Abstract
In order to analyze emergency stop vibration of the friction vertical lifting system under different loads, a loading experiment was carried out, and the longitudinal vibration characteristics of the carriage, frame, and steel rope were measured during the emergency braking process of an elevator. Accordingly, it is found that the load mass does not affect the peak deceleration value of the car frame and the wire rope during downwards emergency stop. Then, vertical vibration is explored using the time-varying vibration analysis theory. The obtained results show that when analyzing the vibration of objects on both sides of the traction wheel, the deceleration of the wire rope on both sides of the traction wheel are not equal, and the influence of the pressure change during the traction-wheel friction should be considered in calculations. This article may provide a reference to calculate the steel rope tension of the elevator and mine hoist.
1. Introduction
Elevators are the most widely used friction lifting systems in different industries [1–3]. Accordingly, the smooth and safe operation of elevators has a direct impact on people's safe movement. One of the most important concerns in elevator safety is the dynamic characteristics of elevators in the emergency braking process [4–7]. However, current industrial test methods and analyses of the performance of the elevator emergency braking can hardly meet the strict requirements of elevators. It is obvious that the emergency braking requirements of elevators are much higher than that of brakes in a normal operation [8]. Studies reveal that vibration during the emergency braking process directly affects the performance of the elevator traction system, thereby affecting the safety and reliability of elevators.
The emergency braking process of elevators can be mainly divided into three phases, including the idling, braking, and free vibration phases [9]. It should be indicated that the imposed force on the braking system in each phase is different so that each phase should be analyzed separately. Hoist rope stores/releases large amounts of energy during the deceleration/acceleration and emergency braking processes of the elevator. In particular, considering the sudden increase of braking force during the emergency braking process, the elevator carriage and the counterweight stop urgently. Consequently, the braking load on the steel rope increases drastically under the effect of inertial force, and stronger vibrations are imposed on the elevator carriage and the counterweight.
Further investigations show that under the effect of strong impact forces, the friction loss between hoist rope and traction sheave increases [10, 11]. Moreover, strong vibrations affect the contact force between the hoist rope and the traction sheave. As a result, relative slippage or even slip may occur between the hoist rope and the traction sheave. The foregoing discussions indicate the importance of investigating the emergency stop vibration of the traction system and analyze its vibration responses under different loads.
Watanabe and Okawa [12] investigated vertical vibrations of the elevator traction system and found that these vibrations are maximized during the braking operation. Moreover, they analyzed the effect of braking torque on the vertical displacement of the compensation wheel, but the vibration of the car and the counterweight were not analyzed. Lonkwic and Różyło [13] applied the free-fall method to conduct a braking test and analyzed the impact of different loads on the effective braking distance and descent speed during emergency braking. Then, they performed simulations in this regard. However, considering the limitations of the model, the actual engineering problems cannot be completely restored. Barkand [14] studied the emergency braking characteristics of mine hoists and designed electric, pneumatic, and traction sheave braking, respectively, but did not consider the impact of the load on the car. Liang [15] focused on elevator brakes and analyzed the failures of brake-related components. Ungureanu et al. [16] studied the characteristics of the elevator position during the emergency braking and analyzed the variations of elevator position under no-load and full-load conditions. But the sliding characteristics of the wire rope are not considered. Khazanovich et al. [17] established the dynamic equations for starting, steady-state motion, and braking phases of a system composed of traction machine, steel rope, carriage, and counterweights and calculated the equivalent load of the elevator power unit. Accordingly, a basis was provided to analyze the elevator electrical response, but no comparative analysis has yet been performed in this regard. Zhu and Chen [18] studied the dynamic characteristics of elevator rope and free and forced vibration characteristics of the elevator carriage but did not consider the impact of these parameters on the weight.
