Load Identification and Deflection Monitoring of Opening Beam on Well-Hole Freight Trains

In railway freight transport of over-size cargos, elastic deflection of overloaded structures is the main cause of train-line collision in running. Deflection monitoring remains a challenge for the non-uniform and opening beam on well-hole freight cars. This work presented a new approach by strain perception and Finite Element Analysis (FEA). In theoretical modeling, support locations and the geometry symmetry were taken into account, to identify the support loads with bottom strains in single loading. Deflection calculation was developed by mathematically correlating bottom deflections with support loads, and further extended to the concerning region of the non-uniform and opening beam. Validation underwent in loading simulation and tests. The identified deflection deviates from the read and measured within 5.98%. In application, in-transit monitoring reveals that the most unfavorable vertical cargo movement, which is calculated with the identified support deflections and the measured suspension displacement, climbs up to 231.6 mm in synthetic evaluation, when the train runs on a 400-m radius line curve at the speed of 19.6 km/h. The detecting maximum is within but very close to the limit dimension between cargo bottom and rail top, 250 mm. Hence, it is recommended to measure the limit after the transformer is loaded. Research outcome indicates that the proposed approach enables the real-time deflection monitoring and safety evaluation in railway freight transport, which offers scientific evidence for its operation maintenance and structural optimization.


I. INTRODUCTION
Railway freight transport has always been a strong support for state grid construction programs, especially in delivering over-size cargos including transformers and generator stators [1]. In transport safety, the main concern focuses on the intrusion between the cargo and railway facilities, due to dynamic movement of both the train and cargo [2]. To ascertain safety, dimension check is performed at the two sides and top of loaded cargo according to the loading reinforcement rules [3]. Clearance check of operation facilities is required The associate editor coordinating the review of this manuscript and approving it for publication was Jesus Felez . along railway lines before transport. However, the risks of collision between cargo bottom and railway bed ballast or station platforms remain unknown. The conflict will damage the cargo, the train body structure [4]- [6] and even result in serious operation accidents including train overturning and derailment, followed with tremendous economic loss and negative social impact [7]- [10].
In railway freight transport, well-hole cars are used to carry transformers. The transformer is loaded on four support bases of two load-carrying beams, which are connected with adjustable bars to fit in transformers of different size. To stop the transformer from relative movement when running on line curves, in acceleration or deceleration, 4 lateral stops are set beside support bases to stop sliding along its width, and 2 longitudinal stops are designed between two beams to avoid sliding in running direction as Fig. 1.
In running, vertical movement of the loaded transformer consists of two categories, the rigid movement at different suspension and elastic deflection at support bases of loadcarrying beams. Vertical rigid movement can be detected by draw-wire displacement sensors at suspensions. But the elastic beam deflection can't be directly measured due to limited space between rail track and transformer (250 mm), not to mention the targeting uncertainty on line curves. Hence, theoretical approach was put forward by formulating the mechanical relation between the elastic deflection and longitudinal strains at support bottoms of D 26B -type well-hole cars [11]. The proposed method enables real-time deflection monitoring by multiple strain perception in transit, but unable to work for the DK 36 -type well-hole car. Because there is no analytical strain-deflection solution of its load-carrying beams, which are non-uniform with opening holes.
Different from the theoretical model of D 26B -type well-hole car [8], no analytical solution can be found for the non-uniform opening beam of DK 36 -type. In this work, a theoretical methodology is proposed for load-carrying beams of DK 36 -type well-hole freight car. In the second section, mechanical relation of the vertical support loads, strains and deflections at support bottoms, are theoretically modeled via single loading in FEA. The theoretical model is then validated by simulation of random coupled loading, as well as on-site loading test in third section. In the fourth section, the proposed method is applied in real-vehicle test. The maximum deflection and safety evaluation are discussed. The framework of this paper is shown as Fig. 2.

II. THEORETICAL MODELING
Load-carrying beam of DK 36 -type well-hole car, with nonuniform sections and opening holes, is simply supported on the lateral supporting beams at the two ends. Vertical support loads at the two support bases, are defined by F 1 and F 2 , respectively. Longitudinal strains and vertical deflections at support bottoms, are denoted by ε 1 and ε 2 , ω 1 and ω 2 , respectively. In transformer loading, geometrical dimensions and external forces of the beam model is illustrated in Fig. 3. The material is HG70 high-strength steel for the beam, and Q345 low-alloy steel for linking bars. The elastic modulus (E) is 210000 MPa, the Poisson ratio (µ) is 0.3 and the density (ρ) is 7680 kg/m 3 . Geometry dimension of the load-carrying beam is listed in Table 1.
