Home

Propeller vibration

  • Propeller vibration. the hub, the center, and the tip. Oct 8, 2012 · Can the 2010 Pilot with 4wd be driven with the propeller shaft between front and rear axles removed? I have a vibration that starts at 40 mph and slowly goes away about 60 mph. The ACES 2020 ProBalancer Kit includes all the vibration analyzing and balancing equipment required to improve the performance of your helicopter or plane. Have better strength and durability. Nov 9, 2016 · Category 8 of Method 514. Gives good low-speed handling and performance. A propeller Propeller. The good news is that my vibration problem seems to be going away or else I just don't notice it as much anymore. The best static balance is completed with the spacer attached, and using an end mount type balance stand. This reduces vibration where there is interference between the propeller tip vortex and the adjacent hull and unloads the forward low pressure face reducing any tendency for cavitation at the blade tip. The topics discussed in this document are unrelated to imbalance or dynamic balancing, which is the process for removing the Apr 7, 2024 · Purpose This paper presents a comprehensive investigation into ship propeller shaft vibration control, aiming to enhance the stability and efficiency of maritime propulsion systems for smoother operation and optimized engine performance. 5x the tach frequency; Prop-wash will be dominate at 2x the tach frequency for a two-bladed prop (proportional to the number of blades). Jan 29, 2024 · The model used was a three-bladed cast propeller, typical of industrial boat motors, with a 230 mm diameter made from an aluminum alloy. This sort of vibration sometimes happens with Carriden's Martec folding prop and the solution is to throttle down to idle Keywords: Marine propeller, Propeller-induced hull pressures, Ship vibration, Propeller phase angle, Super-yacht 1. marine. New low-cost, convenient experimental and analytical techniques are described for evaluating the excitations—propeller airborne pressures on the fuselage shells, slip-stream-induced forces on the wing and tail, and Jul 13, 2015 · Expert Opinion Article: Combat the Oft-ignored Dangers of Airframe and Engine Vibration with Cessna Propeller Dynamic Balancing. B. Jun 16, 2023 · Ship Propeller – The efficient operation of ship propellers is crucial for the maritime industry. The complexity of the problem makes the mechanism Propeller singing mainly occurs by the resonance between the natural frequency of propeller tip and vortex shedding frequency at trailing edge. For complex aircraft, constant-speed propellers are used, and are in fact their own system. Therefore, the minimization of vibration intensity of propeller shaft has received much research attention. Oct 18, 2023 · NOTE: If you experience prop vibration, oftentimes removing the prop, rotating it 180°, and re-installing the prop will lessen or eliminate the incidence of vibration as all props and shafts are not 100% symmetrical. You can feel it in the seat of your pants. The DynaVibe Classic displays the magnitude and phase of propeller vibration allowing precise weight adjustments for balanced and smooth engine operation. 7 simulates the vibration environment for cargo carried in propeller aircraft. Hydrodynamics of Ship Propellers, Cambridge University Press, 1994 Chertock, G. 1. Dryden and L. These high-frequency oscillations are the ones that hurt metal propellers the most. How to Replace the Propeller. As is proposed in [14], it is relatively straightforward to spot the vibration level of quadrotors in a preflight stage. The vibration of a propeller are strongly related to the variation in inflow velocity ( wake-field ), the clearance from propeller tip to hull surface and blade geometry. ”. Nov 1, 2023 · The coupling vibration and acoustic radiation of propeller-shaft-hull involve the global vibration and acoustic effects of propellers in complex flow fields, long shaft systems with multiple supports, and whole ship structures from pressure hull to light hull from bow to tail (Qi et al. Apr 27, 2021 · Bubbles stick to surfaces and essentially increase the thickness of propeller blades, with the result that more power is needed to increase or maintain speed. 1 An Open-Water Efficiency Based Speed Change Strategy With Propeller Lifespan Enhancement in All-Electric Ships Propeller excitation forces. Each propeller generates thrust by spinning and pushing air down, allowing the drone to ascend, descend, hover, and maneuver. Some vibration is unavoidable, but an unbalanced propeller can cause problems for both an aircraft and its pilot. 