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Physical aspects

Physical aspects. Content. Static and Dynamic Friction Force and Elongation Creep and Slip Energy and Efficiency Temperature and Humidity. Static and Dynamic Friction. Definition of coefficient of friction m. Coulomb’s law. 1 Conveyed goods 2 Supporting surface F n Normal force

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Physical aspects

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  1. Physical aspects

  2. Content Static and Dynamic Friction Force and Elongation Creep and Slip Energy and Efficiency Temperature and Humidity

  3. Static and Dynamic Friction

  4. Definition of coefficient of friction m Coulomb’s law 1 Conveyed goods 2 Supporting surface Fn Normal force Ff Frictional force Fa Tractive force m is influenced by • Two friction partners • Surface material and structure • Conditions (dirt, humidity, oil, temperature etc.)

  5. Static and dynamic friction m0 = Coefficient of static friction (friction of rest) mG = Coefficient of dynamic friction (friction of motion, sliding friction)

  6. Examples of coefficient of static friction Measuring of the coefficient of friction Examples of coefficient of dynamic friction Measurement device Davenport

  7. Force and elongation

  8. Stress-strain behavior of synthetics  A [mm2] l [mm] Force-path diagram Stress-strain diagram  F [N]

  9. Modulus of elasticity / pull for 1% Zone of Hook: Stress and strain (elongation) are proportional In the “zone of Hook” applies: s . 100 [ ] 2 = / Modulus of elasticity E N mm e [%] In the belting business instead of the E-modulus the pull for 1% is used: Pull for 1% = Tensile force for 1% elongation per unit of width [N/mm]

  10. Relaxation, pull after running in If a belt is elongated to a constant length and the tensile force F is measured, a reduction of force can be observed during several hours relaxation For power transmission belts the pull value is measured on a power transmission test bench after the relaxation phase, that means after running in  pull1% after running in (pull1% a.r.i.)

  11. Significance for belt drives To avoid high FW peak  2 step tensioning  Decrease of the shaft load FW within 2-3 hours after tensioning  After relaxation FW = constant Fw = 2T0

  12. Remaining elongation Once a tensioned synthetic belt is slackened, it will contract immediately elastic recovery A certain amount of the elongation recovers gradually over a long period of time  viscoelastic recovery The initial length will not be reached, this means it remains a certain  remaining elongation

  13. Structural elongation / emin  Traction layers of conveyor belts are made of fabric. The stress-strain behavior of fabric is different to solid tapes  The warp threads have to be stretched tight before tensile force is submitted This “forceless” elongation is called structural elongation

  14. Minimal initial tension emin of conveyor belts  Conveyor belts are normally tensioned according to the actual application (load, operation conditions etc. )  However, the structural elongation has to be considered. Recommended minimal initial tension emin : Belts with PES-fabric tensile member emin = 0.3 % Belts with PA-fabric tensile member emin = 0.5 %

  15. Admissible tension eadm / admissible tensile force Pulladm  The admissible tension adm of conveyor belts is limited by the tensile strength of the joint  The strength of a fingerspliced joint is influenced by the finger geometry, the temperature and the humidity  Provided that T < 80°C, the admissible tension for conveyor belts (PES fabric) is adm 1.6%  Hence, the admissible tensile force per unit of width is Pulladm  1.6 · k1% [N/mm]

  16. Creep and Slip

  17. Arc of adhesion, arc of creep Belt contracts from a1 to a2 when changing from F1 and F2 Belt elongate from a2 to a1 when changing from F2 and F1 Relative movements take place in the arc of creep bG Power transmission takes place in the arc of adhesion bA With increasing power transmission  arc of creep bG increases If arc of creep bG displaces arc of adhesion bA  slip occurs

  18.      Creep v1 > v2  Belt is driven in bA with the speed v1 (corresponding n1)  Belt moves backwards relative to the pulley in bG deceleration  Belt leaves driving pulley with reduced speed v2  Belt drives pulley in bA with the speed v2 (corresponding n2)  Belt moves forward relative to the pulley in bG acceleration  Belt leaves driven pulley with increased speed v1

  19. Slip  The arc of creep bG increases with increasing power transmission  If arc of creep bG displaces adhesion bA  slip occurs Slip must be avoided !  Maximum possible power transmission if F1 = max. and F2 = min.  Equation of Eytelwein

