Machine Design 5
Laboratory report
Experiment 3: Screw mechanisms and joints.
The purpose of the experiment is to determine stresses in screw mechanisms, bolts and fasteners and the efficiency of the screw mechanism.
1.1 Stand diagram:
1. bolt
2. nut
3. thrust washer
4. compound strain gauge transducer sleeve
5. strain gauge transducer sleeve
1.2. Measurement principles and results calculations.
The bolt built into the stand has an M30 thread. According to ISO standard the dimensions of thread are:
α = 60 deg
pitch: P=3,5 mm
thread major diameter: d=30mm
According to ISO standard:
thread minor diameter: d3=25.71 mm
nut minor diameter*: d1=26.5 mm
The dimensions of the bolt:
dW = 20 mm
dZ = 25 mm
As the wrench is being turned the torque moment gradually increases. The strain gauges mounted on element 4 (compound strain gauge transducer sleeve) are used to measure the axial stress Q as well as the torque of the thread resistance MG, while the strain gauge mounted on element 5 measures the friction torque of the feet of the bolt MP. The fourth measured quantity is the torque moment applied using the key MKL.
These 4 measurements are stored in a PC type computer using an analog/digital converter.
The μ’ (apparent friction coefficient of the thread surface) and μP (coefficient of friction on contact plane at the base of the bolt) are calculated using relations derived from following equations (for case when bolt is turned clockwise):
Resulting in
μ'=2MGdsQ-tanγ2MGdsQtanγ+1
μP=2MPdmQ
where :
- where ρ’ is the apparent angle of friction
dm = ½(dw+dz) - average friction diameter of bolt base
ds = ½ (d+d1) - average friction diameter of thread surface
γ = atan(P/πds) - average helix angle
(note: R. L. Norton in his Machine Design proposed a different formulae ds=d-0.649519P)
The PC program available at the stand does not calculate μG, however this calculation could also be automated.
The program calculates the thread efficiency using following formulae (derived in experiment instructions):
ηG=LuLw=QP2πMG=tanγtanγ+ρ'
1.3. Main stand components and stress distribution diagrams:
1.4. Measurement errors:
Due to an automated registration of data the errors of measurements in this experiment.
The accuracy of measurement of voltage is estimated at ∆UCZU=0.002, resulting in following measurement errors:
∆QQ=∆UQUQ=0.022
∆MGMG=∆UGUG=0.022
∆MPMP=∆UPUP=0.042
The values of errors of calculated parameters therefore are:
∆μG=∂μG∂Q∆Q+∂μG∂MG∆MG=cos∝2∂μ'∂Q∆Q+∂μ'∂MG∆MG==cos∝2μ'+tanγ1-μ'tanγ1+tan2γ∆QQ+∆MGMG==cos∝2μ'+tanγ1-μ'tanγ1+tan2γ0.044
∆μP=∂μP∂Q∆Q+∂μP∂MP∆MP=2MPdmQ∆QQ+∆MPMP=0.064μP
Errors for ∆μG, ∆μP and the values of μG for 5 selected points re are:
1.5. Closing conclusions:
The error interval boarders in μP graph are not aligned correctly. This is due to the fact I was reading values from unfiltered graph. I expect the same kind of error in case of hand drawn μG graph, however smaller since the source graph μ’ is somewhat smoother.
Filtering the graphs cannot be done manually and it would be good to introduce it as a function of used program. Another possible improvement would be to draw μG automatically.
The graphs show the friction coefficients first decreasing but above some Q being more or less constant. The friction coefficient at the feet of the bolt being larger than the apparent and real friction coefficients of the thread surface.
The efficiency of mechanism seems to be constant for changing values of Q.
However the broad error interval does not allow for certainty.
The best observed for this experiment is the linear relation between torque and axial force in the bolt. This is also what theory suggests.
MEiL