Design methodology of a reduced-scale test bench for fault detection and diagnosis

Mechatronics 47 (2017) 14–23

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Design methodology of a reduced-scale test bench for fault detection and diagnosisR E. Esteban a, O. Salgado b,∗, A. Iturrospe c, I. Isasa d a

Mechanical and Manufacturing Department, Mondragon Unibertsitatea, Loramendi 4, 20500 Mondragon, Spain Mechanical Engineering, IK4-Ikerlan, J. M. Arizmendiarrieta 2, 20500 Mondragon, Spain c Department of Electronics and Computer Sciences, Mondragon Unibertsitatea, Loramendi 4, 20500 Mondragon, Spain d Mechanical Engineering, Orona EIC S. Coop., Orona Ideo, Jauregi bidea s/n, 20120 Hernani, Spain b

a r t i c l e

i n f o

Article history: Received 30 July 2015 Revised 27 June 2017 Accepted 4 August 2017

Keywords: Test bench Dimensional analysis Scaling law Similarity Diagnosis

a b s t r a c t Condition monitoring is a crucial task for electromechanical system reliability and quality enhancement, which leads to early electrical and mechanical faults detection. In this paper, the design of a scaled test bench including its main subsystem components at initial stage is presented for the assessment of new methods dedicated to electrical and mechanical faults detection and diagnosis in electromechanical systems. In this paper a design methodology is proposed for developing a reduced-scale test bench dedicated to condition monitoring. Dimensional analysis is applied for ensuring the similarity between the scaled test bench and the full-size systems to be emulated. In addition, the scaled test bench includes the required instrumentation as well as an acquisition platform for development of condition monitoring strategy to batch condition monitoring of full-size systems. Finally, the similarity is evaluated by comparing both the simulation and the experimental results. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Condition monitoring for electromechanical systems has received increasing attention both from academia and industry during the last decade [1]. This development is motivated by the growing demands on cost efficiency, reliability and product quality of industrial electromechanical systems [2], being essential to reduce unscheduled downtimes and minimize operation and maintenance costs. In general, implementing condition monitoring in electromechanical systems requires to understand the dynamic behavior of the global system and its faults [3,4]. For this purpose, system identification techniques combined with experimental testing is usually required [5]. These techniques can be classified according to model-based or data-driven approaches [6,7]. Datadriven approaches [8] are suitable for applications where a limited a priori knowledge of the monitored system is available [9,10]. The performance of data-driven approaches is also highly dependent on the quality and the quantity of the available data [11,12]. Regarding model-based approaches, they rely on the availability of a mathematical model for the monitored system, which can be derived from physical modeling principles [13]. The performance of model-

R ∗

This paper was recommended for publication by Associate Editor T. H. Lee. Corresponding author. E-mail address: [email protected] (O. Salgado).

http://dx.doi.org/10.1016/j.mechatronics.2017.08.005 0957-4158/© 2017 Elsevier Ltd. All rights reserved.

based techniques depends on a large extent on the accuracy of the model when describing the dynamics of interest [14]. Model-based approaches have been successfully employed for electromechanical systems monitoring and control applications [15–18]. Nevertheless, both model-based and data-driven approaches make use of data from available sensor measurements. In this paper the studied electromechanical system is a roped 1:1 elevator [19]. An elevator installation comprises both a mechanical subsystem and an electrical subsystem, as it is shown in Fig. 1. The mass of the elevator car is balanced by a counterweight in order to reduce the torque demanded by the machine. An electrical machine drives the system through a pulley onto the suspension ropes which interconnect the elevator car and the counterweight. Both the car and the counterweight move vertically, constrained by a pair of rails each. The installation shown in Fig. 1 is driven by an electrical machine which is controlled using a field oriented control (FOC), where the velocity signature profile is generated for each ride, depending on the starting car position and its final destination. Despite of several attempts, the application of novel signal processing methods for condition monitoring of elevator installations are still an active field of research. The development of new methods dedicated for elevator condition monitoring needs a validation before its installation on a real elevator. Currently, there is a wide range of elevator dimensions and the validation of new methods

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15

Fig. 1. Simplified schematic description of an elevator installation.