In theoretical modeling, FEA method is adopted to acquire the mechanical relation between longitudinal strains at support bottoms (ε 1 and ε 2 ) and vertical loads at support bases (F 1 and F 2 ). In a same way, correlation between support bottom deflections (ω 1 and ω 2 ) and identified support loads (F 1 and F 2 ) is given by single loading simulation. As a result, deflection calculation is modeled where the measured strains at support bottoms (ε 1 and ε 2 ) are the input parameters, vertical deflections (ω 1 and ω 2 ) are the output. Output deflections are extended to acquire deflections at all location of loadcarrying beam in concerning safety-relevant region.

A. LOAD IDENTIFICATION
The loading frame of DK 36 -type well-hole car is subjected to vertical forces from transformer through support bases, lateral curve-running centrifugal force from lateral stops, longitudinal forces from acceleration or deceleration through longitudinal stops. Lateral and longitudinal forces can be directly measured by pressure sensors installed between VOLUME 8, 2020  transformer and stop structures. But for the vertical, it's unlikely to perform a direct measurement because the transformer base and support base are welded together. Hence, the vertical forces are identified by detecting the strains, which locates at the support bottom. The linear correlation between support bottom strains and support loads in the elastic mechanical stage, is created by single loading simulation, as in Fig. 4. In load identification, further step is taken to fit the model in different support locations due to different transformer size.
In single support loading at base 1#, the vertical load is denoted by F 1 , strains at two support bottoms are denoted by ε 1_F1 and ε 2_F1 , respectively. In linear elastic stage, bottom strains are formulated as where a 1_F1 and a 2_F1 are the fitting coefficients between load at support base 1# and strain at two support bottoms, respectively.
In support loading at base 2#, the vertical load is denoted by F 2 . Strains at two support bottoms, which are denoted by ε 1_F2 and ε 2_F2 , respectively, are formulated as where a 1_F2 and a 2_F2 are the fitting coefficients between load at support base 2# and strain at two support bottoms, respectively.
The detected strain at each support bottom, respectively denoted by ε 1 and ε 2 , is composed of strains induced by the two support loads, respectively. Thus, Accordingly, the support forces are identified by In transformer loading of DK 36 -type well-hole car, the geometry dimensions remain constant except the support location (L F ) because of different transformer size. To make a general solution, mechanical relation between strain-force coefficients and support location (L F ) is mathematically modeled with simulation results in 9 different support locations. Locations are determined by the range of support base distance when loading transformers with different weight and size.
Considering the geometry and loading symmetry, we have The support load identification can therefore be simplified as in (6).
In deflection calculation, the identified support load serves as medium variable to relate the deflection and the measurable strain. Likewise, the deflection is decoupled into deflections induced by each support load, as in Fig. 5, and transferred into the formulation based on the strain acquired in the previous section.
In single loading at base 1#, support bottom deflections are denoted by ω 1_F1 and ω 2_F1 , respectively. Mechanical relations are given with different support locations as where g 1_F1 (L F ) and g 2_F1 (L F ) are the coefficients between support load F 1 and deflection at two supports, respectively. In single loading at base 2#, vertical deflections at two support bottoms are denoted by ω 1_F2 and ω 2_F2 respectively. Formulations are given as where g 1_F2 (L F ) and g 2_F2 (L F ) are the coefficients between support load F 2 and deflections at two supports, respectively.
The practical deflection at each support bottom is composed of deflections induced by the two support loads, respectively.  Because of the geometry and loading symmetry, we have: g 1_F1 (L F ) = g 2_F2 (L F ), g 1_F2 (L F ) = g 2_F1 (L F ). Therefore, the support bottom deflections are calculated by To calculate the mathematic function of strain-load (f 1_F1 (L F ), f 2_F1 (L F )) and load-deflection (g 1_F1 (L F ), g 2_F1 (L F )), support location L F is defined in the range of 13500∼16000 mm according to historical transport of transformers, the weight of which varies from 1670 kN to 3400 kN, as in Fig. 6.
To better fit the correlation between support location and strain-load coefficient, as well as load-deflection coefficient, the support location range is divided into 8 segments, 9 locations. At each location, vertical support load is defined into 4 step loads, the maximum of which is the mean of the total 4 support loads at the transporting limit of DK 36 -type, 3600 kN.
