1. Dipl. eng. Leonov D., PhD Ivanov A., Phd Lilov I.
METHODOLOGY FOR OPTIMIZING THE INFLUENCE OF SURFACE ROUGHNESS ON THE FUNCTIONAL PROPERTIES OF DETAILS IN MECHANICAL ENGINEERING
Dipl. eng. Leonov D., PhD Ivanov A., Phd Lilov I.

2. Purpose of the report
The article deals with a fundamentally new methodology for optimization, assessment, and control of the roughness of surfaces that can be applied in all production facilities. What is meant by optimization is the choice of the most appropriate roughness from among all the practically possible values that can be achieved in certain production conditions. The given methodology is used as a basis for the assessment of the influence of surface roughness on the strength of a joint formed through the process of hot pressing.

3. Roughness parameters according to ISO 4287
Rmax l yp yv y m
Roughness parameters according to ISO 4287

4. The profiles with equal parameters
The profiles describing absolutely different microrelief have equal parameters

5. Non – paramterical approach for evaluation and control of surface roughness
A method by using non-parametric criterions and as such the graphics of different functions are taken :
functions of distribution of the ordinates of the profile or the tangents of the angles of the profile’s gradien ;
density of distribution of the ordinates of the profile or angles’ tangents of the profile’s gradient .

6. The physical sense of non-parametric criterions

7. Object of testing D l d
A hot-pressed joint with a nominal diameter of contact area D = 20 mm, external diameter of the threaded collar d = 30 mm, length of contact area l = 20 mm. Under exploitation the joint is loaded with axis force F = 6,65.10³ N.

8. Technology of manufacture of each model
Numbers of the groups of models
Mechanical processing
Modes of machining
Surface roughness (Rz), μm :
threaded collar/shaft 1
Turning
S=0,7 mm/rev, n=355 rev/min
15,04
17,64 2
Grinding
N=180 rev/min, V=35 m/s
12,69
10,05 3
Polishing
N=1400 rev/min
2,1
2,65
S – Feed rate, V - Cutting speed, N – Rotational speed, Rz - Average maximum height of the profile

9. Graphics of the groups of models
               
The graphics of non-parametric criteria „Density of distribution of the angles’ tangents of the profile’s gradient” of models: а) for the threaded collars, b) for the shafts. The X axis – value of the angles’ tangents of the profile’s gradient. The Y axis – frequency of emergence of the angles’ tangents of the profile’s gradient.

10. Strength of un-pressing , N
Results
Numbers of the models
Strength of un-pressing , N
Actual preload, mm
1 group 1
10,9·103
0,023 2
11,8·103
0,024 3
13,3·103
0,028
2 group 4
15,4·103
0,025 5
17,6·103 6
16,2·103
0,027
3 group 7
22·103
0,026 8
24,6·103 9
24·103

11. Results and discussion
- a mathematical model relating the optimization parameter with the technological modes of processing and making it possible to forecast the level of force required for un-pressing with variations of the above-mentioned factors ;
- technological modes of processing which produce an optimal surface roughness, guaranteeing the highest level of force required for un-pressing S threaded collar = 0,43 m/min, V threaded collar = 37,5 m/s, Sshaft = 0,467 m/min, Vshaft = 36 m/s
- optimal surface roughness of the following machine parts «Threaded collar» and «Shaft», which can be controlled through the use of non-parametric criteria

12. Control of the roughness
The optimal graphics “Density of distribution of the angles’ tangents of the profile’s gradient” and the deviation tolerances for: а) the threaded collars, b) the shafts. The X axis – value of the angles’ tangents of the profile’s gradient. The Y axis – frequency of emergence of the angles’ tangents of the profile’s gradient.

13. Conclusion
The use of standard parameters to assess and control the surface roughness of machine parts, appliances and machines has only one advantage – the simplicity of its practical use. When we are looking for a complex criterion dependent on several factors, it is simply impossible to apply numerical criteria because they do not allow for the optimal characteristic (the most appropriate of all the possible ones) of the normed functional property of the surface to be accurately defined with a practicable degree of accuracy. The functions of density of distribution and the functions of distribution of ordinates and tangents of the angles of inclination of the pattern unequivocally define the roughness of surfaces and fully satisfy the legitimate requirement of a thorough and comprehensive definition.