Just as the weight of the product can be measured using a scale, the product ruggedness can be measured with dynamic inputs. A shock machine is used to generate a damage boundary curve, and a vibration system is used to map out the natural frequencies of a product.
Shock – Damage Boundary
The damage boundary theory is a testing protocol which determines, in an engineering sense, which shock inputs will cause damage to a product and which will not. There are two parts of a shock which can cause damage, the acceleration level and the velocity change. The velocity change, or the area under the acceleration time history of the shock, can be thought of as the energy contained in a shock. The higher the velocity change the higher the energy content. There is a minimum velocity change which must be achieved before damage to the product can occur. This level is called the critical velocity change. Below the critical velocity change, no damage occurs regardless of the input acceleration level. In essence, there is not enough energy in this region of the damage boundary to cause harm to the product. Exceeding the critical velocity change, however, does not necessarily imply that damage results. If the change in velocity occurs in a manner which administers acceptable doses of acceleration to the product, the velocity change can be very large without causing damage. However, if the critical velocity and the critical acceleration are both exceeded, damage occurs.
A typical damage boundary curve can be found in Figure 6. It is a plot of the damage causing parameters of a shock pulse and defines the region where certain combinations of acceleration and velocity change will cause damage. If the combination of acceleration and velocity change fall in the clear band outside the damage region, no damage occurs. For example, if the velocity change of the input is below that of the product’s critical velocity change, then the acceleration level of the input can be in the 100s G’s, 1000s G’s, 10,000s G’s, or even infinite without causing damage. In practical terms, to achieve these very high accelerations means that the duration of the shock must be very short. If we think of it in a graphical sense, we have a certain amount of area or velocity change which we can re-arrange to produce a shock pulse. If we decide to make the pulse very tall, i.e. very high in acceleration, then because of the limited amount of area that the pulse can contain it must also be very short in duration. In fact, the duration is so short that the product cannot respond the acceleration level of the event, only the energy input. Because the input velocity change did not exceeded the critical velocity change of the product, no damage has occurred.
When the velocity change of the input exceeds the critical velocity change of the product, however, the only way to avoid damage is to limit the input acceleration to a level below that of the product’s critical acceleration. This is usually one of the functions that a cushioned package performs. It translates the high acceleration events experienced on the outside of the container to lower acceleration events experienced inside at the unit.
To determine a damage boundary requires running two sets of tests. A step velocity test is used to determine the product’s critical velocity change and a step acceleration test is used to determine the critical acceleration.
Step Velocity Test
To run the step velocity test, the unit is fixtured to the table of the shock machine and subjected to a short duration pulse with a relatively low velocity change content. It is important that the duration of the event be so short that the unit cannot respond to the acceleration level of the shock, only the velocity change. Most commercial machines intended for use in this type of testing produce a half sine pulse 2-3 msec in duration. Following the input, the test unit is examined for functional, physical and aesthetic damage. If none has occurred, it is given an input with a slightly larger velocity change component, but with roughly the same duration. This process is repeated until damage to the unit has occurred. The last non-failure input defines the critical velocity change for the unit in the orientation in which it was tested.
The critical velocity change can be equated to an equivalent free fall drop range (EFFDR). These numbers describe how far the unpackaged unit can fall onto a rigid surface before damage will occur. The process for calculating the EFFDR is demonstrated in figure 7. In essence, it describes the ranges of heights that the bare product may fall before damage will occur, based upon the type of surface it impacts. Undoubtedly, if you drop the unit onto something soft, you can drop it farther without damage than you could if you dropped onto something hard. This is why a range of heights is defined, rather than one specific height above which damage will occur and below which damage will not occur.
