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Hayward Gordon Mixers Mechanical Design Fundamentals

Hayward Gordon Mixers Mechanical Design Fundamentals. JC van Grieken Mixer Applications Engineer June 26, 1999. Why do Mechanical Analysis?. After determining the HP, RPM, Impeller size and positioning we can do a mechanical analysis.

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Hayward Gordon Mixers Mechanical Design Fundamentals

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  1. Hayward Gordon MixersMechanical Design Fundamentals JC van Grieken Mixer Applications Engineer June 26, 1999

  2. Why do Mechanical Analysis? • After determining the HP, RPM, Impeller size and positioning we can do a mechanical analysis. • Determines whether shaft will fail due to stress (shear or tensile). • Ensures no critical speed (vibration) problems. • To determine deflection at critical points. (not covered)

  3. What Will be Covered? • Tensile and Shear - the two types of stresses and their equations. • Combination of these stresses. • Impeller Hydraulic Force (Fh). • Critical Speed - What is it and how does it affect us? • Sample problem by hand.

  4. Two Types of Stress • Stress is basically Force / Area (psi) •  - tensile stress denoted by sigma •  - shear stress denoted by tau All calculations are in the Elastic Range

  5. Occurs in pure bending (as in shafting with a radial load) Tensile Stress ()

  6. Tensile Stress () • The moment at A is responsible for the tensile stress.

  7. Shear Stress () • Occurs in torsion (as in a shaft transmitting torque).

  8. Shear Stress () • The torque (T) in the shaft above the impeller is responsible for the shear stress.

  9. Combination of Stresses • Now that we have the tensile and shear stresses acting on the element we have to find the combined stresses.

  10. Combination of Stresses • Using Mohr’s circle we can find the maximum tensile and shear stresses encountered in the element.

  11. Mohr’s Circle • Both (0,-) and (,) lie on the perimeter of the circle. • Simple geometry gives:

  12. Hydraulic Force • Action / reaction between impeller and fluid. • Assumed random in both direction and magnitude. Must consider the worst case. • Acts in radial direction.

  13. Hydraulic Force • D is impeller diameter (in) • Cf is the impeller condition factor. Used to account for different loading conditions.

  14. Vibration Analysis • Must be done on every agitator. • Every system that has mass and elasticity has the potential for free vibration. (ie: vibration with no external excitation). • The Natural frequency (Nc) or Critical Speed is the frequency at which this free vibration can occur. (ex: hitting a shaft with a hammer will excite the shaft to vibrate at Nc). • All calculations assume rigid support.

  15. Vibration Analysis • Nc must be avoided at all costs. • If a force with a frequency of the natural frequency acts on the system (ie: RPM=Nc) then resonance occurs. • The force will ‘pump’ energy into the vibration and increase its amplitude until failure occurs.

  16. Calculation of Nc • Mixing Assist uses the Raleigh Method (lumped mass version) to determine Nc. • Basically conservation of energy.

  17. Calculation of Nc • Low to moderate damping has little influence on Nc. • Damping will only lessen the amplitude of the vibration. • Nc depends only on the mass and stiffness of the system

  18. Critical Speed Multiplier • Hayward Gordon designs to a maximum of 75% of Nc. • Lightnin designs to 40% Nc without stabilizers and 80% Nc with stabilizers. • Hayward Gordon accounts for higher stresses when closer to Nc with a critical speed multiplier (Fcrit).

  19. Critical Speed Multiplier

  20. Critical Speed Multiplier • Direct multiplier to the contribution from pure tensile stress only. • End result - as you approach Nc, the stresses go to infinity (ie: failure).

  21. An Example • Shown is a typical impeller and shaft arrangement. • Need to find the pure stresses, the critical speed and then the combined stresses.

  22. An Example • From experience we know the maximum stresses will occur at the lower bearing. • For stress we need to find the Impeller forces and the Moment about the lower bearing.

  23. An Example • We will also need to work out the Moment of Inertia (I), the Polar Moment of Inertia (J) and the torque in the shaft at the lower bearing.

  24. An Example • Now find the Pure Tensile Stress () at the bearing. • Now find the Pure Shear Stress () at the bearing.

  25. An Example • Determine approximate Nc for this system. • Mixing Assist uses Rayleigh’s lumped mass method - not suitable for hand calculation. • We will use the following equation:

  26. An Example • Now lets find Fcrit.

  27. An Example • Finally we can find the maximum combined shear and tensile stresses.

  28. Summary of Steps for Mechanical Design of Agitators Once HP, RPM, Impeller Size and Positioning are known then we can do a mechanical analysis. 1. Find the hydraulic forces from the impellers and resolve to a moment about the section of interest. 2. Find the torsion in the shaft at the point of interest. 3. Calculate the pure shear and tensile stress. 4. Determine the 1st critical speed of the system and find the critical speed multiplier. 5. Calculate the maximum shear and tensile stresses. 6. Find deflections at critical points. (not covered)

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