Design of Springs

PPT on Helical Spring and Leaf Spring

1. Government Engineering College, Raipur (C.G.) Department of Mechanical Engineering Prepared By: Suraj K umar Chand Assistant Professor 02-12-2017 1 Department of ME, GEC Raipur

2. SPRING 02-12-2017 2 Department of ME, GEC Raipur

3. CONTENT Introduction Function and Applications Types of spring Terminology of helical spring Styles of end Stress and Deflection equation Series and Parallel equation Spring materials and manufacturing process Design of helical spring Surge in spring Helical torsion springs Multileaf spring Equalised stress in spring leaves (nipping) 02-12-2017 3 Department of ME, GEC Raipur

4. INTRODUCTION Springs are flexible machine elements used primarily to deflect under load with the ability to return to its original shape when unloaded. They are designed to store energy, measure a force, or absorb shocks and vibrations. The popular types of mechanical springs are helical compression spring, helical extension spring, helical torsion spring, and multileaf spring. There are three criterions in design of springs which is sufficient strength to withstand external load, desired load deflection characteristic and sufficient buckling strength. 02-12-2017 Department of ME, GEC Raipur 4

5. FUNCTIONS AND APPLICATIONS Springs are used to absorb shocks and vibrations, e.g., vehicle suspension springs, railway buffer springs, buffer springs in elevators and vibration mounts for machinery. Springs are used to store energy, e.g., springs used in clocks, toys, movie-cameras, circuit breakers, and starters. Springs are used to measure the force, e.g., springs used in weighing balance and scales. Springs are used to apply force and control motion, e.g., in cam follower mechanism to maintain the contact between them, in clutch it provides the required force to engage the clutch. 02-12-2017 5 Department of ME, GEC Raipur

6. TYPES OF SPRINGS Helical spring : the helical spring is made from wire, usually of circular cross-section, which is bent in the form of a helix. There are two types of helical spring- Helical compression spring II. Helical extension spring 02-12-2017 6 Department of ME, GEC Raipur

7. In helical compression spring, the external force tends to shortens the spring while in helical extension spring, the external force tends to lengthen the spring. In both the cases, the external force acts along the axis of the spring and induces torsional shear stress in the spring wire. The words ‘compression’ and ‘extension’ are related to total spring and not to stresses in spring wire. The helical springs are sometimes classified as closely-coiled helical spring and open-coiled helical spring. A helical spring is said to be closely-coiled helical spring, when the spring wire is coiled so close that the plane containing each coil is almost at right angle to the axis of helix. (Helix angle ≤ ) A helical spring is said to be closely-coiled helical spring, when the spring wire is coiled in such a way, that there is a large gap between adjacent coil. (Helix angle > ) ADVANTAGES They are easy to manufacture. They are cheaper than other types of springs. Their reliability is high. The deflection of spring is linearly proportional to the force acting on the spring.   02-12-2017 7 Department of ME, GEC Raipur

8. Helical torsion spring : The construction of this spring is similar to that of compression or extension spring, except that the ends are formed in such a way, that the spring is loaded by a torque, about the axis of the coils. It is used to transmit a torque (P x r) to a particular component in a machine or a mechanism. It is used in door-hinges, brush holders, automobile starters and door locks. The helical torsion spring resists the bending moment (P x r), which tends to wind up the spring. The bending moment induces bending stresses in the bending wire. 02-12-2017 8 Department of ME, GEC Raipur

9. Multileaf spring : A multileaf or laminated spring consists of a series of flat plates, usually of semi-elliptical shape. The flat plates, called leaves, have varying lengths. The leaves are held together by means of U-bolts and center clip. The longest leaf, called master leaf, is bent at the two ends to form spring eyes. The leaves of multileaf spring are subjected to bending stresses. They are widely used in automobile and railroad suspensions. 02-12-2017 9 Department of ME, GEC Raipur

10. TERMINOLOGY OF HELICAL SPRING The main dimensions of helical spring subjected to compressive force are as follows: d = wire diameter of spring (mm) inside diameter of spring coil (mm) outside diameter of spring coil (mm) D = mean coil diameter (mm) Therefore,   02-12-2017 10 Department of ME, GEC Raipur

11. There is an important parameter in spring design called spring index. It is denoted by letter C . the spring index is defined as the ratio of mean coil diameter to the wire diameter, The spring index indicates the relative sharpness of the curvature of the coil- A low spring index means high sharpness of curvature. When the spring index is low (C < 3), the actual stresses in the wire are excessive due to curvature effect. Such a spring is difficult to manufacture and special care in coiling is required to avoid cracking in some wires. when the spring index is high (C > 15), it results in large variation in coil diameter. Such a spring is prone to buckling and also tangles easily during handling. Therefore spring index from 4 to12 is considered better for manufacturing consideration.   02-12-2017 11 Department of ME, GEC Raipur

