Springs & Types Metal & Rubber Springs PDF

Gépelemek 1. SPRINGS & TYPES METAL & RUBBER SPRINGS Authors: Dr. Kerényi György Molnár László, Dr. Marosfalvi János, Dr. Horák Péter, & Dr. Baka Ernő Rugók | GÉPELEMEK 1. előadás 1 Springs Gépelemek 1. The commonly used material model of machine and structural elements: homogeneous, isotropic...

Gépelemek 1. SPRINGS & TYPES METAL & RUBBER SPRINGS Authors: Dr. Kerényi György Molnár László, Dr. Marosfalvi János, Dr. Horák Péter, & Dr. Baka Ernő Rugók | GÉPELEMEK 1. előadás 1 Springs Gépelemek 1. The commonly used material model of machine and structural elements: homogeneous, isotropic, linearly elastic material. Hooke's law is valid: σ = E·ε. Therefore, we often model the structural elements as springs (see: analysis of the force play of bolted connections), but then we only allow small deformations! Springs are those structural elements whose characteristic is that: they change their shape to a great extent under load without damage. Rugók | GÉPELEMEK 1. előadás 2 Springs (functions) Gépelemek 1. Elastic clamping, holding force (eg. Engine valve springs, furniture springs, etc.) Energy storage, damping, return (eg. dampers, bumpers, watch springs, etc.) Dynamic systems matching: tuning, tuning out (eg. Resilient couplings, clutches, vibration machines, etc.) Vibration damping (eg. Machine base, dampers, etc.) Load/torque limitations (eg. Safety valves, safety clutches, etc.) Load/torque measurement, regulation (eg. Spring scales) Others: joints, arrangements, force balancing, etc. Rugók | GÉPELEMEK 1. előadás 3 Springs (functions) Gépelemek 1. 1. Elastic clamping valve spring 2. Energy storage, eg. single acting cylinders Rugók | GÉPELEMEK 1. előadás 4 Springs (functions) Gépelemek 1. 3. Damping motion energy, eg. Buffers, bumpers, pallet stoppers Rugók | GÉPELEMEK 1. előadás 5 Springs (functions) Gépelemek 1. 4. Dynamic systems matching: tuning vibration transport pipeline vibration feeder Rugók | GÉPELEMEK 1. előadás 6 Springs (functions) Gépelemek 1. 4. Dynamic systems matching: tuning out Automotive clutch Rugók | GÉPELEMEK 1. előadás 7 Springs (functions) Gépelemek 1. 5. Vibration damping: Shock absorbers Rugók | GÉPELEMEK 1. előadás 8 Springs (functions) Gépelemek 1. 6. Force, torque measurements: torque wrenches 7. Force limitation: spring safety valve Rugók | GÉPELEMEK 1. előadás 9 Characteristics of the load case Gépelemek 1. progressive Strored energy & stiffness linear degressive Rugók | GÉPELEMEK 1. előadás 10 Characteristics of the load case Gépelemek 1. 𝑑𝐹 𝐹 Stiffness: 𝑠 = = 𝑑𝑓 𝑓 𝑁 𝑚𝑚 Spring constant: 𝑐(𝑑) = 1 𝑓 = 𝑠 𝐹 𝑚𝑚 𝑁 at torsion springs analogy 𝐹 → 𝑇, twisting torque, f → 𝜑, twisting angle, 1 𝑊 = 𝑇 ⋅ 𝜑 stored energy 2 Rugók | GÉPELEMEK 1. előadás 11 Characteristics of the load case Gépelemek 1. If the stored energy is not fully recovered when a spring is unloaded, then a part of it is lost, usually converted into heat. (dissipate) This is the physical meaning of damping. Damping factor: Illustration of a typical hysteresis loop under loadingunloading compressive conditions (a) Energy dissipated during the loading-unloading phase ΔW and (b) graphical representation of the energy U. 𝑊𝑙𝑜𝑠𝑡 Ψ= 𝑊𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 Rugók | GÉPELEMEK 1. előadás 12 Phisical principles of damping Gépelemek 1. − − − − − external Coulomb friction (structural damping), (eg. Leaf springs, volute springs) internal, property of the material of spring (viscous damping), (eg. rubber-, polymer springs) stream losses, (eg. capillar tube) constant or intermittent electrical back forces, (eg. induction clutches) other phisical effects. Rugók | GÉPELEMEK 1. előadás 13 Rheology of damping Gépelemek 1. External Coulomb friction (structural damping), Hookeelement Saint-venant element Rugók | GÉPELEMEK 1. előadás 14 Rheology of damping Gépelemek 1. internal, property of the material of spring (viscous damping), Hookeelement Kelvin-Voight