Table 1 Value range of the elevator dimensions. Range

l [m]

ml [kg]

v [m/s]

a [m/s2 ]

j [m/s3 ]

t [s]

min max

3 45

0 630

1 1

0.7 0.7

1 1

5 35

The rest the paper is organized as follows. Section 2 describes the similarity conditions required to design a versatile elevator scaled test bench. In Section 3 the dimensional analysis are obtained and the scaling laws are derived. Section 4 addresses the design solution of the scaled test bench. Finally, in Section 5, fifteen real elevator are emulated in the scaled test bench and they are evaluated by equivalent elevator simulations. 2. Similarity

in them can be laborious or even time-consuming to perform [20]. The range of 1:1 elevator dimensions to be validated is summarized in the following Table 1. The dimensions of these elevator installations range from one floor building (3 [m]) up to fifteen floor buildings (45 [m]) whereas the range of the car load varies from 0 [kg] up to 630 [kg]. The rated speed, acceleration and jerk of the electrical machine are assumed to be equal for all 1:1 elevators. In order to reduce the effort of performing test and facilitating the validation of new methods, a test bench can be designed with the capacity of emulating all the elevator dimensions of Table 1. The specifications of this table involves that the test bench needs to be designed for emulating different mechanical subsystems dimensions while maintaining the electrical subsystem. Designing a test bench based on the aforementioned requirements cannot be done in an ad-hoc manner as demonstrated in other test bench designs with similar requirements in transportation systems [21–25]. In these test bench designs, the dimensional analysis [26] is proposed as a tool for designing scaled test benches which are equivalent to real systems. The reason to use dimensional analysis is that it is strongly based on concepts of similarity and that similitude has been proved to play a central role in designing equivalent systems [27–32]. This paper aims to design a scaled elevator test bench for performance assessment of condition monitoring techniques. With the application of dimensional analysis, could be possible to form dimensionless groups and formulate scaling laws in order to ensure the similarity between the test bench and the full-size elevator installation to be emulated [33]. In addition, the design of the scaled elevator test bench includes the design solution of both the mechanical and the electrical faults which are going to study using the developed condition monitoring techniques [34]. Regarding the faults, the electrical type of faults included in the design of scaled test bench are the torque ripple [35] and the encoder phase error, whereas the mechanical type of faults are the elevator car-rail and counterweight-rail misalignment [36], the sliding shoe friction conditions [37], rope prognosis [38], and the elastomeric mount characterization [39].

A scaled test bench is similar to a real application if both the scaled test bench and the real application share geometric, kinematic and dynamic similarity [40]. Similarity is achieved when testing conditions are created such that the test results are applicable to the real design. The following three criteria are required to achieve the similarity: • Dynamic similarity. Dynamics deals with forces. Two bodies are dynamically similar if their corresponding bodies experience the same forces in corresponding times. The force includes mainly concentrated force, distributed forces and torques. The physical modeling principles is usually employed to describe the system dynamic response [41]. In the use case selected, the dynamic similarity criteria can be obtained by modeling the dynamics of the elevator installations. A simple vertical dynamic model of an elevator [42], is shown in Fig. 2. This model comprises two lumped masses (the car and the counterweight), a mass-less driving pulley and two springs. The imbalance between the elevator car and the counterweight exerts a torque in the pulley that is actively balanced with the electromagnetic torque applied by the machine. The mechanical and electrical subsystems are coupled by the following torque balance equation,

τ = r ( fw − fc )

(1)

where τ is the torque exerted by the machine and the rope tensile force on the car side and counterweight side are denoted by fw and fc respectively. Based on the force balance in each inertial element, the equations that govern the system dynamics are expressed as,

fc = m(g + a ) + frc

(2)

fw = mw (g − a ) − frw

(3)

where the car-rail and counterweight-rail friction forces are denoted by frc and frw and the elevator car and counterweight

