Jing Zheng
Problem 7-1 (10%)
Statements: Two 3 x 5 cm blocks of steel with machined finish Ra = 0.6 mm are rubbed together with a normal force of 400 N. Estimate the true area of contact between them if their Sy = 400 MPa.
Hints:
Not much except that the compressive yield strength is the same as the tensile yield strength. You need to read Chapter 7.2 “MATING SURFACES” before you try this problem.
Problem 7-2 (10%)
Statements: Estimate the dry coefficient of friction between the two pieces in Problem 7-1 if their Sut = 600 MPa.
Hints:
Not much except that the compressive yield strength is the same as the tensile yield strength. You need to read Chapter 7.3 “FRICTION” before you try this problem.
Problem 7-8 (20%)
Statements: A paper mill processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50 m outside dia (OD) by 0.22 m inside dia (ID) by 3.23 m long and has an effective modulus of elasticity in compression of 14 MPa and n = 0.3. Determine the width of its contact patch when it sits on a flat steel surface, loaded by its own weight.
Hints:
(a) (25%) Find the weight of the paper roll. Determine the radii of the contacting bodies (R1 and R2).
(b) (50%) Read Chapter 7.8 and 7.9. Determine the geometry (B) and material constants (m1 and m2). For your convenience, the Young’s modulus and Poisson’s Ratio are E = 207 GPa and n = 0.28 respectively.
(c) (25%) Calculate the contact patch half-width and width. Is this a spherical contact case or a cylindrical contact case?
Problem 7-13 (20%)
Statements: Estimate how long it will take to file 1 mm off a 2-cm cube of HB150 steel if the machinist applies 100 N over a 10-cm stroke at 60 strokes per minutes.
(a) If done dry.
(b) If done lubricated.
Hints:
(a) (25%) Read Chapter 7.4 and 7.5, find the Wear Coefficient K for Abrasion for file under dry surfaces and lubricated conditions.
(b) (25%) Construct an equation that consists time t as an variable.
(c) (50%) Combine the constructed equation with equation 7.7b, and then solve for time, t (with dry and lubricated condition).
Problem 7-15 (10%)
Statements: Create a table of acceptable materials to run against a steel shaft based on their metallurgical compatibility. Rank them as to suitability.
Hints:
Figure 7-6 is the compatibility chart for metal pairs. Find the right row or column.