DuPont Advanced CAE Solutions for High Performance Plastic Gears

Tailored integrated plastic gears can lead to significant weight reduction. The reliance on mathematical analysis and simulations can reduce the design cycle iterations and result in huge cost and time savings. Developing high throughput plastic and hybrid plastic gears through reliable predictive engineering techniques may reshape the future of automotive, healthcare, and aerospace industries.

Plastic gears are continuing to displace metal gears in a widening arena of applications. Increased transmission efficiency, lowered NVH, increased wearing performance, and weight reduction are main characteristics of a plastic gear system. The need for weight reduction in many industrial applications, e.g. electronic cars and bikes, has led to a rapid increase in plastic and hybrid metal/plastic gear applications. DuPont is one of the industry leaders in replacing metals with plastics in a wide range of applications. The reliance on mathematical analysis and predictive engineering can reduce the design cycle iterations and result in huge cost and time savings. Successful predictive engineering techniques for plastic gear designs should be able to capture different failure mechanisms. For example, fatigue failure in plastic gears can be classified into tooth root failure, thermal damage due to self-heating, excessive wear due to localized contact, and environmental attack. Most of to-date predictive engineering techniques have been developed for metal gears and they are not designed to accurately predict plastic gears’ characteristics such as fatigue life, load sharing, and wear damage. On the other hand, standard design scopes, e.g. VDI2736 [3], rely on expensive gear experimental testing where only limited data is available in the literature for plastic gears. DuPont advanced CAE team provides world class capabilities to assist customers in their product developments. DuPont’s computational design tool for plastic gears offer a realistic simulation of plastic gears’ lifetime, durability, and load sharing. The developed methodology is verified through assessment of its performance in capturing several experimental testing results. The developed design tool is based upon the state-of-the-art Continuum Damage Mechanics (CDM) and provides an efficient tool for lifetime prognosis of plastic gear systems. Several factors that can affect the fatigue life of plastic gears including creep, surface finish, humidity, aging, self-heating and frequency can be considered with this approach. Using this design platform, design engineers can monitor fatigue crack initiation/propagation, cyclic plasticity, creep and shifts in the load sharing of plastic gears through their lifetime. This may aim design engineers to better understand the basic differences between fatigue mechanisms in metal and plastic gears, and may provide a design tool for optimization tasks.

Let’s focus on fatigue failure in plastics and compare their fatigue damage mechanisms to the metallic counterparts. When a fatigue crack is initiated in a metallic part, usually more than 70% of the useful life has already been passed and the part needs to be repaired or replaced. On the other hand, plastic parts are much more energy absorbent compared to metals, which means they have excellent crack arresting characteristics. Thus, a fatigue crack can be initiated in a plastic but will be arrested and part can sustain many more cycles. Due to the key difference between metal and plastic fatigue damage mechanisms, the fatigue theories developed for metals might be too conservative or even errorous for plastic applications. Most recently, a fatigue analysis tool for unfilled polymers has been developed and reported by [1,2]. The developed tool is based upon Continuum Damage Mechanics (CDM) and allows for simulation of progressive fatigue damage in unfilled polymers [1]. The proposed fatigue tool was extended to capture the effect of self-heating by [2]. The developed methodology is applied to plastic gear designs in order to investigate the role of progressive damage mechanisms on lifetime of gears. Most of to-date thermoplastic gear designs are based upon VDI 2736 [3] design scope in which assumptions in DIN 3990 [4] are enforced to calculate the bending strength. These assumptions imply that the teeth is rigid and therefore deformation of teeth under load is neglected When plastic teeth are subjected to cyclic loads, progressive fatigue damage, cyclic plasticity, creep, and viscoelastic responses decisively affect the load sharing, operational behavior and fatigue endurance. There are several research studies in the literature that show the deformation of teeth undermine the fatigue life of plastic gears [5,6].