In FEA, Hypermesh was used to create the finite element mesh of the load-carrying beam, and the simulation was performed in ANSYS. The thickness of the beam is only 18 mm comparing with its length (36m) and height (12.47m), the thin-walled structure is therefore meshed with shell elements. The minimum size of beam boundaries in irregular shapes, is smaller than 60mm. In order to ensure adequate efficiency and accuracy in FEA, the mesh size was set to 20 mm. The load-carrying beam is modeled and meshed with 145060 nodes and 147613 shell elements, as in Fig. 7.
Translation constraints are defined at both ends of the beam model. Longitudinal translation is released at one end to let go the movement in longitudinal deformation. Concentrating forces are defined at two supporting area of 600 mm×220 mm, describing the actual area of support bases, as in Fig.7.
The vertical displacement and longitudinal strain at the bottom line of load-carrying beam, which ranges from −6000 mm to 6000 mm centering its symmetry axis, is responsible for large deflection. The bottom deflection in the concerning region under single support loading of 900 kN, which is 1/4 of the loading capacity of well-hole car (3600 kN), is given in Fig. 8(a) with different support locations. It is revealed that as the support location approaches the middle, there is an increase on the maximum deflection (52.95∼57.17 mm) and deflection at support bottoms (51.92∼56.84 mm at support 1#, 44.68∼54.54 mm at support 2#). Despite the holes in the beam, vertical deflection monotonically rises from two sides to the peak, revealing a different rule as longitudinal strains depicted in Fig. 8(b). The inflection point of longitudinal strain arises at hole boundaries where its semicircle and rectangle meet, as the red bar describes in Fig. 8(b). In addition, minor strain changes can be observed at the middle axis of the hole and between holes, as the dash dot line suggests. To find mechanical relation between support forces, bottom strains and support locations, mathematical formulation between strain-load coefficient and support location is given in priority.
Reading the longitudinal strains and vertical deflections at support bottoms, simulation results and fitting coefficients of strain-load, deflection-load are given in Fig. 9 under single loading with 4 load magnitudes and 9 support locations, in an attempt to make a more precise model.
Linear correlation between strain-load and displacementload is observed in simulation, by fitting the data of strain and displacement in different load magnitudes, but at the same support location. However, strain-load coefficient and support location L F follows a 4 th -order polynomial correlation where the fitting degree can reach 0.99. Different from strain-load coefficient, there is a linear correlation between deflection-load coefficient and support location. The analytical expression of strain-load coefficient and deflection-load with respect to support location, are given by (12).
Based on theoretical modeling and FE simulation, support load identification and bottom deflection calculation are formulated by (6), (10), (11) and (12). Only the deflection at two support bottoms is concerned because it accounts for the vertical beam deformation that brings about the vertical movement of the transformer.

C. DEFLECTION EXTENSION
In the previous part, support loads and deflections are formulated with pre-calculated constants. Support load and deflection calculation via strain measurement, is a simple arithmetic operation. If there is a need to observe deflections along the bottom beam in concerning region, the polynomial fitting method is employed between deflection curve and identified support loads.
At the 9 predefined support locations, the deflection curve can be formulated by fitting each under the single support loading of 900 kN, whereas the fitting constants can be linearly formed with other load magnitudes at the same support location. In this way, the fitting equations of vertical displacement in the concerning region are given at support locations ranging from 13500 mm to 16000 mm, under load magnitude of 900 kN, as seen in Fig. 10(a). Also, the correlation between fitting constants A i , B i , C i , and support locations (as in Table 2), based on which the deflection curve can be modeled under 900-kN load magnitude, are then given as in (13).
where ω F 1 (x) is the deflection expression in single support loading. A, B and C are the fitting constants in different support locations under load magnitude of 900 kN. For constants A, B, and C, the fitting coefficients with respect to support location L F are denoted by and C C2 (82.10 mm), according to the fitting results in Fig. 10(b). The deflection calculation can be extended with respect to the load magnitude F 1 and support location L F , by blending the four equations from (13) with linear conversion from magnitude of 900 kN to others. The ultimate formulation of vertical deflection under single loading is given in (14) as follows: Taking account into the geometry and loading symmetry, the beam deflection curve ω F2 (x) can be re-formulated in single support loading of F 2 , by letting t = −x and F 1 = F 2 , VOLUME 8, 2020  as in (15).