Performed investigations reveal that considering testing limitations, experiments cannot fully fit the actual working conditions of elevators. In order to resolve this shortcoming, the present study is mainly focused on the vibration analysis of elevators. In this regard and to truly reflect the vibration characteristics of different components of elevators during emergency braking, a conventional elevator with a traction ratio of 1 : 1 is taken as the experimental object. Then, the elevator is loaded with 10%, 20%, 40%, 60%, and 80% of maximum allowable load, respectively. Longitudinal vibrations of the carriage, frame, and steel rope of the elevator are tested in the emergency braking process. Results of the present study are expected to provide a design guide for vertical lifting mechanisms, such as elevators, cranes, and mine hoists, and provide a technical support for the safe operation of the friction vertical lifting system.
2. Theoretical Analysis of Time-Varying Vibration of Friction Vertical Lifting System
Figure 1 shows that the lifting traction system of an elevator is mainly composed of a carriage, frame, traction sheave, and traction steel rope. The steel rope is connected to the elevator carriage at one end and the counterweight at the other end and is suspended on the traction sheave. Accordingly, upward and downward movements of the elevator carriage and counterweight are realized by the friction between the steel rope and the traction sheave groove. It should be indicated that the elevator traction steel rope directly lifts the elevator carriage or counterweight. Generally, each elevator has 5–10 steel ropes. Depending on the height of the building, the length of the wire rope may vary from a few meters to hundreds of meters. Accordingly, the elevator traction system can be considered a slender flexible friction system with vertical lifting.
The applied load on the elevator originating from passengers or cargo affects the static tension of the steel rope at the carriage side. Moreover, the elevator has reciprocating up and down movements in the hoistway during the operation [3, 19–22]. The steel wire rope is a continuous elastomer. When the elevator operates, the length of the steel wire rope at the side of the car and at the opposite weight changes constantly. Therefore, it is of significant importance to analyze the emergency braking of elevators during the upward and downward movements to calculate the tension characteristics of the hoist rope.
In order to study the vibration characteristics of the carriage and the frame, the elasticity between them should be considered. Accordingly, it is of significant importance to accurately describe the elastic characteristics of the wire rope when the friction vertical lifting system is established. Meanwhile, because the elevator car and guide rail are in contact with the pulley, the transverse vibration can be ignored. Consequently, only the longitudinal vibration characteristics of the elevator should be analyzed.
The lifting system can be simplified to a system consisting of carriage, frame, wire rope, traction wheel, and a counterweight. The carriage and frame are connected by a steel rope, and the frame is connected to the counterweight by a wire rope. Because the main objective of the present study is to investigate the emergency stop vibration in the vertical direction of the system, and considering the restraint of the car and the heavy guide rail, lateral vibration of the system is small. Therefore, transverse vibration can be ignored, and the longitudinal vibration model is used in the analysis, considering the time-varying characteristics of the wire rope.
In all calculations, masses of the frame and carriage are assumed to be and , respectively. The carriage and the frame are connected by a spring with a length and stiffness . The frame and the traction wheel are connected by a steel wire rope of length L. To simplify the calculations, the rope group composed of multiple wire ropes is considered as a string with the equivalent modulus of elasticity E, equivalent cross-sectional area S, and equivalent linear density ρ.
Applying the Hamilton principle, vertical vibration differential equation of the system in the absence of external interference can be established. In this regard, the kinetic energy of the system can be expressed as follows:where the differential operator is defined in the form below.
Moreover, potential energy of the system can be expressed aswhere represents the equivalent tension at point of the string at time t and
Because the wire rope only moves along the vertical direction, the contact between the wire rope and the traction wheel can be simplified as a supported constraint. Therefore, the boundary condition at is given as follows:
Substituting (1) and (3) into the Hamilton principle yields the following expression:
3. Experiment Object and Method of Variable Load Emergency Stop
In order to analyze the vibration characteristics of the steel rope, frame, and carriage, the test elevator with a traction ratio of 1 : 1 was considered in the analysis. Figure 2 indicates that upward and downward emergency stop experiments were performed for each load.
A maintenance expert performs the following operations in the elevator room: loading different masses (i.e., , , , , and ) in the elevator carriage. After loading, the elevator performs upward and downward emergency stops. In the present study, five masses of 100, 200, 400, 600, and 800 kg are utilized in the experiment.