element Damping force is proportional with velocity Rugók | GÉPELEMEK 1. előadás 15 Materials of springs Gépelemek 1. • metal springs, • rubber- and polymer (elastomer) springs, • air- and gas springs, • liquid springs, • Other phisical fields (eg. magnetic) application. Rugók | GÉPELEMEK 1. előadás 16 Some types of springs (metal, polymer, rubber) Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 17 Materials of springs Gépelemek 1. Spring steels – Light alloy, – Alloy, eg.: Si-Mn, Cr-V Rm~1100 -2500 [Mpa] σv~350…450 [Mpa] σmeg~0,7·Rm (for bending) τmeg~60…240 MPa (for twisting) σmeg’~0,8 ·σmeg (for fluctuating loads). ...and other alloys eg.: copper alloys Rugók | GÉPELEMEK 1. előadás 18 Materials of springs Gépelemek 1. The key difference between hot working and cold working is that hot working is done at temperatures above recrystallization temperature of the metal whereas cold working is done at temperatures below the recrystallization temperature! Spring steels in cold working Spring steels in hot working Patented steel: A, B, C, D Annealed steel: FD, VD Max. Up to 10 mm wire diameter. Patenting, annealing. Tensile strenght (dependent upon wire diameter): 1000-2000 N/mm2 Coiling in hard „phase” From 16 mm wire diameter Annealing Tensile strenght (not dependent upon wire diameter): 1000-1400 N/mm2. Heat treatment after „coiling” Rugók | GÉPELEMEK 1. előadás 19 General manufacturing steps of springs (eg. coil) Gépelemek 1. Step One – The manufacturing process starts with coiling the spring. This can be done with either cold or heated wire. Cold winding starts with a wire that is at room temperature and involves winding the wire around a shaft. The process of hot winding is used for thicker wire or bar stock. The metal is heated beforehand to increase wire flexibility and then the steel is coiled around a shaft while it is still extremely hot. After it has been coiled, it is immediately taken off of the shaft and dipped into the oil so that it can cool and harden at a rapid rate. Step Two – Once this step is complete, the steel needs to completely harden. The coiling process causes stress in the wire, which is alleviated by heat treatment. The spring is heated in an oven for a specific amount of time at a set temperature and then placed aside to cool slowly. Step Three – The following step is called shot peening and using a machine to strengthen the steel to prevent metal fatigue, which could cause cracking during its use. Step Four – The next step is called setting. It sets the spring to function correctly and remain stable at a certain length. During the process, it is completely compressed, usually multiple times, so that all the coils are completely pressed up against their bordering coils. Step Five – The final step in the creation of the spring is usually coating. This is done to prevent corrosion, and the whole surface of the spring is coated with liquid rubber or plated with another metal such as chromium or zinc. Rugók | GÉPELEMEK 1. előadás 20 Types of metal springs Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 21 Calculation of springs Gépelemek 1. Calculation of springs in various designs – shape, stress – or it is checked with the relations of elementary strength theory. These can be found in manuals, handbooks. The designer's work and preliminary planning are often helped by nomograms, detailed catalogs and auxiliary tables of manufacturing companies. linear progressive curved hysteresis Rugók | GÉPELEMEK 1. előadás 22 Calculation of metal springs (load case) Gépelemek 1. Utilization factor: energy stored in a unit volume. (compares the energy stored in a unit volume with the energy we would get if the spring had the same state of stress everywhere.) Tensioned (compressed) beam (homogeneous state of stress) Elongation: Working stress: const. Stored energy: 𝐹𝑙 𝑓= 𝐴𝐸 𝐹 𝜎= 𝐴 1 𝑊 = 𝐹𝑓 2 The volume: 𝑉 = 𝐴𝑙 Utilization factor: 𝑊 1 𝜎2 = 𝑉 2 𝐸 Rugók | GÉPELEMEK 1. előadás 