The resultant deflection is the summation of two individual deflection curve induced by each single loading, as in (16).
The constant of quadratic term (A i ) remains negative, a maximum of deflection as well as its location can therefore be found as follows: where ω MAX is the maximum deflection and x MAX is its location in concerning region.
Hence, (16) offers a theoretical model for calculating the deflection curve in identified support loads, and (17) gives a calculation of the maximum deflection and its location.

III. VALIDATION
Validation goes in numerical simulation and on-site loading experiment. In simulation, support location, load magnitude at two support bases are randomly generated as load cases in the range of practical scenarios. 10 load cases of coupled support loading are given to verify the proposed model. The difference is compared between the identifications and given loads as well as read deflections in simulation.
In loading experiment, strains and deflections are measured at support bottoms before and after transformer loading. The measured strains are substituted into the proposed model to identify the support forces and static deflections, which are compared with practical forces and measured deflections.

A. NUMERICAL SIMULATION
The FE model and boundary condition of single beam in simulation validation remain the same as in theoretical modeling. To compare the results of each beam on the full assembled loading frame, simulation validation is also conducted on the loading frame. The frame is modeled and meshed with 418475 nodes and 425799 elements, including 424399 shell elements for load-carrying beams and 1400 beam elements of linking bars, as in Fig. 11. Likewise, in single beam, the mesh size of loading frame was set to 20mm. The two marked areas at the bottom of lateral beam on one end, are defined with full constraints except the rotation about car width direction. Symmetric areas on the other end are defined with only vertical constraint. Vertical loads are defined the same way as in single load-carrying beam.
To cover possible loading scenarios, 10 load cases were generated by random method concerning the range of two support forces and support locations. Since the theoretical modeling is carried out on single support loading, only coupled loading at two support bases is taken into account here. Single beam and loading frame model are involved in validation, the two support forces and loading location are the same on the two beams of loading frame in accord with practical circumstance. The support force varies in the range of 0∼900 kN at each base. The loading location ranges from 13500 mm to 16000 mm. Validation load cases are listed in Table 3.
For each load case, longitudinal strains at two support bottoms are read and substituted into the load identification and deflection calculation model. The identified support load magnitude and deflection (denoted as 'ID') are compared with the given loads and read deflections (denoted as 'GV') in Table 4. Relative deviation is calculated by |'ID' − 'GV'|/'GV'×100% and plotted in a 3D bar as Fig.12.
Comparison indicates that the deviation (|'ID' − 'GV'|) between identified and given loads, varies within 35.5 kN for load magnitudes, and 2.4 mm for support deflections. The relative deviation ranges within 5.98% and 3.28% for load magnitudes and support deflections, respectively. Relative deviation goes no more than 6%, which suggests good agreement of the proposed method with simulation. It is also seen that the relative deviation is smaller in single beam validation than that in loading frame. In load validation, the maximum relative deviation is 2.12% in single beam simulation and 5.98% in loading frame simulation. In deflection validation, the maximum relative deviation is 0.64% in single beam and 3.27% in loading frame. To explain the difference, the mechanical response of the lateral supporting beam, which support the two load-carrying beams at two ends, are taken into account. The bending effect of lateral beams give rise to a higher deviation, but fortunately no greater than 6%.

B. LOADING EXPERIMENT
In transformer loading, two load-carrying beams are adjusted in a distance of 3560 mm, and the lateral distance between side beam and transformer boundary is 60 mm. The loaded transformer weighs 3170 kN (denoted as F G ), the support distance of which is 6650 mm in its length. The geometric center of the loading frame deviates 200 mm from transformer gravity center in longitudinal, but coincides laterally. Loading dimensions of both frame and the cargo is depicted in Fig. 13.
During the loading test, strains at support bottoms are measured by strain gauges and read from data acquisition system (DAQ). Deflections are measured with steel tape and plumb line, in terms of the displacement at assembly ends, support bottoms and middle bottom of load-carrying beam, as in Fig. 14. Displacement measurement is carried out in a way that the distance is characterized by the length of plumb line in strict vertical direction to rail head, and measured by steel tape afterwards. Loading deflections are calculated by measured displacements as in (18).
