Introduction to Mechanical Systems and Machine Elements

Posted on Nov 4, 2024 in Technology

Mechanical Systems (Static Machines)

Concept 1: Machine

A machine is a device that performs work and is devoted to the transformation of energy.

Concept 2: Mechanism

A mechanism is a set of components that serve to guide, transmit, and modify movement.

Concept 3: Design

Design is both functional and aesthetic and is subject to three forces: static, kinematic, and dynamic. It determines if a machine can carry out its intended function.

Equilibrium of Material Points and Rigid Bodies

Material Point

A material point is a body with a given size, but not too large. According to Newton’s 1st law, if the net force (F) acting on a material point is zero (F = 0), it is either at rest or in uniform rectilinear motion (MRU).

Rigid Body

A rigid body is a body with a given mass in which the distance between any two points does not change, regardless of the forces acting upon it. This also follows Newton’s first law.

Moment of a Force

The moment (or torque) of a force (F) on a point (O) is equal to the product of the force and the perpendicular distance from the point to the line of action of the force. It is measured in Newton-meters (Nm):
MO (Nm) = F (N) x d (m)

Torque

Torque is produced by two forces with parallel but opposite directions. It is also measured in Newton-meters (Nm):
F = D x (d + d)

Free Body Diagram

A free body diagram is a drawing of the body being analyzed in isolation from the other bodies in contact with it. All the forces acting on the body are drawn on the diagram.

Simple Machines

The performance of a machine is ideally 100%, meaning the work or energy it receives is the same as the work or energy it supplies. The work done by a machine to overcome a load is called resistant work, while the work we do to operate the machine is called motor work.

Lever

A lever is a rigid bar that rests on a fulcrum or pivot point. For a lever in equilibrium, the sum of the moments about the fulcrum is zero:
ΣMO = 0, F1 x d – R2 x d = 0

Wheel

A wheel reduces the force required to move a load by allowing it to roll instead of being dragged. For a wheel in equilibrium, the sum of the moments about the axle is zero:
ΣMO = 0, F (N) = N (N) x rt (m) / a (m)

Winch

A winch is a lifting machine designed primarily for freight. It consists of a cylinder-shaped drum with handles at both ends that allow it to rotate. A rope or cable is wound around the drum, and loads are suspended from the rope. For a winch in equilibrium, the sum of the moments about the axis of rotation is zero:
ΣMO = 0, F1 = R x r2 / r

Differential Pulley

A differential pulley consists of two concentric cylinders of different diameters fixed to the same axis. When the larger cylinder is rotated, the rope unwinds from it and winds onto the smaller cylinder, lifting the load. For a differential pulley in equilibrium, the sum of the moments about the axis of rotation is zero:
F = R x (r2 – r1) / 2 x r1 x ç

Inclined Plane

An inclined plane is a simple machine that has been used since antiquity and is still used today in other machines such as screws and wedges. For an object on an inclined plane in equilibrium, the sum of the forces along the plane is zero:
ΣMO = 0; F – Fx – Ff = 0
F = G x (sinα + μcosα)

Screw

A screw is essentially an inclined plane wrapped around a cylindrical surface. The relationship between the force applied to the screw (F), the radius of the screw (r), the load being lifted (R), and the pitch of the screw (p) is given by:
2π x F x r = R x p
R (N) = 2 x F x D / P
R = (2 x F x D / P) x C, C = tanα / tan(α + φ) [tanα = p / πd and 2πr x tanφ = μ]
R = M / tan(α + φ) x rc

Elements of Machines

Machine elements are the different parts that make up a machine and its mechanisms. They function to hold or unite different parts (e.g., screws, cotter pins) and serve as guides or for the mechanical transmission of forces and motion (e.g., wheels, pulleys).

Fixed and Detachable Joints

Fixed Joints

Fixed joints are used when the union must withstand significant mechanical stresses and dismantling is not necessary. Examples include the structure of a metal crane or the chassis of a car. Two common types are soldered and riveted joints.

Detachable Joints

Detachable joints allow for easy assembly and disassembly of parts. Examples include cotter pins, bolts, and screws. An example application is holding the wheel of a car.

Riveted Joints

Riveted joints are used to join thin, flat pieces that cannot be welded or where welding could cause internal stresses and deformation. A rivet is a cylindrical fastener with a head on one end. It is inserted into pre-drilled holes in the pieces to be joined, and the headless end is deformed to secure the joint. There are different ways to distribute riveted joints:

  • Lap joints: the two pieces overlap.
  • Butt joints: the two pieces are in the same plane and joined together by a cover plate that is riveted to both pieces.
  • Double butt joints: the two pieces are in the same plane and joined together by two cover plates, one on each side.

