Application of finite element method to design of progressive crush buffer concepts for elevators

ABSTRACT

 

This paper presents a new design concept of buffer for elevators, which is based on dissipating impact energy by means of non-recoverable plastic deformation, but maintaining similar performance requirements of typical hydraulic buffers on a wide range of impacting masses and velocities. Firstly, it is presented an aluminium tube with specific geometry which provides folding behaviour under impact conditions. The design process and geometry optimisation are performed by means of explicit finite element (F.E.) crush simulations with the adequate material model for the aluminium, including strain rate stiffening of the material. The tube geometry is optimised for fulfilling a maximum average acceleration requirement within the specified ranges of cabin mass and impacting velocity, being finally validated with experimental results on full size prototypes. An alternative concept is shown as well, as combination of plastic deformation buffer with a simplified oil-based damper to satisfy critical vertical strokes requirements without modifying general geometry of buffer.

 

 

  1. INTRODUCTION AND OBJECTIVES

 

Elevators are always equipped with emergency braking systems which ensure that cabin is stopped when an overspeed situation occurs. These systems are calibrated to be activated for stopping the cabin when a speed over a 115% of nominal velocity occurs. However, in other particular situations, the cabin could fall into the pit from the bottom floor position and reach its stroke end before reaching this overspeed limit. In these situations, overspeed brakes would be therefore not actuating, causing a safety risk for elevator users.

 

To cover these emergency situations, buffers of different types can be disposed in the pit to stop the cabin under safe deceleration conditions. Nowadays, the best technology to achieve this function is based basically on hydraulic buffers, which are usually expensive devices compared to the general cost of elevators.

 

The present paper proposes a new design concept of buffer for elevators, which is based on dissipating impact energy by means of non-recoverable plastic deformation (progressive folding behaviour), but maintaining similar performance requirements of typical hydraulic buffers on a wide range of impacting masses and velocities, with simple geometries and easy manufacturing processes and, therefore, of reduced cost.

 

The work is presented in three parts according to their specific objectives: In the first part, the new buffer concept is designed for fulfilling the deceleration specifications (see Figure 1) on a particular case of cabin mass and velocity. The geometry of the buffer is fitted by means of virtual prototyping techniques, in this case, explicit finite element (F.E.) simulations which are later validated by experimental cabin free fall tests on full size samples. The use of F.E. simulation includes to develop specific material models and to adjust the boundary conditions which reproduce adequately the real conditions of the buffer in the test. In the second part, buffer design is optimised for fulfilling same deceleration specifications under defined ranges for cabin mass and velocities using same F.E. techniques. Finally, it is conceptually adapted for specific design conditions which include elevator installations with limited pit depth.

 

  1. GENERAL DESIGN SPECIFICATIONS

 

The general specifications for the new design of plastic deformation buffer concept are detailed below, according to the previous objectives:

  • First concept design for fixed cabin mass and velocity:
  • Cabin mass: 1000 Kg
  • Speed: 115% of 90m/min (103.5 m/min)
  • Average sustained deceleration: 1G
  • Deceleration peaks under 2.5G or shorter than 0.04 seconds.
  • Second optimised concept design for ranges of cabin mass and velocity:
  • Cabin mass (m):                        from 700 to 1300 Kg.
  • Speed (v):                     from 22% to 115% of 90m/min  (20 to 103.5 m/min).
  • Final concept solution for limited pit depths, adding following specifications:
  • Stroke:              Maximum, 180 mm.
  • Device length:              Maximum, 600 mm

 

  1. DESIGN OF PROGRESSIVE CRUSH BUFFER BASED ON FE-METHOD FOR FIXED CABIN MASS AND VELOCITY

 

3.1. Conceptual design: shapes and materials

In the previous section, the general specifications that must fulfil the elevator buffer in this preliminary design phase have been presented. The concept design is based on absorbing the impact energy of the elevator cabin in free fall conditions by means of non-recoverable plastic deformation of the buffer, as it is done in vehicles design, where energy absorption is solved by means of engineered structures with tailored crashworthiness characteristics (Xiang et al. 2006). For this, a novel concept design, newly applied in elevator industry, which is based on an aluminium tube with progressive folding behaviour is presented. The folding behaviour is ensured by means of an specific geometry of the tube. Figure 1 shows the ideal deceleration curve defined as requirement for the component.

 



 

 

XG

1/25 sec.