where D S1 and D S2 are the static deflection at two support bottoms. D M is the deflection at the middle bottom. D 1_UL and D 2_UL are the distance of lateral support beams from railhead before loading. D 1_LD and D 2_LD represent the distance of that after loading. D S1_UL and D S2_UL are the distance of the two support bottoms from railhead before loading. D S1_LD and D S2_LD are the distance of that after loading. D M_UL and D M_LD are the distance of the middle bottom from railhead before and after loading, respectively. The support forces are theoretically calculated due to the difficulty in performing direct measurement, because the support bases are welded with the cargo bases. Identified support forces are then compared with theoretical calculations at support bases, which are given in (19) using the force and moment equilibrium as follows: where F 1_L and F 2_L are the theoretical support forces on the left beam, F 1_R and F 2_R are the theoretical support forces on the right beam. The direction of two beams is distinguished when the train is moving forward in top view. L S is the longitudinal distance between support bases on each beam, here L S = 6650mm. L W is the lateral distance of support base   Strain measurement output is set to zero before loading. Strains at 4 support bottoms of two beams are read from DAQ system after loading, ε 1_L = 735 µε and ε 2_L = 708 µε at two support bottoms on the left beam, ε 1_R = 744 µε and ε 2_R = 726 µε at two support bottoms on the right beam. Measured strains are substituted into the model, in an attempt to acquire the support forces and vertical deflections by the proposed method. Comparison is made between identified and given results in loading experiment as Table 5.   Result listed above reveals that the strains, support forces and deflections at support base 1#, measured or identified, are greater than that on support base 2#. Identified support forces deviate from theoretical calculations within 2.41% and 3.38% on the left and right beam, respectively. Identified deflections deviate from measurement within 2.39% and 1.83% on the left and right beam, respectively. Results suggest good agreement between the proposed method and on-    site loading experiment, which lays evidence for the method validation when performing deflection calculation via multiple strain measurement. The static deflection is extended by the identified support forces in concerning region, as seen in Fig. 15.
Deflection deviation by identification and extension ranges from 0.2 to 3.1 mm. Relative deviation between deflection measurement and extension calculation is within the range of 0.94∼2.52%. The static deflection is the evidence for transferring the synthetic deflection into dynamic deflection in on-vehicle experiment.

IV. MONITORING AND EVALUATION A. EXPERIMENT OVERVIEW
In-transit monitoring and evaluation was carried out during the railway freight transport from Shanhaiguan to Huade in China. Total transport distance is about 1400 km. Transformer weight and loading dimensions are the same as described in on-site loading experiment.
For well-hole freight train, a notable change of support force on load-carrying beams can be observed when the train runs on line curves, in terms of increase on one side and decrease on the other. Resulting deflections of the two beams VOLUME 8, 2020   follow the same rule, either positive in dynamic compression or negative in alleviation of support loads. Therefore, of all detections during the transport, only measurement on line curves is taken into account. For loaded DK 36 -type wellhole train, defined speed limit on different curve radius are given in Table 6.
For strain measurement, strain gauges were arranged in full Wheatstone bridge, three of which are bonded on a dummy block. The material of the dummy block is the same with load -carrying beam. And its location is beside the strain measuring point, so as to compensate the environmental temperature drift. Dynamic strain signal were collected by IMC DAQ system at a sampling frequency of 256 Hz, so as to cover the main vibration frequency of loading frame, 7.4 Hz for the 1 st -order vertical bending in modal analysis [52]. Before analysis, strain data were processed with low-pass filtering at frequency of 40 Hz [53].
Running speed of freight train was detected by Stalker-S3 type velocimeter, precision of which is within ±1km/h. Running mileage, which describes the train location, is calculated with the running speed and time interval. The running mileage is consistently updated with railway mileage post to eliminate location errors. Thanks to the railway administration, information including curve radius, corresponding superelevation and mileage location are given, to analyze with monitoring results.

B. RESULTS DISCUSSION
In monitoring of bottom strains underneath load-carrying beams, the identified support forces, support deflections will be analyzed with relevant parameters, including the running speed, curve radius and superevelation. For railway line curves, the curve direction is defined the same with the centrifugal force when running forward.
Line curves scatter in different section between railway stations. Bottom strains on straight line are far lower than those on line curves. Therefore, curve-related data are intercepted from sections and spliced together. Dynamic deflection in transport is extracted from synthetic deflection, by subtraction of the static deflection measured in loading experiment. A time-history of dynamic bottom strains, synthetic support forces and synthetic support deflections are given in Fig. 17. The dynamic support deflection is calculated by the subtraction of identified synthetic and measured static support deflections. Dynamic support deflections and maximum deflection are listed in Table 7.
