Gear Failure & Reliability Analysis

The gears are subjected to high cyclic or alternating stresses. There are three common modes of tooth failure:

  • Pitting is a fatigue phenomenon and occurs as a result of repeated stress cycles which lead to surface and subsurface cracks.
  • Bending fatigue leading to tooth breakage. It is caused by the root bending stress imposed by the transmitted load. In some cases pitting or wear may weaken the tooth to the extent that breakage occurs.
  • Scuffing is a form of surface damage on the tooth flanks, which occurs when the lubricant film fails allowing metal to metal contact.

Bending Stress Calculation

Gear overload or cyclic stressing of the gear tooth at the root beyond the endurance limit of the material causes bending fatigue and eventually a crack originating in the root section of the gear tooth and then the tearing away of the tooth or part of the tooth.

The bending stress calculation is predicted by the Lewis equation, which is crucial in determining the tooth width. The equation considers the gear tooth to be a cantilevered beam and uses the bending of the cantilever beam to simulate the bending stress acting on the gear.

Gear Materials

When specifying gear materials, properties such as resistance to wear, good fatigue strength as well as a low coefficient of friction are desirable. Alloy steels are most commonly used in the manufacture of gears. They offer high strength and a wide range of heat treatment properties. The material composition below indicates how properties vary with commonly used alloy materials:

  • Nickel – Increases hardness and strength.
  • Chromium – Increases hardness and strength but the loss of ductility is greater. It refines the grain and imparts a greater depth of hardness. It has a high degree of wear resistance.
  • Manganese – It gives greater strength and a high degree of toughness than chromium.
  • Vanadium – The hardness penetration is greatest. The loss of ductility is also more than any other alloys.
  • Molybdenum – Increases strength without affecting the ductility.
  • Chrome – Nickel Steels – The combination of the two alloying elements, chromium and nickel, adds the beneficial qualities of both. Gears made from 300 series stainless steel, containing 18% chromium and 8% nickel, are essentially nonmagnetic and cannot be hardened by heat treatment. They are recommended for low torque applications as their mechanical properties and resistance is low. The steel gears are usually heat-treated in order to combine properly the toughness and tooth hardness. It is NOT essential for both pinion and wheel gears to be of the same material. As the smaller gear will have to rotate more turns than the larger gear, it is more prone to wear and fatigue. It is common, therefore, to choose a material with improved properties for the pinion to give a gear pair with a near-matching strength and durability.

Simplified Rules of Thumb for Design of Gears

  • The face width of spur gears should be 3 to 5 times the circular pitch.
  • If possible, the ratio of face width to pitch diameter should be kept small (<2) for less sensitivity to misalignment and uneven load distribution due to load-sensitive deflections.
  • Increasing the face width will decrease wear and fatigue, but the dynamic load will increase.
  • A coarser tooth (smaller diametral pitch) will improve the fatigue performance but not the wear performance. For a given tooth design, only a harder material will improve the wear.
  • Larger pitch diameters have lower tangential forces and lower dynamic loadings.
  • Decreasing the tooth error decreases the dynamic loading.

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