Gear undercut causes more design rejections than any other gear manufacturing issue we see. From medical device gears to precision robotics components, preventing undercut early saves costly redesigns and ensures reliable performance.
Gear undercut is prevented by using profile shift coefficients, increasing pressure angle from 20° to 25°, or maintaining minimum tooth counts (17+ teeth for standard gears). Profile shift is the most common solution as it eliminates undercut while preserving gear ratios and center distances.
Discover the exact tooth count thresholds, proven elimination methods, and when undercut exceptions make sense — backed by real manufacturing experience.
Table of Contents
What is gear undercut and how does it affect gear strength?
Gear undercut reduces tooth strength by 15-30% and occurs when tooth count falls below 17 teeth (20° pressure angle) or 12 teeth (25° pressure angle). It creates stress concentrations at the tooth root, leading to premature failure and reduced contact ratio between mating gears.
Testing data shows undercut gears fail at significantly lower torque loads compared to non-undercut designs. In precision applications like medical actuators or robotics, this translates to oversized gearboxes, higher material costs, or frequent replacements. The weakness isn’t gradual — it’s a distinct failure threshold that catches engineers off-guard during prototype testing.
Undercut isn’t dimensioned on drawings because it’s a manufacturing artifact, not a design feature. CAD software won’t warn you about it, and finite element analysis may miss the localized stress concentration. This creates a disconnect between design intent and manufactured reality, often discovered only when quotes require expensive modifications or parts fail qualification testing.
According to gear engineering principles, undercut becomes critical when the cutting tool removes material below the base circle during gear generation. Parts with undercut require either design changes or accept reduced load capacity — both costly decisions late in development.
Design Takeaway: Before finalizing gear designs, use this decision framework:
- High-precision/high-load applications: Keep ≥17 teeth (20° PA) or use profile shift for smaller pinions
- Moderate-load applications: Consider 25° pressure angle to allow 12+ teeth with standard tooling
- Cost-sensitive/low-load applications: Undercut may be acceptable below 14 teeth if strength requirements allow 20-30% reduction
- Wire EDM or 3D printed gears: Undercut geometry possible without manufacturing constraints
At what tooth count does undercut become a problem?
Undercut becomes problematic below 17 teeth for 20° pressure angle gears and below 12 teeth for 25° pressure angle gears. Practical threshold depends on application: high-precision systems need strict limits, while cost-sensitive applications may accept undercut down to 14 teeth.
The formula z_min = 2/sin²(α) gives theoretical minimums of 17.1 teeth (20°) and 11.2 teeth (25°). These thresholds apply universally regardless of module size.
Undercut severity increases dramatically below thresholds:
- 16 teeth (20° PA): Minor undercut, often acceptable
- 12 teeth: Severe undercut, causes premature failure under load
- 8 teeth: Extreme material removal, may fail during testing
Industry practice uses 14 teeth as practical minimum for general applications. Medical and aerospace maintain 17-tooth minimum for reliability.
Design Takeaway: Use 17 teeth minimum for precision applications, or consider 25° pressure angle for fewer teeth with standard tooling.
Why do manufacturers flag small tooth count gears as problematic?
Small tooth count gears require special manufacturing considerations, increase scrap risk, and need custom tooling that adds 2-4 weeks lead time plus 15-30% cost premium.
Standard processes create undercut below minimum thresholds. Solutions require:
- Profile shift: Custom hob modifications, extra setup time
- Wire EDM: Eliminates undercut but costs significantly more
- Accept undercut: Higher rejection rates, handling damage risk
Manufacturers flag these designs because engineers often discover performance issues during prototype testing, creating costly redesign cycles and project delays.
Design Takeaway: When quoting gears under 17 teeth, specify load requirements and whether custom tooling costs are acceptable. State “undercut acceptable” to avoid unnecessary engineering discussions.
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Does undercut affect all gear types — or only spur gears?
Undercut affects all generated gear types including spur, helical, bevel, and worm gears, but helical gears can achieve lower tooth counts due to their transverse pressure angle being higher than the normal pressure angle used for cutting.
Spur gears follow the standard z_min = 2/sin²(α) formula directly. For helical gears, the effective pressure angle in the plane of rotation increases based on helix angle: a 30° helix with 20° normal pressure angle creates approximately 23° transverse pressure angle, reducing minimum teeth from 17 to about 11.
Standard helix angles for common tooling availability: 15°, 23°, 30°, and 45°. Most CNC shops stock these angles, avoiding custom tooling delays. Higher helix angles provide greater undercut reduction but introduce thrust loads requiring appropriate bearing selection.
Choose helical gears when: packaging requires fewer than 17 teeth, slight noise increase is acceptable, and thrust loads can be managed. Avoid for high-speed applications where thrust forces become problematic or when axial space is limited.
Bevel gears use profile shift as standard practice in Gleason systems. Internal gears often have severe undercut constraints. Wire EDM and 3D printing eliminate manufacturing undercut but don’t improve tooth strength.
Design Takeaway: For tooth counts below 17, helical gears with 30° helix angle offer the best balance of standard tooling availability and undercut elimination. Consider thrust bearing requirements and housing modifications for axial load management.
Can profile shift eliminate undercut while maintaining gear ratio?
Profile shift completely eliminates undercut while preserving gear ratios, but requires custom tooling that adds 2-4 weeks lead time and increases cost by 15-25%. Success depends on finding manufacturers with profile shift capabilities.
Profile shift uses coefficient x = (17 – z)/17 for 20° gears. An 8-tooth pinion needs x = 0.53 shift. The gear ratio stays identical since tooth count remains unchanged. Center distance may increase unless mating gear receives compensating negative shift.
