Engineering homework help

3.1

CHAPTER 3 ___________

TRANSPORTATION

3.2

The Transportation Environment

During transportation truck trailers move in the 6 ways shown below. Surge, sway and heave refer to linear motion in the longitudinal, lateral, and vertical directions respectively. Roll, pitch and yaw are angular motions. Roll is rotation around the longitudinal axis, pitch is rotation about the lateral axis, and yaw is rotation about the vertical axis.

Trucks When a truck encounters a raised bump that spans the width of the road, like an elevated concrete slab, both the left and right side wheels of the trailer rise up at the same time. The trailer reacts by pitching and heaving. When the truck encounters a bump or pothole on one side of the trailer, only the wheels on that side rise up. The trailer reacts by heaving and rolling. When the truck makes turns, the trailer yaws and sways. When it brakes or accelerates, it surges. Even if there are no bumps, accelerations or turns, the trailer still moves in all 6 ways because the road is never perfectly smooth.

The reaction of a package or pallet load to all of this motion can be complicated. If the trailer encounters a sufficiently large bump, the heaving floor can literally launch pallet loads and crates upward into the air. Surge and sway can cause tall items to tip over. Back and forth rolling can cause pallet loads to shake themselves apart.

Placement of the load in the trailer can also affect the stability of the load. The front of the trailer is usually quieter than the back and the center (midway between the sides) is usually quieter than along the sides. When the load varies a lot in size and weight, carriers often place heavier items on the driver's side of the trailer. This offsets the effect of the "crown" in the road (there for water runoff), which causes the load to lean a little to the right. Keeping the load vertical is important so that it doesn't lean against the walls or each other.

3.3

Studies of trucks traveling over various roads have revealed the following general characteristics: ! Vibration in the vertical direction tends to be more severe than lateral and longitudinal vibration.

! The amplitude of vibration depends on road roughness. City streets usually generate much higher amplitudes than do freeways because they are rougher.

! Floor accelerations depend on the total weight (trailer itself + load). Greater weights produce lower the accelerations and therefore quieter rides.

! Floor accelerations depend on the truck's speed. Lower speeds produce lower accelerations.

! Floor accelerations can be as high as 20 g’s when the truck goes over bumps or potholes. Most of the time however, the acceleration is less than ½ g (background vivration).

! The greatest movement is usually in the rear of the trailer because the back end hangs out over the rear axle, like a diving board. The highest g-levels however are usually over the support beams and axles.

! Truck trailers equipped with "air-ride" suspension systems usually give a smoother ride than trucks with conventional "leaf-spring" suspension. Leaf springs (left) are flat steel bars banded together and attached to the trailer and axle. They flex like a bow. In an air ride suspension system, the leaf springs are replaced with large air-filled shock absorbers (right).

3.4

! The bottom package in a stack of packages tends to move less than the top package. The higher up the stack, the more movement. The top package could be bouncing around on top of the stack while the bottom package is relatively calm. The most likely location for product damage is the top of the stack because movement is greatest there. The most likely location for package damage is the bottom of the stack because compression forces are highest there.

Railcars Railcars move like trucks with some important exceptions: ! There are no bumps or potholes, so there is almost no pitching or heaving. ! Railcars have a shock absorber in the longitudinal direction known as a "draft gear" (below). The coupler is connected to the car body by a spring. When the couplers on connecting cars lock up, the shock from the impact is partially absorbed by the springs on both cars. Hydraulic and friction type draft gears are also used. Sideways shocks up to 1 g are common. This is enough to cause the load inside to shift or even topple over.

! Railcars rock from side to side as they go down the track. This is referred to as "hunting", meaning the wheels trying to follow an uneven track (below).

3.5

Types of Damage

Loading and Unloading Damage to packages often occurs during loading and unloading with fork trucks. The left photo below shows a large package (turned over) that sustained damage when a fork truck attempted to lift it by sliding the forks underneath it. Placing the package on a skid or pallet would have prevented this. The right photo shows damage to a corrugated box caused by an attempt to squeeze too many packages into the trailer.

A number of warnings are placed on packages. Examples are "Do Not Drop", "Do Not Stack", and the ones shown below. These warnings are often ignored.

3.6

Bad Pallets Sometimes the pallets themselves are the problem. The 3 photos below show poorly constructed pallets. The block in the left pallet is made from particle board, which has poor nail holding ability. The deckboards on the center pallet have been re-used too many times. The ends split apart when nailed. This allows the pallet to "parallelogram", as in the right photo. The wood used in the right pallet was good. The problem was the nails. They were too spaced close together, allowing the deckboards to pivot.

