Determination of accidental forklift truck impact forces ondrive-in steel rack structures

Author

Gilbert, Benoit P, Rasmussen, Kim JR

Published

2011

Journal Title

Engineering Structures

DOI

https://doi.org/10.1016/j.engstruct.2010.10.022

Copyright Statement

© 2011 Elsevier. This is the author-manuscript version of this paper. Reproduced in accordancewith the copyright policy of the publisher. Please refer to the journal's website for access to thedefinitive, published version.

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http://hdl.handle.net/10072/42539

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Determination of accidental forklift truck impact forces on drive-in steel rack structures Benoit P. Gilbert(1), Kim J.R. Rasmussen(2) (1) School of Civil Engineering, The University of Sydney, Australia Now, School of Engineering, Griffith University, Australia (2) School of Civil Engineering, The University of Sydney, Australia Abstract: The paper addresses the problem of determining the accidental forklift truck impact forces on steel storage racks. Based on first principles of mechanics, simple models of a loaded forklift truck and a drive-in racking structure are presented. Model masses, as well as stiffness and damping coefficients are calibrated against experimental results obtained from tests of a forklift truck and a drive-in racking structure. Comparisons between experimental results and solutions obtained from the simple mechanical models show that the simple models accurately reproduce the static and dynamic behaviours of their associated structures. Based on the drive-in rack impact test results presented in a companion paper ([1]) and the simple mechanical models for drive-in racks, actual impact forces are calculated and presented. Finally, using the impact test results and the simple mechanical models, the actual motion of the forklift truck body is calculated. This motion, being a common characteristic to all drive-in racking impacts, allows impact forces to be obtained for various pallet loads, impact elevations and rack characteristics. Thus, the paper concludes with a general method for calculating forces generated under forklift truck impact. Keywords: Steel storage rack, drive-in rack, impact force, forklift truck behaviour, drive-in rack behaviour. 1 Introduction This paper addresses the problem of determining the accidental forklift truck impact forces on steel storage racks. As presented in the companion paper ([1]), different types of forklift truck impact can occur on steel storage racks. This paper focuses on down-aisle impacts occurring on drive-in racking structures but the methodology and methods presented herein can be easily extended to any type of rack or steel structure in general. Contrary to classical “selective racks”, by storing pallets on rail beams on the first-in, last-out principle “drive-in racks” minimise floor space allocation and are often a more economical alternative solution to selective racks. To allow the forklift truck passage, drive-in racks can only be braced at the back (spine bracing) and at the top (plan bracing) leading to slender uprights in the down-aisle direction, only restrained at the bottom by the base plate assembly and at the top by the portal beam. When subjected to a forklift truck impact in the down-aisle direction, the bowing of the upright may trigger progressive failure by allowing the pallets to drop through. The literature review shows that no investigation is available for determining the accidental forces that develop between a storage rack and a forklift truck during an