23 Calculation of metal springs (leaf springs) Gépelemek 1. Simple leaf spring sagging: 𝑓 = 𝐹⋅𝑙3 3⋅𝐼⋅𝐸 𝑀 bending stress: 𝜎 = 𝐾 𝑊 1 1 𝜎2 utilization factor: = ⋅ ⋅ 𝑉 9 2 𝐸 therefore 1 𝜂= 11% − 𝑜𝑓 𝑢𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 9 Varying cross-sectional 1 𝜂= improved; 3 33% − of utilization Rugók | GÉPELEMEK 1. előadás 24 Applications of various springs Gépelemek 1. Leaf spring Coil spring Spiral spring Rugók | GÉPELEMEK 1. előadás 25 Coil springs (Twisting) Gépelemek 1. Manufacturing: from extruded wire hot or cold working process Main use: twisting (& shearing, generally ignored). No damping capability 𝐹 𝑑4 ⋅ 𝐺 Stiffness 𝑠 = = , where 𝑛𝑚 number of threads, 3 𝑓 8 ⋅ 𝐷 ⋅ 𝑛𝑚 8⋅𝐹⋅𝐷 operat𝑖𝑜𝑛 𝑠𝑡𝑟𝑒𝑠𝑠 𝜏 = 𝑘 3 𝑑 ⋅𝜋 𝐷 where 𝑡 is coil coefficient − 𝑡 = − 𝑎𝑛𝑑 𝑘 𝑓𝑟𝑜𝑚 𝑡𝑎𝑏𝑙𝑒 (𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟) 𝑑 Rugók | GÉPELEMEK 1. előadás 26 Coil springs Stress distribution (theory) Correction factor [k] Stress distribution (reality) Vertical centerline Vertical centerline Gépelemek 1. Coil coefficient [t] Rugók | GÉPELEMEK 1. előadás 27 Spiral springs (Bending) Gépelemek 1. Main use: constant bending moment 𝑀=𝑇 Angular rotation: = 𝑀⋅𝑙 𝐼⋅𝐸 𝑠𝑡 = Stiffness: Spring unfolded lenght: 𝑀 𝜑 = 𝑀= 𝐹⋅𝐿 𝐼⋅𝐸 𝑙 𝑖 2 𝑀 𝑘𝑡 ⋅ 𝑒 𝐼 𝑙 ≈ 2π𝑖 𝑟0 + ℎ Operating bending stress: 𝜎= 𝑙 ≈ 𝐷𝜋𝑖 where 𝑘𝑡 correction factor, t coil coefficient: 𝐷 𝐷 𝑡 = circular cross−section, t = rectangular cross−section. 𝑑 Utilization: circular: 𝜂 = 1 , 4 𝑉 1 rect𝑎𝑛𝑔𝑢𝑙𝑎𝑟: 𝜂 = 3 Rugók | GÉPELEMEK 1. előadás 28 Various coil springs Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 29 Coil springs Gépelemek 1. For grabbing of tensioned coil springs & fine tuning of them: It can be seen how to switch threads in & out. Stifness: 𝐹 𝑑4 ⋅ 𝐺 𝑠= = , 𝑓 8 ⋅ 𝐷 3 ⋅ 𝑛𝑚 where 𝑛𝑚 threads in use. Rugók | GÉPELEMEK 1. előadás 30 Coil springs Gépelemek 1. For grabbing of tensioned coil springs & fine tuning of them: Rugók | GÉPELEMEK 1. előadás 31 Automotive (torsion) suspension Gépelemek 1. A torsion bar is of spring steel with one end rigidly fixed to the frame. The bar twists as the other end rotates with movements of the suspension lower arm Rugók | GÉPELEMEK 1. előadás 32 Automotive (leaf & coil) suspension Gépelemek 1. A coil spring is simply a spiral of resilient steel rod. It is stretched or compressed by the vertical movement of the wheels. A leaf spring is fixed to the axle by U-bolts that clamp the centre of the stack of steel strips. As the spring deflects , its leaves flatten, make greater contact with one another and stiffen the spring. As the leave flattens, it lengthens so one end has a pivoted shackle. Rugók | GÉPELEMEK 1. előadás 33 Disc springs Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 34 Disc spring stacking Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 35 Spring systems Gépelemek 1. Progressive characteristcs with coil springs F Rugók | GÉPELEMEK 1. előadás 36 Spring systems Gépelemek 1. Various characteristcs with coil springs with series and/or parallel connections. F F Rugók | GÉPELEMEK 1. előadás 37 Spring systems in engineering Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 38 Spring systems in engineering (railway bogie) Gépelemek 1. Primary Suspension Coil A steel coil spring, two of which are fitted to each axlebox in this design. They carry the weight of the bogie frame and anything attached to it. Secondary Suspension Air Bag Rubber air suspension bags are provided as the secondary suspension system for most modern trains. The air is supplied from the train’s compressed air system. Rugók | GÉPELEMEK 1. előadás 39 Examples of metal springs Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 40 Rubber & polymer springs Gépelemek 1. Material of rubber and polymer (elastomer) springs: viscoelastic, that is, their state of strength and deformation depends on temperature and time. Polymer specifics: - creep, - relaxation, - visco-elastic behaviour. Advantageous use: mainly