In this issue, we help to answer a question submitted by an engineer working at one of the world’s leading manufacturers of sustainable industrial floor maintenance equipment. Their products clean high traffic industrial surfaces such as airports, warehouses and even the floors of the White House and Yankee Stadium.
For two weeks, the engineer who submitted this problem researched the best ways to find a solution.
He needed to protect the steel shaft and die-cast aluminum brush hub of a hard floor scrubber machine from failure in a locked-rotor condition. He knew that one method of protection is to design a shaft key that fails before there is any damage to more expensive parts.
Can a steel key protect the shaft and the brush hub of a floor scrubber from damage?
What We Know:
The shaft of a hard floor scrubber machine is made of steel and has a diameter of 11/16 in. The output torque is 250 in-lbf at 200 rpm. The driven brush hub is made of die-cast aluminum. The destructive shear stress for the shaft material is 32,000 psi, and destructive compressive stress for die-cast aluminum is 24,000 psi.
The questions are:
- What are the recommended dimensions of the shaft key?
- Will the 1/4×1/4×1 in steel shaft key with destructive shear stress of 30,000 psi shear off and fully protect the shaft and the brush hub?
- Is an aluminum or softer key needed to protect the driven hub in a locked-rotor condition with full torque impact load?
Finding the recommended dimensions
We start with a search for ‘key size for shaft diameter’. (Click to run search)
And open Table 1, Key Size Versus Shaft Diameter in Machinery’s Handbook (27th Edition) & Guide to Machinery’s Handbook:
From this table, the recommended dimensions of the key are 3/16 × 3/16 in.
Now let’s find the equations for calculation of the torque moment for the shaft and shaft key.
A quick search for ‘shaft key’ retrieves the chapter Design of Transmission Shafting in Machinery’s Handbook (28th Edition) & Guide to Machinery’s Handbook.
There is an equation for calculation of the shaft diameter on page 301:
Using this equation we can calculate the torsion moment corresponding to 80% of the dangerous stress in the shaft.
From Table 1 on page 302, we find that the Kt factor is 1.5 and factor B=1 because the shaft is solid. Opening chapter 17., Design of Shafts and Keys for Power Transmission on page 155, we find equations for the torque moment versus dimensions of the key:
In the equation, “2″ represents the compressive stress of the hub material. It is used because the value is smaller than the destructive stress of the steel.
When we appy the values to the equations, the result is:
As we can see, the torque moment at which the shearing stress in the key is dangerous is greater than the torque at 80% of dangerous compressive stress in the hub — and even greater than the torque at 80% of dangerous shear stress in the shaft. So the steel key of these dimensions will not protect the hub and even the shaft.
Let’s calculate the destructive shearing stress for the material of the key required to protect the hub and the shaft. In order not to damage the shaft and the hub, the torque moment of key shear should not exceed the moment Tc:
Therefore, to protect the shaft and the hub with the key of these dimensions, we have to use a material with a destructive shear stress that is not more than 9,600 psi. The allowable shear stress should not to be less than….
to handle the maximum output torque of 200 lbf-in. We then use Data Search to restrict our results to interactive properties data. Entering the field name shear strength and our value of 9,600 psi,
(Click to enlarge)
we find the interactive table Estimated Minimum Mechanical Properties of Wrought Aluminum Alloys – (engineering units) in the Aluminum Alloy Database.
In this table, we learn that 1060 H16 tempered alloy satisfies our requirements:
This alloy has an ultimate shear stress of 8,000 psi and a yield shear stress of 6,000 psi, which is higher than 2327 psi, allowable shear stress in the key calculated earlier for 200 lbf-in torque. Hence, this alloy is able to handle output torque of 200 lbf-in safely. Reviewing the properties of this material, we notice that the key thickness has to be increased to prevent failure due to crushing.
- The recommended dimensions of the key for the shaft of 11/16 in diameter are 3/16 × 3/16 in.
- The 1/4 × 1/4 ×1 in steel key will not protect the hub and the shaft. It is stronger than these components.
- A softer key material, e.g., 1060 H16 aluminum alloy, would protect the hub and the shaft.