impact. International racking standards only consider arbitrary impact forces, the equations for which have no scientific justification. Furthermore these standards only deal with selective racks and are not applicable to drive-in racks. The present study is motivated by the high failure rate of drive-in racks compared to other types of racks and steel structures in general. Further details on the behaviour of drive-in racks and available literature for this type of structure are given in the companion paper ([1]). Based on first principles of mechanics, the paper first develops a simple model of a loaded forklift truck. Model masses, as well as stiffness and damping coefficients are calibrated against experimental results obtained from isolated tests of an actual forklift truck. Subsequently, also based on first principles of mechanics, a simple model of a loaded drive-in rack is developed. Model masses, as well as stiffness and damping coefficients are calibrated against experimental results. Comparisons between experimental results and solutions obtained from the simple mechanical models show that the simple models accurately reproduce the static and dynamic behaviours of the forklift truck and the loaded drive-in rack. Using the result of experimental impact tests and the simple model of the drive-in rack, actual impact forces are calculated and presented. Finally, using the experimental impact test results and the two simple mechanical models, the actual motion of the forklift truck body is determined. This motion, being a common characteristic to all drive-in racking impacts, allows impact forces to be obtained for various pallet loads, impact elevations and rack characteristics. Thus, the paper concludes with a general method for calculating forces generated under forklift truck impact. 2 Forklift truck behaviour 2.1 Static and dynamic tests on a loaded forklift truck To measure the static and dynamic behaviour of a forklift truck, tests have been performed on a NICHIYU FB20 forklift truck model, 2 tons load capacity. Three different loads (300 kgs, 775 kgs and 1175 kgs) are placed sequentially on a pallet, with the centre line of the pallet located at a distance H from the centre line of the bottom connection between the mast and the forklift truck, as shown in Fig. 1. H is set to be equal to the impact elevation associated with the impact tests performed on a drive-in rack structure and presented in the companion paper ([1]). A hydraulic jack with a quick release system applies a horizontal load in the impact direction at the location of the impact point with the rack. Two LVDTs (Linear Variable Displacement Transducer) record the horizontal displacements of the pallet at the jack location (LVDT 52) and of the forklift truck mast at the jack elevation (LVDT 53), as shown in Fig. 1. The location of the LVDTs allows the bending and torsion of the pallet/mast system to be measured. In the first phase, the jack pulls statically on the pallet at a low displacement rate and the static stiffness of the forklift truck is recorded. In a second phase, the load is quickly released leaving the system free to oscillate and the dynamic response of the system is recorded at a rate of 50 Hz. Three tests are performed for each pallet load.

Figure 1: Forklift truck test set-up

The test results show that during the static phase of the test both LVDT 52 and 53 increase linearly with the load. During the dynamic phase of the test, LVDT 52 and 53 have similar displacement frequencies and proportional amplitudes, indicating that the bending and torsional responses of the mast are coupled. Detailed test results are reported in [2]. 2.2 Simple mechanical model of the forklift truck Typically, the mast of a forklift truck is attached to the forklift truck body at two distinct points. A bottom hinge corresponding to the front wheel axis allows the mast to rotate forward and backward while restraining the mast from rotating sideway. Two hydraulic jacks, referred to as “tilt hydraulic jacks” and positioned at a distance h above the bottom hinge and on each side of the mast control the tilting motion about the bottom hinge. A forklift truck has usually two wheels at the front and one or two wheels at the back linked to the body by the means of shock absorbers. Fig. 2 shows a photo of the NICHIYU forklift truck used in the experimental tests. Fig. 3 shows a simple mechanical model of the forklift truck, in which a vertical member at a horizontal distance l1 from the bottom hinge represents the mast and a horizontal member at a vertical distance H from the base of the mast represents the forks. A rotational stiffness kB representing the rotational stiffness of the bottom hinge combined with the rotational stiffness provided by the forklift truck shock absorbers restrains the mast from rotating sideway about its base. Two horizontal springs with stiffness kJ, located at a distance dJ on each side of the mast, represent the tilt hydraulic jacks and restrain the mast against torsion. Due to the nature of their connections with the mast, the two tilt hydraulic jacks are considered to be pinned at theirs ends, unable to transfer shear. The damping of the forklift truck mast is found to be a “drag force damping” type, i.e. proportional to the square of the velocity. This type of damping is found when an oscillator is immersed into a fluid and is for the forklift truck related to the action of the tilt hydraulic jacks. Being significant, this torsional damping from the tilt hydraulic jacks is considered to be the predominant source of energy absorbtion in the system and all other sources of damping are ignored. A damping coefficient CJ for each tilt hydraulic jack is considered in Fig. 3. A mass m representing the combined mass of the load, the pallet and forks is considered at the centre of gravity of the load, i.e. at a vertical distance HCoG and at a horizontal distance l1 + l3 from the bottom hinge of the mast. The pallet mass and the mass of the

forks are estimated to be 50 kgs each. A load F representing the impact load/jack load is applied on the forks at a horizontal distance l1 + l2 from the bottom hinge of the mast.

