This article gives you a comprehensive guide about springs. Read further to learn more about the following.
Springs are a flexible machine elements that store mechanical energy when subjected to tensile, compressive, bending, or torsional forces. When the spring is deflected, it stores energy and, at the same time, exerts an opposing force. The relationship between the amount of deflection and the force exerted depends on the characteristics of the spring. The most common form is a cylindrical, helical spring with a constant pitch. This type of spring is a round wire spooled into a cylindrical form. It is commonly seen in vehicle suspension systems, engine valves, dampers, and so on.
Hooke‘s law is used to model the behavior of springs. It states that the force applied to the spring is directly proportional to its deflection, provided that it is within the elastic range. To find the magnitude of the force (F), the elongation distance is multiplied by a spring rate.
F = -kx
Where k is the spring rate and x is the elongation distance. The negative sign is only a convention to indicate that the spring force acts in the opposite direction.
For a given cross-sectional area of the spring, the force can be converted into stress, while the deflection can be described as strain. Hooke‘s law can then be defined as the proportionality between the stress and strain of a material. The ratio between stress and strain is called Young‘s modulus. Young‘s modulus is more extensively used to model the behavior of springs since it is an intrinsic property of a material. On the other hand, the spring constant varies with the length of spring making it an extrinsic property.
Hooke‘s law only applies until a certain limit, called the proportionality limit. Sometimes, the elastic limit is considered. Beyond this point, the linearity between stress and strain does not hold. The material is plastically deformed, which means it will not return to its original shape or length when the stress is removed.
A spring does not deflect through tension or compression. They change their dimension mainly due to torsion or shear. To further visualize, suppose the spring is unwound into a straight wire, typically with a round cross-section. The resulting free body diagram then becomes the cross-section of the wire with shearing forces acting on its periphery.
Since the spring is wound into a helix, the spring‘s curvature must be considered. The curvature effect is due to the shorter length of the inner side than the outer. The shear strain experienced by the inner and outer sides differs with the dimensions of the wire and torsional force. Moreover, the cross-section of the wire is subjected to direct shear. Direct shear is developed as the wire resists the applied load. More accurate models will use a term to account for the curvature of the wire and the direct shear stress, known as the Wahl correction factor. The resulting maximum shear stress (τ) is stated as,
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
In designing a helical spring for a particular application, the parameters usually known are the applied force and the length of the spring. In actual cases, there will be two conditions: the operating condition and the installed condition. When a spring is in its installed condition, it is subjected to an initial force and deflection. When an external force is applied, this is known as the operating condition.
To proceed with the design, initial values must be assumed. Typically, the type of material is initially selected. The objective of the design then becomes finding the geometry of the spring that can operate under the applied force and deflection. Wire dimensions, coil length, and the number of active coils are assumed initially for trial calculation. These values are correlated through tables and charts from spring design handbooks or manufacturer datasheets. The values are verified if the theoretical stress experienced by the spring with trial dimensions is within the maximum allowable stress of the material operating at a given type of service. If the theoretical stress calculated exceeds the maximum allowable stress, another set of trial dimensions is used.
The relationships stated above are only applicable for cylindrical, helical springs with constant pitch, and round wire coils. There are other types of springs that are governed by different equations and factors. Moreover, this discussion only tackled the relationships between force, deflection, and stress. Designing springs can also involve determining the right type of ends, critical buckling, fatigue life, and performance in vibration and surging.
Springs can be classified according to the type and nature of the force acting on the spring. These can be further categorized by their geometry, form, and construction. The most common form of spring is a helical spring, which is made from a wire with a circular cross-section. Springs with special constructions exist for absorbing heavier loads or for fitting in mechanisms with small clearances.
These are springs that are designed to deflect under compressive loads. They are the most commonly used and represent 80 to 90% of all springs manufactured. Compression springs geometries can be cylindrical, conical, convex, or concave.
These are springs that operate with tensile loads. The free length of tension springs is almost equal to the solid length to allow more deflection when stretched. The design of tension springs is the same as compression springs but with more emphasis on the design of end hooks and the initial tension. Tension springs represent about 10% of all springs manufactured.
This spring operates with an angular force or torque different from the previous two springs, which deflect under linear, axial forces. Torsion springs are designed to wind up from the free position. This winding subjects the wire cross-section to bending, instead of the torsion models used in tension and compression springs.
When torsion springs are twisted, they store mechanical energy and exert force in the opposite direction of the applied force. The most important aspect of torsion springs is their winding, which can be right or left-handed. Right-hand wound springs are wound clockwise, while left-handed wound ones are wound counterclockwise. The winding of a torsion spring can only be seen by looking at the end of the spring.
These are non-helical springs with geometries such as wound strips, cantilever beams, disks, and bars. The cross-section of the spring material is subjected to different types of stresses, mostly combinations of bending and torsional stresses.
The types of ends available for springs depend on the spring type since extension, compression, and torsion springs have different options regarding the types of ends they may have. Each spring has standard ends that easily conform to its type. Additionally, manufacturers offer customized ends to meet the needs of unique and unusual applications.
The main objective of spring design is to determine the right combination of spring geometry and material to achieve safe working stress at a practical cost. The desired properties to achieve this are high strength, high elastic limit, fatigue resistance, and hardness, with added properties such as corrosion resistance and machinability. Regarding the mechanical properties, the role of heat treatment is important in altering the stress-strain characteristics of the metal. All of these must be considered in selecting the right material. Common spring materials are summarized below.
Iron in itself is a soft metal. Alloying it with carbon increases its strength and hardness. Its carbon content can range from 0.05 to 0.30% for mild steels and 0.30 to 1.70% for high carbon steels that can still respond to heat treatment. Enumerated below are some of the steels used as spring materials.
These are steels with additional alloying elements such as chromium, vanadium, phosphorus, and silicon. Each element enhances different properties of steel, such as strength, hardness, and machinability.
Stainless steel is an iron alloy containing 10.5% chromium, which is the minimum amount to impart corrosion resistance to the metal. Other alloying elements such as nickel, manganese, and molybdenum are present to enhance its corrosion resistance and mechanical properties. Corrosion resistance is achieved by creating a thin film of metal oxides that acts as protection against corrosive materials. There are a wide array of stainless steel grades available, but only a few are used in spring manufacturing.
These are alloys with a base metal other than iron. Common base metals used for spring materials are copper and nickel. Copper alloys generally have high electrical and thermal conductivity, good corrosion resistance, and machinability. Nickel alloys, on the other hand, have superior elevated temperature properties.
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