The lathe's original headstock is a metal pipe with seated bearings locked in place to a steel plate welded along the web of an I beam. The shaft of the headstock is the axle of a truck with a locking hub for a front differential. A cylinder and plate are welded to the wheel hub with ground spikes secured through the plate to skewer the logs.
Headstock Replacement Specifications and Constraints
Facilitate Wasatch Timber’s product offering of 6-inch diameter logs. The primary requirement is that the cutting heads must have a ¼ inch clearance with the faceplate during operation. Additional requirements are that the shaft have a centering spike to line up the logs, have a fatigue life of 10^6 cycles, and a safety factor of 3 against yielding. The bearings must be rated for the dynamic load of the log. Furthermore, the skewering teeth must be no longer than 1.5 inches with a safety factor greater than 2, and they should be easily replaceable.
Prototype Design
The prototype headstock is a shaft with removable keyed faceplate secured by keyed shaft collars. The faceplate has eight replaceable bolts machined to a point to skewer the log. The assembly is secured to a plate with two tapered roller bearings. The skewering teeth’s dimensions are determined by Wasatch Timber’s requirements for the teeth to be no longer than 1.5 inches from the faceplate.
Failure Analysis
The largest logs weigh up to ~4,300 lbs. The minimum shaft diameter was determined to be 1.75 inches while still satisfying the required fatigue life with a safety factor of 3 against yielding as shown below.
The initial analysis was conducted using MATLAB for determining the minimum acceptable shaft diameter and the minimum acceptable minor diameter for the bolts that would guarantee an operational safety factor of 2. The results show that the minimum acceptable shaft diameter is 1.75 inches while the minimum acceptable minor diameter for the bolts was approximately 0.46 inches given that 9 bolts were used.
Testing Methods
To validate the final headstock design two finite element models were created. The first model created was used to simulate the loading along the headstock assembly to analyze the shaft and bolt stresses and displacements. The second model was used to simulate the stress acting on the faceplate under maximum load with the addition of preloaded bolts.
1st ANSYS Model Setup: Shaft and Bolts
The first ANSYS model was created to analyze the shaft and the bolts. After importing the model from SolidWorks, the following boundary conditions were applied: the feet of each pillow block was fixed (A-B), the end of the shaft was fixed (C), a torque of 378 lb*in (applied from the motors) was applied along the faceplate (D), and a force of 237.16 lbf (½ max log weight divided by number of teeth) was applied on each tooth (E-J)
2nd ANSYS Model Setup: Faceplate Setup
For the second ANSYS model, the same boundary conditions were applied as the first ANSYS model with the addition of a preload force acting through each of the bolts. The preload force was calculated to be 17,040 pounds.
Results
1st ANSYS Model Results: Shaft and Bolts
From the results of the simulation, the maximum stress for the shaft was found to be located where the shaft coincides with the front face of the first bearing, and the maximum stress found in the bolts (teeth) was located along the minor diameter in the thread closest to the nut as was expected for both.
Using FEA, after applying a point load at the end of the rod of 2134.5 lbf for ½ max log weight, the maximum stress in the shaft was found to be 23.37 ksi. The expected maximum stress acting on the shaft was calculated to be 22.3 ksi. This was calculated by treating the shaft as a cantilever rod with a length that was equivalent to the length from the end of the shaft to the front face of the first bearing (5.5 inches). The difference between the FEA results and hand calculations for the maximum shaft stress was 4.29%.
The maximum stress that was found for the bolts with FEA was 59.87 ksi while the expected maximum stress was calculated to be 59.80 ksi. This resulted in a difference of 0.12% between the FEA results and hand calculations.
The total deformation of the headstock assembly was also analyzed using the FEA model. The maximum deformation seen in the model was approximately 0.039 inches. The image below shows the location of the maximum displacement to be at the tip of one of the teeth.
2nd ANSYS Model Results: Faceplate
Additonal Images
