This article gives you a comprehensive guide about springs. Read further to learn more about the following.
Springs are versatile mechanical components that store energy when subjected to tensile, compressive, bending, or torsional forces. As a spring deflects, it stores energy and simultaneously exerts an opposing force. The relationship between deflection and the force exerted depends on the spring’s characteristics. The most common type is the cylindrical helical spring, which features a round wire coiled into a cylindrical shape with a constant pitch. This design is frequently used in vehicle suspension systems, engine valves, dampers, and other applications.
Hooke’s Law is used to model how springs behave. It states that the force applied to a spring is directly proportional to its deflection, as long as the spring remains within its elastic range. To calculate the magnitude of the force (F), multiply the elongation distance by the spring rate.
F = -kx
In this equation, (k) represents the spring rate, and (x) is the elongation distance. The negative sign is included to indicate that the spring force acts in the opposite direction of the applied force.
For a given cross-sectional area of a spring, the applied force can be converted into stress, and the deflection can be described as strain. Hooke's Law can then be interpreted as the proportional relationship between stress and strain in a material. This ratio is known as Young's modulus. Young's modulus is often preferred for modeling spring behavior because it is an intrinsic property of the material. In contrast, the spring constant, which can vary with the spring's length, is considered an extrinsic property.
Hooke's Law applies only up to a certain limit known as the proportionality limit. Beyond this point, sometimes referred to as the elastic limit, the linear relationship between stress and strain no longer holds. When this limit is exceeded, the material undergoes plastic deformation, meaning it will not return to its original shape or length once the stress is removed.
A spring does not deflect solely through tension or compression; instead, it primarily changes dimensions due to torsion or shear forces. To better understand this, imagine unwinding the spring into a straight wire, typically with a round cross-section. In this scenario, the free body diagram would represent the cross-section of the wire, showing shear forces acting on its periphery.
Since the spring is wound into a helix, the effect of curvature must be taken into account. The curvature arises because the inner side of the spring is shorter than the outer side. This difference in length causes varying shear strains along the inner and outer sides of the wire, depending on the wire dimensions and applied torsional force. Additionally, the cross-section of the wire experiences direct shear as it resists the applied load. To achieve more accurate modeling, the Wahl correction factor is used to account for both the curvature of the wire and the direct shear stress. The resulting maximum shear stress (τ) is given by:
τ = Kw 8FD ⁄ d³
Kw = 4C - 1 ⁄ 4C - 4 + 0.615 ⁄ C
F is the force, D is the coil diameter, lowercase d is the wire diameter, Kw is the Wahl correction factor, and C is the spring index (D/d).
The spring‘s elongation distance (x) can be expressed as linear deflection (δ). The linear deflection can be derived from the angle of twist (θ) formula,
θ = TL ⁄ GJ
where: T is the torque, L is the length of the wire, G is the shear modulus, and J is the polar moment of inertia of the wire cross-section. In terms of spring design variables, the linear deflection of a spring is expressed as,
δ = 8FC³N ⁄ Gd
where: N is the number of active coils of the spring. Modifying this equation to obtain the spring rate (k) results in the equation,
k = F ⁄ δ = Gd ⁄ 8C³N
When designing a helical spring for a specific application, the key parameters typically known are the applied force and the spring length. There are generally two conditions to consider: the installed condition and the operating condition. In the installed condition, the spring is subjected to an initial force and deflection. When an additional external force is applied, this constitutes the operating condition.
To proceed with the design, initial assumptions must be made. Typically, the choice of material is selected first. The goal is then to determine the spring's geometry that can handle the applied force and deflection. Initial assumptions are made for wire dimensions, coil length, and the number of active coils for trial calculations. These values are compared with data from spring design handbooks or manufacturer datasheets. The design is verified by checking if the theoretical stress on the spring with the trial dimensions falls within the material's maximum allowable stress for the intended service. If the calculated stress exceeds this limit, alternative trial dimensions are used.
The relationships described above apply specifically to cylindrical helical springs with a constant pitch and round wire coils. Other types of springs follow different equations and factors. Additionally, this discussion has focused on the relationships between force, deflection, and stress. Designing springs also involves other considerations such as selecting the appropriate type of ends, assessing critical buckling, evaluating fatigue life, and analyzing performance under vibration and surging conditions.