12. Solid length : Solid length is defined as the axial length of the spring which is so compressed that the adjacent coils touch each other. In this case, the spring is completely compressed and no further compression is possible. Solid length = d Where = total number of coils Compressed length : compressed length is defined as the axial length of the spring, which is subjected to maximum compressive force. In this case, the spring is subjected to maximum deflection δ . There should be some gap between the coils at the maximum deflected position to avoid clashing between them. The clashing allowance or total axial gap is usually taken as 15% of the maximum deflection. Sometimes an arbitrary decision is taken and it is assumed that there is a gap of 1 mm or 2 mm between adjacent coils under maximum load condition, in this case- Total gap = ( -1) x gap between adjacent coils Free length : Free length is defined as the axial length of an unloaded helical compression spring. In this case there is no external force acts on the spring. Free length = compressed length + δ = solid length + total axial gap + δ   02-12-2017 12 Department of ME, GEC Raipur

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14. Pitch : The pitch of the coil is defined as the axial distance between adjacent coils in uncompressed state of spring. It is denoted by p . p = Stiffness : The stiffness of the spring is defined as the force required to produce unit deflection. Therefore, k = Active and inactive coils: Active coils are the coils in the spring, which contribute to spring action, support the external force and deflect under the action of force. A portion of the coil at each end, which is in contact with the seat, does not contribute to spring action and called inactive coil. These coils do not support the load and do not deflect under the action of external force. The number of inactive coils is given by, Inactive coils = ( - N)   02-12-2017 14 Department of ME, GEC Raipur

15. STYLES OF END : Helical compression spring Type of ends Numbers of active turns Plain ends Plain ends (ground) ( Square ends ( Square ends (ground) ( Type of ends Numbers of active turns Plain ends Plain ends (ground) Square ends Square ends (ground) 02-12-2017 15 Department of ME, GEC Raipur

16. STYLES OF END : Helical extension spring For helical extension springs, all coils are active coils. The number of active coils ( N ) is the same as the total number of coils ( ).   02-12-2017 16 Department of ME, GEC Raipur

17. STRESS AND DEFLECTION EQUATION There are two basic equations for the design of helical springs : Load-stress equation Load-deflection equation Load-stress Equation 02-12-2017 17 Department of ME, GEC Raipur

18. The dimensions of equivalent bar are as follows: The diameter of the bar is equal to the wire diameter of the spring (d). The length of one coil in the spring is ( π D). There are N such active coils. Therefore, the length of equivalent bar is ( π DN). The bar is fitted with bracket at each end. The length of this bracket is equal to mean coil radius of the spring (D/2). Torsional moment, Torsional shear stress, or …..(a) When the equivalent bar is bent in the form of helical coil, there is additional stresses on account of following two factors: There is a direct or transverse shear stress in the spring wire. When the bar is bent in the form of coil, the length of inner fibre is less than the length of outside fibre. This results in stress concentration at the inside fibre of the coil.   02-12-2017 18 Department of ME, GEC Raipur

19. The resultant stress consists of superimposition of torsional shear stress, direct shear stress and additional stresses due to the curvature of the coil. 02-12-2017 19 Department of ME, GEC Raipur

20. There are two factors to account for these effects: = Factor to account for direct shear stress = factor to account for stress concentration due to curvature effect The combined effect of these two factors is given by, K = The direct shear stress in the bar is given by = = ......(b) Resultant shear stress, τ = + = …...(c) The shear stress correction factor ( ) is defined as, = or Hence τ = …..(d) Where K is called stress factor or Wahl factor and is given by K =   02-12-2017 20 Department of ME, GEC Raipur

21. Load-deflection equation : The angle of twist for the equivalent bar is given by, θ = = or θ = …..(e) The axial deflection ‘δ’ of the spring, for small value of θ, is given by, δ = θ x (D/2 ) = …..(f) The rate of spring (k) is given by, k = = …..(g) The energy stored in the spring E = Area under load-deflection line = δ   02-12-2017 21 Department of ME, GEC Raipur

22. SERIES AND PARALLEL CONNECTIONS Series connection Parallel connection   k = +   02-12-2017 22 Department of ME, GEC Raipur

