Normal Stress Due to Tool Calculator

Normal Stress Formula:

\[ \sigma_n = \frac{\sin(\phi) \times F_r \times \sin(\phi + \beta - \gamma_{ne})}{A_c} \]

Shear Angle:

rad

Resultant Cutting Force:

Mean Friction Angle:

rad

Working Normal Rake:

rad

Chip Cross Sectional Area:

m²

Tolerance:

Normal Stress (Pa):

Tolerance Range (Pa):

1. What is Normal Stress Due to Tool?

Definition: Normal stress is the stress component perpendicular to the cutting plane caused by the tool's action on the workpiece during machining.

Purpose: It helps engineers analyze cutting forces and optimize machining parameters for better tool life and surface finish.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_n = \frac{\sin(\phi) \times F_r \times \sin(\phi + \beta - \gamma_{ne})}{A_c} \]

Where:

\( \sigma_n \) — Normal stress (Pascals)
\( \phi \) — Shear angle (radians)
\( F_r \) — Resultant cutting force (Newtons)
\( \beta \) — Mean friction angle on tool face (radians)
\( \gamma_{ne} \) — Working normal rake angle (radians)
\( A_c \) — Cross sectional area of uncut chip (m²)

Explanation: The formula calculates the normal stress component by considering the cutting geometry and forces.

3. Importance of Normal Stress Calculation

Details: Understanding normal stress helps in tool design, predicting tool wear, and optimizing cutting parameters for efficient machining.

4. Using the Calculator

Tips: Enter all angles in radians, force in Newtons, and area in square meters. The tolerance field (default ±5%) accounts for calculation uncertainties.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q2: What's a typical shear angle value?
A: Shear angles typically range between 5°-40° (0.087-0.698 radians) depending on material and cutting conditions.

Q3: Why include a tolerance value?
A: Machining conditions vary, so the tolerance provides a realistic range accounting for measurement and calculation uncertainties.

Q4: How do I measure resultant cutting force?
A: Use a dynamometer during cutting tests or estimate from power consumption and cutting parameters.

Q5: What affects normal stress values?
A: Workpiece material, cutting speed, feed rate, tool geometry, and lubrication all influence normal stress.