In assistance with the strain time-history, 3D contour map of the synthetic deflection in concerning region, are given as in Fig. 18(a) and Fig. 18(b) for the left and right beam, respectively. And dynamic deflection contour map are given in Fig. 18(c) and Fig. 18(d) for the left and right beam, respectively.
From the above monitoring and identification, the maximum detected strain of the left beam occurs on a 400-m radius line curve (superelevation: 105 mm) when the train is running at the speed of 19.6 km/h. Identified synthetic support loads and support deflections climb up to the maximum, 1286.3 kN and 135.2 mm at support 1#, 1008.1 kN and 133.7 mm at support 2#. For the right beam, the maximum strain detection arises on a 400-m radius line curve (superelevation: 105 mm) at the running speed of 17.5 km/h. Identified synthetic support loads and deflections rise up to 1232.4 kN and 130.7 mm at support 1#, and 1149.6 kN and 129.5 mm at support 2#.
Dynamic monitoring reveals that, on right line curve there is a dynamic compression on the right beam, which brings about a positive dynamic strain and deflection at support bottom. While an alleviation happens on the left beam, which arouses a negative dynamic bottom strain and deflection. The same rule follows when the train is passing through a left line curve. Results also suggest that there is an opposite trend of dynamic deflection concurrently observed between the left  Explanations were introduced in a similar way as stated in [11]. Mechanical analysis of the transformer when the train is running on a right line curve is given in Fig. 19.
Taking the transformer as the analysis object, in the view of its section along width direction, the gravity force (denoted VOLUME 8, 2020  as F G ) and centrifugal force (denoted as F C ) are acting at the gravity center. The supporting forces (denoted as F L and F R respectively for the left and right beam) are working from the 4 support bases. And the lateral forces (denoted as F T ) act from the lateral stops which only offer an inner stop force at an individual beam. When the support force F L from the left beam is greater than that from the right beam F R , the lateral force F T locates from the right beam to balance the moment about the gravity center, as demonstrated with red arrows in Fig. 19. The circumstance turns out the opposite when support force F R from the right beam exceeds that from the left beam F L . The lateral force F T comes from the left as the force depicted with blue arrows in Fig. 19. According to the force and moment equilibrium, the difference of support forces from the two beams is given in (20) [11].
where H S is the vertical distance between lateral force F T and transformer gravity center. m is the mass of transformer. g is the acceleration of gravity (9.8 m/s 2 ), v is the running speed, R is the curve radius, θ is the curve superelevation angle.
To better understand the difference of support forces on beams, the lateral acceleration parameter is defined by J NRL and calculated by J NRL = (g · sinθ − v 2 /R · cosθ). The scatter diagram of J NRL vs. (v 2 /R) is given by re-calculation of running speed, curve radius and superelevation from Table 8, as in Fig. 20.
Calculations indicate that all J NRL values are positive, which certifies that the supporting force from the beam at outer track side is greater than that at inner on line curves. The centrifugal force directly relates to the running speed and geometric radius of line curves. While the speed limit defined for the well-hole car, fails to create adequate centrifugal force to balance the centripetal force from the transformer gravity, but works with the lateral stops on the beam at the inner track side. In addition, the dynamic support deflections can be linearly correlated with the lateral acceleration parameter, in an approximate linear relation as seen in Fig. 21.
The fitting formulation is helpful in estimating the maximum dynamic support deflection in railway freight transport, wherein the same loading weight but different line curves and running speed are involved. The most unfavorable deflection of the transformer, locates at the transformer boundary at the tilting side rather than the support bases on the beam, when there is a difference between deflections at two support bases. But the deflection increase is no bigger than 1mm according to the calculations in [11], the deflection at support bases of load-carrying beam thus describes the most unfavorable displacement of the transformer in safety evaluation.

C. SAFETY EVALUATION
Transformer movement in vertical direction, which contains the elastic deformation of load -carrying beams and rigid displacement at suspensions, is concerned in safety evaluation. It has been discussed that the support deflections on the beam account for the most unfavorable vertical transformer movement. Thus, the maximum dynamic and synthetic deflection at support bottoms are included to assess the safety limit of 250 mm, dynamic for post-loading when the limit is measured after loading, synthetic for pre-loading when the measurement goes before loading.
