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MEDICAPS INSTITUTE OF TECHNOLOGY & MANAGEMENTDepartment of mechanical engineering

Merchants circlePrepared by:

Sumit shrivastava Shubham jawara Rajpal singh yadav

ME-b (batch 2013)

outline Brief introduction to Merchants Circle.Assumptions for Merchants Circle Diagram. Construction of Merchants Circle. Solutions of Merchants Circle. Advantages of Merchants Circle. Need for the analysis of cutting forces. Limitations of Merchants Circle. Conclusion

introduction Merchants Circle Diagram is constructed to ease the analysis of cutting forces acting during orthogonal (Two Dimensional) cutting of work piece.

Ernst and Merchant do this scientific analysis for the first time in 1941 and gives the following relation in 1944

It is convenient to determine various force and angles.

Metal cuttingOrthogonal cuttingOblique cutting

Cutting Edge is normal to tool feed.

Here only two force components are considered i.e. cutting force and thrust force. Hence known as two dimensional cutting. Shear force acts on smaller area. Cutting Edge is inclined at an acute angle to tool feed. Here only three force components are considered i.e. cutting force, radial force and thrust force. Hence known as three dimensional cutting. Shear force acts on larger area.Metal Cutting is the process of removing unwanted material from the workpiece in the form of chipsTerminology : Rack angle : Frictional angle : Shear angle Ft : Thrust Force Fn: Normal Shear ForceFc: Cutting Force Fs: Shear Force F: Frictional Force N: Normal Frictional Force V: Feed velocityRAKE ANGLE Back Rake Angle: It is the angle between the face of the tool and measured in a plane perpendicular to the side cutting edge Side Rake Angle: It is the angle between the face of the tool and measured in a plane perpendicular to the baseFront ViewBack Rake AngleSide Rake AngleFrictional Angle It is the angle between the resultant ,of the Frictional Force & Normal Force, and Normal Reaction.

= tan-1 : coefficient of frictionPFRNShear Angle It is the angle made by the shear plane with the direction of the tool travel.FsFtFcFnFNVShear Force Resistance to shear of the metal in forming the chip. It acts along the shear plane.Normal Shear Force Force on the chip provided by the workpiece. Acts normal to the shear plane.Friction Force Resisting force acted at the tool workpiece interface to resist the motion of tool.Thrust Force This force acts normal to the cutting force or the velocity of the tool.Normal Friction Force It act at the tool chip interface normal to the cutting face of the tool and is provided by the tool.Cutting Force Force acted along the velocity of tool

Cutting force increases as speed increases and decreases as rake angle decreasesAssumptions for merchants circle diagram Tool edge is sharp. The work material undergoes deformation across a thin shear plane. There is uniform distribution of normal and shear stress on shear plane.The work material is rigid and perfectly plastic. The shear angle adjusts itself to minimum work. The friction angle remains constant and is independent of . The chip width remains constant. The chip does not flow to side, or there is no side spread.FNFTConstruction of merchants circleFSFCFR-NVForces included in metal cutting Fs , Resistance to shear of the metal in forming the chip. It acts along the shear plane.

Fn , Backing up force on the chip provided by the workpiece. Acts normal to the shear plane.

N, It at the tool chip interface normal to the cutting face of the tool and is provided by the tool.

F, It is the frictional resistance of the tool acting on the chip. It acts downward against the motion of the chip as it glides upwards along the tool face.solution of merchants circleKnowing Fc , Ft , and , all other component forces can be calculated as:The coefficient of friction will be then given as :On Shear plane,

-FSFTFCFNFNRV

Now,

Now shear plane angle

The average stresses on the shear plane area are:

solution of merchants circle-FsFtFcFnFNRVLet be the shear angle

Where,solution of merchants circleAssuming that is independent of , for max. shear stress-FsFtFcFnFNRV

Now the shear force can be written as:

and

TNeed of analysis of forcesAnalysis of cutting forces is helpful as:-

Design of stiffness etc. for the machine tolerance.Whether work piece can withstand the cutting force can be predicted. In study of behavior and machinability characterization of the work piece. Estimation of cutting power consumption, which also enables selection of the power source(s) during design of the machine tool. Condition monitoring of the cutting tools and machine tool.advantages of merchants circleProper use of MCD enables the followings :-

Easy, quick and reasonably accurate determination of several other forces from a few forces involved in machining.

Friction at chip-tool interface and dynamic yield shear strength can be easily determined.

Equations relating the different forces are easily developed.limitations of merchants circleSome limitations of use of MCD are :-

Merchants Circle Diagram (MCD) is valid only for orthogonal cutting.

By the ratio, F/N, the MCD gives apparent (not actual) coefficient of friction.

It is based on single shear plane theory.Conclusions/resultsFollowing conclusions/results are drawn from MCD :-

Shear angle is given by For practical purpose, the following values of has been suggested:

= for >15o = 15o for