🎓 Lesson 8 D5

Feed per Tooth vs. Chip Thickness Ratio

Feed per tooth is how far the cutting tool moves forward each time one of its teeth cuts into the material, while chip thickness ratio compares the thickness of the chip before and after cutting to show how much the material deforms.

🎯 Learning Objectives

✓ Calculate feed per tooth given spindle speed, feed rate, and number of flutes
✓ Analyze chip thickness ratio to estimate shear angle and predict cutting force trends
✓ Apply chip thickness ratio principles to select optimal feed and depth-of-cut combinations for hard rock drill bits
✓ Explain how variations in chip thickness ratio affect tool life and surface integrity in percussive drilling

📖 Why This Matters

In mining drilling and rock fragmentation, controlling chip formation determines bit wear, penetration rate, and energy efficiency. A poorly managed feed per tooth can cause chipping, overheating, or premature bit failure—costing thousands in downtime and replacement. Understanding chip thickness ratio helps engineers diagnose inefficient cutting, optimize blasthole drill parameters, and extend bit life in abrasive formations like quartzite or granite.

📘 Core Principles

Feed per tooth governs material removal per cutting edge and sets the baseline for chip geometry. Chip thickness ratio (r = h₁/h₂) emerges from the mechanics of orthogonal cutting: as r decreases (i.e., chips thicken due to plastic flow), shear angles shrink, friction increases, and cutting forces rise. In percussive rotary drilling—common in blasthole applications—the effective feed per tooth is modulated by hammer frequency, rotation speed, and thrust. Real-world chip formation deviates from ideal models due to rock heterogeneity, bit wear, and slurry effects; thus, r serves as a diagnostic proxy rather than a fixed constant.

📐 Key Calculations

Two interrelated formulas anchor this lesson: feed per tooth links machine parameters to edge-level engagement, while chip thickness ratio quantifies deformation severity. Both are foundational for predicting tool loading and thermal load.

💡 Worked Example

Problem: A DTH hammer drills at 120 rpm with a feed rate of 0.8 m/min using a 3-flute button bit. Rock core analysis shows undeformed chip thickness h₁ = 0.15 mm and measured chip thickness h₂ = 0.42 mm. Calculate f_z and r.

1. Step 1: Convert feed rate to mm/min → 0.8 m/min = 800 mm/min.

2. Step 2: Apply f_z = f_v / (n × N) where f_v = 800 mm/min, n = 3 flutes, N = 120 rpm → f_z = 800 / (3 × 120) = 2.22 mm/tooth.

3. Step 3: Compute r = h₁ / h₂ = 0.15 / 0.42 = 0.357.

4. Step 4: Interpret: r ≈ 0.36 indicates significant plastic deformation (typical r for hard rock = 0.2–0.4); combined with high f_z (>2.0 mm/tooth), this suggests excessive load per flute — likely accelerating carbide button fracture.

Answer: f_z = 2.22 mm/tooth; r = 0.36. Both values exceed recommended ranges for medium-hard rock, indicating need to reduce feed rate or increase RPM to lower f_z and improve chip evacuation.

🏗️ Real-World Application

At the Antamina Mine (Peru), operators observed rapid wear on 165-mm DTH bits in andesite (UCS ≈ 180 MPa). Vibration and torque data revealed intermittent high-load spikes. Post-blast bit inspection showed localized carbide spalling—not uniform wear. Engineering review calculated average f_z = 2.6 mm/tooth and r = 0.29, confirming overload per flute. By increasing RPM from 110 to 145 and reducing feed pressure by 12%, f_z dropped to 1.8 mm/tooth and r rose to 0.38—restoring stable shearing, extending bit life by 37%, and improving hole straightness tolerance by ±1.2°.