Draw-wire displacement sensors (WSS-0500-D40-22V0) are set at different suspensions, serving in displacement measurement during static transformer loading, and dynamic monitoring in transit, as in Fig. 22. In measurement, six displacement sensors were set wherein two at the primary suspension of two sides of the first wheel, two at the second suspension of both sides of small frame, and the other two at the third suspension of medium frame, all in forward direction. In static loading and on-vehicle transport, the displacement changes were read from the IMC DAQ system. Static, dynamic and total displacement at all suspensions, as well VOLUME 8, 2020 as the maximum identified support deflections are listed in Table 8 and Fig. 23.
Safety evaluation undergoes in dynamic and static terms. The dynamic evaluation puts the safety limit, 250-mm space between transformer bottom and rail top, as the measured dimension after the transformer is loaded. Accordingly, the synthetic evaluation contains the limit before the transformer is loaded. Hence, according to the monitoring and calculations in Table 8, the total displacement is acquired by adding the total suspension displacement with the maximum support deflection at each side, in dynamic or synthetic way. In dynamic evaluation, the estimated total displacement reaches 87.6 mm and 76.4 mm at the left and right side, respectively. While the estimation climbs up to 231.6 mm and 220.4 mm at left and right side in synthetic evaluation. It is observed that the maximum vertical movement of the transformer does not exceed the safety limit, but pretty close to when taking account into synthetic evaluation. Therefore, it is suggested that the limit measurement be done after the transformer is loaded.

V. CONCLUSION
In this work, load identification and deflection calculation approach of opening beam on well-hole freight car is proposed. The presented model is validated by coupled loading simulation and static loading experiment, and applied in safety evaluation in transport. Conclusions derived are as follows: (1) Support load identification is modeled by blending the mechanical relation of strain-load in single support loading with the other. Deflection calculation is formulated with the identified support loads, which takes account into different support locations in practical engineering. The proposed methodology offers a safety evaluation means for nonuniform and opening beams of well-hole freight car.
(2) Simulation validation goes in random coupled loading. Results reveal that the load deviation between identification and the given is no more than 5.98% for single beam and loading frame, respectively. The deflection deviation between calculation and what read is no greater than 3.28%. Experiment validation reveals that the measured strains, identified support forces and deflections at support base 1#, are larger than that on support base 2#. Load deviation between identification and theoretical calculation ranges from 2.41% to 3.38%. Deflection deviation between identification and measurement ranges from 1.83% to 2.39%. Validation suggests good agreement of the proposed method with simulation and experiment.
(3) On-vehicle monitoring gives a maximum detection of 356.3µε for dynamic support bottom strains, identification of 1286.3 kN for synthetic support loads, 43.2 mm and 135.2 mm for dynamic and synthetic support deflections, respectively, when the train runs at the speed of 19.6 km/h on a 400-m line curve. It is proved both experimentally and theoretically, that the supporting force on the beam at the outer track side is greater than that at the inner, due to the speed limit defined on line curves. It also suggests that all positive dynamic deflection occurs on the left beam whereas negative on the right when running on left line curves. Same rule follows when the train is running on right line curves.
(4) In safety evaluation, the rigid displacement at all suspensions and the elastic deformation on the load-carrying beam are taken into account. With the displacement measurement via draw -wire sensors at three suspensions, the most unfavorable vertical movement of transformer rises up to 87.6 mm and 231.6 mm in dynamic and synthetic evaluation, respectively, within the range of the safety limit, 250 mm. The synthetic evaluation approximates the safety limit, it is therefore suggested that the limit dimension be measured after the transformer is loaded.
(5) Research outcome reveals the reliability and accuracy of the proposed method, and thus enables real-time deflection monitoring and safety evaluation in freight transport. In the future, the load identification model will be serving as an important part in multi-load identification, including the vertical support loads, the lateral loads and longitudinal loads from stop structures. All external loads work in cooperation to form the real-service load spectrum of the loading frame in assistance with FEA method, so as to perform the fatigue damage estimation and structural optimization for the car.
YITONG WU is currently pursuing the master's degree with the School of Traffic and Transportation Engineering, Central South University, Changsha, China. Her major interest is vehicle operation engineering and her research interests include safety monitoring and evaluation of railway freight transport.
XIFENG LIANG received the bachelor's and the master's degrees from the School of Energy and Environment Engineering, Southeast University, Nanjing, China, in 1985 and 1988, respectively. He is currently a Professor with Central South University. His research interest includes train operating safety and environment, especially in structural safety evaluation.