Sometimes the load is too long or too wide. The top left photo below shows a long package on a pallet that will only fit in the trailer lengthwise. The forklift driver can only carry it up to the trailer but not into the trailer, unless it is carried as in the top right photo. If the fork tips extend beyond the center of gravity (CG) of the load, there shouldn’t be a problem. If they don't, the load tips forward and the top and/or bottom deck boards pop off (bottom left figure). Sometimes the product has feet or other parts that protrude through the top deck (bottom right photo). These will get damaged when the forks hit them.

3.7

Cosmetic Damage The floor of a truck trailer vibrates up and down about 5 times a second during transportation. This forces packages and pallet loads to do the same. It can cause products to rub against cushions, the box, and other objects. At this rate, there could be as many as 5x60x60 = 18,000 back and forth rubs every hour of travel. The advertisement below is an example The label on the left below is new. The one on the right was worn by rubbing against the inside of the box during a cross country truck ride.

Flex-Cracking of Packages Vibration can cause plastic film, metal foil and paper to crack from being repeatedly bent back and forth. Cold weather magnifies the problem because materials become more brittle at low temperatures. This makes them less effective as a barrier against a gain or loss of moisture, heat and air.

Static Charge Buildup Rubbing different materials together can generate static electricity, especially in dry air. If the charge buildup is sufficient, a spark could occur. This can easily destroy sensitive electronic components like circuit boards. To prevent this, special "antistat" bags are used to protect them. A charged surface also tends to attract dust. This could be a problem for medical devices that require sterile conditions.

Settling Products in the form of pieces, like cereal and aspirin, tend to settle during transportation. The constant up and down motion combined with side-to-side shaking moves the contents around, causing them to sink and fill voids. Everything moves toward a configuration with the lowest center of gravity. This is also true for larger systems like a truckload of loose loaded boxes. Settling of lightweight materials like cereal may give the impression that the package was under filled. This is why cereal is sold by weight, not volume.

3.8

Settling of heavy pieces in boxes can cause damage to the pieces themselves and the box. This happened to the bulk loaded (randomly packed) apples on the left below. Due to their mass and shape the pieces tend to wedge themselves between their neighbors. This pushes the walls of the box outward and reduces the compression strength of the box. Enough wedging can cause the box to tear open. This usually happens only when there are boxes stacked on top. The added pressure compacts them even more.

Placing the apples in trays with partitions eliminates the wedging effect but can create a new problem (below, right). Loose fitting partitions allow two distinct types of bruises, "point" and "roller" bruises. Vibration can cause apples in the top tray to roll. This forms a bruise in the shape of a continuous band around the apple. Apples at the bottom of the box tend to show point bruises because they are held in place by the weight of the apples on top.

Separation Some foods are "suspensions". Ketchup and salad dressing are examples. They contain solid particles suspended in liquid. If the particles are more dense than the liquid, they eventually sink to the bottom, similar to settling. If less dense, they rise to the top, which is the case for the salad dressing below. This results in a separation between solids and liquids over time. The process is normally slow because the difference in solid and liquid densities is small. Vibration can accelerate the separation process from days to minutes. Flexible containers may add to the problem by amplifying the vibration as they flex.

3.9

Leaky Closures Screw-on caps on bottles can "back off" (unwind) during transportation. Vibration can alter the forces that hold the cap in place, allowing it to unwind over time. Liquid can leak out and lubricate the threads, making it easier for the cap to back off even more.

An easy way to check for backoff is to put a mark on the cap and another mark on the neck of the bottle just below it. If the marks remain aligned after transportation, the cap has not backed off. If not, then the cap must either be tightened more or locked in place. "Shrink- bands" and "break-tabs" are common ways to do this.

But closures can still leak even if the cap doesn't unwind. Bottle in packages that have no headspace tend to have this problem, especially when stacked. Any weight on top of the bottle can cause the liner to compress more. Going over a bump can compress it a lot. The liner does not immediately rebound back to its original thickness when the bump is over, so there is a temporary gap that can allow liquid to leak out. You can demonstrate this by pressing your fingernail into a liner and watching it slowly recover. Tightening the cap more doesn’t necessarily solve the problem because bumps still over-compress the liner.

Pulp (paper) liners can leak even if they are not over-compressed. Paper is porous so it absorbs liquids easily. If the liquid soaks into the liner, it could leak out. Water-proof coatings are usually applied to the inside face of pulp liners to stop liquids from reaching the paper.

Regardless of the type of liner, too much application torque can tear it. The liner is more likely to tear if it is glued to the cap. It has no choice but to slide along the rim of the bottle as the cap is tightened. A liner that is pressed into the cap (not glued) tends to stick to the rim while the cap spins on top of it. This is better because sliding takes place on top of the liner where it doesn't matter.

