Reduced Modulus at the Contact of Two Metals - Report Example

Q1. a) Reduced modulus at the contact of two metals (Eeffective) is given by the following equation. Where E1 = Elastic modulus of metal E2 = Elastic modulus of metal 2; 1 = Poisson’s ratio of metal 1 and 2 = Poisson’s ratio of metal 2 In this case, as both the metals are the same (copper). Therefore, E1 = E2 = 140 GPa and 1 = 2 = 0.3 Therefore, i.e. GPa Q1. b) For copper Hardness H = 700 MPa = 7*108 Pa and Elastic modulus E = 140 GPa = 1.4*1011 MPa Elastic strain at the yield stress or p is given by Q2. A conical indenter of a hard material under normal load N produces an indent with into a metal surface of hardness H and the radius (r) of the indentation mark on the metal surface is given by the following equation Here, Normal load N = 10 N and Hardness H = 700 MPa = 700*106 N/m2 Therefore, Half the width of the scratch (r) will be Therefore, Width of the scratch = 2r = 190 m The coefficient of ploughing friction () is given by the following equation 0.17 Here  is half angle of the conical indenter. Q3) Life of a ball bearing (L) is when multiplied with third power of the applied load is a constant i.e. W3L = constant Where W is applied load in N and L is life in number of cycles Therefore, or, Where L1 and L2 are life of a Ball Bearing at loads W1 and W2 respectively. Here, W1 = 2 kN, W2 = 8 kN and L1 = 108 cycles Therefore, Life of the Ball Bearing at 8 kN load will be Q4.) Combined average roughness (RA) of two surfaces is given as Here, RA1 = RA, Steel = 0.5 m and RA2 = RA, Brass = 0.6 m Therefore, Combined Roughness = 0.781 m Parameter M is calculated in the following manner Here, ft is the thickness of the oil film under operating condition = 4 m and RA is combined average roughness = 0.781 m Therefore, Because the ‘M’ parameter is between 5 and 10, therefore, the sliding interface is operating in ‘Hydrodynamic Lubrication Regime’. Q5) Four important limitations of liquid lubricants are the following. (i) Practical or Design Limitation in Accessibility of the Mating Surfaces The mating surface should be accessible during service of the component so that liquid lubricants can be applied at regular intervals to replace the degraded lubricant. But this is not possible in many cases due to either design reasons or the operating atmosphere itself may be either toxic or radioactive and thus limiting the access of the mating surface. (ii) Limit on Operating Temperature Viscosity and therefore lubricating ability of liquid lubricants decrease significantly with increasing temperature. Therefore, liquid lubricants are not suitable for high temperature applications. Besides, liquid lubricant may get either degraded or even vaporize if temperature spikes up during operation due to some fault. (ii) Ineffective at High Load, Low Speed At low speed the oil film thickness is less and if the load is high then thin thin lubricating film cannot maintain desired gap between the mating surfaces which touch each – other causing significant wear. Thus liquid lubricant is not effective when the rpm is low and load is high. (iv) Clean Applications? Liquid lubricants spread on the shop floor making the shop floor dirty. In fact liquid lubricants are single most contributors towards a dirty shop floor. These lubricants attract dust and other particles and add further to the uncleanliness of the shop floor. Besides, there are environmental issues associated with disposal of a liquid lubricant. Therefore liquid lubricants are not preferred for clean applications. Q6. Referring to the figure below. Elastic Modulus of Steel E1 = 208 GPa = 2.08*1011 Nm-2 Poisson’s Ratio of Steel 1 = 0.28 Elastic Modulus of Copper E2 = 69 GPa = 6.9*1010 Nm-2 Poisson’s Ratio of Aluminium 2 = 0.28 Radius of the steel Ball R = 25 mm = 2.5*10-2 m P = ? H = 700 MPa = 7*108 Nm-2 Effective modulus (Eeffective) at the interface of steel ball and aluminium plate will be i.e., Eeffective = 58.3 GPa = 5.83*1010 Nm-2 Radius of the indentation (a) on the top surface of the Al plate is given by Herz equation ……….. (1) Maximum Pressure (Po) ………. (2) Maximum Shear Stress (max) ………. (3) Shear stress required for the aluminium plate to yield first ……… (4) For most of the metals y = 3H, where ‘H’ is hardness of the material. Equating the value of shear stress in equations (3) and (4), ……………. (5) i.e., kN The corresponding