Milling Surface Roughness Formula | Ball Nose and Feed Pitch

Surface roughness in milling is mainly determined by tool radius and feed pitch, and can be predicted by geometric formulas.

Structured Content

Surface Roughness Concept

Machining type:

• Ball nose end mill
• Radius end mill

Machining mode:

• Feed interval cutting
• Contour machining

Key parameters:

• R: tool radius
• P: feed pitch
• h: surface roughness

Formation Principle

Concept:

• Surface formed by tool path overlap

Cause:

• Radius controls curvature
• Feed controls spacing

Result:

• Larger feed → rough surface
• Larger radius → smoother surface

Surface Roughness Formula

Formula:

h = R × {1 − cos [ sin⁻¹ ( P / 2R ) ] }

Parameters:

• R: tool radius
• P: feed pitch
• h: roughness height

Parameter Effect

Tool radius:

• Larger R → smoother surface
• Smaller R → rougher surface

Feed pitch:

• Larger P → rougher surface
• Smaller P → smoother surface

Data Table Application

Usage:

• Quick roughness estimation
• Parameter selection

Optimization Strategy

Tool:

• Large radius cutter

Cutting:

• Reduce feed

Method:

• Multi-pass finishing

Common Problems

High roughness

Cause:

• High feed

Solution:

• Reduce P

Low efficiency

Cause:

• Too low feed

Solution:

• Increase feed

Wave marks

Cause:

• Large step over

Solution:

• Reduce step

Engineering Focus

Key factors:

• Radius
• Feed

Results:

• Better surface
• Predictable quality