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E. Esteban et al. / Mechatronics 47 (2017) 14–23

acceleration a and jerk j as follows,

t =tv + 2 ta + 4 t j tv =

Vq = R iq + Lq i˙q + p θ˙ (Ld id + λ )

−

a ; j

ta =

v a

a ; j

−

iqre f =K ps (ωre f − θ˙ m ) + Kis Vq =K pq (iqre f − iq ) + Kiq

(4)

The torque exerted by the machine, τ is calculated using the electrical dynamics of a PMSM, described by the following equations [43]:

3 p[λ iq + (Ld − Lq )id iq ] 2

v a

tj =

a ; j

(7)

The FOC architecture can be modeled analogously to [46] as follows,

masses are m and mw respectively. Note that the loads of the car can vary from 0 [kg] to 630 [kg], thus, the car mass parameter groups not only the mass of the cabin, mc , but also the loads, ml , as follows,

τ=

−

where, tj , ta and tv denote respectively the time periods when the nominal jerk, j, the nominal acceleration, a, and the rated speed, v, remain constant in time [44]. This velocity profile model undergoes the time rates and motion required to move the elevator car up to different height of buildings. This velocity signature profile is also the input of the FOC as it is shown in Fig. 3. The FOC architecture has two separate control loops: a velocity loop and a current loop. The velocity loop has a PI controller for controlling the angular velocity of the rotor. The output of the velocity loop is the current signature reference iqre f for the current loop. The aim of the current loop is to maximize the active power for maximizing the exerted axial electromagnetic torque [45]. The direct current id is related to the reactive power and it is minimized by setting idre f to zero.

Fig. 2. Lumped parameter model of the mechanical subsystem.

m = ( mc + ml ).

l

v

(5) (6)

where, V, i and L denote the voltages, current and inductance, and the subscripts d and q denote the direct and quadrature axis respectively. The resistance of the stator is denoted by R, λ is the magnetic flux linkage and p is the number of machine pole pairs. • Kinematic similarity. Kinematics deals with motions. Kinematic of both the model and real application must undergo similar time rates and motions. Therefore, the involved variables are length and time. Two systems are kinematically similar if corresponding bodies experience the same motion in corresponding times. This criteria comprises both linear and angular displacements, velocities, and accelerations. In the use case selected, the time rates and motion of an elevator installation can be obtained by modeling the speed profile of the elevator based on the starting car position and its final destination. The time periods of the speed profile can be calculated for any value of the ride distance l, rated speed v,



t

0 t

 0

(ωre f − θ˙ m ) dt (8)

(iqre f − iq ) dt

where the proportional gain and the integral gain of the PI controls are denoted by Kpi and Kii respectively. • Geometric similarity. Two different-sized objects are geometrically similar if the scaled test bench can be brought to exact coincidence with the full-scale system. The scaled test bench is usually scaled to the application using the geometric proportionality. In the use case selected, the geometric similarity criteria is obtained principally by scaling the height of the hoistway. This is important in the design of a scaled test bench, where strict geometric similarity often cannot be obtain and distorted models have to be used [47]. In this application, the powertrain and the guiding system of the scaled test bench are distorted. The guiding system is distorted geometrically because the Tshape guides have to be slender and the powertrain is distorted geometrically because the radius of the driving pulley is small. Furthermore, the size of the pulley has to be different for each elevator configuration. Therefore, instead of using a strictly scaled driving pulley, a pulley radius equal to the real elevator is maintained and the powertrain is distorted geometrically. 3. Dimensional analysis and scaling laws In order to apply the dimensional analysis, let N be the number of system parameters, and let M be the number of basic di-

Fig. 3. Field oriented control architecture.

