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Advancing Microelectronics • Volume 28, No. 2 • March/April 2001
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Shock-Protection Suspension Design For Printed Circuit Board
Suresh Goyal, Edward K. Buratynski, Gary W. Elko, Lucent Technologies Bell Laboratories, 600 Mountain Avenue, Rm. 1B-212, Murray Hill, NJ 07974, 908-582-5959, FAX: 908-582-6228, Email: goyal@lucent.com
ABSTRACT
This paper presents the central results of the Shock Response Spectrum (SRS) approach in the context of designing a compliant suspension for a Printed Circuit Board (PCB) inside a wireless telephone handset, for shock amelioration. The dynamic response of the PCB is measured for a rigid suspension and for three versions of a grommeted compliant suspension. The resulting SRS plot shows clearly the resonant response of the PCB, and the effectiveness of the compliant suspensions in reducing shock pulse amplification during resonance. The results also illustrate the usefulness of high damping of the suspension materials in reducing peak accelerations. The guidelines generated through this study are applicable for packaging design for a wide-array of electronic products, especially those pertaining to communications/computing.
Introduction
Impact-tolerance, or the ability to safely withstand accidental drops and bangs, is becoming an increasingly important aspect of the reliability of telecommunication network components and enablers [1]. This includes, for example, fragile components like ceramic substrates, optical sub-systems, notebook computers, etc. The shock-tolerance of a product is generally determined by the fragility of its 'weakest' components. Invariably, impact-induced forces and deformations are not uniform throughout a product and depend strongly on the location within the object and the 'connections' leading to that location. Hence one of the challenges for the product designer is finding/creating 'safe' locations within the object for the placement of fragile components.
Frequently, during the design of rugged products, a decision has to be made whether a component like a Printed Circuit Board (PCB) or a disk drive be mounted rigidly inside an outer chassis or be connected compliantly through elastomeric-grommets and the like. In this paper we highlight the importance of accounting for the Shock Response Spectrum (SRS) in making the above decision. The work is presented through the example of designing an elastomeric suspension for the PCB inside the housing of a wireless telephone. For completeness we first review the theory underlying the SRS. We then present the design of the PCB suspension tackled in this paper: the initial experimental results, and the full shock response spectrum evaluation of the PCB that followed using various suspensions.
The value of this work lies as an illustration of the tenets of the SRS (based primarily on linear systems theory) in a real-world problem, and the applicability of our results to a wide-array of related products that have similar scale and construction.
Shock Response Spectrum Approach
Modeling or measuring impact forces is a difficult problem because of the multitude of factors involved and the extreme nature (high magnitudes, low durations) of the events. The complicated interactions that occur between (and within) the components of an electronic product during impact make the task of estimating impact loads and deformations even more difficult. Instead of trying to model impact loads in their entirety, the SRS approach – explained in detail in [2,3] – focuses on the failure of components suspended internally to the main structure of the product. The dynamics of small internal parts during an impact is known as shock response.
To fall within the scope of the SRS analysis, a fragile component must: a) be considerably smaller in mass than the system to which it is joined; b) not be a load-bearing structural element; c) in combination with its suspension elements, be well approximated by a linear model; d) have its limiting (damaging) conditions defined by its peak acceleration or its peak displacement exceeding some critical value acr or xcr respectively. Common examples include a PCB suspended inside a product chassis, ceramic substrates or Micro-Electro Mechanical Systems (MEMS) in portable communication/computing terminals, the display or disk drive of a laptop computer, or a product in its shipping container (the classic application). The subject of shock modeling for such systems divides naturally into two parts: impact-induced motion of the 'suspension point' that supports the fragile element and the consequent dynamic response of the element. For each of these parts, the SRS approach is to classify typical behaviors; the resulting potential for damage is then either intuitively obvious or can be assessed easily.
The general shock problem arises from the impact of a moving (falling) object with a floor, or a fixture, generally something more massive by far. The magnitude of the collision is defined by the velocity of impact (or the drop height). The first step in shock analysis is to recognize that the suspension point of a fragile component undergoes a sudden variation in velocity due to a collision-induced acceleration, or shock pulse ab(t) . Although the exact nature of ab(t) may be very hard to predict, just a few characteristics are important. First, there is the net change of mean velocity of the suspension point,
where t is the duration of the shock pulse.
The essence of ab(t), frequently a unimodal pulse, can be characterized simply by its magnitude and duration. A particularly useful measure of pulse duration is its effective duration,
A more complete pulse specification must include its shape, but it has been found that a broad range of pulse shapes is more or less similar. The key information relates to spectral content: does the pulse rise and fall relatively gently? Or do level changes occur extremely rapidly, and thus contain significant high frequency components. Finally, the shock pulse need not be unimodal and the suspension point may continue to oscillate or 'ring' after the change in mean velocity Dv.
