This article gives you a comprehensive guide about springs. Read further to learn more about the following.
- What is a spring?
- Overview of spring design
- Types of spring
- Common spring materials
Chapter One – What is a Spring?
Springs are a flexible machine element 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 on 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. The Young’s modulus is more extensively used to model the behavior of springs since it is an intrinsic property of a material. The spring constant, on the other hand, 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.
Chapter Two – Overview of Spring Design
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 turning it 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 wire dimensions 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. To have a more accurate model, a term to account for the curvature of the wire and the direct shear stress is used. This is 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
Where: F is the force, D is the coil diameter, 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 usually known parameters 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 are 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.
Chapter Three – Types of Springs
Springs can be classified according to the type and nature of the force acting on the spring. These can be further categorized from 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.
Helical Compression Springs: 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.
Cylindrical Springs: This is the most common type of spring. The pitch on these springs is equal. Since the pitch and coil diameters do not change along the length of the spring, the spring rate is constant.
Conical Springs: The main characteristic of these springs is their nesting coils. The solid length of conical springs is designed to be equal to the diameter of one or two wires. They can be used for larger deflections than cylindrical springs. Also, they are more resistant to buckling and lateral forces. Because of the different coil diameters, the spring rate is not linear which is desired in dynamic applications. The coils with larger diameters tend to deflect faster. To make the spring rate linear, the pitch must be varying.
Barrel (Convex) and Barbell/Hourglass (Concave) Springs: These are helical springs with double cone geometries. They have the same advantages as that of conical springs.
Variable Pitch, Cylindrical Spring: As the name suggests, these are cylindrical springs with varying pitch. This enables the spring to have a varying spring rate which is desirable for dynamic applications.
- Cylindrical Springs: This is the most common type of spring. The pitch on these springs is equal. Since the pitch and coil diameters do not change along the length of the spring, the spring rate is constant.
Helical Tension Springs: 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.
Tension/Extension Springs: These springs are cylindrical in shape and have close spaces between coils. In this type of springs, the end hooks experience more stress than the coil which becomes the initial site for failure.
Drawbar Springs: These are helical compression springs used in tension. This design is safer than helical tension springs since being in compression prevents the spring from deforming excessively. This also protects the spring from permanent deformation. The maximum deflection is the solid height.
- Tension/Extension Springs: These springs are cylindrical in shape and have close spaces between coils. In this type of springs, the end hooks experience more stress than the coil which becomes the initial site for failure.
Helical Torsion Springs: This spring operates with an angular force or torque which is different from the previous two springs that 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.
Special Springs: 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.
Flat Spring: The model for this type of spring is a flat, beam supported either on one end or both ends. When supported on one end, it is considered as a cantilever spring. Its shape can be rectangular or tapered at the free end. With regards to the cross-section, the geometry is usually rectangular. The deflections for this type of spring are small which is only about 25% of the spring length. Common applications of flat springs are electrical switches.
Leaf Spring: A leaf spring is made of one (mono-leaf spring) or multiple flat springs or leaves layered on top of each other. The layers are held together by metal clips at each end. Leaf springs are usually formed into an elliptical, semi-elliptical, or parabolic shape with progressively shorter leaves. They absorb and store energy through bending of the multiple flat springs and the friction between the layers. They are stronger than helical springs and are used for shock absorbers of heavy vehicles.
Belleville Washers: These are springs shaped into discs with a slightly conical shell. The load is applied parallel to the axis of the cone which flattens the washer. Belleville springs can carry heavy loads with small deflections. Also, they can be stacked on top of each other which can be in series or parallel. The series stack is for multiplying the allowable deformation while the parallel stack is for multiplying the load capacity. They are used in holding nuts and bolts in place by absorbing shocks and vibrations.
Garter Spring: A garter spring is a helical spring with the ends attached. The force returned by a garter spring acts radially outward or inward. Garter springs that exert an outward force are compression garter springs while garter springs that act the opposite are tension garter springs. They are commonly used in 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 attached to a shaft or wheel. The spring stores energy when the shaft is rotated. This is used as a balancing element in mechanical watches that gives the oscillating time controller its natural frequency. Thus, in watchmaking, they are also called balance spring or hairspring.
Constant-force Spring: Constant-force springs are similar to spiral or power springs in construction, but instead of storing rotational kinetic energy, they store linear kinetic energy. It works by pulling the outer end of the spiral unrolling the spring. When the tension is released, the pulled end is retracted back due to the elasticity of the spring. They are commonly used in cable and rope retractors.
Volute Springs: These are thick metal strips wound into a tapered spiral forming a cone. Their function is similar to conical compression springs, but they are able to support heavier loads. They are used sparingly because of their high cost.
Torsion Bars: These are long metal bars supported on one end while the other end is attached to a lever or arm. When a force is applied to the arm, the bar is twisted with respect to its axis. These are used in automotive chassis.
- Flat Spring: The model for this type of spring is a flat, beam supported either on one end or both ends. When supported on one end, it is considered as a cantilever spring. Its shape can be rectangular or tapered at the free end. With regards to the cross-section, the geometry is usually rectangular. The deflections for this type of spring are small which is only about 25% of the spring length. Common applications of flat springs are electrical switches.
