Relationship of torque and shaft size

A rudimentary understanding of how shaft sizes are determined can be helpful to anyone who works with pumps, fans, elevators or any other motor-driven equipment. Engineers often design using an ample safety factor, but consider modifying a shaft only with good engineering support. The greater the consequence of failure, the more generous the safety factor should be.


Figure 1: A fire pump such as this does not run often, but it had better work when you need it! Courtesy: EASAHave you ever wondered why various types of electric motors with the same horsepower/kilowatt ratings have different shaft diameters, or why some pump shafts are so much smaller than the shafts of the motors that drive them? And what about those hollow-shaft motors? A rudimentary understanding of how shaft sizes are determined can be helpful to anyone who works with pumps, fans, elevators or any other motor-driven equipment.

Bigger is better—or at least used to be

Owing partly to tradition, the shafts of electric motors are often larger than those of the equipment they drive. Engineers were very conservative a century ago when electric motors first came into widespread industrial use, so they typically designed in a sizable margin of error. Today’s engineers haven’t changed much in this respect. For example, standard NEMA frame dimensions, which have been revised only once since 1950, still specify much larger shaft sizes than commonly accepted principles of mechanical engineering would require.

Shaft design basics

Shaft size is dictated by torque, not horsepower. But changes in horsepower and speed (rpm) affect torque, as the following equation shows:

Torque (lb-ft) = hp x 5,252/rpm

Accordingly, an increase in horsepower would require more torque, as would a decrease in rpm. For example, a 100 hp motor designed for 900 rpm would require twice as much torque as a 100 hp motor designed for 1,800 rpm. Each shaft must be sized for the torsional load it is expected to carry.

Two basic approaches are used to determine the required minimum shaft size for motors, both of which yield conservative results. One method calls for making the shaft large enough (and therefore strong enough) to drive the specified load without breaking. Mechanical engineers define this as the ability to transmit the required torque without exceeding the maximum allowable torsional shearing stress of the shaft material. In practice, this usually means that the minimum shaft diameter can withstand at least two times the rated torque of the motor.

Figure 2: Effluent pumps application. Courtesy: EASAAnother way to design a shaft is to calculate the minimum diameter needed to control torsional deflection (twisting) during service. To engineers, this means the allowable twisting moment, or torque, is a function of the allowable torsional shearing stress (in psi or kPa) and the polar section modulus (a function of the cross-sectional area of the shaft).

Machinery’s Handbook provides the following equations for determining minimum shaft sizes using both design approaches: resistance of torsional deflection and transmission of torque. Both sets of equations are based on standard values for steel, with allowable stresses of 4,000 psi (2.86 kg/mm2) for power-transmitting shafts, and 6,000 psi (4.29 kg/mm2) for line-shafts with sheaves (sometimes called pulleys). Some of the equations also are specific to keyed or non-keyed shafts, which is handy for pump users who need to know how to calculate both keyed and unkeyed shafts.

Transmission of torque approach

Most motor shafts are keyed, which increases the shear stress exerted on the shaft. Considering this, motor shaft designs typically use no more than 75% of the maximum recommended stress for a non-keyed shaft. This is another reason why the shafts of electric motors are often larger than the pump shafts they drive.

> > See the following pages for Equations 3-5 and Examples 1-4.

<< First < Previous 1 2 3 Next > Last >>

No comments
The Top Plant program honors outstanding manufacturing facilities in North America. View the 2015 Top Plant.
The Product of the Year program recognizes products newly released in the manufacturing industries.
Each year, a panel of Control Engineering and Plant Engineering editors and industry expert judges select the System Integrator of the Year Award winners in three categories.
2017 Lubrication Guide; Software tools; Microgrids and energy strategies; Use robots effectively
Prescriptive maintenance; Hannover Messe 2017 recap; Reduce welding errors
Safety standards and electrical test instruments; Product of the Year winners; Easy and safe electrical design
Infrastructure for natural gas expansion; Artificial lift methods; Disruptive technology and fugitive gas emissions
Mobility as the means to offshore innovation; Preventing another Deepwater Horizon; ROVs as subsea robots; SCADA and the radio spectrum
Future of oil and gas projects; Reservoir models; The importance of SCADA to oil and gas
Diagnostic functions for system safety; Specifying industrial enclosures; Effective decision support for a crisis
Transformers; Electrical system design; Selecting and sizing transformers; Grounded and ungrounded system design, Paralleling generator systems
Natural gas for tomorrow's fleets; Colleges and universities moving to CHP; Power and steam and frozen foods

Annual Salary Survey

Before the calendar turned, 2016 already had the makings of a pivotal year for manufacturing, and for the world.

There were the big events for the year, including the United States as Partner Country at Hannover Messe in April and the 2016 International Manufacturing Technology Show in Chicago in September. There's also the matter of the U.S. presidential elections in November, which promise to shape policy in manufacturing for years to come.

But the year started with global economic turmoil, as a slowdown in Chinese manufacturing triggered a worldwide stock hiccup that sent values plummeting. The continued plunge in world oil prices has resulted in a slowdown in exploration and, by extension, the manufacture of exploration equipment.

Read more: 2015 Salary Survey

Maintenance and reliability tips and best practices from the maintenance and reliability coaches at Allied Reliability Group.
The One Voice for Manufacturing blog reports on federal public policy issues impacting the manufacturing sector. One Voice is a joint effort by the National Tooling and Machining...
The Society for Maintenance and Reliability Professionals an organization devoted...
Join this ongoing discussion of machine guarding topics, including solutions assessments, regulatory compliance, gap analysis...
IMS Research, recently acquired by IHS Inc., is a leading independent supplier of market research and consultancy to the global electronics industry.
Maintenance is not optional in manufacturing. It’s a profit center, driving productivity and uptime while reducing overall repair costs.
The Lachance on CMMS blog is about current maintenance topics. Blogger Paul Lachance is president and chief technology officer for Smartware Group.
The maintenance journey has been a long, slow trek for most manufacturers and has gone from preventive maintenance to predictive maintenance.
Featured articles highlight technologies that enable the Industrial Internet of Things, IIoT-related products and strategies to get data more easily to the user.
This digital report will explore several aspects of how IIoT will transform manufacturing in the coming years.
Maintenance Manager; California Oils Corp.
Associate, Electrical Engineering; Wood Harbinger
Control Systems Engineer; Robert Bosch Corp.
This course focuses on climate analysis, appropriateness of cooling system selection, and combining cooling systems.
This course will help identify and reveal electrical hazards and identify the solutions to implementing and maintaining a safe work environment.
This course explains how maintaining power and communication systems through emergency power-generation systems is critical.
click me