Study and Analysis of Geometric Effect of Ball Burnishing Process of Different Materials and Evaluation of Forces and Strain for Ballizing Process

The process consists of forcing an oversized ball of a hard material through a premachines hole in softer material .The interference between the ball and the hole causes the hole to expand such that its deformation is partly plastic and partly elastic. The elastic deformation of the hole is recovered due to elastic spring back whereas the plastic deformation results in a slight permanent increase in the hole diameter after ballizing. Ball burnishing or Ballizing is a production process for improve the accuracy and surface finish of holes. This process is a mass production process for sizing and finishing holes. The sizing and finishing of holes depends upon the interference adopted for ballizing process. This paper is an attempt toward comparing surfaces effects ,Estimation of deflection, deformation, radial strain, stress and finished dimensions of Mild steel and Aluminium.

We get a finished desired diameter of hole, after the ball of definite diameter is passed from the initial diameter.These data of initial and final diameters of hole and diameters of ball are based on the data accumulated by trial and error experimentation as discussed earlier.
By dividing with D (the diameter of ball) we have made the values of interference and plastic deformation.Non-Dimensional these nondimensional quantities are plotted which give a linear relationship as shown.

Construction of mathematical Models & equations
When the linear relationship is combined with the Hertz's theory of contact stress of elastic bodies the equation is During the process, the ball and hole both will under go elastic deformation, although ball is hardened and bush is made of a softer material.
There fore interference = i f = i p + e h + e b ...( 1) If we plot i f against X axis and i p against y asix we get.The author has observed in his study of ballizing experiments that during the travel of the ball, the bush indicates a marked bulge and the ball bas less likelihood of strain.It may be pointed out that for excessively thick walled bushes the value of e B cannot be adopted as zero.
A detailed theoretical model can be developed for estimating the values of strain e H .This model is based on the Classical contact stress analysis founded by H. Hertz and presented in next section.In Ballizing there is almost rectangular strip contact between ball and the hole.A comparison of experimental results with Authors model is indicated in fig. .

Evaluation technique and methodology (For Strains) Mathematical Model for strains in Ballizing
Referring the fig. is the length of contact and 2b is the breadth or width of contact.The interference between the ball and the hole wall gives rise to say pressure P per unit length.
The max. deflection is obviously occurring along xx.
We have to find an expression for this max.deflection.
It is true that the uniform pressure P along the line contact will give rise to semi elliptical pressure distribution as shown in the side view over the width of contact.
Adopting a simplified assumption that the pressure distribution is uniform of intensity q instead of semi elliptical (Based on Timoshenko and Goodier.Theory of Elasticity) a model is developed in this article.
Load Distributed over a part of the Boundary of a semi-infinite solid referring to (Formula for calculation of deflection) Substituting in the expression for w, q = P ave For calculating the radial strain in the wall of the hole b = width of strip of contact and is calculated by the equations ... (5) Where adopting δ = i f /2 Thus the radial strain in the wall of the hole Ballizing.

RESULT AND DISCUSSION
a.Evaluation and analysis of different interference and with help of Fig.

Calculation for Radial Strain Aluminium Bushes
It is observed that with 150 and 50 microns interference respectively the final diameters obtained are 15.08 mm and 15.16 mm respectively.In the two bushes of 180 microns interference, from very rough surface as shown in fig. the final surface finish obtained was of 0.29 CLA, which indicates that a very good surface finish is obtained In the two bushes, in which interference was kept only 50 microns, the surface finish was not so good as it gave the C.L.A. value as 0.65 .

Calculation for Radial Strain
For Mild steel Bush with 80 Microns interference For Aluminum Bush of 180 microns interference E = 0.675 x 10 6 kg/cm 2 µ = 0.34 R 1 = 0.9 cm R 2 = 1.8 cm 2a = 2 p R 1 = 5.677 cm.b= 0.0114 c, p = 3342.70kg/ sqcm The value of e H calculated from the equation e H = 2.41 x 10 -3 cm The intercept on the Y axis is 1.35 microns according to authors model and aimed at adopting equal to 1.
A value of 50 microns has been adopted for strain calculations in the case of steel, whereas an interference of 150 microns is adopted for Aluminum because of sinking in tendency of Aluminum, under the load of an indenting ball.From C.L.A. equation as well as C.L.A. plots it is clearly seen that improvement in surface finish is obtained material and more interference, axial load has increased.However, load is found to be independent of velocity.