E. Esteban et al. / Mechatronics 47 (2017) 14–23

17

The π -groups are extracted from the dimensional set matrix as follows,

Table 2 Dimensional set matrix. System parameters Basic dimensions (M) π -groups (N − M )



Repeating parameters

B E

π1 = v

A C

τ  t τ

π5 = mensions required to describe all the N parameters in the governing equations Eqs. (1)–(7). The N dimensional parameters can be converted into (N − M ) dimensionless groups by means of a dimensional set matrix procedure [48]. The dimensional set matrix procedure is shown in Table 2. The repeating parameters, dimensions, and dimensionless π -groups are represented in a matrix form. Each column of the matrix represents the dimensional exponents of a given parameter. The matrices related with the system parameters, B, the matrix of the repeating variables A and the matrix E, which usually is the identity matrix, are known a-priori. The C matrix relates the dimensional exponents of the system parameter with the repeating parameters in order to define the dimensionless π -groups. This C matrix is calculated according to the following equation [33],

C = −(A−1 B ET )T

(9)

To apply dimensional analysis to designing an elevator scaled test bench, firstly the basic dimensions of the variables that describe their behavior must be determined. The dimensional expression for designing an equivalent elevator test bench based on the Eqs. (1)–(8) is,

z = f(τ , f, m, k, c, θ , l, v, a, j, t, K ps , Kis , K pq , Kiq , R, L, λ, i )

(10)

where this expression represent the dynamic response of the coupled electromechanical model of an elevator. This dimensional expression comprises N = 19 dimensional physical quantities. For the elevator test bench design, the repeating parameters selected to form the dimensionless groups are the ride distance l, the car mass m, the torque τ and the machine electrical current, i because they are easily measured and contain the four basic dimensions (M = 4 ) that need to be scaled: length [m], mass [kg], time [s] and current [A]. The dimensional set matrix of the coupled electromechanical elevator model is given in Table 3,

π6

m

l m k l2 = ; Kis L

λ

τ

π3 = j l 2

;

  m 3 τ

π4 =

;

f l

τ

;

;

τ

π11 =

π2 =

;

aml

;

cl ; τm Kiq L = 2 ; R

π7 = √

π8 = θ π 9 =

π12

π13 =

R i2 t

τ

;

K ps R

λ

π14 =

π10 =

;

L i2

τ

;

K pq ; R

π15 =

λi . τ

(11)

It can be observed that the four π -groups, (π 9 , π 10 , π 11 and π 12 ), solely relates the parameters of the field oriented control with the parameters of the electrical machine. These four π -groups are the dimensionless gains of the PI controllers for both the velocity loop and the current loop. As these dimensionless gains are solely related with the electrical parameters, the similarity conditions for mechanical subsystem is decoupled from the electrical subsystem. Therefore, it is possible to design a test bench which emulates different mechanical subsystem dimensions while maintaining the electrical subsystem and control. The last three π groups are the dimensionless expressions of the electrical machine and the rest of the π -groups are the dimensionless expressions of the mechanical subsystem. Both electrical and mechanical subsystem dimensionless groups can be interpreted as work-energy principle [49], which are calculated after performing some mathematical operations as detailed in Appendix A. The π -groups describes the relationship between the scaled test bench and the application. The values of the dimensionless parameters are held to be the same for both the scaled test bench and the application (e.g. π1e = π1b ) in order to derive scaling laws which prescribe scaled test bench testing conditions. Three main scaling laws are obtained for emulating different elevator dimensions: the car mass, the torque and the ride distance as follows,

sl =

le ; lb

sτ =

τe me ; sm = ; τb mb

(12)

where the scaling law sl is the ride distance ratio between the real elevator and the test bench. In the same manner, the sτ and sm are the machine torque and the car mass ratio respectively. These

Table 3 Dimensional set matrix of the elevator system. v

a

j

f

t

k

c

θ

Kps

Kpq

Kis

Kiq

R

L

λ

l

τ

m

i

Length [m] Time [s] Mass [kg] Current [A]