2,5G

1G

Figure 1. Design targets: Ideal deceleration curve


The ideal curve from Figure 1 starts with an initial peak load with minimum value of 2.5G and unlimited maximum value (but restricted within a time period not longer than 1/25 sec.), and continues with a sustained average load of 1G. This requirement is combined with the maximum height specification of the buffer design, which is similar to consider that all the impact energy must be absorbed in less than a given displacement since the elevator cabin initiates contact with the buffer.

 



 

To fulfil these ideal requirements, it is proposed a buffer design with the geometry which is shown in next Figure 2, including corner holes to ensure progressive folding.

 



 

The geometrical parameters have been adjusted by means of preliminary F.E. analysis until design requirements are accomplished. In addition, ellipsoidal holes are machined in the lateral walls to perform during crushing as triggering mechanisms when the elevator cabin impacts the upper tube, avoiding therefore general buckling of the component, and also reducing the initial deceleration peak. The selected material is a commercial aluminium alloy that can be also produced by extrusion, being the selected cross‑section of the tube compatible with the typical commercial cross sections available. This improves also the ?low-cost? design concept of the product.

Total height of the component is finally fixed to 400mm, which has been adjusted to be long enough to absorb all the kinetic energy of the elevator cabin. Finally, the tube is fixed to the lower bench by means of an internal massive plunger.


 

 

Figure 2: Sketch of the proposed bufer design



 

 

3.2. F.E.M.-based design of progressive crush buffer

The present section describes the Finite Element model that has been carried out to simulate the progressive folding behaviour of the aluminium buffer. This phase is completed with the validation of the simulation results with experimental test run on real buffer samples. The F.E. code used for the simulations is ABAQUS Explicit v6.4 (Hibbitt et al. 2003). Several assumptions have been made in order to obtain an accurate enough F.E. model with also low computational cost.

 

The buffer has been modelled by means of 4-node ?shell? elements with reduced integration (S4R). This type of element has been used due to the possibility of modifying material thickness without changing the mesh in previous phases of design adjustment.

 

Material considered in the calculations is a commercial aluminium alloy. The mechanical properties have been introduced in ABAQUS by means of a material model which considers elastic-plastic mechanical behaviour (Cooper and Warrior 2002). It should be taken into account that material model does not include failure, instead of that, it has been assumed that material does not increase its stress level once it reaches the maximum elongation value. After this point, material keeps on deforming, thus absorbing energy. In addition, stress-strain curves consider increase of material stiffness due to high deformation rates, which has been modelled by means of the Johnson-Cook material model. The mechanical properties introduced in the ABAQUS model have been adjusted with the tensile tests carried out at ITA installations. In addition, the parameters of the strain rate dependent model have been adjusted according to existing values in literature.

 

In the F.E. model, the buffer is the deformable body, using the previously commented S4R shell elements, which are available in the ABAQUS library. The impacting cabin has been modeled by means of a rigid surface which has an initial velocity of 115% of rated speed of 90m/min, and which is considered on free falling. The cabin mass has been considered by means of a point mass applied on the reference node of the rigid surface. In addition, the weight of the cabin has been considered by means of gravity acceleration affecting the point mass of the reference node of the rigid surface (free fall conditions). Next figure shows the modelization of the impacting cabin and the boundary conditions applied to the reference node of the rigid surface which models it.

 



 

 

Point mass = 1000Kg

Impacting velocity = 1.73m/s

Gravity acceleration = 9,8 m/s2

Impacting cabin

 

 


Figure 3: Impacting cabin modelization

 

 

Next, Table 1 shows the F.E. results obtained in terms of deceleration of the rigid surface which simulates the cabin. The table shows also the total crushing time and the total cabin displacement once all kinetic energy is absorbed:

 

Accel. Peak [m/s2]

Tpeak

[sec]

Average accel. [m/s2]

49

0, 001682

12,5848

 

 

 

Cabin stopped

Total time [sec]

Displacement [mm]

0,139

120

       

Table 1: Results obtained for the explicit crush simulation

 



 

Figures 4 and 5 show the deceleration and velocity curves obtained for this configuration in F.E. simulation:

 

Figure 4: Deceleration over cabin displacement

Figure 5: Cabin speed over crushing time

 

 

Next the deformed shape evolution of the buffer is shown. It can be observed the progressive folding behaviour achieved with the present buffer design concept:

 

t = 0s

t = 0.01s

t = 0.02s

t = 0.035s

t = 0.07s

t = 0.1s

t = 0.15s

Figure 6: Deformed shape evolution

 

 

3.3. Design validation with experimental tests

The present section shows the results obtained after the crush tests performed on real full-size samples of the buffer design concept. Afterwards, the obtained experimental results will be compared with the numerical ones obtained using the explicit code ABAQUS which have been shown in previous section. This correlation is done to validate the explicit F.E. simulation procedure and the aluminium material model adjustment that will be used to optimise the buffer design (next section 4) under different conditions of cabin mass and impacting velocity.