The consequences of concern to this forcing input at the suspension point are the fragile-body peak acceleration and displacement. Hence the most common shock response calculations are those evaluating peak fragile-element acceleration due to a range of acceleration pulse inputs. It turns out that the relationship of teff to the time period of free vibration of the suspended fragile system, Tn, is critical for determining this response. The most useful facts for shock-protection that emerge from the above calculations are the limiting behaviors, that is, fragile-component response to short duration and long duration shock pulses [3].
If teff is considerably shorter than Tn, the peak fragile-element acceleration will depend only on the velocity change of the base and not on the time period over which it occurs. This gives rise to the very important notion of 'velocity shock' (applicable generally to all well-behaved systems): a base acceleration for a sufficiently short time period whose effects depend only on the net velocity imparted, not on the pulse's shape, peak magnitude, or precise duration. A velocity shock just great enough to cause damage defines a critical velocity, vcr .
If teff is considerably longer than Tn, there are two cases to consider. If the shock pulse increases and decreases gently (like a very wide half-sine), there will be no suspended object transients and it will respond quasistatically to the imposed acceleration. In this case fragile part peak acceleration afmax = abmax and damage will occur only if the imposed acceleration exceeds acr. The second case is if the shock pulse has a rapid rise time, no matter how broad it is, its frequency content will excite overshoot.
The shock-protection implications of the above limiting behaviors are:
• If the suspended fragile component will be subject to shock pulses that result in an impulsive velocity change of its base Dv < vcr, no damage will occur irrespective of how great the peak acceleration of the shock pulse may be, and no protection is necessary.
• If the shock pulse causes a velocity change Dv ³ vcr, two cases have to be considered
1) If the shock pulse has magnitude abmax < acr, it will cause no damage and any Dv is permitted.
2) If abmax ³ acr, the shock pulse will cause damage. Shock-protection in this case could either involve the usage of cushioning to increase the effective duration of the shock pulse so abmax < acr; modification of the suspension (stiffness decreased and sway space increased) to make vcr > Dv; or ruggedization of the fragile component itself to increase its acr > abmax [e.g., 3].
The concepts of the SRS approach can be reinforced through the example of the system illustrated schematically in fig. 1.
Representing Shock Response
Fig. 1 shows a fragile component of mass mf connected to a heavier chassis through a suspension modeled by a combination of a spring and damper. The chassis may be covered by a cushioning material to increase the duration of, or soften, the impact. The net force exerted on the fragile mass, that which may cause damage, is given by its mass times its acceleration af(t). The forcing input is a suspension point acceleration pulse, ab(t), that is produced when the cushioned chassis hits the ground.
Since the system of fig. 1 is linear its dynamic response can be represented through a so-called 'base pulse response ratio R', given as:
To characterize this response ratio analytically for a large variety of shock pulses (differing in shape, spectral content, and duration), simple, analytic, unimodal acceleration pulses of various shapes (like rectangular, sinusoidal, versed sine, triangular, etc.) are applied to the suspension point.
The resulting peak fragile component acceleration afmax due to the above shock pulses, either during or after the pulse, can be determined analytically by solving the equation of motion for a forced spring-mass-damper system [4]. Collating the response ratios of the fragile component to various shock pulses, the SRS approach plots R as a function of effective shock pulse duration (normalized by the time period Tn of free vibration of the fragile system). Fig. 2 presents the SRS for an undamped system, i.e., the system of fig. 1 with zero damping. Although fig. 2 plots the SRS for a few, but representative, pulse shapes, plots for other well-behaved pulse are not too different and have an upper-bound represented by the response for a rectangular pulse [4,3]. Observe in fig. 2 that for teff /Tn < 1/6, the SRS does not depend on pulse shape and is approximately a straight line through the origin. This means, for example, that for a given pulse shape, halving shock pulse duration and doubling its amplitude, that is applying the same Dv, leaves the internal peak accelerations unchanged. This is the short-pulse response discussed earlier.
The highest R for any pulse shape occurs for a pulse duration teff » Tn /2, which is similar to the phenomenon of resonance experienced with sustained-periodic excitation (vibration). The value of R at resonance depends on the pulse shape, being highest for a rectangular pulse. At long pulse lengths the SRS approaches a horizontal line, of a level depending only on pulse rise time. This is the long-term response discussed earlier and it clarifies the role of cushioning: to transform a given velocity change into an acceleration pulse of longer duration and lower magnitude.
The addition of damping to the suspension tends to reduce R for a given pulse shape and amplitude, particularly around resonance. For velocity shocks, moderate damping is beneficial. For reducing the peak fragile component acceleration to long duration pulses, the more the damping, the lower the R [4,3].