Figure 2: NICHIYU FB20 forklift truck

Figure 3: forklift truck simple model

The system shown in Fig. 3 is simplified to the statically equivalent model given in Fig. 4, in which the tilt hydraulic jacks are replaced by an equivalent single torsional spring with stiffness kT and associated damping coefficient CT.

Figure 4: Forklift truck equivalent simplified model

2.3 Equations of motion For the model presented in Fig. 4 and for small displacements, the kinetic energy KE, potential energy PE and damping energy DE (from the generalised Rayleigh dissipation function) are given as,

( )2

2311 ..21

++=••θθ llHmKE COG (1)

22

21 2

121 θθ TB kkPE += (2)

••

⋅= 2223

1 θθTCDE (3)

where θ1 and θ2 represent the bending and torsional angles respectively, as shown in Fig. 4. The equations of motion for θ1 and θ2 under external loading are obtained using the general Lagrange equation (Bangash [3]),

i

iiii

MDEPEKEKEdtd

=∂

∂+

∂∂

+∂∂

−

∂

∂••θθθθ

(4)

where Mi represents the external bending or torsional moment. Eq. (4) applied to θ1 and θ2 gives,

( ) HFllHmkHm COGBCOG ....... 231112 =+++

••••θθθ (5)

( ) ( ) ( )2113122222

31 ......... llFllHmCkllm COGTT +=+++++••••••θθθθθ (6)

2.4 Model calibration 2.4.1 Bending and torsional stiffness kB and kT The bending stiffness kB and torsional stiffness kT of the forklift truck mast are calculated from the static test results as, HFkM BB ⋅=⋅= 1θ (7) ( )212 llFkM TT +⋅=⋅= θ (8) where MB and MT are the bending and torsional moments induced by the jack force F respectively. θ1 and θ2 represent the bending and torsional angles respectively, as shown in Fig. 4. For small displacements, θ1 and θ2 are given by,

( )12531 .1 ldH

θθ −= (9)

2

53522 l

dd −=θ (10)

where d52 and d53 are the recorded displacements of LVDTs 52 and 53 respectively. The stiffness kB and kT are hence calculated combining Eqs. (7) to (10) as,

2

152

2

153

2

1

.

lld

lld

HFkB

−

+

= (11)

( )5352

221 .dd

lllFkT −+

= (12)

Table 1 gives the values of kB and kT found for each experimental test using a linear interpolation during the static phase and the values of H, l1 and l2 given in Table 2. It is observed from Table 1 that while the bending rotational stiffness kB is essentially constant with increasing pallet load, the torsional stiffness kT increases with the pallet load. The increase in stiffness kT is related to the increase in oil pressure in the tilt hydraulic jacks required to prevent the mast from tilting forward when increasing the pallet load. The increase in oil pressure increases the stiffness kJ and hence the stiffness kT. In view of the results shown in Table 1, throughout this paper kB is considered constant for all pallet loads and equal to its mean value 873418 kN.mm/rad. kT is considered to vary with the pallet load and linear interpolation is applied to the data shown in Table 1 to obtain kT for pallet loads between 300 kg and 1175 kg. For pallet load less than 300

kgs or greater than 1175 kgs, kT is taken as 88590 kN.mm/rad and 148334 kN.mm/rad respectively. 2.4.2 Damping coefficient The damping coefficient CT is calculated against experimental test results by numerically solving Eqs. of motion (5) and (6) using the commercial software FlexPDE [4]. The quick release system being not strictly perfect, the applied load F was found to decrease linearly from its initial value to zero between 0.16 and 0.26 sec. The decreasing rate of F is considered for each test when solving Eqs. (5) and (6) numerically. CT is found by best matching the numerical results to the experimental test results. The obtained values of CT are given in Table 3. It is observed from Table 3 that the damping coefficient CT increases with the pallet load which is probably related to the hydraulic pressure in the tilt jacks increasing with the pallet load. As for kT, CT can be linearly interpolated in Table 3 for different pallet loads. 2.5 Validation of the forklift truck model Ignoring the damping of the underdamped system when calculating its natural angular frequencies, the natural frequencies ωi of the system shown in Eqs. (5) and (6) are evaluated using the determinant method as,

( )( ) ( )

0.....