Chapter Four – Common Spring Materials
The main objective of spring design is to determine the right combination of spring geometry and material that will 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.
- Music Wire (ASTM A228): This is the best carbon spring steel material. Music wires have high tensile strength, high elastic limit, and high fatigue resistance. These superior mechanical properties are imparted by patented cold work done in drawing the wire through dies. Its surface is coated with a liquid tin solution during cold work which creates an excellent surface quality ready for secondary processes such as electroplating. They are typically used to make small springs subjected to high loads and cyclic conditions.
- Oil-tempered (ASTM A229 Class I and II): These carbon steels with good quality characterized by black or gray color. Oil-tempered spring steels have comparable mechanical properties with music wire and are used in most applications where the cost of music wire is impractical.
- Hard-drawn (ASTM 227): These are the cheapest of the spring materials with inferior qualities compared to music wire and oil-tempered steels. Hard-drawn wires are also cold worked similar to music wires, but the drawing process used is less controlled than that of music wires.
- High-Carbon Valve Spring Steel (ASTM A230): These are high-carbon steels with uniform quality and temper. They are drawn the same way as oil-tempered steels, but their heat treatment is more controlled. As the name suggests, they are used as valve springs in automotive and aircraft engines which require corrosion resistance, fatigue resistance, and good performance at high temperatures.
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.
- Chromium-Vanadium Valve Spring Steel (ASTM A232): Chromium-vanadium steel alloys have the highest quality among the alloy steels in terms of valve spring applications. These are available as annealed, cold-drawn, or oil-tempered wires. Springs made from these alloys are used in high fatigue, high shock loadings. Their service temperatures are higher than high-carbon valve springs.
- Chromium-Silicon Alloy (ASTM A401): These are available in cold-drawn or oil-tempered conditions. Chromium-silicon steel alloy can be heat treated to high hardness without losing much ductility. They are suitable in high impact loadings such as firearm recoil springs.
Stainless steel is a type of 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 is a wide array of stainless steel grades available but only a few are used in spring manufacturing.
- Austenitic Stainless Steels, 300 Series: These are stainless steels with an austenitic crystalline structure that is achieved by alloying nickel. Because of their austenitic structure, they are not hardenable by heat treatment. Their hardness and high tensile strength are acquired through cold working. Its main alloying elements are nickel and chromium which have concentrations ranging from 8 to 11.5% and 17.5 to 18.5%, respectively. 300 series stainless steels used for springs are grades 301, 302, 304, and 316.
- Martensitic Stainless Steels: These steels are alloyed by chromium and molybdenum for corrosion resistance with a low percentage of nickel. They have a lower chromium content that ranges from 12.5 to 17%. Thus, they have lower corrosion resistance than austenitic stainless steels. The advantage of using martensitic stainless steel is its ability to harden through heat treatment. Popular grades for making springs are 420 and 431.
- Precipitation Hardening Stainless Steels: Precipitation hardening is a heat treatment process that significantly enhances the mechanical properties of the material. On top of that, the heat treatment process can be optimized which is important to achieve a balance between hardness and ductility. Typical grades used are martensitic 17-4PH and semi-austenitic 17-7PH.
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.
- Phosphor Bronze (ASTM B159): Phosphor bronze is an alloy of copper, tin, and phosphorus. This is the most widely used copper-base spring alloy. They have good electrical conductivity coupled with the ability to withstand repeated bending. However, they are not hardenable by heat treatment.
- Beryllium Copper (ASTM B197): Beryllium copper is another popular copper-based alloy characterized by its ability to be heat treated. They are initially cold drawn which is then precipitation hardened after forming. Like phosphor bronze, they have good electrical conductivity and fatigue resistance.
- Monel 400: Monel 400 is a nickel-based alloy composed of around two-thirds nickel, one-third copper. They are the least expensive and with the lowest tensile strength of the nickel alloys used in spring manufacturing. Monel 400 alloys can only be hardened through cold working.
- Monel K-500: Its composition is similar to Monel 400 but with additions of small amounts of aluminum and titanium. The addition of aluminum and titanium allows it to be heat treatable through precipitation hardening.
- Inconel 600: This is an alloy composed of nickel, chromium, and iron. These are more expensive than stainless steel but are particularly useful for higher service temperatures. Inconel 600 cannot be hardened through heat treatment.
- Inconel X-750: Like Inconel 600, this alloy is composed of nickel, chromium, and iron but with the addition of aluminum, titanium, and columbium. The addition of these alloying elements makes Inconel X-750 a precipitation-hardenable alloy.
- A spring is a flexible machine element that stores mechanical energy when subjected to tensile, compressive, bending, or torsional forces.
- Hooke’s law states that the force applied on the spring is directly proportional to its deflection provided that it is within the elastic range.
- The most common form of spring is a helical spring which is made from a wire with a circular cross-section.
- The main objective of spring design is to determine the right combination of spring geometry and material that will achieve safe working stress at a practical cost.
- Spring materials are made from alloys such as steel, stainless steel, copper alloys, and nickel alloys.