Materials, Tribology And Surface Engineering – Math Problem Example

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Materials, Tribology and Surface Engineering AssignmentQuestion One(a). Brass (CW614N - CZ121) has a Young’s modulus of 97GPa and a Poisson’s ratio of 0.34.Calculate the effective modulus at the interface when two brass plates are loaded together. (b) Copper has a modulus of 140 GPa and a hardness of 150 MPa. Estimate the elastic strain in copper at the yield stress(10 marks)SOLUTION: (a) (b) Strain, ε is given by σ/ E= (150x103)/ (140x106)Strain =1.07x10-3Question TwoA steel shaft with a Ra value of 0.4μm is rotating in a brass bush with a Ra value in its inner diameter of 0.7μm.

The shaft and bush are immersed in oil and, during operation; an oil film thickness of 5μm is developed. In which lubrication regime is the sliding interface operating? Your answer should be supported by suitable examples and references. (10 marks)SOLUTION: Boundary lubricationSince the value of film parameter obtained falls in the range: 5≤4.55≤10, the lubrication regime can be classified as Elastohydrodynamic lubrication. Question3.Using appropriate examples or references discuss four limitations of liquid lubricants. (10 marks)Discussion: Liquid lubricant lubricants are manufactured from vegetable oils, animal fats and mineral oils. Limitations: Vegetable oils are rapidly oxidized and less stable at high temperature environments.

They also contain high levels of natural boundary lubricants. Examples of these oils include Castor oil and Rapeseed oil. Compared to solid and semi-solid lubricants, liquid lubricants, especially from animal fats, are easily contaminated by presence of debris. In addition, they easily contaminate surfaces that they come into contact with. Examples include of animal fat oils include tallow oil and fish oil. These lubricants usually have challenges in controlling loss of lubricant by creep, leakages, absorption by porous surfaces, evaporation and chemical reactivity of the lubricant and contact surfaces.

Loss of lubricant from the required area of working makes it lose its function as a lubricant. Liquid lubricants extracted from vegetable oils and animal fats generally exhibit variations in temperature in their viscosity cause variation on system efficiency or torque on the load bearing component. Question4. It is found that a polymer-based bearing supporting a rotating steel shaft has a depth wear rate of 0.25mm in 1000 hours both at a bearing pressure of 10MPa and speed of 10-1ms-1, and at a pressure of 1 MPa and a speed of 1ms-1.(a) Show that the bearing is operating in the range where the specific wear rate is constant. SOLUTION: (6 marks)Assumption: The volume of the wear material is a unit. Case I: Normal load, F= 10MPaSpeed = 10-1ms-1Wear rate = 0.25mm in 1000 hours= 2.5x10-4 mm/hrSpecific wear rate, k = (volume of material wear)/ (Normal force x sliding distance)Sliding distance= (10-1ms-1x1000x3600) = 3.6x105mk1=1/ (10x3.6x105m) = 2.8 x 10-7Case II: Normal load, F= 1MPaSpeed = 1-1ms-1Wear rate = 0.25mm in 1000 hours = 2.5x10-4 mm/hrSpecific wear rate, k = (volume of material wear)/ (Normal force x sliding distance)Sliding distance= (1ms-1x1000x3600) = 3.6x106mk2=1/ (1x3.6x106m) = 2.8 x 10-7

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