.....2

312

312

31222

=++−+−+−+−

TiCOGi

COGiBCOGi

kllmllHmllHmωkHmω

ωω (13)

Eq. (13) allows a unique solution given by,

( )( )BTCOG

TB

kllkHmkk

...

231

2 ++=ω (14)

Table 4 compares the natural frequencies calculated using a Fourier Transform of the dynamic experimental tests with the natural frequencies calculated using Eq. (14). In Eq. (14), the values of kB and kT found in Table 1 are used with the distances (l1, l3, HCoG) given in Table 2, in which HCoG is the average value for the 3 different loads. Table 4 shows an excellent agreement between the experimental test results and solution obtained from the simple mechanical model introduced in Fig. 4, thus validating the simple mechanical model of the forklift truck. 3 Structural behaviour of drive-in rack 3.1 Static and dynamic tests on drive-in racks Static and forklift truck impact tests on a drive-in rack structure loaded with two different pallet loading configurations (namely “Impact BC” and “Impact CD”, see [1] for details) have been performed using a hydraulic jack and the forklift truck analysed in Section 2 respectively. In “Impact BC”, the pallets are not loaded in the vicinity of the

impacted upright allowing this upright to freely deform under impact. In “Impact CD”, the pallets are loaded in the vicinity of the impacted upright allowing the investigation of the restraining effect of the pallets on the upright deformation. During the static tests, a hydraulic jack pulls on the impacted upright in the down-aisle direction at the impact elevation, while during the impact tests, the forklift truck impacts the rack in the down-aisle direction with its load raised at the impact elevation. Displacements of the impacted upright and overall rack are recorded in the down-aisle direction. The complete test results are presented and detailed in the companion paper. 3.2 Simple mechanical model for drive-in racks When subjected to an impact force, a drive-in racking structure resists the impact by an overall displacement of the structure and by bending of the impacted upright. The stiffness ko associated with the overall displacement of the rack and the stiffness ku associated with the bending of the impacted upright at the impact point were determined from the previously mentioned static experimental tests. A simple mechanical model of a drive-in racking system is given in Fig. 5 where mo and mu represent the associated masses of the overall rack displacement and the impacted upright respectively. Co represents the damping coefficient of the overall rack and Fu represents the damping of the impacted upright in form of a friction force. While the overall damping of the rack may be assumed to be linear due to classical energy loss in the system, the damping associated with the impacted upright is non-linear and is generated by the friction between the pallets and the rail beams. In Fig. 5, Fimp represents the impact force on the rack, xF represents the displacement of mass mu and xo represents the displacement of mass mo.

Figure 5: Rack simple mechanical model with frictional damping

In order to simplify the previous mechanical model, the frictional damper of the impacted upright will be replaced by a linear damper without significant loss of accuracy as shown in [2]. The new simple mechanical model is shown in Fig. 6 where Cu is the linear damping coefficient of the impacted upright.

Figure 6: Rack simple mechanical model

3.3 Equations of motion The equations of motion for xF and xo of the system presented in Fig. 6 are,

( ) impoFuoFuFu FxxkxxCxm =−⋅+

−⋅+⋅••••

(15)

( ) 0=−⋅−

−⋅−⋅+⋅+⋅•••••

oFuoFuoooooo xxkxxCxkxCxm (16)

3.4 Model calibration The values of ku, ko, mo, mu, Co and Cu are obtained from the experiments detailed in [2]. The values of ku and ko are calculated from static tests performed on the drive-in rack structure and reported in Table 5. mo and Co are obtained from the impact test results using the recorded free oscillation of the overall rack displacement xo after impact. mo is calculated using the natural frequency of the overall rack in Eq. (17), while Co is obtained from the logarithmic decrement given in Eq. (18) over one period To. Calculated values for mo and Co are reported in Table 5.