Springs can be classified based on the type and nature of the force acting upon them, as well as their geometry, form, and construction. The most common type is the helical spring, which is made from a wire with a circular cross-section. There are also specialized springs designed to absorb heavier loads or to fit into mechanisms with limited clearances, featuring unique constructions tailored to specific applications.
These springs are designed to deflect under compressive loads and are the most widely used, accounting for 80 to 90% of all springs manufactured. Compression springs can have various geometries, including cylindrical, conical, convex, or concave shapes.
Cylindrical Springs: These are the most common type of spring. In cylindrical springs, the pitch is uniform throughout, and both the pitch and coil diameters remain constant along the length of the spring. As a result, the spring rate is also constant.
Conical Springs: A defining feature of conical springs is their nesting coils. The solid length of these springs is designed to match the diameter of one or two wires. They can accommodate larger deflections compared to cylindrical springs and offer greater resistance to buckling and lateral forces. Due to the varying coil diameters, the spring rate is nonlinear, which is advantageous in dynamic applications. Coils with larger diameters deflect more quickly. To achieve a linear spring rate, the pitch must be adjusted accordingly.
Barrel (Convex) and Barbell/Hourglass (Concave) Springs: These are helical springs with double cone geometries. They share the same advantages as conical springs, including improved resistance to buckling and the ability to handle larger deflections. The barrel shape has a convex profile, while the barbell or hourglass shape features a concave profile, both designed to enhance performance in various applications.
Variable Pitch Cylindrical Springs: As the name implies, these are cylindrical springs with a varying pitch along their length. This variation allows the spring to have a changing spring rate, which is particularly advantageous in dynamic applications where different force requirements are needed at different deflections.
These springs are designed to operate under tensile loads. The free length of tension springs is nearly equal to their solid length, which allows for greater deflection when stretched. While their design is similar to compression springs, there is a greater focus on the design of end hooks and the initial tension. Tension springs account for about 10% of all springs manufactured.
Tension/Extension Springs: These springs are cylindrical with tightly spaced coils. In tension or extension springs, the end hooks endure more stress compared to the coils, making them the primary point of potential failure.
Drawbar Springs: These are helical compression springs specifically designed to operate under tension. Unlike helical tension springs, drawbar springs are inherently safer because they are kept in compression, which helps prevent excessive deformation and protects the spring from permanent damage. The maximum deflection of drawbar springs is equal to their solid height.
This type of spring operates with an angular force or torque, in contrast to the linear, axial forces of compression and tension springs. Torsion springs are designed to wind up from their free position, causing the wire cross-section to experience bending rather than the twisting seen in tension and compression springs.
When torsion springs are twisted, they store mechanical energy and exert a force in the opposite direction of the applied torque. A key characteristic of torsion springs is their winding direction, which can be either right-handed or left-handed. Right-hand wound springs are twisted clockwise, while left-hand wound springs are twisted counterclockwise. The winding direction is typically determined by inspecting the end view of the spring.
These are non-helical springs with various geometries, including wound strips, cantilever beams, disks, and bars. Unlike helical springs, the cross-section of these springs experiences different types of stresses, primarily combinations of bending and torsional stresses.
Flat Springs: This type of spring is modeled as a flat beam supported at one or both ends. When supported at one end only, it is known as a cantilever spring. Flat springs can have a rectangular or tapered shape at the free end, and their cross-sectional geometry is typically rectangular. Deflections for flat springs are generally small, about 25% of the spring length. Common applications include electrical switches.
Leaf Spring: A leaf spring consists of one (mono-leaf spring) or multiple flat springs, or leaves, stacked on top of each other and held together by metal clips at each end. Leaf springs are typically shaped into elliptical, semi-elliptical, or parabolic forms, with progressively shorter leaves. They absorb and store energy through the bending of the flat springs and the friction between the layers. Leaf springs are stronger than helical springs and are commonly used as shock absorbers in heavy vehicles.