Screwed Joints

Screwed joints are used for quick assembly and disassembly of parts. They are commonly used in machine building and can also serve to fasten two or more pieces together. A typical screwed joint consists of a screw, a nut, and a washer.

Characteristics of a Screw and Nut

  • Thread: A helical groove on the surface of a cylinder (screw). When this groove is engaged with a corresponding internal thread in a hole (nut), it allows for relative motion between the screw and nut.
  • Hand of thread:
    • Right-hand thread: the thread spirals upwards to the right. Turning the screw clockwise causes it to advance.
    • Left-hand thread: the thread spirals upwards to the left. Turning the screw counterclockwise causes it to advance.
  • Thread geometry: There are many different thread forms with different utilities:
    • Triangular: e.g., ISO metric thread, suitable for general-purpose applications.
    • Square: used for transmitting large forces.
    • Trapezoidal: used for lead screws and power transmission.
    • Rounded: used for sealing (e.g., fire hydrants).
    • Knuckle: used for thin sheet metal.

Standardized Threads: ISO Metric Thread

Threads are standardized to ensure interchangeability. The ISO metric thread is the most common standard. It defines the geometry of the screw, the clearance between the nut and bolt, the radius of the screw tips, the angle of the thread, and the inner and outer diameters. The ISO metric thread has a triangular profile with a 60-degree angle. Another common standard is the Whitworth thread, which has a 55-degree angle and dimensions expressed in inches.

Screws, Nuts, and Washers: Types and Graphical Representation

  • Screws and nuts: used to join two pieces together. They must have the same dimensions and geometrical characteristics to ensure proper fit.
  • Washer: a thin, flat ring, typically made of steel, that is placed under the head of a screw or nut. It serves several purposes:
    • Distributes the load over a larger area.
    • Prevents the screw or nut from damaging the surface of the material being fastened.
    • Provides a smooth bearing surface.
    • Increases the clamping force.
  • Types of screws: screws are classified by their thread metric, head shape, and length. Common types include: countersunk screw, hexagonal head screw, square head screw, round head screw, and wing screw.
  • Graphical representation: the profile of the screw thread is represented by a thin line.

Systems for Joining and Fixing with Screws

There are various methods for securing screws, primarily to prevent loosening due to vibrations.

Joining Machine Components: Cotter Pins, Keys, Splines, and Dowel Pins

When joining two cylindrical parts (e.g., a shaft and a pulley), cotter pins (steel pieces inserted into slots or holes in the shaft and hub) are often used. Cotter pins can be classified based on the type of load they resist: transverse cotter pins, longitudinal cotter pins, and taper pins.

Keys and Splines

  • Keys: used to join two cylindrical parts under tension or compression. They are typically wedge-shaped on one side and have a slight taper (1 to 5%) on the other side to prevent loosening. They are designed to resist shear stresses.
  • Splines: used to transmit torque and ensure the immobility of the parts. They consist of multiple teeth or ridges on the shaft that engage with corresponding grooves in the hub. They provide a more secure connection than keys and can handle higher torques.

Dowel Pins and Spring Pins

  • Dowel pins: used for light loads and simple positioning. They are cylindrical or conical pieces of wood or metal that are inserted into holes drilled through both parts. They are easy to install and provide a secure fit.
  • Spring pins: used for light to medium loads and can handle some misalignment. They are cylindrical pins with a slot cut along their length, allowing them to be compressed slightly during installation. This provides a tight fit and prevents loosening.

Longitudinal Keys

Longitudinal keys are used to transmit torque and ensure the axial immobility of the parts. The top face of the key contacts the top of the keyway in the hub, and the bottom face contacts the shaft. They have a slight taper to prevent axial movement. The pressure between the key and the shaft is very high (1200 kp/cm2), allowing the two parts to rotate together without slipping. If it is not possible to provide a taper, the key can be secured with screws.

Woodruff Keys

Woodruff keys are used when axial displacement of the hub along the shaft is required while still transmitting torque. They are semi-circular in shape and fit into a corresponding keyway in the shaft. They are typically used for light to medium loads.

Splined Shafts

For parts that must be rigidly attached and subjected to high torques, splined shafts are used. They have multiple teeth or ridges around their circumference that engage with corresponding grooves in the hub. This provides a very secure connection and can handle very high torques.

