Gouge and interference avoidance in surface contouring

A method of determining a tool geometry and tool orientation for any prescribed path along a workpiece of a cutting tool, comprising:

• providing a parameter set, where parameters of the parameter set include tool geometry and tool orientation relative to a surface of the workpiece;
• determining values of the parameters in the parameter set such that no local interference or global interference occurs, where local interference occurs when a portion of the tool immediately adjacent a cutting edge of the tool contacts a sidewall of a groove already cut by the cutting edge, and global interference occurs when a portion of the tool away from the cutting edge contacts a sidewall of a groove already cut by the cutting edge;
• and
• providing a physical cutting tool and tool orientation according to the determined values of the parameters to avoid interference,
• wherein the tool path is generally along the z-direction with modulation in the x-direction, and the direction into the workpiece is perpendicular to the x-direction and z-direction,
• wherein the tool geometry includes a top face oriented toward the workpiece surface, a first side clearance face and a second side clearance face, γ is the side clearance angle of the first and second side clearance faces with respect to the workpiece surface before any rotation of the tool, the tool is oriented so as to be rotated about the x-axis by an angle δ such that the side clearance angle γ becomes an effective clearance angle γn defined by
• tan(γn)=[(cos(δ)sin(φ)−sin(δ)cos(φ)sin(α))/cos(φ)sin(α)], where α is a half included cut angle, (π/2-φ) is the angle between first clearance face and the top face, and where the following conditions hold for all points on the first and second side clearance faces for all positions along the path:
• γn>tan−1|X(Z)−X(Z−ΔZ)/ΔZ|,
• where X(Z) is the value of the x-coordinate for a point on one of the side clearance faces when a tip of the tool is at the position Z along the z-axis, and Z−ΔZ is the position of the tool tip at an earlier time.

A method of determining a tool geometry and tool orientation for any prescribed path along a workpiece of a cutting tool, comprising:

• providing a parameter set, where parameters of the parameter set include tool geometry and tool orientation relative to a surface of the workpiece;
• determining values of the parameters in the parameter set such that no local interference or global interference occurs, where local interference occurs when a portion of the tool immediately adjacent a cutting edge of the tool contacts a sidewall of a groove already cut by the cutting edge, and global interference occurs when a portion of the tool away from the cutting edge contacts a sidewall of a groove already cut by the cutting edge;
• and
• providing a physical cutting tool and tool orientation according to the determined values of the parameters to avoid interference,
• wherein the tool path is generally along the z-direction with modulation in the x-direction, and the direction into the workpiece is perpendicular to the x-direction and z-direction,
• wherein the tool geometry includes a top face oriented toward the workpiece surface, a first side clearance face and a second side clearance face, wherein the cutting tool has a V-shaped cross section having a half included angle α oriented about the x-axis by an angle δ such that the cutting tool will cut modulated V grooves in the surface of the workpiece having a half included angle αn defined by tan(αn)=[tan(α)]/cos(δ).

A method of determining a tool geometry and tool orientation for any prescribed path along a workpiece of a cutting tool, comprising:

• providing a parameter set, where parameters of the parameter set include tool geometry and tool orientation relative to a surface of the workpiece;
• determining values of the parameters in the parameter set such that no local interference or global interference occurs, where local interference occurs when a portion of the tool immediately adjacent a cutting edge of the tool contacts a sidewall of a groove already cut by the cutting edge, and global interference occurs when a portion of the tool away from the cutting edge contacts a sidewall of a groove already cut by the cutting edge;
• and
• providing a physical cutting tool and tool orientation according to the determined values of the parameters to avoid interference,
• wherein the tool path is generally along the z-direction with modulation in the x-direction, and the direction into the workpiece is perpendicular to the x-direction and z-direction,
• wherein the tool geometry includes a top face oriented toward the workpiece surface, a first side clearance face and a second side clearance face, and the cutting tool is oriented about the x-axis by an angle δ, the relative x-direction deviation ε of a cutting tool profile from the prescribed path cut by the rotated cutting tool on the workpiece surface due to δ is given by:
• ε(δ)=C.δ.tan(θ)=C.tan(θ).δ.
• where θ is the angle of the prescribed path with respect to the z-axis and C is the depth of cut of the cutting tool into the workpiece.