05 ips throughout the course of the Ship vibration resulting from the propeller excitation forces depend on the response of the vessel to the applied forces; henced, the magnitude of the excitation should always be evaluated with respect to the vibration level it causes. The propeller is a potential source of noise and vibrations in a ship. Feb 5, 2014 · Per USAF requirements, propellers must be balanced to 0. Aerodynamic Imbalance. Has a better holding power in rough seas. The faster the blades cut through the water, the lower the pressure on the suction side of the blades becomes. In vibration analyses, superstructure vibration is treated separately from hull girder vibration, and methods to carry out these calculations are recommended by classification societies. occur, are due to resonant vibrations of the propeller or the propeller-engine. Analyses were conducted to determine the correlation between vibration in the dynamic movement of a balanced and an imbalanced propeller using a laser vibrometer (portable digital vibrometer) PDV-100, to determine the corre (a) The applicant must determine the magnitude of the propeller vibration stresses or loads, including any stress peaks and resonant conditions, throughout the operational envelope of the airplane by either: Apr 25, 2021 · The main excitations of superstructure vibration are propeller induced forces and low speed diesel engine. Fig. According to the analysis results, propeller singing frequencies can be estimated from free vibration analysis and Feb 24, 2022 · Propeller vibration, in the engineering sense with respect to vibratory loads, is a very different topic than vibration due to balance; No level of static or dynamic balancing can mitigate or remove propeller operating restrictions; Sensenich Support Documentation. It mostly occurs when the rotation of the propeller is not installed in the most appropriate area by the technicians. Apr 3, 2014 · It's a function of Amplitude. First, the shaft might be bent, either as a result of impact to the propeller, or because of mishandling during shipment or installation. In conclusion, cavitation can have a range of negative effects on a ship’s propeller. Ventilation, on the other hand, is the propeller sucking in air. Nov 4, 2020 · A 4 blade propeller has the following characteristics: The manufacturing cost is higher than the 3 blade propellers. Oct 16, 2019 · However, a vibration meter is not exempted from monitoring vibrations brought about by weather and turbulence in the air. 40, No. A mechanical failure of the propeller could cause a forced landing or create vibrations sufficiently severe to damage the aircraft, possibly causing it to become uncontrollable. In this paper, vibration mode characteristics of propeller blade in a ship are investigated by the vibration analysis using MSC/NASTRAN. Jun 15, 2023 · In this paper, the unsteady exciting characteristics of a marine propeller influenced by the shafting whirling vibration effect are numerically studied by employing the dynamic sliding multi-region method and a Reynolds-averaged Navier–Stokes equation model. This article presents a methodology used for the forced vibrations analysis of Jun 10, 2023 · In this work, we conduct a numerical investigation of aerodynamics and aeroacoustics of propeller blades with vibrations, which could occur in practical unmanned aerial vehicles as the blades are often made of lightweight materials. Noise The collapsing cavities give rise to noise effects which, accompanied by high-frequency vibrations, can be extremely unpleasant to passengers and crew if they are A PROPELLER-VIBRATION INDICATOR. I checked the prop again and it is on there correct and tight. g. Below is our archive of product support documents. This is the only way I can rule out the drive shaft. The vibration response of the propeller has been analyzed at three points, respectively the hub, the center, and the tip of the blade, to determine the point having the largest value of the 2. Vibration can also cause pilot and passenger fatigue. COMPLETE isolation of the airplane propeller from the engine, except for a very flexible torque drive, appears to be the only satisfactory solution of the vibration problem in the future, Mr. The simulations resolve the sound generation from the unsteady turbulent flows using an acoustic-wave preserved artificial compressibility method. After decades of flying legacy systems on E-2 and C-130 variants, your crew will notice considerable reduction in vibration and interior noise, as well as a notable improvement in reliability and performance. These transducers are placed at locations of The propeller is the means by which an engine transmits horsepower to thrust. This advisory circular (AC) provides guidance and describes methods, but not the only methods, for demonstrating compliance with § 35. Engine accessory vibrations can be identified using the ratios listed in the type certificates Jan 28, 2016 · AC 20-37E is a great resource for field propeller maintenance, and it includes a very useful checklist for propeller annual inspection. To address these challenges, researchers and engineers have developed various methods and Mar 29, 1996 · Propeller Vibration Checklist. , 2010; Huang et al. Small corrections that balance a propeller can dramatically reduce vibration throughout an aircraft. It might