Drawing specification requirements: Call out “Profile shift coefficient x = 0.5″ with operating pressure angle and modified center distance. Include both standard and operating pitch diameters for manufacturing verification. Many shops require this information upfront to quote accurately.
Vendor capability varies significantly: Larger gear shops and specialists can handle profile shift, but many general CNC shops cannot. Verify capability before sending RFQs to avoid delays. Some shops maintain common shift coefficients (x = 0.3, 0.5, 0.7) to reduce custom tooling requirements.
Alternative comparison: Profile shift provides highest strength but costs most. 25° pressure angle offers middle ground with standard tooling. Helical gears provide best cost-performance balance for most applications requiring low tooth counts.
Design Takeaway: Use profile shift for critical applications where maximum strength is required. For cost-sensitive projects, consider 25° pressure angle or 30° helical gears as more economical alternatives with shorter lead times.
Does increasing pressure angle prevent undercut formation?
Increasing pressure angle from 20° to 25° reduces minimum tooth count from 17 to 12 teeth, effectively preventing undercut in smaller gears while maintaining standard tooling availability and no custom setup requirements.
The mathematical relationship z_min = 2/sin²(α) shows pressure angle impact directly. At 20°, minimum teeth = 17.1; at 25°, minimum = 11.2 teeth. This 35% reduction in minimum teeth makes 25° pressure angle ideal for compact gear trains requiring high reduction ratios.
Manufacturing advantages of 25° pressure angle: Standard hobs and gear cutters readily available, no lead time penalties, and most CNC gear shops can produce without special setup. Tooling costs remain identical to 20° gears, unlike profile shift solutions requiring custom modifications.
Performance trade-offs: Higher pressure angles create stronger tooth roots but increase separating forces by approximately 15-20%, resulting in higher bearing loads. Efficiency drops slightly (1-2%) due to increased sliding action, and noise levels may increase in high-speed applications.
Application examples: Heavy equipment commonly uses 25° for slow-speed, high-load applications. Planetary gearboxes benefit from 25° pressure angle to reduce involute interference in internal designs NASA aerospace testing showed 25° and 35° pressure angles performed well in high-speed applications with synthetic lubricants.
Design Takeaway: Choose 25° pressure angle when you need 12-16 teeth with standard tooling. Expect 15-20% higher bearing loads but gain immediate availability and cost savings over custom solutions like profile shift.
When is undercut acceptable in gear design applications?
Undercut is acceptable in low-load, cost-sensitive applications where 15-30% strength reduction doesn’t compromise function. Common examples include consumer electronics, toys, small appliances, and prototype testing where performance validation matters more than longevity.
Load and speed thresholds: Undercut becomes problematic above 2-3 Nm continuous torque or 1000+ RPM where dynamic loads amplify stress concentrations. Below these limits, undercut gears can provide adequate service life while reducing costs and lead times by 15-25%.
Application-specific acceptance criteria:
- Prototype/testing gears: Undercut acceptable for proof-of-concept validation
- Consumer electronics: Short duty cycles allow undercut in positioning mechanisms
- Low-duty applications: Intermittent operation systems can accept reduced strength
- Backup systems: Rarely operated emergency systems tolerate undercut well
Implementation guidance: Calculate gear capacity using AGMA 2001-D04 standard methods or equivalent gear strength calculators. Apply 60-70% safety factor to calculated capacity when accepting undercut. Specify on drawings: “Note: Undercut acceptable, max root thickness reduction 25%” to prevent manufacturing confusion.
Validation approach: Test prototypes at 150% expected load to verify undercut acceptance for your specific application. This confirms theoretical calculations against real-world performance before committing to production.
Design Takeaway: Accept undercut when total applied torque stays below 60-70% of calculated AGMA capacity, duty cycles are intermittent, and cost reduction outweighs performance optimization. Always specify undercut acceptance criteria clearly on engineering drawings with load limitations.
Conclusion
Gear undercut prevention requires balancing design constraints with manufacturing realities. Profile shift offers maximum strength but increases cost and lead time, while 25° pressure angles provide standard tooling solutions for moderate reductions. Helical gears deliver the best cost-performance balance for compact applications requiring low tooth counts.
Contact us to explore manufacturing solutions tailored to your gear design requirements.
Frequently Asked Questions
Yes, but ensure all gears maintain identical pressure angles and modules for proper meshing. Common combinations include 25° pressure angle pinions with standard 25° gears, or profile shifted pinions meshing with standard gears at modified center distances.
Calculate thrust force as: F_thrust = F_tangential × tan(helix angle). For 30° helix gears, thrust loads equal 58% of tangential loads. Specify this in bearing selection and ensure housing can handle axial loads without deflection affecting gear mesh.
Larger gear shops and AGMA-certified manufacturers typically offer profile shift services. Ask specifically about “addendum modification” or “profile shift coefficient” capabilities during RFQ. Request examples of previous profile shift work and verify they can calculate operating pressure angles and modified center distances.
Bearing radial loads increase proportionally to tan(pressure angle). For 25° vs 20°, expect approximately 18% higher radial loads: tan(25°)/tan(20°) = 1.18. Factor this into bearing selection and housing design to avoid premature bearing failure.
Run durability tests at 150% expected torque for 10,000+ cycles. Monitor for tooth root cracking, excessive wear, or noise increase. If gears survive this overload testing, undercut is likely acceptable for your application’s actual operating conditions.
Consider wire EDM cutting, which eliminates undercut manufacturing constraints entirely. While per-part costs are higher, it avoids custom tooling expenses and allows any tooth geometry. Alternatively, accept undercut with appropriate load derating for non-critical applications.