  20. Can creep be influenced or avoided?  In frictional engaged drives creep is system inherent and can not be avoided !  The extend of creep can be influenced by the E-modulus, k1%-value resp. : High k1%-value  small De  small amount of creep  v1 v2 Low k1%-value  high De  large amount of creep  v1> v2

  21. Energy and Efficiency

  22. Definitions Energy W = P · t [Ws = Nm = Joule] Example: Lamp of 100 W, 24 h alightEnergy consumption: W = 100 W · 24 h · 3600 s = 8.64 · 106 Ws, Joule  2.4 kWh Power Efficiency [%] P = Power [W] Pin = Power input [W, kW] t = Time [s] Pout = Power output [W, kW]

  23. Possible origins for energy losses  Energy losses due to material deformation  bending around pulleys and rollers  flexing of friction cover  Energy losses due to friction  Energy losses due to creep

  24. Energy losses due to cyclic bending  Considerable deformation may occur when a belt runs around a pulley  Most of the energy required for the bending is returned at reverse bending  A small part of the energy is lost in form of heat  hysteresis Flexible belts increase efficiency and energy savings ... but also permit to run over small pulley diameters ... and have positive effect on belt service life

  25. Energy losses due to flexing of friction cover  Each contact with a pulley or roller will cause a deformation of the belt surface  energy loss  Relevant factors for energy consumption:  material, thickness and structure of the belt cover  hardness and damping coefficient of the belt cover  pulley/rotor diameter and pressure force

  26. Energy losses due to friction and creep Conveyors - Friction between belt and slider bed - Bearing friction (roller conveyors!) - Friction between belt and con- veyed goods (with accumulation/ divertion) - Friction of belt on installation parts (has to be avoided!) - Creep on driving pulley (negligible) Drives - Normal friction between belt and pulleys (negligible) - Friction if slip occurs (has to be avoided!) - Bearing friction (negligible) - Friction between flanks and grooves (V-belts!) - Ventilation (e.g. with arm pulleys) - Creep on driving and driven pulley

  27. Summary of influences ConfigurationCreep Bending Flexing Friction Open drive X   Many bendings X  X small pulleys Tangential driveLive roller conveyors X   Conveyors  Decisive X considerable  negligible

  28. Measures to increase efficiency  Select large diameters of pulleys and rollers Avoid unnecessary bending, minimize number of pulleys/rollers Minimize pressure and deflection on pressure rollers Use flexible belts with high modulus of elasticity Determine belts as narrow as possible (small cross section) Set initial tension not higher than necessary Avoid belt vibrations Protect belt, pulleys and bearings from dirt, oil and humidity Avoid overdimension of electro motors (influence of cos j) Smooth starting (permits use of thinner and smaller belts) Select flat belt instead of V-belt

  29. Temperature and Humidity

  30. Influences Temperature and humidity strongly influence synthetic material:  Dimensional stability  elongation / shrinkage  Modulus of elasticity, k1% value  elongation under load, take-up  Strength of the joint  tensile strength of belt  Wear resistance, layer adhesion  pulley diameter, service life  Aging of cover material, hydrolysis  service life

  31. Min./max. admissible temperature  The admissible temperature given in the product data must be observed  The admissible temperature refers to the temperature resistance of the belt material at 50% rel. humidity  Restrictions apply when min./max. adm. temperature coincides with other factors such as small pulley diameters, high belt speed, high humidity, etc.  In cold environments, until -30°C, thermoplastic Polyurethane (TPU) has to be favored  Note: At low temperatures, synthetic belts loose their flexibility!

  32. Dimensional stability  Change of dimensions due to influence of temperature and humidity are negligible for belts with PES or Aramide traction layer  The influence of temperature on the dimensional stability plays an important role for thermoplastic belts without traction layer (e.g. elastic machine tapes, Polycord)  This influence of humidity is important with regard to belts with Polyamide traction layer

  33. Influence of humidity on PA-belts  Polyamide is hygroscopic, it changes its water content with the humidity of the ambient climate  This goes along with a change in length  Test with unloaded belt (stock situation)  < 80% rel.h.: Reversible dimensional change  > 80% rel.h.: Irreversible shrinkage

  34. Hydrolysis  Degradation of TPU at high temperature (> 65°C) andhigh humidity (> 80% relH)  Effects primarily the bonding agent and leads to layer separation  Softening and wear out of the TPU cover

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