be vibrating above 3200RPMs but if it is I cant feel it. To determine if the propeller is the culprit, observe if there are significant vibrations during higher RPMs. Kearns believes. Jan 22, 2018 · Engine mounts, magnetos, instruments, avionics, control systems, and just about every part of the aircraft can be affected by excessive vibration. If the direction of engine whirl is the. If you are finding loose rivets and cracking in the aircraft cowling or spinner, it pays to see what the vibration is at the propeller. Attention: DynaVibe Products may not be cancelled or returned. Propellers are subject to constant vibration stresses from the engine and airstream, which are added to high motor/propeller that is the source of the vibration is isolated, this may be used for maintenance; in the case of vehicles with actuator redundancy (e. Jan 6, 2022 · Driveline vibration starts at around 25 MPH and keeps going. 6: Steady vibration stress in the propeller shaft Fig. Collins NP2000 system features an Electronic Propeller Control System (EPCS), eight modular composite blades and other modernized components. The pulsatility of main engine, the non-uniformity of propeller working area and the unbalance of shaft misalignment, which cause the FIV more complex (Shi et al. Under such conditions, he explains, much lighter propeller blades May 1, 2021 · The vibration mathematical model of ship propeller-shaft longitudinal two-stage vibration isolation system is established. The design and material of the propellers greatly affect the drone’s performance, making The American Bureau of Shipping recognizes the study of overall ship vibration as an important measure in providing the habitability, safety and functionality of vessels. 390185. This supported under NASA Grants NSG-1308 and NSG-3304 421 Dec 6, 2021 · Propeller: Everything you need to know from the definition, how it works, types, construction, size, issues, and improvements. Vibration is entire vehicle and is like being in a helicopter. It is NOT RPM dependent - I even dropped it into neutral at around 35 MPH and the vibration is constant. If Aries is out of the water then check that both blades are moving freely. The damping performance depends on the type and location of the piezoelectric transducers with respect to the mode Mar 14, 2024 · These Varifold propellers also come with a 15% pitch relief on the tips. Reduce Vibration. Severe wake-structure interaction induces intense vibrations and noises. , 2019). Dec 9, 2015 · The propeller blades are one of the main sources of turboprop engine vibration. I recommend 3M double-side foam tape from Amazon . The non-uniform wake around the propeller generates fluctuating forces on the propulsion shaft. 3 Noise and Vibration Mitigation Techniques. The workaround in the Cessna was to adjust prop and throttle to get the desired power level with a different RPM. For basic aircraft, a fixed-pitch propeller is fixed to reciprocating engines to produce the desired thrust performance. Not to mention, dealing with vibration is physically and mentally stressful for Oct 10, 2019 · The vibration analysis was conducted on a carbon fiber 2-blade propeller by comparing the results of vibration tests with the propeller blade contour. Oct 11, 2019 · The effect of a propeller vibration is depicted in Figure 2, where z is the reference axis, and +Z and −Z is the propeller displacement, due to its vibration along the direction orthogonal to Vibration is created due to the unsteady nature of the cavitation and is termed as the periodic deflection of the structure in a vertical, horizontal or torsional manner. Then, the sound Aug 1, 2021 · Experimental investigation introduces an approach for the propeller vibration damping using piezoelectric transducers in conjunction with appropriate shunt circuit. Jun 25, 2023 · Triblade Propellers: Feature three blades for improved lift and control, reducing noise and vibration for smoother flight experiences. Factors influencing vibration generation and propagation include the propeller’s rotational speed, blade count, blade shape, material properties, and the nature of the engine-propeller coupling. e. This presentation will discuss briefly methods of calculating the dynamic behavior of a propeller and will present some results obtained to date on a NASA research grant to The Pennsylvania State University. 13-inch Stops noise and vibrations. This excessive vibration can lead to various issues, including cracks in the airframe, cowling, and spinner, damaged exhaust systems, and premature engine wear. Propeller Vibration Definitions Hartzell often receives comments about “propeller vibration”, which is generally discussed in the context of propeller imbalance. Introduction Over the last few decades, noise and vibration standards have been constantly evolving, along with the comfort environment which can be experienced on board luxury passenger ships. This paper describes an instrument to be mounted on the end of the. The vibration response of the propeller has been analyzed at three points, respectively the hub, the center, and the tip of the blade, to determine the point having the largest value of the Jul 1, 2016 · The simple way to increase the efficiency is reduction of blade area, increasing load near the tip and adopting a larger diameter with low RPM. assembly. 