2.
Temperature does not rise so much during ballizing that it may affect the surface finish.

3.
After, ballizing internal diameters of bushes were measured; which established the fact that ballizing is a microsizing process.4.
There is very slight increase in diameter when interference is less.Keeping the same oversized ball.

5.
Theoretically as well as experimentally it is confirmed that if ballizing is done with more interference high velocity and on moderate BHN value, improved surface finish is obtained.

6.
Small circular contacts will be observed on the entire circumference as shown in Fig. 6.1.

7.
Co-relation factor for C.L.A. equation is 0.9583 whereas for load equation correlation factor is calculated to be 0.8677.8.
Both the results show values are quite high and curve fitting is satisfactory in both the cases.9.
Variation of load on the length of bush shown that, nearly at the center of the bush length the load is maximum.10.
Vibration in he load curve may be due to variation in the geometry accuracy while boring.

Objectives of the Proposed work
Sizing of bushes and final results will be of utility to industries.This will help in achieving high precision by selecting appropriate "Ball-Tube" combination.Surface finish evaluations using qualitative and quantitative measures.
Some of the application are listed below 1.
Honned and Lapped surfaces can be further smoothened.

2.
Sizing and finishing of cross hole recesses.
Slight tapers can be removed.

6.
Good results can be obtained by ballizing for the following materials.7.
Case hardened surfaces can also be ballized, but these should be free from hard chromium layer.
Calculations applies equally for the β line starting at any points in AB wide range of application and being used as a noble process (ballizing), it has some Observations, Concluding remarks can be made are listed below : 1.
Interference (i f ) should never exceed 2x of the hole diameter.

2.
It has given very good results for bores ranging from 0.5 mm to 125 mm diameter.

3.
The length to diameter ratio has also been recommended length should not be more than 10 times or less than 1/10 of the bore diameter.

4.
Wall thickness should also be greater than 1/10th of bore diameter.

5.
Ballizing gave good results for hole diameters of 1.5 mm to 25 mm.

6.
Part to be ballized should not be harder than 45 Rc.The balls must be more hard than 65 Rc.(65 Rockwell C scale).7.
Materials should be homogeneous.8.
Wherever ballizing length is more, arrangement, for pressing or pulling the ball though the bore has to be devised.9.
Porous, spongy or parts that wave hard spots due to casting, ballzing does not give uniform surface finish, 10.
Although some cast parts are successfully ballized.11.
Every curved tubing cannot be ballized.12.
Parts that have case hardened layer upto 0.4 mm, can be ballized, but beyond 0.4 mm case hardened depth, ballizing connot be carried out successfully.13.
When heat treatment is done after ballizing, sizing and finishing of the ballized hole get disrupted.14.
It has given a relationship of Ball over size and bore undersize to obtain the final diameter desired.15.
It has established that in a particular soft material (Medium Carbon Steel) 16.
When ballizng is done with a hard material ball the required bore diameters can be obtained as mentioned in the diagram (Fig. ) = interference = d b -d i and permanent plastic deformation = i p = d f -d i .
value of m and C can be obtained.Referring to figs it is seen that the slope m of the linear relationship line is of the order of unity.However from the authors model it was proposed that.This suggests that the value of e B is negligible.Thus it can be inferred that if the value of e B = 0 Hence m =1

Fig. indicate
Fig. indicate comparison between authors model and Experimental results.
based on the theory of elasticity (Hertz contact stress equations) and theory of plasticity involving slip line field solutions.(c) Strain models -Graph between i p and i f .(d) Axial force models (calculation of F for ballizing) (e) A comparison of the Mathematical Models of the Ballizing process with experimental Investigations.(f)