3.10

Mechanical Failure Individual components inside a product can vibrate violently during transportation even though the package may appear to be calm from the outside. A compressor inside a refrigerator can vibrate so much that it breaks the solder connections on the metal tubing carrying the refrigerant to and from it. Circuit boards can bend and break electrical connections.

The photo below shows wine glasses shattering due to a phenomenon known as "resonance". A loudspeaker was pointed at the glass and the frequency of vibration of the sound (the pitch) was varied until it matched the natural frequency of the glass. When this happened, the glass vibrated so much that it shook itself apart.

LTL vs TLShipments During transportation, the constant vibration of the floor of a truck trailer causes loose loaded boxes and pallet loads to move around. This is especially a problem in "less than truckload" (LTL) shipments because the trailer is not full, so packages are not always supported by other cargo. The left photo below shows a poorly arranged LTL shipment. This will not make it to its destination without looking like the center photo. The packages on top can fall from as high as 8 ft. The right photo shows a pallet load of sand in 50 lb paper sacks. The rolling motion of the trailer caused the load to come apart. Truckload (TL) shipments fare best because there is much less room for movement.

3.11

Tipovers When a truck accelerates, decelerates and turns, packages, pallet loads and crates will either 1) remain motionless, which is the desired outcome, 2) slide across the floor, or 3) tip over. Short loads tend to slide and tall loads tend to tip. The photos below show glass sheets in a wooden crate. The crate tipped over in a turn because it was too tall and wasn't blocked by other cargo or by the trailer wall.

In general, whenever the height of the pallet load or crate is greater than twice the base dimension, the tendency is to tip rather than slide. In the left figure below, package A is likely to tip over when the truck accelerates or brakes because 80/30 >2. It tends to slide when the truck turns right or left because 80/50 < 2. Package B is likely to tip over when it turns and slide when it accelerates or brakes. Tall loads should be strapped to the walls of the trailer as shown in the right photo. The trailer walls must be equipped with hooks or cleats that allow this. Otherwise, the load should be blocked and braced with other cargo.

3.12

Reducing Transportation Damage

Damage can be greatly reduced by limiting the amount the product moves during transportation. Limiting movement inside the package is done through package design, usually by cushioning the product or by including partitions or dividers. Limiting movement in a pallet load can be done by stretch-wrapping the load. Limiting movement in the trailer can be done by using dunnage and by blocking and bracing with other cargo.

Stretch Wrap "Stretch-wrap" is usually low density polyethylene film on rolls 1-3 feet wide and 50 to 80 gauge thick (0.5 mil to 0.8 mil). Wrapping is done on either a rotary platform, where the pallet load spins on a turntable while the film comes off a stationary roll (below), or by an orbital stretch-wrapper, where the pallet load remains stationary and the roll of film orbits around it.

The recommended procedure for wrapping a pallet load of boxes is shown below. The stretchwrap should start on the bottom 2" below the pallet deck. This helps to prevent the load from sliding off the pallet. After applying 2 complete horizontal wraps on the bottom, the wrap should spiral upward such that there is 50% overlap between successive wraps. When the wrap gets 2" beyond the top, 2 more horizontal wraps are applied on top. The tension on the wrap tends to fold this excess over and holds the top boxes down. The wrap should then spiral downward, again with 50% overlap, ending with 2 more horizontal wraps on bottom.

3.13

Plastic wrap works best if it is "pre-stretched" before it is wrapped around the load. When stretched past its elastic limit and immediately wrapped around the load, it will contract over the next few minutes and squeeze the load. Prestretching also has the advantage that less stretchwrap is used. When the proper amount of prestretch is used, a 1000 ft roll of wrap can be stretched into a 3000 - 5000 ft roll.

Pre-stretch is done on a machine. The film is stretched between two sets of rollers that turn at different speeds (left figure below). Film is drawn off a roll of wrap by the first set of rollers, which turn slowly. There is very little tension on the film at this point. It is then pulled into the second set of rollers, which turn much faster. The second set draws film in faster than it comes out of the first set, so the film between the rollers stretches. The amount of stretch can be controlled by adjusting the roller speeds. Once the film emerges from the second set of rollers it is quickly wrapped around the pallet load before it has a chance to fully contract.

Walking around the load holding a roll of wrap does not produce the required amount of stretch, no matter how hard you pull on it (right photo below). You will pull the boxes off the pallet before you even get close to the necessary tension. Pre-stretch must be done by a machine.