Step Acceleration Test
For the step acceleration test, a new unit is fixtured to the table of the shock machine and given a low acceleration square wave pulse with a relatively large velocity change content. The velocity change of the input must be at least 1.57 times the critical velocity change defined in the step velocity test. This will ensure that the test is conducted past the knee of the damage region. This knee occurs where the product shifts from being velocity sensitive to being acceleration sensitive. Following the input, the test unit is examined for damage and if none has occurred the unit is subjected to a slightly higher acceleration level with roughly the same velocity change. This process is continued until damage to the unit has occurred. The last non-failure input defines the critical acceleration for the unit in the orientation in which it was tested.
The designer now has all the information necessary to set the shock protection requirements of his product. The critical velocity change shows the designer the maximum drop height the bare product can be subjected to before damage will occur. If that drop height is less than the design drop height specified in STEP 1, a package or interface material is necessary. If a package system is necessary, it must transmit less than the critical acceleration to the unit, when dropped from the design drop height.
In a rigorous testing program, damage boundary curves are generated for each orientation of the unit. To do this requires damaging 2 units per orientation, one for the step velocity test and one for the step acceleration test. Rarely are this many units available for destructive testing in the prototype stage of a product’s life, the most beneficial time to do this type of work. Compromises are often made to limit the number of units which must be damaged. In certain situations it is possible to perform the testing only along the three orthogonal axes. In addition, the unit can often be repaired between tests, so that one unit and a few spare parts may be used to perform all of the testing.
It should be noted that the square wave used to determine the critical acceleration provides conservative results. In general, a square wave of a given acceleration and duration is the most severe waveform possible. It contains not only the fundamental frequency associated with the pulse duration, but also all the higher harmonics associated with the quick rise and decay of the waveform. What this means is that square wave can cause damage, at a given acceleration level and velocity change, while other waveforms do not. Figure 8 displays examples of the damage regions which various waveforms may produce. As can be observed form this plot, the square wave encompasses all damage regions produced by other waveforms. This is useful to the package designer, because in the early stages of development it is not known what shape waveform the package will transmit to the product. By using a square wave for this test, we gain confidence in our final package design. We know that if the unit can pass a square wave of a given velocity change and acceleration level, we can pass any waveform that our package may produce of the same velocity change and acceleration level.
In addition to the engineering reasons, there are also the economic and practical reasons for using the square wave to determine the critical acceleration. As can be noted from figure 8, the square wave produces a flat horizontal line to bound its damage region while other waveforms tend to make scalloped upward sloped shapes. Because of the square wave’s flat line, we can define the critical acceleration with just one set of tests. This is something that can be done in an afternoon. To define the actual shape of the damage region for other waveforms, requires performing tests along the entire length of the velocity change axis. This approach can damage hundreds of units and require weeks or even months to complete. Although it may provide more precise results for a given waveform, it says nothing about how other waveforms may cause damage. Usually the expense and effort to define the critical acceleration in this manner is not warranted because no practical benefits are gained.
Vibration – Resonance Search & Dwell
It is generally agreed that damage due to vibration is unlikely except at those frequencies where the product is most sensitive. The identification of those frequencies, therefore, becomes critical in designing a package system. The purpose of the bare product vibration testing is to identify the natural or resonant frequencies of the critical components within the product.
To run the vibration test, the unit is secured to the table of a vibration test machine and subjected to a low level sinusoidal input over a broad frequency range. The product can be observed for resonances either visually, audibly, or fitted with response accelerometers attached to its critical components. If the unit has been instrumented, the table input and component responses are monitored throughout the test.
Typically, the ratio of the component response to the table input acceleration is plotted as a function of frequency and is called a transmissibility plot (see Figure 9). The transmissibility ratio (response divided by input) reaches a peak at the natural or resonant frequency of the component. The plotting of this ratio comprises the resonance search portion of the testing.
Once the product resonant frequencies have been determined, the vibration system is tuned to those frequencies and the product is forced to dwell there for a predetermined length. This will identify those frequencies which are prone to induce damage or fatigue.
If the unit is likely to be shipped in more than one axis, the vibration sensitivities of the product in those axes should be investigated as well.