The limiting behaviors outlined above are applicable to far more general systems than those of fig. 1 [3]. One such system, a PCB suspended compliantly inside a wireless handset, is described below.
 Suspension Design: Printed Circuit Board
Fig. 3 shows a PCB suspended inside a wireless telephone using six screws and six half-grommets around the screws. The handset was expected to be able to safely withstand 20-30 drops from 1.5m onto vinyl tile and 250 drops from 1m onto vinyl tile. Based on drop testing of a wide range of wireless handsets from similar heights, it was estimated that the telephone chassis would be subjected to shock pulses of durations t ranging from 0.3 – 2.0ms (miliseconds).
The aim was to design a suspension for the PCB that would minimize the resulting peak accelerations on the PCB. The choices for the suspension were either to connect the PCB rigidly to the outer chassis using the six screws, or to connect it compliantly with grommets made from commercially available elastomers. The additional design challenge, common in all portable products where small size and low weight are highly desirable, arose from the fact that the space to accommodate the grommets was quite limited.
Initial impact testing with shock pulses of a fixed duration showed that parts of the PCB experienced acceleration peaks that were considerably higher than the applied pulses and no clear resolution was available for the design choices. It was recognized, then, that these amplifications were a result of the shock response of the dynamic system formed by the compliant PCB, and its suspension had to be tested using a spectrum of shock pulses as detailed below.
Experimental Procedure
SRS testing was done using a Dynatupâ Impact Testing Machine, Model 8250, equipped with a specially designed fixture that allowed it to be used as a drop-table, as shown in fig. 4. The shock pulses were generated through impacts between the falling tup (directly beneath the fixture) and various elastomeric pads placed on a fixed steel. The drop height was set to be 1m and essentially-unimodal shock pulses of durations ranging from 1.5-16ms were obtained.
 The PCB was tested in four configurations: attached rigidly to the test fixture, and attached compliantly with grommets made from three different versions of the elastomer VersaDampä, supplied by E-A-R Specialty Compositesâ (of Indianapolis, IN). The VersaDampä family of elastomers is thermoplastic, with a proprietary formulation. The chosen grades of VersaDampä represented a wide range of stiffness and damping. They were, V2590 (highly damped, Shore A durometer 57), V2750 (moderately damped, Shore A durometer 70), V2325 (lower damping, Shore A durometer 40).
Accelerations were measured at four locations:
1) At the site where impact first occurs between the tup and the elastomeric pads (using the load cell inside the tup).
2) At the base of the suspended PCB (using an accelerometer), to measure the forcing input, ab(t), on the suspended PCB.
3) At a point on the PCB which is close to a support. As expected, the accelerations recorded at this location were not too different from those recorded at the base of the suspended PCB.
4) In the middle of the lower half of the PCB (that is, the most flexible point on the PCB) to measure maximal PCB response, af(t).
Results and Data Analysis
Since the PCB is flexible it has natural vibration modes that couple with those introduced from a compliant suspension. The accelerometer results showed a clear resonance of the PCB at around 350 Hz and a resonance of the test fixture itself at around 1400 Hz. Keeping this in mind, the accelerometer data was passed through a low-pass filter, designed using the software MATLABTM, with a high frequency cut-off at 2200 Hz. The filtering only smoothed accelerometer data for the very short duration, 1.5-1.6ms, shock pulses; it left the data for longer duration pules unaltered. Fig. 5 shows an example of ab(t), and the corresponding af(t).
For each PCB configuration, response ratios R = afmax/abmax were calculated for all the pulse durations they were tested in. The results are displayed in fig. 6 where the ordinate is R and the abscissa is the actual shock pulse duration, t, at the base of the PCB. For a linear, undamped, system with a natural frequency of 350 Hz (that is, Tn » 2.8ms), the SRS approach predicts that sinusoidal shock pulses will yield peak responses at t » 2.2ms (teff » 1.4ms). Observe that for each PCB configuration, the maximum response occurs around t » 2.2ms.
Fig. 6 shows that for pulse durations that excite resonant response, the acceleration on the PCB can be significantly higher than the shock pulse, as predicted by the SRS analysis. This is true for all configurations of the PCB - with and without the elastomeric suspension. The lowest response, near resonance, occurs with the V2590 grommets, illustrating the benefits of using highly damped materials in the suspension. Note that resonant response occurs at a somewhat longer pulse duration, t » 2.5ms, only for the softest suspension, made of V2325. Also observe that the SRS plots for all PCB configurations have the same slope before resonance, highlighting the uniformity of the short-pulse response.