23. SPRING MATERIALS There are four basic varieties of steel wire which are used in springs in the majority of applications- Patented and cold-drawn steel wires (unalloyed) There are two terms related to this type of spring wire which is ‘patenting’ and ‘cold drawing’. Patenting is defined as heating the steel above the critical range and followed by rapid cooling. This operation produces a tough uniform structure that is suitable for severe cold working. They are made of high carbon steel and contain 0.85-0.95% carbon. Least expensive. Patented and cold-drawn steel wires are mainly used in springs subjected to static forces and moderate fluctuating forces. 02-12-2017 23 Department of ME, GEC Raipur

24. Oil-hardened and tempered spring steel wires and valve spring wires Oil hardened and tempered spring steel wire contains 0.55-0.75% carbon. The wire is cold drawn and then hardened and tempered. Valve spring wire contains 0.60-0.75% carbon. It is the highest quality of oil hardened and tempered steel wire. There are two grades of unalloyed, oil-hardened and tempered spring steel wire and valve spring wire which is SW and VW. Grade SW is suitable for spring subjected to moderate fluctuating stresses, where as grade VW is recommended when the spring is subjected to a high magnitude of fluctuating stresses. Oil-hardened and tempered steel wires (alloyed) There are two varieties of alloy steel wires, namely chromium-vanadium steel and chromium-silicon steel. Chromium-vanadium steel contains 0.48-0.53% carbon, 0.80-1.10% chromium, and 0.15% vanadium. These wires are used for applications involving higher stresses and for springs subjected to impact or shock loads. Chromium-silicon spring steel contains 0.51-0.59% carbon, 0.60-0.80% chromium and 1.2-1.6% silicon. These are also used for shock or impact loading. 02-12-2017 24 Department of ME, GEC Raipur

25. Stainless steel spring wires . Stainless steel springs, which exhibit an excellent corrosion resistance, are ideal to work in steam or other corrosive medium. Costly. SPRING MANUFACTURING PROCESSES If springs are of very small diameter and the wire diameter is also small then the springs are normally manufactured by a cold drawn process through a mangle. However, for very large springs having also large coil diameter and wire diameter (greater than 6 mm) one has to go for manufacture by hot processes. First one has to heat the wire and then use a proper mangle to wind the coils. 02-12-2017 25 Department of ME, GEC Raipur

26. UTS-EXPONENTIAL RELATIONSHIP It is observed that the ultimate tensile strength of spring material varies significantly with wire diameter. Therefore, ultimate tensile strength cannot be specified unless the wire diameter is known. A number of experiment is carried out to find out the relationship between the ultimate tensile strength and the wire diameter and it is concluded that the graph of ultimate tensile strength versus wire diameter is almost a straight line when plotted on a log-log paper. The equation of this straight line is given by, where, A = intercept of straight line m = slope of straight line   02-12-2017 26 Department of ME, GEC Raipur

27. DESIGN OF HELICAL SPRINGS There are three objectives for design of the helical spring- It should possess sufficient strength to withstand the external load. It should have the required load-deflection characteristics; and It should not buckle under the external load. The main dimensions to be calculated in the spring design are- wire diameter, mean coil diameter and the number of active coils . The first two are calculated by load-stress equation, while the third is calculated by load-deflection equation. The factor of safety in design of spring is usually 1.5 or less. τ = Assuming, = 0.75 and = 0.577 τ ≈ 0.3 Generally in design of helical springs, the permissible shear stress ( τ ) is taken from 30% to 50% of ultimate tensile strength ( ) τ = 0.3 or 0.5   02-12-2017 27 Department of ME, GEC Raipur

28. Procedure… For the given application, estimate the maximum spring force (P) and the corresponding required deflection ( δ ) of the spring. In some cases, maximum spring force (P) and stiffness k, which is (P/ δ ), are specified. Select suitable spring material and find out ultimate tensile strength ( ) from the data. Calculate the permissible shear stress for the spring wire by following relationship: τ = 0.3 or 0.5 Assume a suitable value for spring index (C). For industrial applications, the spring index varies from 8 to 10. A spring index of 8 is considered as a good value. The spring index for springs in valves and clutches is 5. the spring index should never be less than 3. Calculate the Wahl factor by following equation: K = Determine wire diameter (d) by, τ = Determine mean coil diameter (D) by following relationship D = Cd   02-12-2017 28 Department of ME, GEC Raipur

