Crane forks are widespread tools used to lift several objects of different weight and shape. These forks are used indoor with overhead travelling crane and also outdoor with every sort of crane.
The fork under investigation is a medium size one. It is approximately 2m high and 0.7m wide. The two teeth are 0.9m long. The height and width data are not fixed because the distance of the teeth are adjustable with a screw mechanism (the “lever” in the top-centre of the real fork highlighted in red,fig.1) in order to be flexible for different shapes and dimensions of load. However, the fork has been studied in one middle range configuration, because the small variations in height and width are thought not to affect considerably the results. There is a third tooth that can be inserted at the centre, between the others, but it is useful only to help the stability of the load and it is not designed to support weight, so it is not considered in this analysis. It is reported that the maximum weight liftable is 1500 kg and the fork mass is 110 kg.
There are two parallel springs, but from now only 1 spring with the total stiffnes is considered. The role of this component in the stability of the load is investigated.
In this project, the fork is thought to be sustained by a cable and to be moved by a overhead travelling crane: the vertical traslation is provided by a cable-pulley sistem, while the horizontal is due to the sliding of the previous system on a beam anchored on the walls.
The objectives of this projects are:
- creating a working model that allows to simulate the behaviour of the fork/load system and extract useful data as maximum angular oscillation and the reaction forces on the joints in different configurations (e.g. vertical or horizontal translations at different velocities, with different loads). Understanding the angular position of the load is crucial to determine whether it stays in its position during the movimentation, while obtaining the forces is important in order to perform a better mechanical design. The goal is the fork weight reduction: with a limited weight liftable by the crane the less the fork is heavy, the more load can be lifted.
- investigating the role of the springs and the changes that occurs varying their stiffness. The goal is defining the optimal stiffness that reduces oscillations and reaction forces.
The modelling problem
The real fork is composed by 7 rigid body (plus the spring). The central part (fig.1) is made by 2 parts with the lower one sliding on the upper one thanks to the screw mechanism as said in the introduction. However, as already mentioned, the fork is studied in a fixed configuration, so the central part is designed with one body and the number of bodies becomes 6. The several bodies have been manually measured, then designed thanks to a 3D software (Solidworks) and later imported in Adams. The six bodies are shown in fig.2 and the joints between them are exposed.
These are the joints used for the fork:
- Revolute between lateral part 1 and central part
- Revolute between lateral part 2 and central part
- Spherical between lateral part 1 and diagonal 1
- Spherical between lateral part 2 and diagonal 2
- Cylindrical between central part and diagonal 1
- Cylindrical between central part and diagonal 2
- Revolute between upper part and central part
- InPlane between central part and ground
It is important to say that the first 6 joints may not be created for the fixed configuration of this project. This is due to the fact that all the bodies, except the upper part, form a single body without relative degrees of freedom. However, using all these bodies and this combination of joints (to avoid redundant contraints) permits to obtain the forces that the parts exchange each other and these forces could be used to design better each body.
The InPlane joint is necessary in order to avoid fork rotations when the initial equilibrium is researched in the first part of simulations.
The spring links the upper and the central part: it is connected to the 2 bodies thanks to the prominences dedicated, as clearly visible in fig.3.
The 2 springs are equal and parallel, so the total stiffness is the stiffness of one spring multiplied by 2.
The springs are helical and they are made by N=30 coils. The steel wire has a 8mm diameter d and the coil has a 36mm diameter D. G has been assumed 81000 MPa. The stiffness of a spring can be calculated with the following model :
The resultant stiffness of a spring is 29.63 N/mm. In Adams it has been created only 1 spring and 60 N/mm stiffnes is assumed.
The load is represented by a generic box on a pallet. All the mass is assigned to the box. The weight and cm position can be manually changed to analyse different weight from 0 to 1500 kg and several cm configurations. Here two fixed joints are applied to link the pallet to the fork and the box to the pallet.
The overhead travelling crane is composed by a beam where the support of the pulley (pulley guide) and the support of a end of the cable (cable guide) slide.