Computational Results
A modal analysis of the PCB, using I-DEASâ software, computed its first mode at 423 Hz. This compares well with the experimentally determined mode of 350 Hz for the PCB, given that the mass of the accelerometers was not modeled and an approximate shape of the PCB was used during analysis. In order to understand why the elastomeric grommets did not alter the response of the PCB dramatically, as hoped, from the configuration when it was attached rigidly to the test fixture, the following approximate analysis can be done.
The flexibilities of the PCB and the grommets are modeled as linear springs, and the mass of the PCB by a lumped mass, to yield a spring-mass oscillator. Using the natural frequency of the first mode of the PCB wPCB = 350 Hz, and its mass mPCB = 0.02 kg, the equivalent spring stiffness for the flexible PCB can be estimated as:
kPCB = mPCB *(wPCB )2= 96.7 N/mm
Using the area of contact Ac = 20 mm2 for each of the six grommets, and l = 1.34 mm as maximal allowable deformation, the equivalent spring stiffness for the six grommets together can be estimated as kgr = 6*E*Ac/l = 90*E mm, where E is the Young's Modulus for the grommet materials. Using the values of EV2590 = 4.8 N/mm2, EV2325 = 2.48 N/mm2, EV2750 = 7.4 N/mm2 from commercial literature, we get:
kV2590=432.0 N/mm,
kV2325=223.2 N/mm,
kV2750=666.0 N/mm.
Comparing the stiffness of the PCB and the grommets, it can be seen that all three of the grommet materials are essentially too stiff to have any softening effect on the suspension of the PCB! However, the softest amongst the three, V2325, does decrease the natural frequency of the suspended PCB somewhat, to about 314 Hz, as mentioned earlier.
Discussion
The main aim in this paper was to explain the reason for a perplexing situation that electronic packaging engineers encounter, measurement of higher shock pulses on internal components of an electronic product than on its outer shell, by describing the response of compliant dynamic systems to a spectrum of shock pulses (called shock response spectrum, or SRS). The work was presented through the example of a suspension design for the PCB of a wireless handset for shock amelioration.
Through measurement of the peak acceleration of the suspended PCB in response to slow-rising shock pulses of different durations, the central message of the SRS – that shock pulse duration, in comparison with suspended fragile component natural response time, is critical in determining suspended component response – was illustrated. It was shown that parts of the PCB experienced peak accelerations that were considerably higher (sometimes almost double) than the magnitude of the applied shock pulse, for pulse durations of around 2.2ms, corresponding to the 'resonant response' predicted by the SRS analysis. It was also shown that the resonant response occurred for all configurations of the PCB, whether it was suspended through grommets or connected rigidly to the outer chassis. However, the peak accelerations at resonance were always lower for the PCB with grommets, than with the rigidly connected PCB, being least severe for the grommets made from the highly damped elastomer V2590. The design implications of this are several.
Amongst the available choices, a compliant suspension with grommets made from V2590 is the most effective in reducing peak accelerations on the PCB near resonance. Additionally, the high damping is useful in combating vibratory loads. The effectiveness of the V2590 grommets can be increased further if the PCB was made a little stiffer (for instance, by adding more support points) so more of the deformation occurs in the grommets. For a given drop height, conservation principles imply that a shorter pulse duration results in a higher amplitude. It can be seen from fig. 6 that for pulses with duration less than 1.5ms, the preferred PCB configuration does not show any amplification; the amplification above that duration may not be damaging because of the lower amplitudes of the applied shock pulses associated with them. If further separation is desired between the resonant response and expected shock pulses, the height of the grommets (that is, available sway space) would have to be increased in conjunction with a much softer and damped material for the grommets. This is illustrated, to some extent, by the results for the V2325 grommets. Finally, fragile components that are susceptible to higher accelerations should be located close to a support point - the grommets.
The results of the SRS analysis are very versatile and applicable for almost all well-behaved systems. Even the results described above are fairly general, being directly useful for a wide-array of products that have similar scale and construction, for example, most hand-held portable electronic products, optical network component packages, etc.
References
1. IEC 68-2-27, “International Standard: Basic Environmental Testing Procedures,” International Electrotechnical Commission, Geneva, Switzerland, 1987.
2. R.E. Newton, “Theory of Shock Isolation,” Shock & Vibration Handbook, McGraw-Hill Book Company, New York, Chapter 31, 1988.
3. S. Goyal, J.M. Papadopoulos, and P.A. Sullivan, “Shock Protection of Portable Electronic Products: Shock Response Spectrum, Damage Boundary Approach, and Beyond,” Shock and Vibration, Wiley, New York, NY, Vol. 4, No. 3, pp. 169-191, 1997.
4. R.D. Mindlin, “Dynamics of Package Cushioning,” Bell Systems Journal, Vol. 24, pp. 353-461, 1945.
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