5 Shafts and Shaft Components I.pdf

SHAFTS AND SHAFT COMPONENTS SESSION I 1 2 3 4

Introduction to Shaft Design Geometric Layout Strengths and Stresses Deflection Considerations

SHAFTS AND SHAFT COMPONENTS SESSION I 1 2 3 4

Introduction to Shaft Design Geometric Layout Strengths and Stresses Deflection Considerations

Questions to ask… • • • •

What is a shaft? For what will we use the shaft for? What will we attach? How? Could the shaft handle the stresses?

INTRODUCTION TO SHAFT DESIGN • Material selection • Geometric layout • Strengths and stresses • •

1 starting point

2 local geometry

Static Variable

• Deflection considerations • • • •

Bending deflection Torsional deflection Slopes at bearings and elements Shear deflection of short shafts

3 global geometry

• Vibrations

Design

What’s next after this design?

SHAFTS AND SHAFT COMPONENTS SESSION I 1 2 3 4

Introduction to Shaft Design Geometric Layout Strengths and Stresses Deflection Considerations

GEOMETRIC LAYOUT Requirements

Configurations

Concerns: (1) axial layout, (2) axial loads, (3) torque transfer

GEOMETRIC LAYOUT Axial Layout Guidelines: • axial layout = f(component layout) • • • • • • • • • •

As much as possible, components are between bearings Pulleys and sprockets are often mounted outboard Cantilever length should be kept short Two bearings are usually satisfactory For long shafts and/or many-component shafts, more than two bearings are necessary but alignment is sensitive Shafts should be as short as possible Axial space is desirable: for lubrication and disassembly Components should be placed near bearings Axial location must be secure unless otherwise required Shaft shoulders can provide axial location of components

GEOMETRIC LAYOUT Requirements

Configurations

Concerns: (1) axial layout, (2) axial loads, (3) torque transfer

GEOMETRIC LAYOUT Axial Loads Guidelines: • •

• •

For transmission of loads to the shaft, shoulders are needed. If axial loads are low, shoulders can be: • Retaining rings in grooves • Sleeves between components • Clamp-on collars If axial loads are very low, shoulders can be omitted. In this case, press fits, pins, or collars with setscrews, can maintain axial location. Usually, only one bearing should carry the axial load, to allow greater tolerances on shaft length dimensions. This is particularly important for long and multi-component shafts.

GEOMETRIC LAYOUT Requirements

Configurations

Concerns: (1) axial layout, (2) axial loads, (3) torque transfer

GEOMETRIC LAYOUT Torque Transfer Guidelines: • • • • • •

Torque transfer requires appropriate machine elements: splines, keys, pins, setscrews, P&S fits These elements are designed to fail before the shaft! For mid-to-high levels of torque: keys are usually used (Dis)assembly is easy because of its slip fit Keys provide angular orientation: useful in some cases For high levels of torque: splines are usually used They can be used for high degree of slip fit (for axial motion) All the rest are used for low levels of torque Early in the design process, these elements should be selected appropriately for the ease of undertaking subsequent design analyses

GEOMETRIC LAYOUT Requirements

Configurations

Concerns: (1) axial layout, (2) axial loads, (3) torque transfer

GEOMETRIC LAYOUT Assembly and Disassembly* Guidelines: • • • •

Largest useful diameter is at the center of the shaft The gearbox itself must position the shaft into its bearings and the bearings into the frame, this is accomplished by providing access at one end For press-fitting, it should not be down a long length of the shaft: this needs extra diameter change For disassembly, considerations are needed for: • Accessibility of retaining rings • Space for bearing pullers • Openings in the housing for press fitting

GEOMETRIC LAYOUT Requirements

Configurations

Concerns: (1) axial layout, (2) axial loads, (3) torque transfer

SHAFTS AND SHAFT COMPONENTS SESSION I 1 2 3 4

Introduction to Shaft Design Geometric Layout Strengths and Stresses Deflection Considerations

SHAFTS AND SHAFT COMPONENTS SESSION I 1 2 3 4

Introduction to Shaft Design Geometric Layout Strengths and Stresses Deflection Considerations

STRENGTHS AND STRESSES Critical Locations • Outer surfaces • Locations of large bending moment • Where torques are present • Where stress concentrations exist

Axial stresses are neglected unless they are deliberately applied. If they only came from helical gears and tapered cylindrical bearings, they are negligibly small compared to bending and torsion.

STRENGTHS AND STRESSES Since shafts are usually solid and round:

von Mises stresses for combined loading:

STRENGTHS AND STRESSES For the DE-modified Goodman criterion:

For design purposes where d is unknown:

Similar equations are provided in the book for other fatigue failure criteria.

STRENGTHS AND STRESSES For testing failure against yielding (Langer): where

Stress Concentrations

≈

STRENGTHS AND STRESSES

Stress Concentrations

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

STRENGTHS AND STRESSES

SHAFTS AND SHAFT COMPONENTS SESSION I 1 2 3 4

Introduction to Shaft Design Geometric Layout Strengths and Stresses Deflection Considerations

SHAFTS AND SHAFT COMPONENTS SESSION I 1 2 3 4

Introduction to Shaft Design Geometric Layout Strengths and Stresses Deflection Considerations

DEFLECTION CONSIDERATIONS deflection = f(stiffness, geometry) stiffness = modulus of elasticity modulus of elasticity of steels is fairly constant.

deflection ≈ f(geometry) Process: • • •

Design according to stresses and reasonable estimates Perform deflection analysis Check linear and angular deflections and slopes at: • •

• •

Shaft components Shaft supports

Balance strength and deflection considerations Do not include fillets, grooves, and keyways and just use the gross geometric dimensions

DEFLECTION CONSIDERATIONS

For unsatisfactory sections:

What if both y and dy/dx are unsatisfactory? Determine the limiting condition (y or dy/dx)

DEFLECTION CONSIDERATIONS

DEFLECTION CONSIDERATIONS

DEFLECTION CONSIDERATIONS