Here the joints that has been used are:
- fixed between the beam and the ground
- translational between the beam and the pulley guide
- translational between the beam the and cable guide
The sliding of the supports is due to 2 translational joint motions assigned to the 2 translational joints. This double-support solution has been chosen to make as simple as possible the vertical and horizontal displacement. This is due to the fact that the cable help section of the software is minimal and an alternative to the winding around the pulley (as a real winch works) was necessary to be found. The pure horizontal displacement of the fork is performed by a synchronized traslation of the supports, while in a pure vertical displacement the pulley guide stays in its initial position and only the cable guide moves.
The cable and the pulley have been created thanks to the machinery/cable section.
The pulley is attached to the pulley guide thanks to a revolute joint and it is made by steel. The dimensions of the pulley are shown in fig.8 and fig.9.
The cable created was a simplified version in which its mass, inertia, transversal and torsional stiffness are neglected. The longitudinal stiffness is due to the density and diameter given as input (steel and 10 mm respectively). The first end of the cable is attached to the cable guide (as already shown in fig.7) and the second end is attached to an hook that sustains the fork (fig.10). The hook is linked to the upper part of the fork by a revolute joint.
After the illlustration of every single part it is time for an overview. The system created has 9 degrees of freedom:
- 5: the triple pendolum composed by hook, fork’s upper part and fork’s lower parts (central part, laterals, diagonals, load) connected by revolute joints has 3 rotational degrees of freedom, plus 2 from the displacement on the YZ plane (fig.12) of this pendulum;
- 3 from the cable (longitudial and lateral displacement and rotation);
- 1 from the rotation of the pulley.
Initially the base of the fork (where it touches the ground) is 6m suspended from the beam. This value has been chosen because approximately 6-8m are typical numbers for the height of a factory roof (fig.11).
Simulations and analysis of results
1. Design of a working model
As written in the objectives, the first simulatons have been designed in order to create a working model that allows to simulate the behaviour of the fork/load system and extract useful data as maximum angular oscillation of the load and the reaction forces on the joints.
The start of a crane or of a winch is never smooth and this may cause vibrations and oscillations. Therefore, displacement step functions have been used as functions for the translational joint motions of the cable and pulley supports and the fork is then let freely oscillate: this will be useful later to obtain the natural frequencies. This is the case chosen for this project, but it is possible to change easily the step functions to other functions to study other scenarios.
An equilibrium analysis is the starting point of every simulation because at the beginning the load/fork is supposed to be suspended and in equilibrium.
Horizontal displacement, base 6m suspended, 1500kg load.
The simulation is done with 1500kg because it is the maximum load liftable by the fork, so it is the most demanding and interesting scenario in order to obtain reaction forces between the bodies. However, to get results for different load and cm positions (now the center of mass is in the center of gravity), it is enough to change manually the weight and cm position of the box and re-run the simulation.
In this case the pulley guide and cable guide move synchronized. So, the step function is the same for both (time in s, displacement in mm):
Horizontal displacement, base 4m suspended, 1500kg load.
In this simulation, at first the cable guide translates of 2m to lift the fork. The movement is slow compared to the step function employed for the horizontal displacement beacuse the aim of this first motion is only to reach an higher point of equilibrium for the fork.
Motion function for pulley guide: step(time,10,0,10.5,1000)
Motion function for cable guide: step(time,1,0,8,2000) + step(time,10,0,10.5,1000)
Vertical displacement, 1500kg load.
In this pure vertical displacement the pulley guide stays in its initial position and only the cable guide moves. The motion applied to the cable support is: step(time,1,0,3,3000)
Force and oscillation
Now it is possible to extrapolate all the reaction forces between the bodies. As an example it is reported the Y (positive from down to up in the videos) and Z (positive from right to left) forces that the upper part acts on the central part.
2. Investigation on the role of the spring
In the previous simulations, a spring of 60 N/mm connects the lower parts and the upper part of the fork. The value of the stiffness has been changed in a stiffer one (10000 N/mm) and in a “softer” one (1 N/mm) to see what changes and to understand better how the springs collaborate.