Figure 3 illustrates the vibration distribution of the steel rope and the frame during the emergency braking experiment. It should be indicated that the acceleration, speed, and displacement changes in the acceleration, uniform speed, and braking stages during the no-load emergency stop test were previously analyzed [23]. Consequently, only vibration distributions of the same direction under different load conditions are considered during the emergency stop experiment of the present study.
Because the emergency stop action is realized by manually disconnecting the power supply of the driving host, different braking positions may be obtained each time. After each braking stop, the distance between the top steel plate of the cab and the top floor slab is measured by a laser rangefinder. Then the distance between the top steel plate and the top floor slab is measured when the elevator is stopped on the top floor. Afterward, is calculated as the distance between the elevator stop position and the top floor. The measured upward and downward stop points are listed in Table 1.
Table 1 indicates that the experimental emergency stop points are located at the lower part of the elevator's stroke. Due to the small lifting height of the tested elevators, the steel rope mass is smaller than the masses of the carriage and the counterweight. It is inferred that small deviations of each stop position have little effect on the vibration test results.
4. Vibrations during the Upward Emergency Stop Test
Under upward emergency braking of the elevator, the steel ropes on both sides of the traction sheave are affected by both the gravitational and the inertial forces. Ignoring the mass of the steel rope and accessories, the applied force originating from the elevator carriage was analyzed during upward the emergency braking. The lifting force of the hoist rope at the emergency stop car side can be expressed in the form below:where is the mass of the empty carriage and its ancillary facilities, Q is the rated load mass, and is the gravitational acceleration.
Moreover, the pulling force of hoist rope at the counterweight side during upward emergency stop condition can be expressed aswhere is the counterweight mass.
4.1. Elevator Carriage
The vibration characteristics of the carriage directly affect the comfort of the elevator. Figure 4 shows the arrangement of sensors in the carriage.
Figure 5 shows the longitudinal vibration curve of the elevator carriage under different loads during the upward emergency stop condition. It is observed that when the load increases from 100 kg to 800 kg, the corresponding deceleration peak increases from 4.33 to 5.50 . The peak change of the deceleration shows that as the load increases, the peak longitudinal deceleration also increases. Because the cushion between the elevator carriage and the frame has a good buffer effect, the carriage vibration distribution under different loads is relatively smooth. It should be indicated that two peaks appear in the braking curve, and there is a more obvious peak drop point in the middle of the braking phase. Moreover, it is found that as the load in the car increases, the peak difference between the second peak and the first peak increases.
4.2. Frame
The car frame is the bearing component of the car, the weight of the car body, and the load in the car are directly transferred from the car frame to the wire rope. Therefore, the car frame needs to have enough strength and stiffness to meet the normal operation of the elevator. The arrangement of sensors on the frame is shown in Figure 6.
Figure 7 presents the longitudinal vibration distribution of the frame under different loads during the upward emergency stop condition. It is observed that when the applied load increases from 100 to 800 kg, the corresponding deceleration peak increases from 4.32 to 6.48 . The peak change of the deceleration shows that as the load increases, the peak of the frame longitudinal deceleration increases too. Moreover, the distribution of the braking deceleration shows that as the load increases, the vibration frequency of the frame increases too. When the load is 100 and 200 kg (light load), the emergency braking curve is smooth, and there is a more obvious peak drop point in the middle of the braking stage. However, when the applied load exceeds 400 kg, the braking curve disturbs and obvious small fluctuations appear throughout the braking process. Moreover, there is still a clear peak drop in the middle of the braking curve, although the degree of the drop is smaller than that of the light load.
The deceleration peaks corresponding to the five loads from small to large are 4.32, 4.4, 6.06, 6.26, and 6.48 . It is observed that as the applied load increase, the corresponding longitudinal deceleration peak of the frame during the upward emergency stop process also increases.