2

2

⋅=πo

ooTkm (17)

( )

( )

+

⋅=oo

o

o

oo Tt at alexperimentx

t at alexperimentxTmC log

2 (18)

Cu is obtained using Eq. (16) and the values of ko, mo and Co calculated previously by averaging the values of Cu calculated for each experimental recording step Δt over the first phase of the impact tests, in which the overall rack essentially stays stationary while the impacted upright bends. mu cannot satisfactory be obtained from previous equations and has to be estimated. In “Impact BC” configuration only the impacted upright, part of the adjacent frame bracing and part of the adjacent rail beams are associated with the relative displacement xF - xo. This leads to a light mass mu, estimated to be about 50 kgs. In “Impact CD” configuration part of the adjacent pallets are also associated with the relative displacement of xF - xo. This leads to a heavier mass mu, estimated to be about 1400 kgs. It is observed that the average damping ratio ζo of the overall rack defined by Eq. (19), is equal to 0.07% which is close to the typical value of damping ratio of 0.1% to 0.9% for steel structures (Bangash [3]).

oo

oo km

C2

=ς (19)

3.5 Validation of the rack model In order to validate the simple mechanical model introduced in Fig. 6, xo obtained from the equation of motion (16) is compared to experimental test results by using xF from experimental tests as input data. The equation is solved by using FlexPDE [4] and the mass, stiffness and damping values given in Table 5. Fig. 7 compares xo for a typical experimental test and the corresponding xo calculated from FlexPDE [4]. The results show excellent agreement between the two values of xo both during and after the impact, thus validating the simple mechanical model of the rack. Comparisons between the two values of xo for all impact tests are reported in [2], all comparisons show excellent agreements.

Figure 7: Comparison between xo from numerical methods and xo for Test 207 -

“Impact BC” configuration 4 Impact force The impact force Fimp developed between the forklift truck and the drive-in rack during the experimental impact tests introduced in Section 3 and detailed in the companion paper ([1]) is now calculated by solving Eq. (15) using FlexPDE in which values of xF and xo obtained from experimental test are introduced as input data. Fig. 8 and Fig. 9 show the impact force Fimp for 15 tests for “Impact BC” configuration and 15 tests for “Impact CD” configuration, calculated using the values of mu, Cu and ku given in Table 5. While performing the impact tests, it was observed that the pallet under the 300 kgs load has a tendency to slide on the forks leading to two distinct sequences of impact. This phenomenon is detailed in [5], and is observed in Fig. 8 and Fig. 9 where the impact load increases to a plateau corresponding to the pallet sliding on the forks. The sliding lasts about 0.3 sec, then the impact force increases again until the forklift truck loses contact with the rack.

Figure 8: Impact forces for “Impact BC” configuration

Figure 9: Impact forces for “Impact CD” configuration

If the pallet sliding effect is omitted, it is observed from Fig. 8 and Fig. 9 that the impact load is rather consistent for each impact configuration and reaches a maximum between 0.1 sec and 0.12 sec for “Impact BC” configuration and between 0.08 sec and 0.1 sec for “Impact CD” configuration. 5 Combining the models for the rack and forklift truck In order to combine the mechanical model of the forklift truck with any rack model representing different rack configurations, pallet loads and impact elevations, a common characteristic to all impacts on drive-in racking structures has to be found. Typically the impact of a forklift truck on a drive-in storage rack is induced by the rotation of the forklift truck body about its front wheel axis as shown in Fig. 10. The rotation of the forklift truck body will essentially remain the same for all impacts on drive-in racking structures and can be taken as a common input for combined forklift truck and rack model. Hence, impact forces and displacement at the impact point can be calculated from the combined model.

