4 shafts and shaft components

Shafts and Shaft Components

Introduction Shaft rotating member used to transmit power or motion Axle non rotating member that carries no torque Shaft Design Interdependencies

Shaft elements (gears, pulleys, bearings, etc) have been partially analysed, and size and spacing tentatively determined from the overall design of the machine.

Introduction Shaft details that need to be examined:

Material Layout Stress and Strength Deflection and Rigidity Vibration due to natural frequency (will not be discussed in this class)

Shaft Materials

Shaft Materials We focus on designing steel shafts, as such: Deflection:

Modulus of elasticity (E) of steels are constant Deflection mainly controlled by geometric decisions, not by material selection

Stress and Strength: Controlled by material and treatment Low/High Carbon CD or HR

Shaft Materials Considerations

Strengthening from heat treatment Often not warranted Trade off between increase in strength vs reduction in endurance limit and increase in notch sensitivity

Design Roadmap Start with low or medium carbon steels (low cost) If strength is an issue, then select a higher strength material Then reduce size until deflection becomes an issue

Shaft Materials Typical Materials

Low Carbon ANSI 1020-1050

Heat Treatable ANSI 1340-50, 3140-50, 4140, 4340, 5140, 8650

Surface Hardening ANSI 1020, 4320, 4820, 8620 If shaft is the journal for a bearing surface

Shaft Layout

Shaft Layout Dependent on the overall design of the machine Must be specified to perform a free body force analysis and to obtain shear-moment diagrams, stress and deflection analyses Common features:

Shoulders Grooves Keyseat Holes

Shaft Layout Considerations

Best to support load carrying components between bearings Pulleys and sprockets often need to be mounted outboard for ease of installation of belt or chain (length of cantilever should be kept short)

Two bearings in most cases. More bearings for long shafts with more load bearing components

Shorter shafts = less bending moment and deflection Load bearing components should be placed near bearings

Decreased bending moment at locations where stress concentrations are present Minimize deflection

Shaft Layout Supporting Axial Load

Shoulders Retaining Rings Pins Collars

Torque Transmission Designed to fail first Keys Splines Setscrews Pins Press or Shrink Fits Tapered fits

Shaft Layout

Shaft Design For Stress

Shaft Design for Stress Critical Locations

Outer surfaces Locations with large bending moments Where torques are present Where stress concentrations exist

Shaft Design for Stresses Torque

Typically enter the shaft at one gear and leaves at another Often relatively constant at steady state operation Shear stress due to torsion is greatest on outer surfaces

Bending Determined by bending moment diagrams Gears and pulleys introduce forces in two planes Resultant moments obtained by summing moments as vectors at points of interest Steady bending moment will produce a completely reversed moment on a rotating shaft

Axial Stresses from helical gears or tapered roller bearings will almost always be negligible compared to bending moment stresses If deliberately applied, do not neglect without checking magnitudes

Shaft Design for Stresses Shaft Stresses Shafts being solid and round

Shaft Design for Stresses von Mises (remember in Fatigue) Axial loads neglected

Shaft Design for Stresses Assessing based on failure criterion (Modified Goodman): For design purposes where d is unknown: Other failure criteria are expressed similarly in p. 369 of Shigley

Shaft Design for Stresses Common case

Bending stress is completely reversed (Mm=0) Torsion is steady (Ta=0)

Necessary to check for yielding at first loading cycle:

Quick check can be done : as

Shaft Design for Stresses: Stress Concentrations

For Shoulders against Bearings (based on common bearing dimensions)

1.2<D/d<1.5 0.02<r/d<0.06 Try to select a bearing with a large fillet radius Create features to reduce stress concentrations

Shaft Design for Stresses: Stress Concentrations

Same analyses can be done on keyseats and retaining ring groves Table below shows Stress Concentration Factors using the worst end of typical values for use on first iterations. Note that once actual dimensions are available, repeat analysis for a more accurate design.

Shaft Design for Deflection

Shaft Design for Deflection Deflection analysis can only be done when geometry of the entire shaft is known. Roadmap:

Design according to stresses and reasonable estimates Perform deflection analysis Check linear and angular deflections and slopes at components and supports Balance strength and deflection

Shaft Design for Deflection Note

For steels: E=207GPa (fairly constant) Fillets, grooves, keyways and other local factors can be neglected Methods for deflection analysis:

Singularity functions Numerical integration Finite Element Analysis

Shaft Design for Deflection Typical Maximum Ranges for Slopes and Transverse Deflections

Shaft Design for Deflection For unsatisfactory deflection or slope,

select the limiting condition (larger dnew/dold ratio) Multiply all diameters by dnew/dold

Shaft Design for Deflection Angular Deflection due to Torsion For constant torque on homogeneous material

Torsional Stiffness

Shaft Components

Miscellaneous Shaft Components Setscrews Keys Pins Retaining Rings

Miscellaneous Shaft Components: Setcrews

Depend on compression for clamping force Holding Power:

Resistance to motion of the collar or hub relative to the shaft Due to frictional resistance and slight penetration

Miscellaneous Shaft Components: Setcrews

Applies to axial and tangential holding power Setscrew length = 0.5(shaft diameter)

Applies to radial thickness of hubs or collars

Miscellaneous Shaft Components: Keys and Pins

Used to secure rotating elements Enable transmission of torque


Design Considerations Failure can be due to bearing or direct shear Standard sizes are available Key length should not exceed 1.5 x shaft diameter Multiple keys can be used Should be the first to fail End of keyseat should be d/10 away from shoulder fillet to prevent combined stress concentrations.


Gib-head key Tapered Prevents relative axial motion Allows adjustment of axial location

Woodruff key Key slot can be positioned away from shaft shoulder Good for smaller shafts because of deeper penetration


Stress Concentrations

Miscellaneous Shaft Components: Retaining Rings

Used instead of a shoulder or sleeve to axially position a component Sizes, grooves, load ratings available on catalogs. Sharp radii on grooves create high stress concentration factors, so care should be taken when using at high bending stress locations

Miscellaneous Shaft Components: Fits

Standards for limits and fits are available depending on purpose.

Clearance running to locational clearance Transition between clearance and interference Interference locational interference to force fit

Serves as guidance for nominal sizes and tolerances


Interference fits Axial and rotational support Causes uniform external pressure on shafts and uniform internal pressure on hubs


= interference d = shaft nominal diameter di = shaft inside diameter do = hub outside diameter


Tangential Stresses Radial Stresses Radial and tangential stresses are orthogonal and should be combined using failure theories

If yielding occurs, full pressure will not be achieved, diminishing the torque that can be transmitted

Compressive stresses improves fatigue strength and can be ignored in analysis Stress concentration in bending at ends of the hub

Can be approximated to be 2


Torque transfer by interference fits Estimated using frictional force at the interface

Torque= frictional force with a moment arm of d/2 Minimum interference should be used to determine the maximum amount of torque that the joint can handle

p = pressure a = Area of interface l = length of hub

4 shafts and shaft components

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