4.3. Hoist Rope
In order to ensure the safety of elevator and passengers, the strength and quantity of wire rope must have a high enough safety factor. Figure 8 is the arrangement of sensors and equipment on the hoist rope. Because the vibration of five hoist ropes is basically similar, only the test results of one hoist rope are selected for analysis.
Figure 9 illustrates the longitudinal vibration curve of the hoist rope under different loads during the upward emergency stop. It is observed that when 100 and 200 kg (light load) are loaded, the vibration is stable. Moreover, the deceleration increases suddenly in the initial stage of braking, and obvious fluctuations appear in the later stage of the braking process. In general, the emergency braking distribution in the entire braking process is smoother at light loads. When the load in the elevator carriage exceeds 400 kg, the corresponding braking distribution becomes rough, and obvious small fluctuations appear throughout the braking process. More specifically, in the free vibration stage of the late deceleration period, the vibration time is longer than the light load time, and the vibration amplitude is higher than that of the light load.
Figure 9 shows that when the elevator carriage is loaded with different loads, the braking curve has a stage where the deceleration amplitude is constant. The maximum value in this phase with small amplitude change is considered as the peak value of the stopping deceleration of the steel rope. The deceleration peaks corresponding to five loads in ascending order are 3.04, 3.25, 3.95, 4.98, and 6.15 . It is observed that as the load in the car increases, the peak value of the rope longitudinal deceleration increases during the upward emergency stop. However, the hoist rope tension decreases due to the braking friction, which slows down the carriage due to the difference between the gravity and the rope traction.
4.4. Upward Emergency Stop Vibration Comparison
Figure 10 indicates that during the emergency braking process of elevators, the longitudinal vibration peaks of the carriage, frame, and hoist rope increase as the applied load to the carriage increases. In general, the frame deceleration is the largest, followed by the carriage weight, whereas the deceleration of the steel rope is minimized. It is observed that the frame vibration curve fluctuates significantly when the load increases from 200 kg to 400 kg. Moreover, the overall change of the car is the smallest, and the change of the steel rope is the largest. From a local perspective, when the load is less than 600 kg, the vibration deceleration peak of the steel rope is minimized. Conversely, when the load exceeds 600 kg, the corresponding peak value of the steel rope exceeds that of the car deceleration.
5. Vibrations during the Downward Emergency Stop
In this section, it is intended to analyze the downward emergency stop and calculate the braking torque of the elevator car during the downward emergency braking operation. In this regard, the pulling force of the hoist rope at the car side during the downward emergency stop can be mathematically expressed as
Moreover, the pulling force of the hoist rope at the counterweight side during the downward emergency stop can be expressed as
5.1. Carriage
Figure 11 illustrates the longitudinal vibration distribution of the elevator carriage under different loads during the downward emergency stop process. It is observed that when the applied load to the carriage increases from 100 kg to 800 kg, the corresponding absolute peak value of the car deceleration decreases from 5.25 to 3.78 . The peak change of the deceleration shows that when the car is going down, as the load in the car increases, the peak value of the longitudinal deceleration of the car decreases. Similar to the upward situation, the vibration curve of the car is smoother under different loads due to the effect of the cushion.
5.2. Frame
Figure 12 shows the longitudinal vibration of the frame under different loads during the downward emergency stop condition. When the load in the car increases from 100 to 800 kg, the peak value of frame deceleration remains almost unchanged, at about . During the braking process, there is a clear peak drop in the middle of the braking deceleration curve, and the drop amplitude increases as the load increases. At 800 kg, there are two drop points with similar shapes. The absolute value of the downward deceleration decreases, indicating the decrease of the steel rope tension. However, due to the elastic effect of the steel rope itself, when the car is loaded less than 600 kg, the steel rope undergoes an elastic contraction at 0.5 s of the braking process. When the car is loaded with 800 kg, the internal tension of the steel rope increases. Therefore, the number of elastic contractions of the steel rope increases to 2, and the braking time is about 0.1 s longer than that of the lighter load.