For injection molded thermoplastic gears, process related considerations such as local orientation of molecular chains, crystallization, residual stress, shrinkage and short-time creep over solidification may profoundly affect the fatigue lifetime. For example, tensile residual stresses may lower the lifetime several orders of magnitude, while a compressive state of residual stress in critical locations may considerably increase the lifetime.

DuPont computational framework is capable of capturing progressive damage, plasticity, and creep cyclic deformation mechanisms, and will provide valuable insight into the design process. As an example, a simple plastic gear system is considered next. Only a portion of the gear is simulated to reduce the computational cost. The gear rotation is simulated via systematically applying contact pressure on each tooth at specific times. With this loading mechanism, the teeth interaction effects can be modeled. Figure 1(a) shows the state of damage at 3000 cycles. Depicted elements by red color illustrate the size and patterns of formed cracks at N=3000 cycles. Figure 1(b) shows the plastic strain at N=3000 cycles. The self-heating effect has also been captured, as depicted in Fig. 1(c). The temperature rise due to the self-heating effects, progressive damage and cyclic plasticity will alter the gear operational behavior through the cycles. The developed modeling technology in this work is able to capture the changes in gear operational behavior through its lifetime. One of the breakthrough of the proposed approach can be the prediction of load sharing ratio through the gear lifetime. It is well-understood now that the initial load sharing ratio can be affected by the teeth deformation and the current model can capture teeth deformations through the life of the gear system.

Due to higher energy absorption properties of polymers compared to metals, capturing the progressive fatigue damage is essential in design optimization tasks. While most of current fatigue analysis techniques for polymers are directly translated from metal fatigue theories, there is an urgent need to develop reliable fatigue prediction tools for polymers. Progressive fatigue damage in unfilled polymers is coupled with cyclic plasticity, creep, and self-heating effects. DuPont fatigue analysis tool for plastic gears provides full coupling between cyclic plasticity, creep, and fatigue damage. This tool provides a step change in predicting short and long-term performance of the plastic gears. DuPont goal is to help our customers to win by reducing their development cycle and optimize their design and material usage. We understand one of the challenges facing the gear manufacturing community is the proof of concept and prototyping cycles and we aim at reducing the cost and time associated with these tasks through reliable predictive engineering techniques. DuPont performance polymers offers DuPont™ Delrin® and DuPont™ Zytel® for light-weight mechanical gears that offer the strength and stiffness of metal gears. Another crucial aspect of an injection molded gear is its dimensional stability after injection molding. DuPont™ Delrin® provides excellent dimensional stability and it has been extensively utilized in high precision applications with zero backlash requirements. Please visit us at http://www.dupont.com/corporate-functions/our-company/businesses/performance-materials.html or contact your local DuPont representative for more information.

References

[1] Amir K. Shojaei, Alan R. Wedgewood, An anisotropic cyclic plasticity, creep and fatigue predictive tool for unfilled polymers, Mechanics of Materials, Volume 106, March 2017, Pages 20-34, ISSN 0167-6636, http://dx.doi.org/10.1016/j.mechmat.2017.01.003.
[2] Amir K. Shojaei, Pieter Volgers, Fatigue Life Assessment of Unfilled Polymers including Self-heating Effects. International Journal of Fatigue, International Journal of Fatigue, Volume 100, Part 1, July 2017, Pages 367-376.
[3] VDI 2736:2014-06, Blatt 2, Cylindrical gears - Calculation of the load-carrying capacity.
[4] DIN3990, Calculation of load capacity of cylindrical gears; introduction and general influence factors, 1987, DIN 3990:1987-12, Tragfähigkeitsberechnung von Stirnrädern.

Autoren des Artikels

Amir Kian Shojaei, Ph.D.

DuPont Performance Materials, Chestnut Run Plaza, Wilmington, DE, 19805, USA, email: Kian.A.ShojaeiDuPontcom

Pieter Volgers, Ph.D.

DuPont Performance Materials, European Technical Centre, CH-1217 Meyrin, Geneva, Switzerland, email: Pieter.VolgersDuPontcom