9: Transient vibration stress in the throw 6 Maximum torsional stress due to the ice impacts, in contradistinction to open water condition, arise within the speed interval 95-100 rpm. and Andersen, P. Mar 12, 2012 · With a folding prop, vibration often occurs when one of the blades is reluctant to unfold, assuming that the blades are not geared to each other. The same evaluation should also be made when addressing the propeller as a noise source. 4 blade propellers are normally made up of stainless steel alloys. It involves breaking an airfoil down into several small parts then determining the forces on them. They must be precisely machined to fit each shaft. An unbalanced propeller can affect a quadcopter’s performance due to vibration, also decreasing its thrust’s yield. The hull form should be optimised to make the wake-field as uniform The propeller is a vital component of the aircraft. Many positive detail changes will have a significant cumulative effect. 00 Inches Per Second (IPS) Peak Amplitude. “The gains are linear,” Platzer says. The methods of damping vary, ranging The propeller’s vibration behavior was compared on three areas of the blade, i. The design is optimized taking a ship propeller-shaft system as an example. Dec 2, 2014 · Analysis of quadcopter propeller vibration based on laser vibrometer 10 October 2019 | Journal of Low Frequency Noise, Vibration and Active Control, Vol. Includes an industry-unique 5-year warranty. Even worse, cavitation can cause vibration because of uneven propeller loads and damage or break equipment. We identified one of the most effective strategies for reducing noise from ship propellers [3–5] as damping the vibrations of the blades at their natural frequencies. However, propeller vibrations can lead to a range of issues, including reduced performance, increased fuel consumption, and structural damage to the vessel. In this study, the rudder is simplified into a plate fixed at two ends. octocopters) the damaged propeller may be disabled. Sep 2, 2023 · The correct propeller size and pitch can significantly improve your boat’s performance and reduce prop slip. [1] A ten-foot self-propelled model designed for the measurement of vibratory propeller forces has been constructed. A local garage said it was the propeller shaft / driveshaft, but said I should go to the Honda dealer. Two types of carbon fiber propeller were used in the analysis, i. Watch this video for a step-by-step on how to replace a prop on your Minn Kota Trolling Motor Feb 25, 2018 · A balanced propeller assembly is important not just for having a smooth flying experience, but also for the health and longevity of an airplane’s engine, instruments and airframe. The Apollo uses the interchangeable hub. It is believed that fatigue failures of aircraft propellers, which occasionally. The ABS Guidance Notes on Ship Vibration have been developed to provide users with specific guidance on the design, analysis, measurement procedures and criteria to achieve Mar 28, 2023 · The prop can also experience vibration due to entanglement with fishing line and seaweed. The calculated data are illustrated by practical examples. The aerodynamic imbalance is one of the leading causes of vibration in aircraft. But there are also harmonics that go well up the range, albeit at lower amplitudes than the 1P boomers we all generally tend to think of as “vibration. These effects can impact efficiency, power, erosion, thrust, noise, vibration, resistance, wear, implosion, scale effects, and more. A proposed design consists Apr 15, 2019 · During the test process, the acquisition of torsional vibration signals is achieved by utilizing a laser torsional vibration transducer (Torque sensor, type: BINSFELD-TT10K) located near the propeller. Various methods can be employed to mitigate noise and vibration in aviation propellers. Luckily, computerized dynamic propeller balancing is a cost-effective route to help dampen those pesky vibrations. and vibration generated by cavitating propellers, including examples of expe Nov 1, 2000 · Any quality propeller balance job will end with a vibration survey performed on the engine assembly. Aug 28, 2018 · Vibration is not only noisy, but it can also cause discomfort and potentially damage avionic systems. Vibration Limits At Propeller RPM DANGER —----- 1. Tuckerman. , 2019a). Three thin piezoelectric transducers macro fiber composite (MFC) type PZT-5A are surface-mounted on the propeller, one at each blade. Oct 24, 2022 · It could be that your airplane propeller is out of balance, causing the airplane to vibrate in its mount. Force measurements have been made with this