compression and/or shearing! Disadvantageous use: for tension and/or twisting is not too good and big elongations, rotations happen. Beneficial property: buffering & damping effect in material (internal friction). Rugók | GÉPELEMEK 1. előadás 41 Rubber & polymer springs Gépelemek 1. For description of rubbers is the Shore hardness. (eg.: Shore° A) Principles & devices of hardness measurement Rugók | GÉPELEMEK 1. előadás 42 Rubber & polymer springs behaviour at fluctuating loads Gépelemek 1. The stiffness of rubber and polymer springs – viscoelastic materials – depends on the rate of load changing velocity. „At fast” load changing they behave „stiffer” The dynamic stiffness (sd) is bigger than the static stiffness (sstat). Sd=tgβd Ss=tgβs sdin = i  sstat Rugók | GÉPELEMEK 1. előadás 43 Behaviour for compression (shape factor) Gépelemek 1. Based on experiments : for compression b.) is better than a.) ka = 1 D  2 h ka = 3 D  2 h Shape factor: (important) 𝑘𝑎 = 𝐴𝑙 loaded clamped surface = 𝐴𝑓 free surface On the above figure the number of bead plates (loaded&free surfaces) make the difference. Rugók | GÉPELEMEK 1. előadás 44 Apparent modulus of elasticity (E* for compression) Gépelemek 1. Apparent modulus On figure: apparent modulus versus shape factor is depicted with dependency on Shore hardness. In case of rubber springs, we can apply the equations known from the theory of elasticity by substituting the apparent modulus (E*) to the place of Youngs modulus (E) [Gpa] (E* is the ε=10%‐percent tangent value) The compression: 𝐹 ⋅ℎ 𝑓= 𝐴 ⋅ 𝐸∗ Shape factor Rugók | GÉPELEMEK 1. előadás 45 Behaviour for shearing (shape factor) Gépelemek 1. Rubber block between 2 bead plates Rubber blocks between 4 bead plates In case of standard rubber sizes there is practically no difference between the two types of design when subjected to shear stress. Rugók | GÉPELEMEK 1. előadás 46 Apparent shear modulus of elasticity (G* for shearing) Gépelemek 1. On figure: apparent shear modulus versus shape factor is depicted with dependency on Shore hardness. In case of rubber springs, we can apply the equations known from the theory of elasticity by substituting the apparent modulus (G*) to the place of shear Young’s modulus (G) Apparent shear modulus Shape factor G* apparent modulus 𝐹⋅ℎ 𝑓= 𝐴 ⋅ 𝐺∗ G real modulus Ratios greater than a given shape factor, the apparent shear modulus of elasticity can be considered constant, i.e. as material constant (G) [Gpa] Rugók | GÉPELEMEK 1. előadás 47 Calculation/checking of rubber/polymer springs Gépelemek 1. Rubber/polymer springs must be calculated & checked for allowable strains. The elasticity equations can be applied with using „apparent moduli” (E*, G*) Compression: 𝜎𝑚𝑒𝑔 = 𝜀 ⋅ 𝐸 ∗ Shearing: 𝜏𝑚𝑒𝑔 = 𝛾 ⋅ 𝐺 ∗ , where because of small angles 𝑡𝑔𝛾 ∼ 𝛾, Cross − section of the spring: 𝐴 = 𝐹 𝜎𝑚𝑒𝑔 , 𝑖𝑙𝑙. 𝐴 = 𝐹 𝜏𝑚𝑒𝑔 , Strain (deformation): 𝑓 = 𝜀 ⋅ ℎ, ill. 𝑓 = ℎ ⋅ 𝑡𝑔𝛾 Rugók | GÉPELEMEK 1. előadás 48 Using situations of rubber springs (state of stress) Gépelemek 1. Compressed block Sheared block Sheared sleeve Twisted sleeve Twisted disc Rugók | GÉPELEMEK 1. előadás 49 Recommended boundary situations (allowable strains) Gépelemek 1. Main use Static Dynamic Rugók | GÉPELEMEK 1. Exteme előadás 50 Rubber spring elements for measuring system bases Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 51 Anti-vibration rubber blocks for machinery bases Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 52 Railway rubber block suspensions Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 53 Air & gas springs Gépelemek 1. Main types: at the start degressive, later progressive characteristics. Pressure limit: 10 bar (1 MPa) Piston type air springs Bellow type air springs Rugók | GÉPELEMEK 1. előadás 54 Bellow & piston type air springs Gépelemek 1. Bellow type air springs Piston type air springs Rugók | GÉPELEMEK 1. előadás 55 Lorry air springs characteristics Gépelemek 1. Rugók | GÉPELEMEK 1. előadás 56