Maximum Screw Torque
Equation for screw survival
For screw root diameters assuming a typical 1 inch screw
with 3:1 ACR where the feed channel depth is 0.180 for 8 L/Dís, straight
compression section 8 L/Dís long (where the next to last flight will then
measure 0.091 channel depth, and the meter 8 L/Dís long at 0.060 inches
as given by Machineryís Handbook, page 263,
T = Ss x Zp
Where, T is the torsional or twisting moment in inch-pounds.
Ss is the allowable shearing stress in pounds per square inch.
Zp is the polar section modulus.
Zp for a circular cross-section, page 266, is given as: 0.196 D3.
There is little published data on the torsional yield stress. The industry rule of thumb is that the yield stress is about two thirds the tensile yield stress. Spirex has published their use of 60% rule.
Our standard screws are made from 135M from Crucible Materials Corporation with a published tensile strength at 145,000 psi and yield strength at 125,000 psi for a hardness of 28-32 HRC.
So, using the conservative 0.60 figure,
0.60 x 125,000 x 0.196 D3 = T
For the following screw root diameters, T =
0.640 = 3,851 inch-pounds
0.810 = 7,805 inch-pounds
0.880 = 9,996 inch-pounds
Assumptions For Engineering Load Location:
In a feed driven screw, the entire load of the mixing,
metering, melting, and feeding is passes through the root of the feed
portion of the screw. This root is the smallest root of the screw. A typical
one inch screw has a 0.640 root diameter for a 0.180 channel depth and a
resultant maximum torque of about 3,850 inch-pounds.
The maximum load exerted on an extruder screw typically comes from the melting zone. The load from a smooth bore extruder is typically given as zero, and the metering section between 10 and 20%. Thus the melting zone generates most of the load. The greatest load possible in the melting zone is at the end of the melting zone where compression is greatest.
For a feed driven screw, all the load still goes through the smallest root. But for a discharge driven screw, the load is not transmitted by the smallest root but by the largest root. It then matters where the maximum load is to be expected. In a discharge driven screw, the maximum load is at the end of the compression section. So, in the discharge driven one inch screw example (from the calculations above 9,996/3,851) is 2.6 times stronger than the one inch feed driven screw. This can be used as a safety margin, for additional torque, or for deeper screws.
Finally, it is important to understand the implication of the Zp term for smaller screws. As a screw decreases in diameter, the screw's strength decreases with the cube of the diameter (while the output decreases with the square of the diameter). Thus, a 3/4 inch screw, for example, is much weaker than a one inch screw, in terms of survivability, when driven through the smallest root. Long practice shows that 1 inch screws usually survive when driven from either end but screws smaller than one inch do not.