Strain Rate Implications in Gear Fatigue Strength

Source: Gear and Power Transmission Research Laboratory, The Ohio State University

Should strain rate be a design concern in transmissions and gearboxes?  Is there any cause for concern when using ultrasonic fatigue testing techniques to produce material data? Existing literature is aggregated and reviewed and a dynamic gear tooth bending analysis of an EV countershaft drivetrain is performed to help answer these questions.


Plasticity behaviors in metals are well known to be dependent on the rate at which strain is applied to the material.  Typically, the range of interest is at least above 100 s-1 (strain per second), and the application is for parts in which the dominate failure mode is a sudden large overloading impact.  Historically, strain rates in high cycle fatigue have not been the subject of much discussion in the gearing industry.  The purpose of this study is to investigate if gearing engineers should start this discussion and if so, to compile as much available material information as possible to help guide that discussion. 

We start by proposing three questions that must be answered

  1. Are gears made of materials with fatigue strengths sensitive to strain rate?
  2. In what regions of material within gears are cyclic strains large enough to cause concern for fatigue fracture in meshing gears?
  3. Are cyclic strain rates in high strain regions in meshing gears significant?

To help answer (1) we review the current literature involving ultrasonic fatigue test methodologies in steels. The state of the art in this topic leads to several broad generalizations

  • Most experimental studies on low and medium carbon steels (<0.6% C) showed a significant difference between fatigue strengths measured at 10-40Hz and 20kHz corresponding to strain rates of 0.063 s-1 and 126 s-1 respectively.
  • Most experimental studies on high carbon (>0.6% C) martensitic steels did not show a sensitivity in VHCF fatigue strength to cyclic loading frequency when the failure mode is from sub-surface inclusion.
  • FCC austenitic steels associated with failures from surface slip bands are insensitive to frequency effects and BCC ferritic steels exhibit fatigue strengths that are strain rate dependent.  Higher strain rates produced higher yield, tensile and fatigue properties. Mixed ferritic and martensitic structures may be sensitive to strain rate effects if the ferritic grains are of sufficient size.

These statements naturally lead to the question of “what are gears made of”. A review of the state of art in automotive gearing shows that gear steels are predominantly low carbon steels that are heat treated though three predominate methods (i) carburizing, (ii) carbonitriding, and (iii) ferritic nitrocarburizing each producing materials of different microstructure.  Carburizing and carbonitriding are performed at temperatures above the austenitic temperature and a microstructure change occurs to FCC and is retained in a layer at the surface while the core remains a pearlite-ferritic structure. Ferritic nitrocarburizing does not involve temperature above the austenitic temperature and the microstructure remains ferritic. Combining the findings yields two observations

  • Carburized and carbonitrided gears may contain ferritic microstructure steel in the core and therefore tooth flank fracture and tooth interior flank fracture fatigue failures may have fatigue strengths which are sensitive to strain rate effects.
  • Nitrided and ferritic nitrocarburized gears may contain ferritic microstructure steel in the case and core meaning that tooth root fracture, tooth flank fracture, tooth interior flank fracture and pitting fatigue failures may all have fatigue strengths which are sensitive to strain rate effects.

The above helps us answer questions (1) and (2) under the assumption that there are use cases of gears producing high cyclic strain rates.  To answer (3), a dynamic gear load distribution model is utilized to predict dynamic strain rates in an electric vehicle gearbox. Thus far, most of the gearing in EV’s is fixed ratio countershaft arrangements at a little over 9:1 with maximum motor speeds of ~18,000 rpm. The trend being to increase motor speed and gear ratio.  The variable use case of automobiles in combination with the two gear meshes creates pitch line velocities from around 1 to 50 m/s.  An example gearset was designed, sized to about 250kW for an on-highway vehicle assuming a maximum motor speed of 18,000 rpm. Dynamic tooth bending strains were then computed for a maximum speed (250 kW) and a highway cruise (20kW) condition and are shown in Figure 1.

Source: Gear and Power Transmission Research Laboratory, The Ohio State University

Figure 1. Tooth bending strains and strain rates at the (a) 250 kW condition and (b) for the 20kW Highway Cruise condition the mesh 1 motor 25 tooth pinion.

Strain rates of 45 s-1 for the 250kW condition and 4.7 s-1 for the 20kW condition were achieved.  To gain perspective on what these rates compare to against pulsator fatigue testing, required test frequencies were computed to achieve the same maximum normal strain assuming sinusoidal loading.  This corresponded to 7,056 Hz for the 250kW condition and 3,238 Hz for the 20kW condition.  These test frequencies are significantly higher than conventional pulsator tests and yet still below the standard ultrasonic test frequency of 20kHz meaning that our gear operate in some intermediate condition as compared to how material fatigue data is collected. 
 

In summary, the presented analysis of the state of the art on strain rate effect in gearing materials leads to a conclusion that nitrided gears may be influenced by strain rate effects on the high cycle and very high cycle fatigue lives in all fatigue failure modes.  Carburized and carbonitrided gears still have fatigue failure modes such as tooth interior flank fracture and tooth flank fracture that occur in softer ferritic portions of the gear and may be influenced by strain rate.  The good news for gear designers is that the evidence suggests that operating at high strain rate will increase cyclic fatigue life.  However, since cyclic accumulation is also inherently faster with increased strain rates, the useful life of a part in terms of mean time to failure may not increase. In addition, gear engineers should still be cautious when using material data collected from ultrasonic test frequencies.  Strain rates from that testing may be considerably higher than what is achieved in application, and in strain rate sensitive materials will overpredict the cyclic fatigue life. 

About the authors:

Isaac Hong, Ph.D.
Research Assistant Professor, Gear and Power Transmission Research Laboratory, Department Mechanical and Aerospace Engineering, The Ohio State University College of Engineering, USA

Dr. Isaac Hong is a Research Assistant Professor in the Department of Mechanical and Aerospace Engineering at The Ohio State University. He received his Ph.D. degree in Mechanical Engineering from Ohio State in 2019. Dr. Hong is a PI in the Gear and Power Transmission Research Laboratory (GearLab) in the College of Engineering and the Rehabilitation Engineering Laboratory (RED Lab) in the College of Medicine School of Health and Rehabilitation Sciences. His research focuses on novel methods to monitor and characterize structural integrity of mechanical devices.

David Talbot, Ph.D.
Assistant Professor, Gear and Power Transmission Research Laboratory, Department Mechanical and Aerospace Engineering, The Ohio State University College of Engineering, USA

David Talbot is an assistant professor in the Department of Mechanical and Aerospace Engineering at The Ohio State University. His research focuses on multi-disciplinary power transmission problems within the aerospace, transportation, wind energy, and industrial gear box industries. His specific research investigations include load distribution modeling of power transmission components, gear, bearing and power transmission system efficiency modeling and measurement, gear dynamics and vibrations, gear manufacturing process simulation, and failure modes of power transmission components.

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