1 −1 0 0

1 −2 0 0

1 −3 0 0

1 −2 1 0

0 1 0 0

0 −2 1 0

0 −1 1 0

0 0 0 0

0 1 0 1

2 −3 1 −2

0 0 0 1

2 −4 1 −2

2 −3 1 −2

2 −2 1 −2

2 −2 1 −1

1 0 0 0

2 −2 1 0

0 0 1 0

0 0 0 1

π1 π2 π3 π4 π5 π6 π7 π8 π9 π 10 π 11 π 12 π 13 π 14 π 15

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 1 −1 0 −2 1 0 0

0 0 0 0 0 0 0 0 0 0 1 1 0 1 0

0 0 0 0 0 0 0 0 −1 0 −1 0 0 0 1

0 1 2 1 −1 2 1 0 0 0 0 0 0 0 0

−1/2 −1 −3/2 −1 1/2 −1 −1/2 0 0 0 0 0 −1 −1 −1

1/2 1 3/2 0 −1/2 0 −1/2 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 2 2 1

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E. Esteban et al. / Mechatronics 47 (2017) 14–23

Table 4 Value range of the scaled test bench parameters.

min max

4. Design solution of the scaled test bench

vb [m/s]

ab [m/s2 ]

jb [m/s3 ]

tb [s]

mwb [kg]

τ b [Nm]

0.11 0.71

0.22 0.60

0.22 3.98

4.27 26.72

10 22

0.05 5.43

three scaling laws from Eq. (12) are then substituted in the dimensionless π -groups in order to get scaling of the rest of parameters related with the elevator mechanical subsystem kinematics and dynamics as follows,

 π1 b = π1 e → v b = v e

sm = ve sv sτ

(13)

π2 b = π2 e → a b = a e

sl sm = ae sa sτ

(14)

π3 b = π3 e → j b =

je s2l

π4 b = π4 e → f b = f e

π5 b = π5 e → t b = t e



sm sτ

3

= je s j

sl = fe s f sτ

1 sl



sτ = te st sm

(15)

(16)

(17)

where the scaling laws sv , sa , sj , sf and st represent the velocity, acceleration, jerk, force and time ratios respectively. These scaling laws are used for finding an optimal design solution, however, there are infinite possible solution due to all the scaling laws, si are a-priori unknown and they are unbounded. Therefore, a design specification sheet is defined in order to fix some values of the scaling laws. The technical data of wide range of real elevator installations (see Table 1) are used in order to bound the maximum and minimum values of le , τ e and me parameters, respectively. Then, the values of the ride distance and the car mass are defined taking into account that the scaled test bench must be handy. A reasonable height of the test bench in order to be accessible for the user is 2.5 [m], with a ride distance of lb ≈ 1.8 [m] and the car mass of m = 15 [kg] (divided in mc = 10 and ml = 5). Then, the kinematic parameters are fixed by defining the maximum and minimum values of the nominal jerk, nominal acceleration, nominal velocity and time. The following value ranges are selected: 0 ≤ jb ≤ 5 [m/s3 ], 0 ≤ ab ≤ 1 [m/s2 ], 0 ≤ vb ≤ 1 [m/s] and 0 ≤ tb ≤ 20 [s] due to the characteristics of the electrical machine and the regulator when generating the velocity profile. Finally, the rest of the test bench parameters are optimized in a least square sense [50]. The parameter value range for the test bench design is shown in Table 4. The maximum values of the table correspond to the most restrictive elevator configuration in terms of ride distance, mass and torque from above limits. Likewise, the minimum values of the table correspond to the less restrictive elevator configuration. The parameter values for the rest of the elevator dimensions are between these two limits. As an example, a real elevator with a ride distance of le = 3 [m], a lifting velocity of ve = 1 [m/s] and without loads (0 passengers) in the elevator car is emulated in the test bench by configuring, the reference signature with vb = 0.43 [m/s], ab = 0.22 [m/s2 ] and jb = 0.22 [m/s3 ] values and adding mwb = 22 [kg] in the counterweight. Note that, time and torque are the result of the combination of the rest of the parameters, tb = 7 [s] and τb = 0.3 [N · m], respectively.