29. Determine the number of active coils (N) by δ = the modulus of rigidity (G) for steel wires is 81370 N/ Decide the style of ends for the spring depending upon configuration of the application. Determine the number of inactive coils. Adding active coils and inactive coils, find out the total number of coils ( ). Determine the solid length of the spring by following relationship, Solid length = d Determine the actual deflection of the spring by, δ = Assume a gap of 0.5 to 2 mm between adjacent coils, when the spring is under the action of maximum load. The total axial gap between the coil is given by, Total gap = ( -1) x gap between two adjacent coils In some cases, the total axial gap is taken as 15% of the maximum deflection. Determine the free length of the spring by following relationship Free length = solid length + total gap + δ   02-12-2017 29 Department of ME, GEC Raipur

30. Determine the pitch of the coil by following relationship p = Determine the rate of spring by k = = Prepare a list of spring specifications. A helical compression spring, that is too long compared to the mean coil diameter, acts as a flexible column and may buckle as a comparatively low axial force. The spring should be preferably designed buckle-proof. The thumb rules for provision of guide are as follows: [Guide not necessary] [Guide required]   02-12-2017 30 Department of ME, GEC Raipur

31. SPRING DESIGN – TRIAL AND ERROR METHOD From mechanical properties of spring wire it is observed that the tensile strength decreases as wire diameter increases. Therefore, tensile strength is inversely proportional to wire diameter. ……….(a) but τ = 0.3 or 0.5 …………(b) hence τ ……………….(c) we know that τ = ……………(d) therefore …………(e) From expressions (c) and (e), it is observed that permissible stress is proportional to (1/d), while induced stress is proportional to (1/ ). The trial and error procedure consists of following steps: Assume some wire diameter (d). Find out the corresponding tensile strength from data book and using this value find out permissible stress by eq. (b). Find out induced stress by eq. (d). Check up whether permissible stress is more than induced stress. If not, increase the wire diameter and repeat the above steps. The above mentioned procedure is repeated till the value of induced stress comes out to be less than the permissible stress.   02-12-2017 31 Department of ME, GEC Raipur

32. DESIGN AGAINST FLUCTUATING LOAD The springs subjected to fluctuating stresses are designed on the basis of two criteria- design for infinite life and design for finite life . let us consider a spring subjected to an external fluctuating force, which changes its magnitude from in the load cycle. = ½ ( + ) = ½ ( - ) Mean stress is given by, where, is the correction factor for direct shear stress and it is applicable to mean stress only. For torsional stress amplitude ( ), it is necessary to also consider the effect of stress concentration due to curvature in addition to direct shear stress. Therefore, where K is the Wahl factor, which takes into consideration the effect of direct shear stress as well as of stress concentration due to curvature.   02-12-2017 32 Department of ME, GEC Raipur

33. A helical compression spring is subjected to purely compressive force, on the other hand, a helical extension spring is subjected to purely tensile force. In general, the spring wires are subjected to pulsating shear stresses, which vary from zero to . is the endurance limit in shear for the stress variation from zero to some maximum value. The data regarding the experimental values of endurance strength of spring wire is not readily available. In absence of such values, the following relationships suggested by H.J. Elmendorf can be used, For patented and cold-drawn steel wires (Grade -1 to 4), = 0.21 ; = 0.42 ……………………………..(a) for oil-hardened and tempered steel wires (SW and VW grade), = 0.22 ; = 0.45 ……………………………..(b)   02-12-2017 33 Department of ME, GEC Raipur

34. The fatigue diagram for the spring is shown in figure. The line GH is constructed in such a way that its slope θ is given by, tan θ = Consider similar triangles XFD and AEB, ; or   02-12-2017 34 Department of ME, GEC Raipur

35. SURGE IN SPRING When the natural frequency of vibrations of spring coincides with the frequency of external periodic force, which acts on it, resonance occurs. In this state, the spring is subjected to a wave of successive compressions of coils that travels from one end to the other and back. This type of vibratory motion is called ‘surge’ of spring. Surge is found in valve springs, which are subjected to periodic force. Methods to avoid surge in springs: The spring is designed in such a way that the natural frequency of the spring is 15 to 20 times the frequency of excitation of the external force. This prevents the resonant condition to occur. The spring is provided with friction dampers on central coils. This prevents propagation of surge valve. A spring made of stranded wire reduces the surge. In this case, the wire of spring is made of three strands. The direction of winding of strands is opposite to the direction of winding of the coils while forming the spring. In case of compression of coils, the spring tends to wind the individual wires closure together, which introduces friction. This frictional damping reduces the possibility of surge. 02-12-2017 35 Department of ME, GEC Raipur

