During machining work in Industry, surface roughness is measured or say compared with standard Comparator plates which are available in market. For precise value there are few contact and non contact measurement techniques are available.

You have to know the tip profile of the tool, the depth penetration of the tip on the turned material,

Roughly, You have to consider the mean value of the integral of the profile generated by the tip :

http://www2.coromant.sandvik.com/coromant/pdf/Metalworking_Products_061/tech_a_1.pdf

There is a pretty good work about it if you want to consider the vibration of the machine and so on (in french) :

http://docnum.univ-lorraine.fr/public/INPL/2008_CROLET_A.pdf

Regards

During Machining of a material surface roughness is measured with a surface roughness measuring testers.

Surface roughness measurement methods include linear roughness measurement, which measures a single line on the sample surface, and areal roughness measurement, which measures an area of the surface. Linear roughness measurement has been the norm until now, but expectations for areal roughness measurement, that can see a surface as it really is, has been rising in recent years.

There are two ways to measure surface roughness: 1)Contact Type and 2) Non-Contact Type (Laser microscope)

Roughness of surface after turnings depends on geometrical and kinematics  profiling of  edge nose in material.

You can calculate the surface roughness using special dependence. Rzt=f^3/8Re (f - feed, Re nse radius. But when value of feed decrase to 0,1 mm/rot height of roughness increase with influecee of minimal value of cutting layer which depends on radius of cutting edge. Details you can see in my paper  "Modeling of Minimal Thickness Cutting Layer Influence on Surface Roughness in Turning" (see Researchgate ). Direction of speed roughness depends on value of speed especialy increase with influence of built up edge.

Sir, is that any relationship of cutting speed with roughness?

Welcome

With increase of speed the surface roughness decrease (in speed direction) but with cutting in buillt up edge phenomena it is some change.  Because built up edge not stabile and it increase in cutting process it depends on suurface roughness. For steel max influence and max Surface roughness is for speed value about 15 m/min. Study BUP  phenomena 

Best regards Tadeusz