ME 3221 - Spring 2012
Homework Set 7
Name:
Due March 30, 2012
1. A plastic clip is designed to temporarily hold a clay pigeon in position on the throwing arm of a clay pigeon thrower, as suggested below. Note that the flexing portion of the clip acts as a cantilever beam. The holding force is developed by deflecting the tip of the clip upward by
0.6 mm when the pigeon is pushed below it.
The clip is designed to be injection molded from an ABS plastic resin whose fatigue strength is reasonably described by the traditional load-life curve used for steel in the range of 10
3 through 10
6
S n
, at 10
6 cycles. The ultimate strength is 44 MPa. The unmodified “endurance limit”, cycles should be taken as 14 MPa, or about 32% of the ultimate strength yield strength is 34 MPa.
1
. The
The modulus of elasticity of the ABS plastic is 2.28 GPa. The surface finish of the plastic part is equivalent to a fine ground finish on a steel part.
Estimate how many pigeons you would expect 99% of the clips to be able to throw before failing. Assume that the normal beam bending models are adequate
2
.
clay pigeon holding clip
9.3
arm pivot pin throwing arm
9.5
1.4 R
(all dimensions in mm)
0.8
F pigeon
(over)
1
In reality, this plastic does not reach an endurance limit at 10
6 the range of 10
3
2 through 10
6 cycles.
cycles, but the steel model is adequate through
A more thorough analysis would explore if this beam is better modeled as a “wide beam”, since its width is many times its thickness.
1

2. A torsion bar spring is fabricated from AISI 1020 solid cold rolled steel round. The spring must rotate 10
◦ when a torque of 100 N-m is applied to it. (The minimum torque is 0.)
Specify the minimum length, l , and minimum diameter, d , that will enable the spring to withstand 10,000 applications of the torque with 99.9% reliability.
y d z l T = 100 N-m x
3. Juvinall & Marshek Prob. 8.52 (Prob. 8.48 in the 4th Edition).
4. The geometry of a shaft is illustrated below. The shaft is grooved to the inside of each bearing to enable holding it in place with snap rings. The groove is machined with a rounded bottom, as shown. The shaft is fabricated from AISI 1040 steel which is quenched & tempered at 425
◦
C. It carries a torque, T , which is modeled as relatively steady, which is 0.2 meters times the force F . The force F is approximated as 800 N for 40% of the life of the shaft, 950 N for 30% of the life, 1050 N for 25% of the life and 1150 N for 5% of the life. The shaft rotates at 1200
RPM. Assume 99% reliability.
Estimate the life of the shaft by applying Miner’s rule.
F
50 300
(All dimensions in mm)
50
F
T
18.5 d
20 d
(Dimensions distorted to clarify geometry)
T
1.2
2