4.1. Description of the test bench The designed scaled test bench is a simplified setup that enables extensive experiments to be performed while maintaining a similarity to a real elevator as shown in Fig. 4. Two main parts can be identified in the scaled test bench (see Fig. 4a): the aluminum truss structure itself, where the elevator car guides, the counterweight guides and the machine are connected, and the two moving parts. The first one corresponds to the counterweight, while the other corresponds to the elevator car. Both of these can move up and down, guided along the guides via sliding shoes. In addition, both are connected to the machine, located at the top of the test bench, by means of a rope. The scaled test bench enables us to change variables, such as car load, velocity, off-center loads and so on, which cannot be changed easily in a real elevator installation. In addition, the elevator car itself can adopt different configurations, simulating an off-center load in the X and Y direction or different loads, with the aim of emulating different elevator car configurations. The test bench used for experimentation was 2.5 [m] high and has lb = 1.8 [m] of usable ride distance. During operation, the following data can be acquired (see Fig. 4b): • Two load cell transducers placed where the wire rope connects to the elevator car and counterweight for measuring the tensile force of the suspension rope. These load cells capture the static and dynamic force by means of four strain gauges in a Wheatstone bridge configuration [51]. The measurements obtained by these two load cell transducers correspond to the fc and fw variables of the elevator model respectively. • Two uniaxial DC accelerometers placed on the elevator car and counterweight for measuring the vertical acceleration of both bodies. The selected accelerometers must be DC because the acceleration profile of the reference signature contains a 0 [Hz] frequency component that can only be directly measured with these sensors. The measurement obtained by these two accelerometers correspond to the ac and aw variables of the elevator model respectively. • a torquemeter placed between the machine and the pulley shaft. This torquemeter measures the static and dynamic torque of the shaft by means of strain gauges and it has a built-in electronics for direct acquisition of the data. The measurement of the torquemeter represent the mechanical force imbalance between elevator car and counterweight, τ . • A draw-wire encoder for measuring the vertical position of the elevator car as in real elevators. • The electrical and mechanical magnitudes from the regulator are also measured. This involves to measuring the angular rotation of the machine rotor shaft by means of an encoder and to measure the magnitude of the voltages and currents. These magnitudes are denoted in the elevator model as θ , Vq and iq . The principal aim of the research is the utilization of modelbased approaches instead of data driven approaches for condition monitoring of elevators. Nevertheless, these sensors deal with the performance comparison of model-based techniques with data driven methods. The latter was earlier carried out for the identification of the rope [52]. 4.2. Design solution of the faults for condition monitoring The scaled test bench design also include both mechanical and electrical type of faults that are commonly studied in elevators [53]. The design solution of these faults are described as follows:

E. Esteban et al. / Mechatronics 47 (2017) 14–23

19

Fig. 4. Description of the scaled test bench.

• The inclusion of the PMSM torque ripple fault is carried out by adding an amplitude and frequency modulated signal in the input signal of the scaled test bench. • Likewise, the PMSM encoder phase error is introduced as an external disturbance of the encoder phase value. • The inclusion of car-rail and counterweight-rail misalignment effect is carried out by changing the guide segments along the ride. • Likewise, friction conditions are obtained using different contact areas between the sliding shoes and the guides. • The rope prognosis is realized employing a multi-groove driving pulley where some grooves are mechanically undercut in order to create different rope slippage effects and eccentricities. • Different elastomeric mounts can be used for its characterization. 4.3. Design solution of the acquisition platform for condition monitoring The condition monitoring system is designed based on the following criteria: • Ability for the acquisition of different types of measurements (voltage, current, acceleration, angular position, torque, forces, etc.) • Ability of batch data processing • Data transmission through Ethernet or USB The design solution of the acquisition platform for recording the data of the aforementioned nine physical variables is shown in Fig. 5. The acquisition platform is composed of 24-bit, 2-input simultaneous sigma-delta analog to digital converter (ADC) modules, 50 kHz maximum sampling frequency with built-in signal conditioning filters for torque, angular position, angular velocity and DC acceleration signals acquisition. Within all analog input modules, three of them are able to directly acquire load cells, motor voltage and currents. An analog output module is implemented in the chassis for generating different scaled velocity profiles from LabVIEW environment. The transmission of data to the PC is performed through USB port system.

