December 2018 - We have all have dropped our smartphones. To reduce the risk of cracking or shattering the screen, we put the phone within a shock-absorbing case. This simple approach reduces the stiffness and impact forces that correspond with the stresses of the phone when dropped. The same is true for dropping material onto a material load table.

It is not an easy task to maneuver material that spans over 12 meters in length and weighs a few tons into a sawing system. Forklifts or gantry cranes are typically employed to  move stock onto a loading table or transfer mechanism. The danger plant managers face is the potential of an inexperienced crane or lift truck operator accidentally dropping a load and damaging both the material and the load table. This uncontrollable interaction may also put the rest of the material handling system at risk for severe abuse. An error-prevention system is needed to guarantee high overall operations effectiveness.

FEA software analysis of heavy load drop contact, reaction forces, and stress as a function of time.

Material load tables and transfer mechanisms often are over-engineered with excessive material in an attempt to prevent damage from dropped loads. Although the strength of the load table may be improved as a result, adding extra support materials can increase the cost—a cost that gets passed onto the customer. A more economical  approach when designing material handling systems is to use advanced engineering practices.

Modern CAD technology, such as SolidWorks, provides powerful tools to calculate and analyze mechanical structures. These programs make it easier to add and test materials that fortify structures in CAD software. The advantage of working in the virtual world is that you can experiment with a variety of materials without adding costs to the prototyping process.

Within these CAD programs, features such as finite element analysis (FEA), can simulate the effects of shock load even before the prototype is produced. This allows for early modifications in the design process at minimal cost, while ensuring the best strength-to-weight ratios.

Theory

The principles of strain energy and conservation of energy help to illustrate that the potential energy before the impact, the kinetic energy right at the impact and the stored elastic energy in a structure (spring) are equal. In the following formula,  is the maximum displacement of the spring, c is the spring rate, m is the falling mass,  is the acceleration of gravity and h is the starting height:

The formula for introducing displacement under a static loading condition  looks like:

The same formula can be written in a different form when applying Hooke’s Law—Fmax is the maximum contact force and  is the static force:

This confirms that a quasi-static calculation with an amplification factor (impulse factor) is possible and that conducting dynamic simulations as a first approach is not necessary. This formula can also be applied to a static displacement calculation of a beam with the use of the Euler-Bernoulli beam theory.

Let’s assume a 100-kilogram mass is hitting a support beam and the contact force and resulting stress needs to be known:

E (Young’s modulus) is 210 GPa, h is 25 mm, I is 1 m, and the beam cross section is a 50 mm x 25 mm rectangle.

Moment of inertia for a rectangular profile is:

The static displacement is:

Bending stress due to static load: M is the maximum bending moment, and W is the moment of resistance:

The impact factor is as follows:

This demonstrates that the impact force from a 25 mm height will be seven times higher while the static load of the mass is 981 N. The bending stress will rise in the same fashion.

The formula for the impact factor shows that an increase in stiffness reduces the static displacement. This increases the impact factor and impact force. The result shows the paradigm that is generally true from machine tools: the stiffer the better; however, this is not necessarily true when dealing with shock loads.

Durability verification

The Transient Nonlinear Dynamic Analysis in FEA software verifies the product in an early stage and conducts damage analysis of it. This provides insight on the contact, reaction forces and the stress as a function of time. The impact takes place in a matter of milliseconds, making the adequate discretization of space and time crucial. The boundary condition represents the interface to the floor. The initial condition is the impact velocity —with  being the gravity constant and the starting height from where a steel billet is dropped.

An example of severe material load table damage experienced from a heavy material drop.

With today’s technology, there are improved ways to design material load tables so they are not overloaded with costs. Generally, designers have two choices:

1. Over-engineer the structure to withstand any heavy shock load, increasing the cost of the load table for the customer.

2. Through the use of FEA software, design the structure to allow elastic flexing while avoiding the effects of plastic deformation. MM

Christian Mayrhofer is the Manager R&D at Advanced Machine & Engineering/AMSAW.