for Series 60 0. With the IPBS, the propeller is continuously balanced to below 0. This is the first step in removing unwanted vibration. The propeller should be removed and a static balance performed. My previous plane, a Cessna 182 had a similar vibration at one particular RPM setting. Contact our sales team today for a quote on our high-performance ACES propeller balancer. Adding blades decreases ideal prop diameter, which increases distance between blade tips and the bottom of the boat. The data for transverse vibration is acquired with an acceleration sensor (Tri-axial accelerometer sensor, type: B&K 4535-B-001). Make sure to consult your boat’s manual or a professional to choose the right propeller. By addressing the propeller diameter, blade shape, blade size and blade pitch, it is possible to reduce the chances that a cavitation burn will start to Purpose. Statically balancing a propeller can help reduce vibrations, but to reduce prop imbalance-induced vibration to the minimum, dynamic balancing is recommended. 25 Inches Per Second (IPS) Peak Amplitude. However, vibration and noise will be the first issues when a designer tries to increase the efficiency of the propeller by these ways. Dynamic propeller balancing is easily accomplished using the DynaVibe Classic, for simple balancing, or the DynaVibe GX2 to balance and complete vibration surveys. “Doubling the tip clearance cuts noise and vibration in half. conversely, the propeller frequency for a reverse engine whirl will be one propeller speed greater than the engine frequency. At Hartzell, we have over 400 different propeller blade designs available, which can be configured in hubs with 2-blade through 6 Sep 19, 2010 · So I put the new Apollo prop on yesterday and today I went for a little ride and there is a vibration now from 1300-3200 RPM's. 8. Double M Aviation provides detailed, and dependable propeller balancing. Jan 18, 2017 · Increase to five blades and only one-fifth of the prop is subjected to that added cavitation. Lower level wide band random vibration is also present due to air flow vibration levels are also dependent to some degree on the propeller dynamics. There have been vibration studies done on the Cessna 188 when converting from a 2 Blade C98 McCauley propeller to a 3 blade propeller of any Flavor, the vibration would get worse I have been told that a certain type of lord mount, made from a different compound which was more rigged was the fix in that application. Propellers inherently cause vibration. Jan 29, 2016 · Abstract and Figures. The vibration environment generated from propeller aircraft are dominated by high amplitude approximately sinusoidal spikes at propeller passage frequency and harmonics. The structural deformation equation is solved via the finite volume method May 6, 2020 · Because a ship’s propeller rotates through the water at an angle of attack, a pressure side and a suction side are created on each of the propeller’s blades. Propeller assembly vibration will be at 1x the tach frequency. Detached eddy simulation is employed to simulate the turbulence in the flow field and propeller wake. Use pre-cut blocks, or cut the blocks to the right size and shape. Thereby the observed vibration phenomenon in the given examples is explained by a bending resonance, for which the bending frequency of the propeller is equal to twice the Oct 10, 2019 · The vibration analysis was conducted on a carbon fiber 2-blade propeller by comparing the results of vibration tests with the propeller blade contour. , "Forces on a Submarine Hull Induced 12 by the Propeller", Journal of Ship Research, Septem- ber 1965, pp 122-130. A method for reducing these vibrations is investigated in this paper. 8: Transient vibration stress in the propeller shaft Fig. SigmaDrive is a low maintenance, high torque, bearing free solution that stops noise and vibration. Aug 9, 2021 · To minimize the vibration of the drone frame, you can attach a piece of double-sided foam tape or velcro to adhere the inner level of the drone body to the frame. Jan 1, 2002 · A ship's main drive shaft axial vibration at propeller blade rate may be transmitted to the hull. These studies show that still feasible to detect fault of propeller imbalance of drone by vibration signals. Aircraft propellers are manufactured to be durable, strong and able to absorb the stresses of flight. A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon a working fluid such as water or air. In the present article, numerical simulations of fluid The blade element theory (BET) is a mathematical process originally designed by William Froude father of Robert Edmund Froude (1878), David W. Apr 18, 2023 · When the propeller runs in the wake field, it will produce pulsating thrust, which will cause the longitudinal vibration of the ship’s propulsion shafting, and it will be transmitted to the hull through the inference bearing and base, causing the structural vibration of the hull. Out of balance propellers. The vibrations