36. HELICAL TORSION SPRINGS A helical torsion spring is a device used to transmit the torque to a particular component of a machine or mechanism. It is widely used in door hinges, brush holders, automobile starters and door locks. Each individual section of the torsion spring is, in effect, a portion of a curved beam. Using the curved beam theory, the bending stresses are given by, ……….(a) y = (d/2) and I = ( π /64) Hence, K is stress concentration factor and is given by, Where and are stress concentration factors at the inner and outer fibres of the coil respectively.   02-12-2017 36 Department of ME, GEC Raipur

37. U = ∫ or U = ∫ We have, θ = And stiffness of the helical torsion spring =   02-12-2017 37 Department of ME, GEC Raipur

38. MULTILEAF SPRING Multileaf springs are widely used for the suspension of cars, trucks, and railway wagons. It consists of flat plates, usually of semi-elliptical shape. The flat plates are called leaves of spring. The leaves have graduated lengths. The leaf at the top has maximum length. The length gradually decreases from the top leaf to the bottom leaf. The longest leaf at the top is called master leaf. It is bent at both ends to form the spring eyes. Two bolts are inserted through these eyes to fix the leaf spring to the automobile body. The leaves are held together by means of two U-bolts and a center clip. Rebound clips are provided to keep the leaves in alignment and prevent lateral shifting of the leaves during operation. 02-12-2017 38 Department of ME, GEC Raipur

39. At the center, the leaf spring is supported on the axle. Multileaf springs are provided with one or two extra full length leaves in addition to master leaf. They are provided to support the transverse shear force. For the purpose of analysis, the leaves are divided into two groups namely, master leaf along with graduated length leaves forming one group and extra full length leaves forming the other. number of extra full-length leaves number of graduated-length leaves including master leaf n = total number of leaves b = width of each leaf (mm) t = thickness of each leaf (mm) L = length of the cantilever or half the length of semi elliptic spring (mm) P = force applied at the end of the spring (N) = portion of P taken by the extra full-length leaves (N) = portion of P taken by the graduated-length leaves (N)   02-12-2017 39 Department of ME, GEC Raipur

40. The group of graduated length leaves along with the master leaf can be treated as a triangular plate. In this case, it is assumed that the individual leaves are separated and the master leaf placed at the center. Then the second leaf is cut longitudinally into two halves, each of width ( b/2 ) and placed on each side of the master leaf. A similar procedure is repeated for other leaves. The resultant shape is approximately a triangular plate of thickness t and a maximum width at the support as ( ). the bending stress in the plate at the support is given by, Or, = And deflection,   02-12-2017 40 Department of ME, GEC Raipur

41. Similarly, the extra full length leaves can be treated as a rectangular plate of thickness t and a uniform width ( ). The bending stress at the support is given by, or, = The deflection at the load point is given by, or,   02-12-2017 41 Department of ME, GEC Raipur

42. The deflection of full length leaves is equal to the deflection of graduated length leaves, = From above relationship it can be derived as, and Using these values the bending stresses can be written as and It is seen from the above equations that bending stresses in full length leaves are 50% more than in graduated length leaves. The deflection at the end of spring ( ) is given by, =   02-12-2017 42 Department of ME, GEC Raipur

43. EQUALISED STRESS IN SPRING LEAVES (NIPPING) As discussed earlier, the bending stresses in full length leaves are 50% more than in graduated length leaves. All leaves should be stressed to the same level in order to utilize the material to the best advantage. One of the method of equalizing the stresses in different leaves is to prestress the spring. The prestressing is achieved by bending the leaves to different radii of curvature, before they are assembled with the center clip and U bolts. The full length leaf is given a greater radius of curvature than the adjacent leaf. This will leave a gap or clearance space between leaves as shown in figure. 02-12-2017 43 Department of ME, GEC Raipur

44. When the center clip is drawn up by tightening U bolts, the upper leaf will bend back and have an initial stress opposite to that produced by normal load P . on the contrary, the lower leaf will have an initial stress of the same nature as that produced by normal load P . When the normal load is applied, the stress in the upper leaf is relieved and then increased in normal way. The initial gap between the leaves can be adjusted in such a way that under maximum load condition, the stress in all leaves will be same. The initial gap C between the extra full-length leaf and the graduated-length leaf before the assembly is called ‘nip’. Such prestressing, achieved by a difference in radii of curvature, is known as ‘nipping’. The initial gap C is given by, C = The initial preload required to close the gap C is given by, And finally the stresses are equal in all leaves is given by,   02-12-2017 44 Department of ME, GEC Raipur

45. THANK YOU 02-12-2017 45 Department of ME, GEC Raipur