 

The experimental tests are based on the UNE-EN 81-2 standard, ?Safety rules for the construction and installations of lifts?. The test consists of a 1000 kg load in free fall which strikes against the buffer sample. The speed at the moment of the strike is 103.5m/min.

 

In the installation, there is a chassis with possibility of vertical movement, guided  by two rails. The chassis can be raised using a crane. In the chassis, several weights have been placed until the 1000 kg load (chassis + weights) is completed. The chassis can be released and put into free fall with an electromagnet located between the crane and the chassis. This system achieves to guide the impacting chassis vertically with low friction. The system deceleration is measured by means of accelerometers placed in the chassis, whereas the velocity is measured by means of a wire sensor. A picture of the testing installation can be seen in Figure 7. Figure 8 shows a sketch of the installation and details the positions where the accelerometers have been placed.

 

The lower bench, where the buffer prototype is mounted for testing, is placed under the chassis along the vertical direction of strike. It consists of a heavy block that stands over a beam joined to the ground. The buffer samples are externally inserted in a plunger which consists of a massive block of 100 mm height mounted on a plate that is attached to the low bench. During the tests, this method has proven to be adequate for preventing lateral instabilities of the tubes, thus allowing uniform crushing.

 

Figure 7: Installation for the crush tests.

 

Figure 8: Schematic view of the testing installation.

 

Figure 9 shows the displacement of the falling chassis of the test bench, measured with the wire sensor along several tests (up to six different crush tests), compared to the F.E. simulation with ABAQUS:

Figure 9: Displacement of the impacting cabin vs. crushing time obtained in experimental tests and obtained with ABAQUS

 

Figure 10 compares the final deformed shape of a tested buffer sample:

 

 

Figure 10: Final deformed shape of a tested sample

 

 



 

With respect to experimental results, the F.E. model reproduces adequately the performed crush tests. Next, Table 2 compares the results obtained with the ABAQUS Explicit model, as described in the previous section, with the average of the sustained deceleration values measured during the six crush tests:

 

 

Design

Average accel. [m/s2]

Displacement [mm]

Test

1,363G

111,8

ABAQUS

1,28G

120

%error

6,50%

7,30%

Table 2: Comparison of numerical (?shell? model) and experimental results

 



 

It can be concluded that the F.E. model reproduces adequately the crushing behaviour observed experimentally in terms of average deceleration, crushing displacement and approximate folding behaviour. Possible deviations may appear due to the fact that the F.E. model does not include material failure which in fact actually occurs in the experimental test in the zones beside the corner holes of the sample. Finally, the presented F.E. model can be used as optimisation tool in the next phase of the buffer concept design.

 

  1. DESIGN OF PROGRESSIVE CRUSH BUFFER BASED ON FE-METHOD FOR CABIN MASS AND VELOCITY RANGES

 

The objective of this section is to present an improved buffer design regarding the crush performance of the tube geometry under different cabin mass and impacting speed ranges. As the cabin load changes by the number of passengers, it is necessary to check the effect of load change. The buffer strike velocity changes also, and it highly depends on the overspeed at the bottom floor. Therefore, the speed variation has to be considered for the buffer design.

The impact conditions that must fulfil the new buffer design are minimum mass cabin (700kg) and maximum mass cabin (1300kg), both with maximum and minimum impact velocity (115% and 22% of rated speed 90m/min). For all the cases, the deceleration requirement described in Figure 1 must be fulfilled as upper limit. The buffer design modifications will imply different hole sizes along tube length and also different tube length, with regard to design presented in chapter 3.

 

Initially, the height of the buffer model was set to 400mm in order to assure that crushing takes place within the holed length of the buffer without reaching the 100 mm plunger, thus, the available crushing length was 300mm.