Springs and Elastic Joints

Springs are used to absorb energy, cushion shock loads, or produce a force or pressure. They are elastic elements that have the property of deforming under load and returning to their original shape when the load is removed. Spring materials are typically alloys of iron, chromium, vanadium, silicon, and molybdenum. They can also be made of synthetic rubber.

Classification of Springs

Springs are classified based on their function, geometric shape, and the type of load they support. Some common types include:

  • Tension or extension springs: made of wire with a circular cross-section, coiled helically. The ends are bent to form hooks. They are designed to withstand tensile forces.
  • Compression springs: similar to tension springs, but designed to withstand compressive forces. The ends are typically flattened to provide a better load distribution.
  • Torsion springs: similar to tension and compression springs, but designed to withstand torsional forces. The ends are shaped to allow for the application of torque.
  • Leaf springs: curved steel blades that are clamped together in the middle with a U-bolt. The ends are attached to the parts being connected. They are commonly used in vehicle suspensions.
  • Spiral springs: flat strips of metal wound in a spiral shape. They are used to store energy or apply torque. One end is fixed, and the other end is attached to the part being moved.
  • Rubber springs: used for vibration isolation, shock absorption, and noise reduction. They can also be used for joints that require no maintenance and can handle small angular oscillations. They can work in compression or shear.

Bearings

Bearings allow a wheel or shaft to rotate freely around an axis with minimal friction. They also support the weight of the rotating element. They are essential for ensuring smooth operation and preventing wear.

Parts of a Bearing

A typical bearing consists of four main parts:

  • Outer ring: the outer raceway for the rolling elements.
  • Inner ring: the inner raceway for the rolling elements. It can be fixed to the shaft or housing.
  • Rolling elements: balls, rollers, or needles that roll between the inner and outer rings, reducing friction. Different types of rolling elements are used for different applications.
  • Cage or separator: keeps the rolling elements evenly spaced.

Types of Bearings

Bearings are classified based on the type of load they support and the type of rolling element they use. Some common types include:

  • Deep groove ball bearings: can handle both radial and axial loads, high speeds, and have low friction. They are the most common type of bearing.
  • Angular contact ball bearings: designed to handle combined radial and axial loads. They are typically used in pairs to support axial loads in both directions.
  • Cylindrical roller bearings: can handle high radial loads and high speeds. They allow for some axial movement of the shaft.
  • Tapered roller bearings: can handle both radial and axial loads. They are typically used in pairs to support axial loads in both directions.
  • Needle roller bearings: have a small cross-section and can handle high radial loads in limited space. They are commonly used in applications where space is a constraint.

Lubricants

Friction between moving parts causes energy loss, heat generation, wear, and reduced performance. Lubrication is essential to minimize friction and wear. It involves applying a substance called a lubricant between the surfaces in contact. Lubricants form a film that separates the surfaces, reducing friction. The coefficient of friction for lubricated surfaces is significantly lower than for unlubricated surfaces.

Characteristics of Lubricants

A good lubricant should:

  • Reduce friction between moving parts.
  • Act as a coolant.
  • Protect against contaminants (water, air, etc.).

Hydrodynamic Lubrication

Hydrodynamic lubrication is a method of keeping moving parts separated by a film of lubricant. This is achieved by pumping the lubricant to the contact surfaces. The lubricant pressure keeps the surfaces apart, preventing direct contact.

Temperature Considerations

Lubricants can be affected by temperature. High temperatures can cause oxidation and degradation of the lubricant, reducing its effectiveness. Additives can be used to improve the thermal stability of lubricants. Recirculation and cooling systems can also be used to maintain the lubricant temperature within the optimal range.

Lubricating Oils

Oils are used for lubrication when temperatures and speeds are high. In addition to reducing friction and cooling, they also help to remove contaminants. Closed oil systems are commonly used to keep the oil clean. Synthetic lubricants, such as SHC (Super High Performance) oils, offer several advantages over conventional mineral oils:

  • Energy savings: due to lower friction.
  • Longer service life: SHC oils can last 5 to 10 times longer than mineral oils.
  • Better oxidation resistance: SHC oils are less susceptible to oxidation at high temperatures.
  • Improved thermal stability: SHC oils maintain their properties over a wider temperature range.

The main disadvantage of SHC oils is their higher cost.

Lubricating Greases

Greases are used for the lubrication of bearings and other components where oil lubrication is not practical. They are semi-solid lubricants that consist of a base oil thickened with a soap or other thickener. The choice of grease depends on factors such as temperature, speed, vibration, and load. It is recommended to follow the manufacturer’s recommendations when selecting a grease.