Merchant’s circle
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This document discusses Merchant's circle analysis for orthogonal metal cutting. It introduces key terms like shear velocity, chip velocity, shear strain, and shear strength. It lists assumptions of the model including a perfectly sharp tool, planar shear surface, straight cutting edge generating a flat surface, and uniform velocities. Merchant's circle analysis relates the cutting forces - feed force F, thrust force Ft, and shear force Fs - to the shear plane angle ø and tool rake angle α through trigonometric relationships. The goal of Merchant's circle is to analyze minimum power consumption during metal cutting.
Merchant’s circle
- 1. MERCHANT’S CIRCLE By- Bishal Das Nit Mizoram
- 2. Nomenclature
- 4. Shear strain
- 5. Velocity triangle Vs-Shear velocity Vc-Chip velocity V-Velocity of uncut chip By Sin law-
- 6. Assumptions: ï‚¢The tool is perfectly sharp and has no contact along the clearance face ï‚¢The surface, where shear is occurring is a plane ï‚¢The cutting edge is a straight line extending perpendicular to the direction of motion and generates a plane surface as the work moves past it ï‚¢The chip does not flow to either side or no side spread. ï‚¢Uncut chip thickness is constant ï‚¢Width moves with a uniform velocity ï‚¢A continuous chip is produced without any BUE ï‚¢Work moves with a uniform velocity ï‚¢The stress on the spear plane are uniformly distributed.
- 7. Nomenclature
- 8. Forces of Merchant’s circle • F=Fcsinø+Ftcosα • N=Fccosα-Ftsinα • Fs=Fccosø-Ftsinø • Fn=Fcsinø+Ftcosø • Fc=Fscosø+Fnsinø • Ft=Fncosø-Fssinø