5. Experimental evaluation of scaled test bench The capabilities of the scaled elevator test bench for emulating different elevator installations were evaluated by fifteen rides, where each test ride emulates a different real elevator. This evaluation consist on a comparison between the simulation of the real elevator installation employing a numerical model and the experimental signals obtained from the test bench. During a test ride the car and counterweight acceleration, the car-side and the counterweight-side rope tensile forces and torquemeter signals are employed as actual measurements. These measurements are then inversely scaled by dividing the magnitude of the signals with their corresponding scaling laws (e.g. le = lb s−1 ). These inversely scaled l signals are then compared to those obtained by simulating the elevator model. The root mean square error (RMSE) has been employed for quantifying the magnitude of the error between the values predicted by the model, yˆ and the values measured experimentally, y, as follows,



RMSE = E (y − yˆ )2 .

(18)

Table 5 shows the characteristics of the fifteen test rides. These fifteen different elevators are emulated in the test bench by configuring, the reference signature with their corresponding values and adding mass in the counterweight, mwb , as detailed in Table 5. The RMSE of the deviation of the actual measurements and the simulations of the fifteen elevator rides are analyzed in a box-plot as it is shown in the Fig. 6. The median of the RMSE for the accelerations, tensile forces and torques are 0.06 [m/s2 ], 4.52 [N] and 0.11 [N · m] respectively. The 50% of the rides are between 0.015– 0.08 [m/s2 ], 3.75–4.55 [N] and 0.075–0.16 [N · m]. Upper and lower whiskers have different length, hence, the box-plot is not symmetric. Lower whisker shows the RMSE of those rides which have lowest imbalance, whereas the upper whisker shows the RMSE of those rides which have highest imbalance. Therefore, the emulated acceleration, forces and torques and their measurements differ mostly when the elevator car is loaded. The reason of this deviation can be attributed to the rail friction which increases as the mass of the elevator car increases. Despite of this deviation, the standard deviation for the accelerations, forces and torques of

20

E. Esteban et al. / Mechatronics 47 (2017) 14–23

Fig. 5. Scheme of the acquisition platform for condition monitoring of elevators. Table 5 Characteristics of elevators to be emulated by the scaled test bench and their corresponding scaled magnitudes. Test name

le

ve

ae

je

mle

lb

mwb

vb

ab

jb

Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev. Elev.

6 6 6 6 12 12 12 12 24 24 24 24 30 30 30

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 630 450 320 0 630 450 320 0 630 450 320 0 630 450

1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8

22 10 10.79 19.43 22 10 10.79 19.43 22 10 10.79 19.43 22 10 10.79

0.305 0.453 0.423 0.315 0.216 0.320 0.299 0.223 0.193 0.286 0.268 0.199 0.176 0.261 0.244

0.22 0.484 0.422 0.23 0.22 0.484 0.422 0.235 0.22 0.484 0.422 0.235 0.422 0.22 0.422

0.323 1.055 0.860 0.356 0.457 1.492 1.216 0.504 0.511 1.668 1.360 0.563 0.56 1.827 1.490

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

of the elevator car are shown. The solid lines are obtained by the measurement of the draw-wire encoder and the DC accelerometer placed on the floor of the elevator car and dividing the scaling laws from Eqs. (12)–(15), (17). The dotted lines are obtained directly from the simulation, using the values of the Table 5. Likewise, the Figs. 7b, 8 b, 9 b shows the dynamics of the Elev 4, Elev. 7 and Elev. 13 test rides respectively, where the rope tensile force of the elevator car and the rope tensile force of the counterweight are represented along the ride. The solid lines are obtained by the measurements of the load cell placed at the end of each side of the rope and dividing the value of the scaling law from Eq. (16). The dotted lines are obtained from the numerical simulation using the values of the Table 5. Good correlation results are obtained and therefore, the scaled elevator test bench is able to emulate different elevator dimensions and the test performed in a scale test bench are equivalent to those made in a real elevator installation.