 



 

After preliminary F.E. analysis considering the new impact conditions, the height was modified to 500mm. In addition, it was checked that global buckling problems were avoided.

 

Therefore, several F.E. analysis have been carried out according to a numerical D.O.E. for analysing the influence on crushing behaviour of the number and size of the tube holes before reaching to final buffer design proposal. Simulation conditions and any other finite element model details are the same as in previous section. The sketch of the final buffer design geometry which fulfils the new specifications, just prior to showing the corresponding experimental-numerical comparison results, is shown at Figure 11.

Figure 11: New buffer design geometry.



 

 

4.1 F.E.M. based optimisation of buffer and experimental check of final design

The installation in which the crush tests have been performed is the same used during the first phase of the present work and described in previous section 3. Experimental numerical comparison has been carried out for the maximum cabin mass conditions (at 115% and 22% of rated speed 1.5m/s) and for the minimum cabin mass conditions (at 115% of rated speed 1.5m/s).

 

Next, the deceleration results obtained in the experimental test are compared to those obtained in explicit F.E. simulation with ABAQUS. In this section, explicit F.E. simulations have been run considering the real impact speeds measured during the experimental testing. The following Tables 4 and 5 show the experimental results of the tests which were performed with 1300kg cabin mass and an impact speed of, respectively, 115% and 22% of rated speed:

 

 


 

average deceleration [G]

stop time [sec.]

buffer stroke [mm]

Tests average

0.810

 

327.4

Abaqus average impact speed (99.5m/min)

1.038

(deviation +28.1%)

0.221

313

(deviation  ?4.4%)

 

Table 4: Numerical comparison: tests and simulation. 1300kg and 115% rated speed test conditions

 

 

 

average deceleration [G]

stop time [sec.]

buffer stroke [mm]

Tests average

0.147

 

207.4

Abaqus average impact speed (21.4m/min)

0.175

(deviation +19%)

0.36

203

(deviation  ?2.1%)

 

Table 5: Numerical comparison: tests and simulation. 1300kg and 22% rated speed test conditions

 

As example, next Figure 12 shows the experimental results, in terms of measured deceleration, which were performed with 700kg cabin mass and 115% of rated speed. Measured deceleration is compared to the one obtained with ABAQUS F.E. simulation. It can be checked that the F.E. results show a very fast initial peak deceleration that is not shown by the accelerometer curves. This initial peak does also occur in the real test, however, it is not possible to register it with the accelerometer due to data acquisition frequency and signal treatment limitations which are unavoidable in the present experimental conditions. In addition, other slower deceleration peaks are also observed in both, the F.E. simulation and the tests, which occur when the tube folding reaches the hole size transition (Figure 12 around time 0.15-0.2 secs.). However, it has been checked that these peaks are also fulfilling the 0.04 sec. restriction for decelerations over 2.5G.

 

Figure 12: Deceleration curves of test conditions 700kg and 115% rated speed

 

 

 

average deceleration [G]

stop time [sec.]

buffer stroke [mm]

Tests average

1.091

 

199.5

Abaqus average impact speed (97.5m/min)

1.232

(deviation +12.9%)

0.169

184

(deviation  ?7.7%)

 

Table 6: Numerical comparison: tests and simulation. 700kg and 115% rated speed test conditions

 

 

Figure 13: Sample of the buffer folding behaviour: 700kg and 115% rated speed test conditions

 

 

As final conclusion, the whole set of results indicate that F.E. prediction shows good match with experiment in terms of deceleration and can be taken as an upper limit for the experimental values. Regarding to design requirements, and for all the conditions tested, it has been checked that experimental results are within design requirements in terms of average deceleration.

 

  1. DESIGN OF PROGRESSIVE CRUSH BUFFER FOR ELEVATORS FOR LIMITED PIT DEPTH.

 

In this section a particular case is studied, adding specifications for some installations where the depth of the pit is limited. Therefore, in this section it is presented a conceptual solution for an elevator buffer designed for pits with limited depth, using a combination of plastic deformation buffer with simplified hydraulic action. Design specifications have been already detailed in section 2.

 

This solution consists of a hydraulic buffer acting in parallel with a crush buffer, whose action is delayed by a certain separation (xb in Figure 14). The decelerating force starts with the hydraulic action at the impact time, the crush buffer acts later as an extra force when the cabin reaches the xb distance.