Belleville Washers: These are springs shaped like discs with a slightly conical profile. When a load is applied parallel to the cone's axis, the washer flattens. Belleville washers are capable of handling heavy loads with minimal deflection. They can be stacked either in series or parallel: stacking in series increases the allowable deformation, while stacking in parallel enhances load capacity. Belleville washers are commonly used to secure nuts and bolts by absorbing shocks and vibrations.
Garter Spring: A garter spring is a helical spring with its ends connected to form a loop. The force exerted by a garter spring acts either radially outward or inward. Garter springs that push outward are known as compression garter springs, while those that pull inward are referred to as tension garter springs. They are commonly used in applications such as oil seals and shaft seals.
Spiral or Power Springs: These are long bands or strips wound into two or more coils, with one end clamped and the other end attached to a shaft or wheel. The spring stores energy as the shaft is rotated. In mechanical watches, this type of spring is used as a balancing element, providing the oscillating time controller with its natural frequency. Consequently, in watchmaking, they are also known as balance springs or hairsprings.
Constant-Force Spring: Constant-force springs resemble spiral or power springs in their construction but are designed to store linear kinetic energy rather than rotational kinetic energy. These springs operate by pulling the outer end of the spiral and unrolling the spring. When the tension is released, the spring retracts the pulled end back due to its elasticity. Constant-force springs are commonly used in applications such as cable and rope retractors.
Volute Springs: These springs consist of thick metal strips wound into a tapered spiral, creating a conical shape. They function similarly to conical compression springs but are capable of supporting heavier loads. Due to their high cost, volute springs are used more sparingly in applications requiring robust load support.
Torsion Bars: These are long metal bars supported at one end, with the other end connected to a lever or arm. When force is applied to the arm, the bar twists along its axis. Torsion bars are commonly used in automotive chassis systems to provide suspension and support.
The types of ends available for springs vary depending on the spring type, as extension, compression, and torsion springs each have different end options. Standard ends are designed to fit the specific type of spring and ensure compatibility with its function. Additionally, manufacturers offer customized end configurations to accommodate unique and specialized applications.
Extension Spring End Options: The ends of extension springs are typically closed loops but can be customized to include hooks. Various types of end shapes are available, such as V hooks, square hooks, coned hooks, eye hooks, and very small hooks. The standard end options for extension springs include:
Compression Spring End Options: Compression springs are categorized based on their end types, which determine their application and functionality. The main end types include closed and square, where the ends are closed and cut square to provide a flat surface for even contact; closed and ground, where the ends are closed and ground flat to ensure precision and stability; double closed, where both ends are closed and often ground flat for uniform contact; and open, where the ends are open, suitable for applications where exact end conditions are less critical.
The main objective of spring design is to identify the optimal combination of spring geometry and material to achieve safe working stress at a practical cost. Key properties to aim for include high strength, high elastic limit, fatigue resistance, and hardness, along with additional properties like corrosion resistance and machinability. Heat treatment plays a crucial role in modifying the stress-strain characteristics of the metal, which must be considered when selecting the appropriate material. Common spring materials are summarized below.
Iron on its own is a relatively soft metal. However, alloying it with carbon enhances its strength and hardness. The carbon content in iron can range from 0.05% to 0.30% for mild steels, and from 0.30% to 1.70% for high carbon steels, which can still be effectively heat-treated. The following are some of the steels commonly used as spring materials:
Alloy steels contain additional elements like chromium, vanadium, phosphorus, and silicon. Each of these elements enhances specific properties of the steel, such as increased strength, hardness, and machinability. These alloying elements help tailor the steel's characteristics to meet the demands of various applications.
Stainless steel is an iron alloy that contains at least 10.5% chromium, which is the minimum amount required to impart corrosion resistance to the metal. Additional alloying elements such as nickel, manganese, and molybdenum are included to further enhance its corrosion resistance and mechanical properties. The corrosion resistance of stainless steel is due to the formation of a thin film of metal oxides on its surface, which protects it from corrosive materials. While there are many grades of stainless steel, only a select few are commonly used in spring manufacturing.
These alloys feature a base metal other than iron, with common base metals including copper and nickel. Copper alloys are known for their high electrical and thermal conductivity, excellent corrosion resistance, and good machinability. Nickel alloys, in contrast, offer superior performance at elevated temperatures, making them suitable for applications requiring high heat resistance.
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