## 1 Introduction  
State-of-the-art high-speed flywheel energy storage systems (FESS) are recognized for several advantageous characteristics including a high charge and discharge rate, lifetimes ranging from 10 to 20 years and high specific energy up to 100 Wh\(\cdot\)kg\({}^{-1}\)[1]. Further, they are unaffected by depth of discharge or cycling effects common to electrochemical batteries and have a relatively high cycle efficiency--up to 95% depending on the electrical components [2]. While the high efficiency and long expected lifetime make FESS an attractive alternative over other short- and medium-term energy storage options, these same attributes pose design and operational challenges. The majority of studies on fiber reinforced polymer (FRP) composite flywheel rotors have focused on instantaneous, or time-independent, behavior of composite rotors and hubs to optimize performance or minimize cost [3; 4; 5]. If rotor failure is considered, it is typically seen as a quasi-static process caused by excessive centrifugal loading exceeding material ultimate strengths [6]. While attempts have been made to predict rotor failure with progressive damage models [7], they largely neglect to incorporate viscoelasticity into the stress and failure analyses. It has been theorized that changes in the interfacial compressive forces could lead to rim separation or creep rupture [8], yet the number of studies on viscoelastic behavior in composite rotors supporting this notion are limited. Some works presented solutions for the boundary-value problem presented by flywheel rotors constructed of viscoelastic materials and discussed creep effects [9; 10]. [PERSON] and [PERSON] [9] focused on flywheel rotors with an outer shell supporting an inner composite rim. Additionally, the rim is of non-uniform cross sections and features a variable winding angle, neither of which are commonly used in modern FESS [11; 12]. [PERSON] [10] discussed a solution to the equilibrium equations to determine creep strain in rotating disks. [PERSON] [13] expanded on previous works by simulating filament-wound composite flywheel rotors with uniform rotor cross section and discussing viscoelastic behavior at 10 years and infinite time (\(10^{10}\) h). [PERSON] showed that viscoelastic stress relaxation of approximately 35% in the radial direction and a corresponding increase of approximately 9% in the circumferential direction can occur over the lifetime of the rotor. [PERSON] [14] conducted experimental investigations on flywheel rotors subjected to three temperatures and speed profiles over the course of 2 months using optoelectronic strain measurements. While rotor creep tests were inconclusive due to a mechanical failure, this work did not rule out any significant impact of creep on strains imposed for the press-fit assembly of the rotor. A similar conclusion was found elsewhere [15]. While there have been developments in the understanding of viscoelastic behavior of flywheel rotors, related insights do not necessarily translate well to typical use cases. For example, FESS in public transit [16] are installed with a vacuum enclosure that minimizes temperature fluctuations. Expected lifetimes are 10 to 20 years. In addition, load cycling occurs every few minutes, with viscoelastic effects effectively being negligible in between cycles. For other promising FESS applications, such as electric vehicle (EV) charging and renewable energy grid support, cycle times are likely much longer than for FESS in public transit, yet temperature conditions and timeframes would be similar. The present study seeks to describe the viscoelastic behavior of composite flywheel rotors during their expected lifetimes using a computational algorithm to predict the stress evolution in the rotor. Additionally, the Tsai-Wu criterion is used to describe the total stress state, combining radial, circumferential, and axial stress to predict rotor failure.