phd doctorate only

A torque wrench is used in a gasket assembly where each ¼” diameter bolt is to have a tensile load of 2826lbs. The specified torque is 8.8foot-lbs. Calibrated torque wrenches are supplied having a single point calibration at 8.8foot-lbs. They have a digital readout with a resolution of 0.1 foot-lbs. The calibration is done in one of 3 “identical” test rigs with load cells having a stated “3 sigma”accuracy of 0.5%. A turnbuckle arrangement in the calibration tool is used to apply the load at a nominal distance of 12 inches from the center of the wrench ratchet assembly. The tool drawing for the test rig has a tolerance for this distance of +/-0.010”. The actual value for any particular test rig is not known but all the tooling has been inspected and found to be within tolerance. The calibration procedure is as follows:

1. Connect the ratchet solidly

1. Apply the load until the digital readout of the load cell reads exactly 8.80 lbs.

1. Adjust the bias of the wrench digital readout to read exactly 8.8 foot-lbs.

During the tightening operation, the mechanic tightens the bolts smoothly and slowly until a reading of 8.8foot-lbs. When observed, they obtain the 8.8 exactly without fail.

Part A. What is the uncertainty in the wrench calibration? T=FD

Part B. What is the uncertainty in the actual torque on the bolts? For this part, consider only the uncertainty due to calibration and the resolution of the wrench which may be considered to be two independent factors. Tactual = Tmeasured + Ecal + Eres

Part C. Estimate the range of values that could reasonably be expected for tension on the bolts at a confidence level of 95%. T=kDP where

T=torque

k = correction factor (nominal value is 0.15 and expert judgment says it may be between 0.13 and 0.17 depending on variation in lubrication and thread characteristics of individual bolts.

D = nominal diameter of bolt (class 2A, ¼-20, coarse thread)

P = tensile clamping force (force on the bolt)