Talking about the horizontal displacement, the angular oscillation and the acceleration of the cm, that are related to the stability of the load, are compared between the different stiffness.
As visible in the previous figures, the solution with a lower stiffness is better in terms of magnitude of the acceleration, while in terms of angular displacent there are not clear differences: K=1 oscillates around a positive average and K=60 and K=10000 oscillate around a negative average, but no solution is clearly the closest to 0. Moreover, the amplitude is approximately the same.
Talking about the centre of mass acceleration, it is clearly visible that lower stiffness is better. What is more, the previous statement is true for other measures like the magnitude of the reaction force exchanged by the load and the fork and by the upper part and the central part (the graphs are not reported, but it is verifiable in the simulatons).
At this point it is interesting to talk about the natural frequencies of the system with different stiffness. They are obtained performing a FFT of the angular oscillation to get the power sprectrum density (PSD). To verify, the same results are achievable performing a linearization around the equilibrium. Stiffness equal to 60 N/mm is taken as example for the following images.
There are other natural frequencies at an higher frequency, but the power associated is very low.
Increasing the stiffness, the first two natural frequencies come closer, the opposite happens reducing the stiffness. This could be one of the reasons why reducing the stiffness is better in the terms previously explained.
The first natural frequency can be analitically verified: the cable/fork system could be thought as a 1DOF simple pendolum and its natural frequency can be obtained as following:
The centre of the mass of the load is sospended approximately 5.8 m from the pulley, so the result is 0.20 Hz, that is similar to the FFT result. Moreover, this is a way to control the general correctness of the model.
The previous results are achieved with the 6m-height analysis, but all considerations are the same for 4 metres.
Vertical displacement, 1500kg load.
For the vertical displacement the magnitude of the reaction forces between the load and the fork and between the upper part and the central part are compared.
Also here there is not clear differences between the original stiffness and a very low one, while a large one makes the situation worser.
To sum up, the less is stiffness of the spring, the better. Taking into account the previous considerations, the spring could be even removed.
So, what is the role of the springs? Why do the manifacturers spend money to install a spring on the crane forks?
After some web researches it has been found that online catalogues call the forks with the spring “self adjustable crane forks” in contrast to “manual balancing crane forks” . A self adjustable crane fork is the fork presented in this project, while a manual balancing crane forks is similar to the one in fig.21.The load is kept horizontal changing manually the position of the hook based on the position of load cm. A self balancing fork does not need manually action because the spring reacts “in the right way” to keep the load horizontal. Fig.22 and fig.23 show how the original stiffness maintain in a good balance the load even if the cm (the red point) is at the two extremities of the teeth, while 1 and 10000 are good only at one extremities, but bad at the other one.
The sentence “the spring reacts in the right way” meaning can be understood looking at fig.24: to balance the load in the right-figure configuration there should be an higher force given by the spring than in the left figure. As shown, the spring in the right is more deformed than in the left, consequently the force is bigger as expected.
The choice by the manufacturer of a stiffness of 60 N/mm originates probably from its experience, through an optimization over years. In the range from 0 to 1500 kg and with this teeth lenght this is best compromise to ensure the horizontal position for every combination of weight/cm position of the load.
The first objective to create a working model has been satisfied. The joints applied, but most of all the double-support (cable guide and pulley guide) solution make possibile to obtain the reaction forces between the bodies for every type of displacement, both horizontal and vertical.
The second part has been more tricky, because the spring is ineffective on what it was expected. There are not remarkable benefits when the center of mass of the load is fixed. The main role of the spring is to keep as horizontal as possible the load with different loads that means different cm positions. This is why this type of forks are called “self adjustable crane forks” in contrast to manual balancing crane forks where the user has to find manually the correct position of the hook.
 Domenico Gentile, “Principi e Metodologie delle Costruzioni di Macchine.”, Slide UniCas, 2011/2012.
 Useful video for cable creation: www.youtube.com/watch?v=eH3Ni20JwJc&t=350s