contact width is 2a i.e. mm Maximum Pressure (Po) will be, GPa Average pressure will be MPa Maximum Shear Stress will be GPa Maximum Shear Stress is located at a depth‘d’, which is given as d = 0.48*a = 0.48*2.28 mm = 1.09 mm below the free surface. Q7. a) Assumptions made for deriving Archard’s adhesive wear equation are the following. (i) There are asperities on any metallic surface. (ii) When two metallic surfaces come in contact, they come in intimate contact at the asperities. (iii) The contact area a2 at the asperities supports the load a2H. (iv) The two materials get bonded at the asperities. (v) Relative motion of the two surfaces cause breaking of this bond and a wear fragment is thus produced. (b) Derivation of wear equation The wear mechanism postulated by Archard is shown schematically in the following figure. Contact area a2 supports the load a2H Where H is the hardness of the soft metal When distance traveled is ‘2a’ Wear volume produced will be (2a3)/3 Thus wear volume per unit length Q = {(2a3)/3}/(2a) = (a2)/3 Thus total wear, Q, in unit slid distance is Q = n*(a2)/3 ‘n’ is number of atoms in contact. Total load is N = n*a2H Therefore, Q/N = 1/3H i.e., Total wear per unit distance Q = N/3H (c) Based on this equation total wear is directly proportional to sliding distance and applied load and inversely proportional to the hardness of the material getting worn out. (d) This equation gives a much larger value for the volume of wear than what is experimentally observed or what is observed in real life. The difference is very high and is 4 to 7 order of magnitude higher than that observed in the experiments. This is because not all but only a very small fraction of the asperity contacts result in wear of the material and therefore, in stead of the equality sign in the Archard’s wear equation, there should be a proportionality sign. When this is done a constant is introduced in the equation whose value is determined experimentally. Thus the revised equation is Q = k(N/3H) Here, ‘k’ is a constant, known as wear coefficient. This is a constant between mating surfaces and its value remains the same for a given pair of mating surfaces for a given operating wear mechanism. Q8. Methods of Increasing Surface Hardness of a Steel Component (a) Without changing composition (i) Surface Hardening: In this method a heat source is scanned over the surface. The heat source causes heating of the surface which takes the surface to austenitic phase. This is an fcc (face centered cubic) phase in which all the carbon dissolves in Fe lattice. As the heat source is moved away the surface is literally quenched due to heat extraction by the underlying cold metal at a very rapid rate. Due to quenching the carbon atom gets trapped into the iron lattice which tries to become bcc but is gets arrested as bct (body centered tetragonal) due to presence of excess carbon in the lattice. This phase is known as maternsite and this phase is very hard. Due to formation of martensite, the steel surface becomes very hard. One can use heat sources like induction coil or a flame or a laser beam. (ii) Shot Pinning In this method the steel surface is blasted with small spherical balls of steel. The steel balls impart shock to the steel surface, which gets hardened due to shock hardening or strain hardening. This is a very good technique as it imparts compressive stress on the surface which improves creep life of a component. (b) By changing surface chemistry (i) Case Carburizing In this process the component is heated in a carbon rich atmosphere. The carbon atoms diffuse into the surface of the steel component and more and more Fe3C (also known as cementite) forms. This leads to hardening of the steel component’s surface as the surface is now high carbon steel and high carbon steel is harder than low carbon steel or mild steel. By controlling time and temperature one can control depth and hardness of the surface. (ii) Ion Implantation In this process ions are implanted into the surface. Suitable ions are produced and accelerated towards the surface in a controlled atmosphere. The ions bombard the surface of the mild steel and get implanted into it. If ions are selected suitably, then this leads to increase in the hardness of the surface. Read More

Q1. a) Reduced modulus at the contact of two metals (Eeffective) is given by the following equation.