 

The hydraulic force is produced by the damping effect of the fluid which flows through several orifices (Figure 14) to the upper chamber as the piston rod advances. The piston and the orifice diameters are selected as design variables to adjust the damping effect. Additionally, a spring is included so as to let the piston mass keep a steady position when no load is applied. Thus, the force provided by the hydraulic buffer can be modelled as: , where x and v are the cabin stroke and velocity, K is the spring stiffness and C a damping coefficient depending on orifice and rod diameters (Manring, 2005).

 

As aforementioned, a crush buffer is added in parallel, for fulfilling the stopping distance criterion. In this case, a double force buffer has been defined, which switches from the force F1 to F2 when the b distance is run (see Figure 14). This force switching is produced at the distance b, by means of different size of holes in the crush buffer, generating a higher deformation force along this zone.

 

Optimisation is performed on the initial design, based on dynamic simulations with a calculation model defined in the software Simulink (Mathwork, 2009). Optimisation is focused on the search for the best combination of the model parameters, taking into consideration that the best results are those ones which accomplish every specification defined for the model. It means that a multi-target optimisation is set with maximum deceleration, average deceleration and limited stroke as design criteria. Results obtained with optimised model are shown in Table 7 for maximum velocity and the full mass range. Table 8 shows results for minimum, medium and maximum masses at the full range of velocities.

 

 

Mass (Kg)

Velocity (m/s)

Stroke (m)

Average deceleration (G)

Maximum deceleration (G)

700

1.73

0.111

0.98

3.24 (*)

750

1.73

0.123

0.84

2.95 (*)

800

1.73

0.136

0.72

2.71 (*)

850

1.73

0.141

0.91

2.49

900

1.73

0.143

0.96

2.29

950

1.73

0.146

0.99

2.12

1000

1.73

0.149

1.00

1.96

1050

1.73

0.153

0.99

1.82

1100

1.73

0.157

0.98

1.70

1150

1.73

0.161

0.95

1.58

1200

1.73

0.166

0.93

1.48

1250

1.73

0.170

0.90

1.44

1300

1.73

0.176

0.87

1.41

 

Table 7. Buffering results with optimised system at maximum velocity (mass range)

 (*) although the deceleration is above the 2.5 G limit, it does not remain for longer than 40 ms, therefore it complies with requirements.

 

 

 

Mass (Kg)

Velocity (m/s)

Stroke (m)

Average deceleration (G)

Maximum deceleration (G)

 

700

0.33

0.092

0.16

1.22

 

0.7

0.095

0.37

1.33

 

1.2

0.102

0.66

1.62

 

1.73

0.111

0.98

3.24 (*)

 

1000

0.33

0.143

0.12

1.47

 

0.7

0.144

0.30

1.50

 

1.2

0.146

0.60

1.55

 

1.73

0.149

1.00

1.96

1300

0.33

0.161

0.12

1.13

 

0.7

0.163

0.29

1.16

 

1.2

0.168

0.56

1.26

 

1.73

0.176

0.87

1.41

 

                     
 

Table 8. Buffering results with optimised system at some masses (velocity range)

 (*) although the deceleration is above the 2.5 G limit, it does not remain for longer than 40 ms, therefore it complies with requirements.

 

This design fulfils all the requirements in the studied ranges for mass and velocity without producing too high deceleration peaks. Figure 14 shows a sketch of the final configuration of the buffering system. Compared to current installations, a smaller hydraulic buffer with a simple design is required, since the crush buffer helps with extra force for completely stopping the cabin, which has been previously slowed down. The simple buffer working alone, for the maximum load case, would result in a velocity of 0.8 m/s when the target stopping distance is reached, far from the specifications, as an idea of the smaller size required of damping buffer when it is combined with the crush buffer.

 

 

 

c

b

xb

Æp

 

 

 

Æo

Figure 14: Buffer system layout with optimised geometry for pits with limited depth

 

  1. CONCLUSIONS

According to the results obtained with the designs shown in the present paper, the following conclusions can be drawn:

  • A complete buffering system based on energy absorption by means of plastic deformation can be used to accomplish safe deceleration conditions in case of overspeed impact, according to the performed F.E. analysis and experimental validations. Results show that the proposed concept of progressive crush

Deja un comentario

Tu dirección de correo electrónico no será publicada. Los campos obligatorios están marcados con *