Optimizing Arc Cutting in CNC Machining Parts with Constant Feed Rates

CNC Machining Parts with Constant Feed Rates

In the world of CNC machining, achieving precision and high-quality finishes on curved surfaces can be challenging. One crucial factor is maintaining a constant feed rate while cutting both inner and outer arcs. Let’s dive into the practical aspects of this technique and see how it can improve your CNC machining parts.

Understanding Constant Feed Rates

When programming CNC machines, it’s essential to calculate the coordinates for each point on the workpiece contour based on the part drawing. Typically, the tool radius is ignored in these calculations. Instead, the programmed radii are based on the drawing dimensions, not the distance to the tool centerline. This means that when cutting arcs, the programmed feed rate is associated with the programmed radius, not the actual radius at the tool center.

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When the tool radius compensation is active, and the arc path is offset by the tool radius, the actual cutting arc radius can be either larger or smaller, depending on the offset value. This results in a reduced radius for inner arcs and an increased radius for outer arcs. Understanding this concept is vital because, in tool radius compensation mode, the cutting feed rate does not automatically adjust. Adjustments are necessary only if the surface finish quality requirements are high or the tool radius is particularly large. This consideration applies specifically to arc movements, not linear cutting.

Setting Feed Rates for Arc Movements

Typically, the feed rate for arc movements is set similarly to linear feed rates. In many programs, there’s no change in feed rate between linear and arc movements. However, if the surface finish of the workpiece is critical, adjustments based on the tool radius, type of arc (inner or outer), and cutting conditions are necessary. The larger the tool radius, the more critical it is to adjust the feed rate for arc cutting.

For instance, an equidistant tool path (using tool radius compensation) can significantly differ from the drawing dimensions in arc programming. Here’s a standard formula for calculating the linear feed rate:

Fi = (r/min) × (F/n)


  • Fi = Linear feed rate (in/min or mm/min)
  • r/min = Spindle speed
  • F = Feed per tooth
  • n = Number of cutting edges (flutes or inserts)

Using this formula, adjustments can be made to the feed rate for arc movements, depending on whether it’s an inner or outer arc.

Adjusting Feed Rates for Outer Arcs

For outer arcs, the feed rate should typically be increased. Here’s the formula:

Fo = F × (R / (R + D))


  • Fo = Feed rate for outer arcs
  • F = Linear feed rate
  • R = Workpiece outer radius
  • D = Tool radius

Adjusting Feed Rates for Inner Arcs

For inner arcs, the feed rate should be decreased. Here’s the formula:

Fi = F × (R / (R - D))


  • Fi = Feed rate for inner arcs
  • F = Linear feed rate
  • R = Workpiece inner radius
  • D = Tool radius

These adjustments ensure a constant cutting speed, maintaining surface quality and reducing tool wear.

Practical Application and Example

Let’s consider a practical example where you need to adjust the feed rates for both inner and outer arcs:

  1. Outer Arc Example:
  • Linear feed rate (F): 20 in/min
  • Workpiece outer radius (R): 2 inches
  • Tool radius (D): 0.25 inches Using the formula:
   Fo = 20 × (2 / (2 + 0.25)) = 20 × (2 / 2.25) ≈ 17.78 in/min
  1. Inner Arc Example:
  • Linear feed rate (F): 20 in/min
  • Workpiece inner radius (R): 2 inches
  • Tool radius (D): 0.25 inches Using the formula:
   Fi = 20 × (2 / (2 - 0.25)) = 20 × (2 / 1.75) ≈ 22.86 in/min

By making these adjustments, the cutting speed remains consistent, improving the machining quality.

Example Data Table

Here’s a simple table summarizing the adjusted feed rates for different arc radii and a constant tool radius of 0.25 inches:

Workpiece Radius (in)Feed Rate (in/min)Inner Arc Feed Rate (in/min)Outer Arc Feed Rate (in/min)

Optimizing arc cutting in CNC machining parts with constant feed rates is essential for achieving high-quality finishes and extending tool life. By understanding the impact of tool radius compensation and adjusting feed rates accordingly, you can maintain a consistent cutting speed and improve the overall machining process. These techniques ensure precision, efficiency, and superior results in CNC machining.

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Want.Net Technical Team

The Want.Net Technical Team has diverse members with extensive education and training in CNC machining. They prioritize precision, efficiency, and innovation to provide high-quality manufacturing solutions globally.

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