6. Conclusions Fig. 6. Box-plot comprising the RMSE of the deviation of simulation and the actual measurements for the acceleration, force and the torque of fifteen elevators.

the rides are less than 0.03 [m/s2 ], 0.85 [N] and 0.06 [N · m] respectively. As detailed examples, emulated kinematics and the dynamics of three test rides are demonstrated in Figs. 7–9, where practically identical amplitude is obtained. The Figs. 7a, 8 a, 9 a represent the kinematics of the Elev 4, Elev. 7 and Elev. 13 test rides respectively, where the ride distance, speed profile, acceleration and jerk

It is noteworthy that the application of condition monitoring in electromechanical systems has increased in the recent years and therefore requires to understand the behavior of the system and its faults. A novel scaled elevator test bench has been designed which emulates real elevators. The dimensional analysis is used to form the dimensionless groups and the scaling laws are formulated. The dimensionless gains of the field oriented control loops obtained in Eq. (11) allows to decouple the similarity conditions of the mechanical subsystem from the electrical subsystem and there-

E. Esteban et al. / Mechatronics 47 (2017) 14–23

Fig. 7. Comparison of the experimental emulation and model simulation (elev. 4).

Fig. 8. Comparison of the experimental emulation and model simulation (elev. 7).

Fig. 9. Comparison of the experimental emulation and model simulation (elev. 13).

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E. Esteban et al. / Mechatronics 47 (2017) 14–23

fore different mechanical subsystem dimensions can be emulated while maintaining the electrical subsystem and control. The dimensionless formulation of these gains should facilitate the tuning of PI controllers for different elevator dimensions. A physical interpretation of work-energy principle have been assigned to the rest of the dimensionless groups. The robustness of the scaled test bench for emulating different elevator motions and dynamics is experimentally validated by fifteen test rides. The dimensionless group formulation of the elevator system could also be applied to other industrial applications where scaled test bench of large systems is required. Finally, the scaled elevator test bench will be employed for the experimental validation of some proposed model-based condition monitoring algorithms in future projects. Acknowledgments This study is partially funded by the Basque Government under the Emaitek 2014 Program (MECOFF project, No. IE13-379) and by the Ministry of Economy and Competitiveness of the Spanish Government under the Retos-Colaboración Program (LEMA project, RTC-2014-1768-4) and the AIRHEM III project. The authors also gratefully acknowledge Orona EIC S. Coop. for supporting this research line. Any opinions, findings and conclusions expressed in this article are those of the authors and do not necessarily reflect the views of funding agencies. Appendix A. Physical interpretation of dimensionless groups The dimensionless groups usually have a physical interpretation. Particularly, nine of the π -groups extracted from the dimensional set matrix are related to the work-energy principle, which can be calculated by performing some mathematical operations as follows,

π12 1 m v2 π2 a m l π3 π5 m j l t = ; πE p = = ; πE j = = ; 2 π8 2 τ θ π8 τθ π8 τθ π7 π12 π5 c v2 t π 1 k l2 π4 f l πE u = 6 = ; πE d = = ; πE w = = ; 2 π8 2τ θ π8 τθ π8 τ θ π R i2 t π14 1 L i2 π15 1 λ i πEh = 13 = ; πE m = = ; πE m = = . π8 τθ 2 π8 2τ θ 2 π8 2τ θ πE k =

(A.1)

where these new nine π -groups represent the ratio between the work demanded by the machine and their corresponding energy transformation as summarized in Table A.6.

Table A.6 Physical significance of dimensionless groups. Name of ratio

Definition

Physical meaning

Kinetic energy ratio, πEk

1 m v2 2 τ θ aml

Translational kinetic energy Rotational work Potential energy Rotational work Jerk energy Rotational work Elastic energy Rotational work Damping energy Rotational work Translational work Rotational work Joule effect Rotational work Storage magnetic energy Rotational work

Potential energy ratio, πE p

τθ

Jerk energy ratio [54], πE j

m jlt

Elastic energy ratio, πEu

1 k l2 2τ θ c v2 t

Dissipation energy ratio, πEd Work ratio, πEw Heating ratio, πEh Magnetic energy ratio, πEm

τθ

τθ

f l

τθ

R i2 t

τθ

1 L i2 1 λi = 2τ θ 2τ θ

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