of the plate operating in the propeller wake are analyzed. abstract. Quad-Blade Propellers : Come with four blades for even more lift and stability, often used in racing drones for their aggressive performance. You have minimized the one-per-revolution vibration induced by an out-of-balance propeller. Mar 4, 2023 · The vibration spectrums were obtained with the drone's accelerometer in different trajectories. I really believe it the drive shaft balance. Nov 10, 2023 · This can cause changes in the pressure field around the propeller, which can lead to cavitation issues. Methods The Nov 1, 2006 · The lower the frequency, the more this vibration will feel like a rumble. Breslin, J. VERY ROUGH —----- 1. Prop shaft couplings transfer all the engine’s thrust to the propeller shaft. The calculation results can identify approximately 2% of the propeller mass imbalance fault. When undesirable vibration is detected, some of the components of the propulsion system, notably the propeller and spinner assembly can be spin trim balanced to improve the running vibration levels of the entire system. Adding more propeller blades can help reduce vibration, improving overall cabin comfort for pilots and passengers. Depending on the model, propeller blades weigh anywhere from a few ounces Sep 6, 2013 · This method is justified by the very great difference in the two natural frequencies of aircraft propeller blades. 37, Propeller fatigue limits and evaluation, of Title 14 of the Code of Federal Regulations (14 CFR). The influence of mass ratio, stiffness ratio and damping ratio of two-stage vibration isolation system is studied. Nov 17, 2020 · This paper gives an overview of recent activities at MARIN related to the im proved prediction and mitigation of noise. Jun 30, 2021 · Propeller-induced vibration of a marine vessel is one of the most complex issues of fluid and structure and the interaction between them. Supports multiple sensor types. By Hugh L. The DynaVibe Classic is an economical, state-of-the-art dynamic propeller balancer designed specifically for the aircraft industry. SigmaDrives can cope with a 3 degree misalignment of the shaft in any direction; 6 degrees in total and, unlike most CV shafts, the DS intermediate shaft coupling can be fitted Dec 25, 2001 · Since around 25 hours, I sometimes notice a slight vibration at the detent (about 2500 RPM) in SR22 #121. Jun 30, 2022 · The diameter of the propeller, the engine rpm and the static pressure around the blades as they move through water can all add up to cause concerns with vibration, corrosion, and cavitation. mental developments in the prediction of pro- peller induced vibration forces on nearby bound- aries", Proceedings of Vibration Characteristics of Aircraft Engine-Propeller Systems. Vibration from weak cylinders gives a peak at 0. If you can’t find the information you are looking for, feel free to contact us at 813-752-3711 or send us an email at info@sensenich. 2 inches per second (ips) of vibration. Propeller can be dynamically balanced; however a large amount of weight will be required. Measurements can be made of total force or surface force with varying longitudinal propeller Oct 27, 2023 · Drone propellers are an essential component of any unmanned aerial vehicle (UAV), playing a crucial role in their ability to fly. 2. May 15, 2017 · In addition to vibration control techniques reducing the bearing and shaft misalignment, investigations have mainly focused on the theoretical and practical methods that guide and support the prediction of the shaft dynamics. He then tried a non SDS prop and said the boat didn't have any vibration but that it had the dreaded prop chatter. To confirm propeller damage, examine it for any broken blades, nicks, bends, pitting, and obstructions. Propeller Checks: (1) If the propeller has been recently repaired or repainted, it MUST be rebalanced statically for horizontal and vertical balance. com. . The effect of propeller rotation is to make the frequency of blade vibration differ from that of the engine whirl by the frequency of rotation. The potential sources and paths by which the propeller produces structural responses resulting in vibration and noise in the cabin of a transport aircraft are discussed. He basically said pick your poison, prop chatter, vibration, or an aluminum prop. P. 6CB parent and V-hull forms with a variety of 4, 5, and 6-bladed propellers. Taylor (1893) and Stefan Drzewiecki to determine the behaviour of propellers. Feb 11, 2021 · A shaft can cause vibration in one of two ways. The compact shaft coupling solution. Specifically, the study focuses on utilizing an H∞ Controller to mitigate vibrations and promote operational tranquility in maritime settings. At a certain speed, the pressure on the suction side is so low that the Apr 15, 2019 · The friction induced vibration (FIV) with discontinuous stick-slip behavior will be frequently excited in the shaft-bearing system (Han and Lee, 2019). dh tb mj bg bt wy he lv zt sm