5.3. Hoist Rope
Figure 13 shows the steel rope longitudinal vibration under different loads during the downward emergency stop condition. When the load in the car increases from 100 kg to 800 kg, the downward braking curve fluctuates significantly at the beginning and the end of deceleration. In the middle of the deceleration, the deceleration value remains unchanged. It should be indicated that the greater the load in the car, the longer the deceleration value. The curve fluctuation of the downward emergency stop is just the opposite of that of the upward emergency stop. The amplitude of the fluctuation is high when the load increases from 100 kg to 400 kg. Moreover, it is more stable when the load increases from 600 kg to 800 kg. Combining the results of the upward emergency stop test shows that the steel rope vibration directly correlated with the loading mass in the elevator's emergency braking process and has obvious directionality. Therefore, when studying the vibration of the elevator traction system, it is necessary to separate the upward and downward conditions for discussion.
5.4. Downward Emergency Stop Vibration Comparison
Figure 14 shows the vibration curves between the frame and hoist rope during the emergency braking. It is observed that the deceleration peaks of the longitudinal vibration of the steel rope and the frame remain unchanged under different loads. However, the deceleration peak value of the steel rope longitudinal vibration is smaller than that of the frame. This is correlated to several factors. One reason is that the elastic effect of the steel rope stretches the steel rope a little during emergency braking. The deceleration sensor used in the experiment is the sensor that collects the voltage signal, which cannot measure the deceleration caused by the elongation of the steel rope. The second factor is that the frame is raised by 5 steel ropes, and the tension of each steel rope is not the same, resulting in a certain difference in the deceleration of each steel rope. Unlike the vibrations of the frame and steel rope, the downward deceleration of the car decreases as the mass increases, showing a more obvious quality correlation, which is due to the cushion effect between the car and the frame.
6. Interpreting the Constant Downward Deceleration
As mentioned in Sections 4.3 and 5.4, the emergency stop tests of elevators A and B show that the absolute value of the deceleration peak during the upward emergency stop condition increases as the load increases. However, the absolute value of the deceleration peak during the downward emergency stop condition remains unchanged. The reasons that change the carriage load, while the deceleration during the downward emergency braking condition remains unchanged, include the influence of the star sealing function of the traction machine and the test experiment error or the steel rope slippage. The three reasons are analyzed as follows:
6.1. Star Sealing Function of the Traction Machine
The permanent magnet synchronous gearless traction machine connects the lead wires of the three-phase windings with wires or series resistors in a star shape, which is called “star sealing” in the industry. Meanwhile, the traction machine is used as a three-phase AC permanent magnet generator, and the unbalanced torque of the elevator's mechanical system drives the traction sheave. The generator absorbs the mechanical energy and converts it into electrical energy. The electrical energy is consumed through the closed loop formed by the star-sealing wire or the resistor [24–26]. When the mechanical torque is balanced with the electromagnetic torque of the motor, the traction machine can run at a uniform speed.
However, because the electromagnetic torque generated by the star sealing function correlated with the rotation speed of the motor, the star sealing torque decreases as the elevator speed decreases. It should be indicated that in the process of the elevator braking, the elevator speed constantly decreases. Even if the star sealing function exists, the elevators cannot keep the deceleration unchanged for a long period during braking, and it is more difficult to keep the deceleration unchanged under different loads in the elevator car. Moreover, because the total stop time is only about 0.6 s, the response speed of the star sealing function is not so fast. Therefore, the influence of the star sealing function is neglected.
6.2. Slip of the Steel Rope
During the downward emergency braking process of the elevator, the tension of the elevator and steel rope at the counterweight side changes significantly due to the sudden braking torque. Moreover, due to the inertial force, the tension of the steel rope at the elevator cabinet side increases, and the tension of the steel rope at the counterweight side decreases. Therefore, the tension difference of the steel rope on both sides of the traction sheave exceeds the critical value. It should be indicated that the friction between the steel rope and the traction sheave is not enough to make the steel rope and the traction sheave static. Meanwhile, the steel rope and the traction sheave slide relatively [27–30].