Figure 10: Forklift impact on drive-in racking structure

Typically, the front wheel axis of a forklift truck corresponds to the bottom hinge connection of the mast with the forklift truck body. Fig. 11 shows the simple mechanical model of the forklift truck introduced in Fig. 4 rotated about the front wheel axis by an angle α. The rotation θ2 is the additional rotation produced by the extension and compression of the tilt jacks. For small displacements, the kinetic energy KE of the forklift truck in Eq. (1) is rewritten as,

( )2

231121

+⋅++⋅=•••θαθ llHmKE COG (20)

Figure 11: Rotating motion of the forklift truck mechanical model

The potential energy PE and damping energy DE in Eqs. (2) and (3) respectively are unchanged. The equations of motion for α, θ1 and θ2 under external loading are obtained using the Lagrange equation given in Eq. (4) as,

( ) ( ) HFllHmllHmkHm impCOGCOGBCOG .......... 31231112 −=+++++

••••••αθθθ (21)

( ) ( ) ( ) ( )212

3113122222

31 ........... llFllmllHmCkllm impCOGTT +−=+++++++••••••••αθθθθθ (22)

Using the geometrical relationship between xF, θ1 and θ2, ( )( )αθθ +++= 2211 .. llHxF (23) the above equations of motion can be rewritten for θ2 and α as,

( ) ( ) ( )

( ) ( ) ( ) HFllHkll

HHllHm

xHkx

HHmll

Hkll

HHllHm

impBCOG

COG

FB

FCOGBCOG

COG

...

..

212131

2

22122131

−=⋅+−⋅

+−++

⋅+⋅⋅+⋅+−⋅

+−+

••

••••

αα

θθ (24)

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )21213131

312222213131

.

...

llFllH

Hllllm

xllH

HmCkllH

Hllllm

impCOG

FCOG

TTCOG

+−=⋅

+−++⋅+

⋅+⋅⋅+++⋅

+−++⋅

••

••••••

α

θθθθ(25)

α is obtained by solving Eqs. (24) and (25) using the software FlexPDE [4] with xF taken from experimental test results. The impact force Fimp is calculated as per Section 4 and the values given in Table 1 to Table 3. Involving simpler equations, it is worth noting that convergence in FlexPDE [4] is more easily achieved by solving Eqs. (24) and (25) for α+θ2 and θ2 instead of α and θ2. α is then retrieved by subtracting θ2 from α+θ2. Fig. 12 and Fig. 13 plot α calculated for all tests shown in Fig. 8 and Fig. 9 respectively. α is only plotted in the domain of validity of Eqs. (24) and (25), i.e. when there is contact between the pallet and the rack, which is considered to be until the impact force reaches zero in Fig. 8 and Fig. 9. If the sliding of the pallet is omitted, results show that α is consistent for all tests and reaches its maximum value at about 0.15 sec. The maximum bay opening occurs at this point as detailed in the companion paper ([1]). It is observed that when the maximum impact load is reached between 0.08 sec and 0.12 sec in Fig. 8 and Fig. 9, α is still increasing. The maximum average value of α at 0.15 sec is equal to 0.023 rad. α is approximated as a multi-linear curve by averaging the results shown in Fig. 12 and Fig. 13 over the first critical 0.15 sec (see Fig. 14), the multi-linear approximation can be used as input in Finite Element models or in solving the equations of motion (15), (16), (24) and (25) to obtain the impact force and rack displacement under impact. The analysis proceeds through the steps:

1) Determine the forklift characteristics (kT, kB, CT), the rack characteristics (mu, Cu, ku, mo, Co and ko) using FE for instance.