Where E1 = Elastic modulus of metal 1;

E2 = Elastic modulus of metal 2;

n1 = Poisson’s ratio of metal 1 and

n2 = Poisson’s ratio of metal 2

In this case, as both the metals are the same (copper).

Therefore,

E1 = E2 = 140 GPa      and

n1 = n2 =  0.3

Therefore,

i.e.                    GPa

Q1. b) For copper

Hardness                     H = 700 MPa = 7*108 Pa                   and

Elastic modulus          E = 140 GPa = 1.4*1011 MPa

Elastic strain at the yield stress or ep is given by

                                      

 Q2. A conical indenter of a hard material under normal load N produces an indent into a metal surface of hardness H and the radius (r) of the indentation mark on the metal surface is given by the following equation

  Here,   Normal load    N = 10 N

and      Hardness         H = 700 MPa = 700*106 N/m2

Therefore,

Half the width of the scratch (r) will be

                       Therefore,

Width of the scratch = 2r = 190 mm

The coefficient of plowing friction (m) is given by the following equation

                        0.17

Here q is the half-angle of the conical indenter.

Q3) Life of a ball bearing (L) is when multiplied with the third power of the applied load is a constant  i.e.  W3L = constant

Where W is applied load in N and L is life in the number of cycles

Therefore,  or,                  

Where L1 and L2 are the life of a Ball Bearing at loads W1 and W2 respectively.

Here,   W1 = 2 kN,      W2 = 8 kN      and      L1 = 108 cycles

Therefore, the Life of the Ball Bearing at 8 kN load will be

 Q4.) The combined average roughness (RA) of two surfaces is given as

Here,   RA1 = RA, Steel = 0.5 mm          and      RA2 = RA, Brass = 0.6 mm

Therefore,

Combined Roughness = 0.781 mm

Parameter M is calculated in the following manner                       

Here,               ft is the thickness of the oil film under operating condition = 4 mm

and                  RA is combined average roughness = 0.781 mm

Therefore,      

Because the ‘M’ parameter is between 5 and 10, therefore, the sliding interface is operating in ‘Hydrodynamic Lubrication Regime’.

Q5) Four important limitations of liquid lubricants are the following.

(i) Practical or Design Limitation in Accessibility of the Mating Surfaces

The mating surface should be accessible during the service of the component so that liquid lubricants can be applied at regular intervals to replace the degraded lubricant. But this is not possible in many cases due to either design reasons or the operating atmosphere itself may be either toxic or radioactive and thus limiting the access of the mating surface.

As the heat source is moved away the surface is literally quenched due to heat extraction by the underlying cold metal at a very rapid rate. Due to quenching, the carbon atom gets trapped into the iron lattice which tries to become bcc but is gets arrested as bct (body-centered tetragonal) due to the presence of excess carbon in the lattice. This phase is known as martensite and this phase is very hard. Due to the formation of martensite, the steel surface becomes very hard. One can use heat sources like an induction coil or a flame or a laser beam.

(ii) Shot Pinning

In this method, the steel surface is blasted with small spherical balls of steel. The steel balls impart shock to the steel surface, which gets hardened due to shock hardening or strain hardening. This is a very good technique as it imparts compressive stress on the surface which improves the creep life of a component.

(b) By changing surface chemistry

In this processions are implanted into the surface. Suitable ions are produced and accelerated towards the surface in a controlled atmosphere. The ions bombard the surface of the mild steel and get implanted into it. If ions are selected suitably, then this leads to an increase in the hardness of the surface.

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