Includes Bent Axis (angle between shaft and block determines displacement) and Swash Plate (inline design). * Radial Piston: Pistons arranged perpendicularly to the shaft axis. Ideal for low-speed, high-torque applications ( $200\,cm^3/rev$ to $10,000\,cm^3/rev$ ) at pressures up to $450\,bar$ .

Motor Performance Metrics

Volumetric Efficiency ( $\eta_{vol}$ ): Ratio of theoretical flow rate to actual flow rate consumed. * $\eta_{vol} = \frac{Q_T}{Q_A} \times 100$
Mechanical Efficiency ( $\eta_{mech}$ ): Ratio of actual torque delivered to theoretical torque. * $\eta_{mech} = \frac{T_A}{T_T} \times 100$ * Theoretical Torque ( $T_T$ ): $T_T = \frac{V_D \times P}{2\pi}$ , where $V_D$ is displacement ( $m^3/rev$ ) and $P$ is pressure ( $N/m^2$ ).
Hydraulic Power vs. Brake Power: Hydraulic power is energy delivered to the motor by fluid; Brake power is energy delivered to the load by the output shaft.

Control Components: Valves

System Segments: 1. Power Input: Prime mover and pump/compressor. 2. Control Segment: Valves managing direction, pressure, and flow. 3. Power Output: Actuators and the physical load.
Categories of Control Valves: 1. Directional Control Valves (DCV): Start, stop, or change flow direction to control actuator movement (Left/Right or CW/CCW). 2. Pressure Control Valves (PCV): Limit or regulate pressure (Force/Torque levels). 3. Flow Control Valves (FCV): Regulate flow rate ( $Q$ ) to manage actuator speed ( $V$ or $N$ ).

Valve Configurations and Actuation

Construction Types: * Poppet (Seat) Valves: Use a ball or disc to block flow. Simple and cheap but require high force to operate; suitable for low-pressure applications. * Sliding Spool Valves: Most common. A spool moves horizontally, using "lands" to block or open ports. Offers high switching power and good pressure compensation. * Rotary Spool Valves: A rotating spool engages with ports in the casing to change flow paths.
Port Designations: * P: Pressure (Pump) port. * T / R / E: Tank, Return, or Exhaust port. * A, B / C1, C2: Working ports connected to the actuator.
Actuation Methods: * Manual: Push button, lever, pedal. * Mechanical: Roller, cam, spring, one-way trip. * Electrical: Solenoid (single or twin windings). * Pressure: Air or oil piloted (pneumatic or hydraulic).

Specific Functional Valves

Check Valve (NRV): Simplest DCV; allows flow in one direction and blocks reverse flow. Usually requires a cracking pressure of approx. $15\,psi$ ( $1.034\,bar$ ).
Shuttle Valve (Logic OR): Has two inlets ( $P_1, P_2$ ) and one outlet ( $A$ ). The outlet receives flow from whichever inlet has higher pressure.
Pressure Relief Valve (PRV): A normally closed valve that limits system pressure by diverting fluid to the tank when a set pressure is reached. Available in direct-acting poppet or spool types.
Needle Valve/Metering Valve: Simplest FCV; an adjustable orifice controlled by a knob. Flow is typically restricted in both directions.
Choke Valve: A needle valve with an integral check valve. It provides restricted flow in one direction and free flow in the opposite direction.

Numerical Examples

Problem 1: Car Body Compressor * Stroke: $2.5\,m$ , Force: $45,000\,N$ , Pump Pressure: $8\,N/mm^2$ , Time: $8\,s$ . * Area: $A = \frac{F}{P} = \frac{45,000}{8} = 5625\,mm^2$ . * Diameter: $D = \sqrt{\frac{4A}{\pi}} = 84.6\,mm$ .
Problem 2: Double Acting Cylinder Analysis * $Q_{in} = 1.5\,Lps$ ( $1.5 \times 10^{-3}\,m^3/s$ ), Load: $4300\,N$ , $D = 50\,mm$ , $d = 25\,mm$ . * Extending Stroke: * Pressure ( $P_{ext}$ ): $21.9 \times 10^5\,N/m^2$ ( $21.9\,bar$ ). * Velocity ( $V_{ext}$ ): $0.764\,m/s$ . * Power: $3.28\,kW$ . * Retracting Stroke: * Pressure ( $P_{ret}$ ): $29.2 \times 10^5\,N/m^2$ ( $29.2\,bar$ ). * Velocity ( $V_{ret}$ ): $1.02\,m/s$ . * Power: $4.386\,kW$ .
Problem 3: Hydraulic Motor Performance * $V_D = 150 \times 10^{-6}\,m^3$ , $P = 85 \times 10^5\,N/m^2$ , $N = 1800\,rpm$ , $Q_A = 5 \times 10^{-3}\,m^3/s$ , $T_A = 185\,N\cdot m$ . * $\eta_{vol} = \frac{V_D \times N}{Q_A} = 90\%$ * $\eta_{mech} = \frac{T_A}{T_T} = 91.2\%$ * Overall Efficiency: $\eta_o = \eta_{vol} \times \eta_{mech} = 82\%$ * Power Output: $P_{out} = T_A \times \omega = 185 \times \frac{2\pi \times 1800}{60} = 34.87\,kW$ .