2) Determine the impact characteristics (H, HCoG, l1, l2, l3 and m). 3) Obtain Fimp by solving the four equations of motion (15), (16), (24) and (25) in

xF, xo, Fimp and θ2 using α as input.

Figure 12: Forklift truck body rotation for “Impact BC” configuration

Figure 13: Forklift truck body rotation for “Impact CD” configuration

Figure 14: Multi-linear approximation of α

6 Conclusions Based on first principles of mechanics, this paper proposes simple models for a loaded forklift truck impacting with a loaded steel drive-in rack. Model masses, as well as stiffness and damping coefficients are calibrated against experimental results obtained from tests of a forklift truck and a drive-in rack structure. The simple models are found to accurately reproduce the static and dynamic behaviour of the forklift truck and drive-in rack. The impact forces developed between the forklift truck and the drive-in rack are calculated using the simple rack model and impact tests on a drive-in rack structure presented in a companion paper ([1]). Finally, combining the two simple mechanical models and using the impact test results, the actual forklift truck body rotation during impact is calculated. This motion, assumed to be a common characteristic to all drive-in racking impacts, allows impact forces to be obtained for various pallet loads, impact elevations and rack characteristics. Thus, the paper provides a general method for calculating forces generated under forklift truck impact. 7 References [1] Gilbert BP, Rasmussen KJR. Impact tests and parametric impact studies on drive-in steel storage racks. Submitted to Engineering Structures. [2] Gilbert BP, Rasmussen KJR. Determination of accidental forklift truck impact forces on drive-in steel rack structures: School of Civil Engineering, The University of Sydney, Australia; 2009. Research Report R902. [3] Bangash MYH. Impact and explosion, analysis and design. Boca Raton, Florida, USA: CRC Press Inc. 1993. [4] FlexPDE. FlexPDE 5.1.0s, User guide: PDE Solutions Inc. 2008. [5] Gilbert BP, Rasmussen KJR, Zhang H. Impact tests and parametric impact studies on drive-in steel storage racks: School of Civil Engineering, The University of Sydney, Australia; 2009. Research Report R903.

Load = 300 kg Load = 775 kg Load = 1175 kg kB

(kN.mm/rad) kT

(kN.mm/rad) kB

(kN.mm/rad) kT

(kN.mm/rad) kB

(kN.mm/rad) kT

(kN.mm/rad) Test 1 849150 84251 783666 126992 875916 138953 Test 2 923214 94981 853181 144406 855504 158301 Test 3 973469 86538 868941 137370 877724 147748 Average 915278 88590 835263 136256 869715 148334

Table 1: Static test results stiffness

H (mm) HCoG (mm) l1 (mm) l2 (mm) l3 (mm) dW (mm) 2425 2648 200 1230 730 250

Table 2: Dimension values for tests

Load = 300 kg Load = 775 kg Load = 1175 kg CT (kN.mm.s²/rad²) CT (kN.mm.s²/rad²) CT (kN.mm.s²/rad²) Test 1 330000 800000 1200000 Test 2 270000 1000000 1300000 Test 3 290000 250000 1300000 Average 296667 683333 1266667

Table 3: Calculated damping coefficients CT Load = 300 kg Load = 775 kg Load = 1175 kg f (hz) f (hz) f (hz) Test 1 1.74 1.42 1.27 Test 2 1.73 1.44 1.28 Test 3 1.75 1.35 1.29 Average 1.74 1.40 1.28 Eq. (14) 1.91 1.40 1.20 Difference (%) 8.73 0.09 7.04

Table 4: Natural frequency of forklift truck

ko (kN/mm) mo (kg) Co (kN/(mm/s)) ku (kN/mm) mu (kg) Cu (kN/(mm/s)) Impact BC 0.762 15051 0.00425 0.300 50 0.0111 Impact CD 0.694 14378 0.00492 1.124 1400 0.0979

Table 5: Drive-in rack simple model characteristics