It is worth noting that the test results of elevator A are used for analysis. The tension changes of the steel rope on both sides of the traction sheave in the emergency braking process are analyzed. It is found that during the emergency braking, due to gravity and inertial forces, the tension of steel rope on the downward side increases, thereby increasing the pressure of the steel rope on the traction sheave. However, the tension of the wire on the upward side decreases under the effect of the gravity and inertial force. The specific analysis and calculation are as follows:
The force balance is performed on the traction sheave in the Z direction, and .
Considering the torque of the traction sheave center, the following equation is obtained: .
Due to the limitation of experimental conditions, the acceleration of the counterweight cannot be measured. The elevator running state when the mass at the elevator cabinet side is equal to the mass at the counterweight side can be equivalent to the counterweight running state. For elevator A, the balance coefficient is 0.42, and the rated load is 1000 kg. Therefore, when the car is exposed to a load of 400 kg, the car and the counterweight are equal in weight.
According to the experimental results of 6.1 and 2.1, when the car is loaded with a load of 400 kg, the upward deceleration of the frame is , and the downward deceleration of the car is . Therefore, when the car is loaded with 400 kg, the counterweight is in the upward state. When the car is loaded with 400 kg, the upward deceleration is equivalent to the counterweight deceleration of this working condition. In other words, and the deceleration on the car side is the actual measured value .
Substituting the values of and into (12) and (13), respectively, it is found that . Because the steel rope slips, it is considered that the friction coefficient remains unchanged during the emergency stop of the car.
Figure 15 shows that substituting the calculated f and the measured downward deceleration of the car into (12) and (13), the curve change of and with the mass in the car is obtained.
Figure 15 shows that the tension of the steel rope at the counterweight side and the support force of the traction sheave to the steel rope linearly correlated with the mass in the car. This is because the change of the traction sheave friction directly correlated with the mass at the downside. Therefore, the deceleration of the elevator car during the upward emergency braking increases as the load in the car increases. However, the deceleration during the downward emergency braking remains unchanged. This indicates that in the standard design of elevators, the method of determining the emergency stop deceleration of the heavy objects on both sides of the elevator traction sheave as a fixed value does not conform to the actual project. Moreover, it should be analyzed in detail according to the operating direction of elevators.
In summary, at the braking stage, due to the effect of the braking force, the rapid change in the tension difference between the two sides of the traction sheave causes the steel rope to slip, and the slip will aggravate the wear of the steel rope and the traction sheave. Therefore, the friction provided by the traction sheave is reduced. Meanwhile, the dynamic friction between the steel rope and the traction sheave will aggravate the vibration of the steel rope, thereby putting the operation of the entire traction system in an unbalanced state.
7. Conclusions
An emergency braking test is performed on elevators that are in use. Moreover, the downward and upward emergency braking and friction transmission characteristics of car, frame, and hoist rope under different loads are investigated. It is found that they exhibit different vibration characteristics. The change of the load has little effect on the change of the braking curve shape, whereas it has significant effects on the peak value of the braking deceleration. When the load in the car increases from 100 to 800 kg, the absolute values of the deceleration peaks of the car, frame, and hoist rope increase as the load in the car increases when rising.
It is found that as the load increases, the peak value of the upward emergency stop deceleration gradually increases. Different from the conventional theoretical expectations, the peak value of the downward emergency stop deceleration is independent of the load mass. It is concluded that the vibration characteristics of different parts of the friction vertical hoisting system are different during the emergency brake condition. It shows that the assumption that the deceleration of emergency stop on both sides of traction wheel is equal in current standards is wrong. The present article may provide a reference to calculate the traction rope tension of the elevator and mine hoist.
In the future, new testing equipment needs to be developed to obtain the elevator emergency stop slip from the elevator traction wheel and wire rope running speed test, so as to obtain the influence of the slip on the elevator emergency stop vibration more comprehensively.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare no conflicts of interest.
Acknowledgments
This research was funded by the National Natural Science Foundation of China (12002391).