According to manufacturers of powered stretch wrap machines, the pre-stretch being used is too low. This results in pallet loads coming apart during transportation and higher film costs because more film is being used than is necessary. The amount of pre-stretch depends on the film being used. The recommended amount is

recommended prestretch = 2/3 of the break point strain for the wrap

The break point strain is usually given on the "technical specifications" published by the film manufacturer. It is also called "percent elongation". If the specification says the percent elongation is 450%, the pre-stretch should be 2/3(450) = 300%. This means that every foot of film gets stretched 3' to a length of 4' just before wrapping it around the pallet load.

3.14

A simple way to verify the amount of pre-stretch is to place two marks on the film a known distance apart before the film enters the stretch rollers. Then measure the distance between them after it has been applied to the pallet load. In the figure above, two marks 10" apart were drawn on the film while it was still on the roll. These marks were found to be 40" apart on the pallet load. The amount of stretch was therefore 40" - 10" = 30", so the pre-stretch was (30"/10") x 100 = 300%. If this matches the recommended amount of pre- stretch, the machine is set up correctly.

Straps/Bands Straps are sometimes used in place of and in combination with stretchwrap. They are made of steel and plastic (PP, PET and nylon) and usually come in rolls ½" wide and 15-30 mil thick. Steel strapping is the strongest and holds tension the best, but is also the most expensive. It is meant for heavy duty applications. Polypropylene is the cheapest plastic strap. It doesn’t retain tension very well. It is meant for light duty applications. PET and nylon are much stronger. They are used in medium duty applications.

Enough straps should be used so that every outside box touches a strap, otherwise missed boxes could vibrate loose and fall off. So strapping is used mostly for large boxes. Small boxes would require too many straps.

Straps have a tendency to loosen up during transportation (top photo). This happens either because:

! the straps deform the packages they are in contact with. Edge protectors (bottom photo) can be used to prevent the strap from digging into corrugated boxes.

! the straps themselves relax. Plastic tends to relax more than metal. In one case, bags on pallets were held down using plastic straps. Pallets were stacked two high and almost reached the ceiling. During transportation, the straps stretched, allowing the stacks of bags to expand upward. By the end of the trip, the bags were wedged between the floor and ceiling. The pallet loads had to be taken apart on the truck to remove the bags.

! the straps were not positioned properly or the cargo was not arranged properly, causing it to shift. This will be considered in the next section.

3.15

Adhesives Adhesives are sometimes used in place of, or in addition to, wraps and straps. The adhesive is usually either a hot-melt glue or a starch-based formulation. It is applied to the tops of boxes as they are being stacked on the pallet.

Hot-melt glue is applied with a heat gun (left photo). Glue sticks are inserted into the back of the gun and trigger pressure forces liquified glue out a heated nozzle in front. One disadvantage is that hot melt glue holds boxes together so well that the corrugated board must be torn to take the boxes off the pallet.

Starch-based adhesives can be sprayed on with an aerosol (right photo). A 16 oz can is usually enough to do three to four average size pallet loads. The adhesive is formulated to have a high shear strength to prevent sliding but a low tensile strength so boxes can be easily lifted off without tearing the corrugated board.

Adhesives do not work well on column stacked pallets. Applying adhesives to only the tops of boxes results in columns that are not connected to each other. Some degree of interlocking is necessary to tie the whole pallet load together.

Cargo Nets Accelerating, braking, and turning can cause sliding and tipping. This can be prevented by using "cargo nets" (below, left). They are connected to the walls of the trailer. These are ideal for LTL shipments. The walls must have hooks or posts to be able to do this. Many do not.

Air Bags Inflatable "air bags" (below, right) are often used to take up space between pallet loads. They are placed between rows of pallets and between pallets and the walls of the trailer.

3.16

Stability

Crates, pallet loads and other large items are often banded together and/or tied to the floor or walls of a truck trailer to limit their movement during transportation. Sometimes the bands or chains loosen up because the load was not positioned correctly. Five examples follow.

Example 1 The figure below shows a crate chained to a flat bed truck. The crate is 6' and 4' away from the anchor points A and D. Will the chain remain tight during transportation?

This can be answered by comparing the length of the path that the chain takes in the crate’s original position (ABCD above) to the path length when the crate is in a slightly shifted position A'B'C'D'. If the path length in the shifted position is greater, the chain would have to stretch in order for the crate to make the shift. This would create more tension in the chain, which would act to restore the crate to its original position, making it stable against movement in this direction. If the path length in the shifted position is less, the chain will loosen up, allowing the crate to move.

In the original position shown above, the path length is

ABCD = AB + BC + CD = (62+52)1/2 + 8 + (42+52)1/2 = 7.810 + 8 + 6.403 = 22.213 ft

Now suppose the crate attempts to shift forward 1 inch due to the truck stopping quickly. In the shifted position, the 6' dimension becomes 6'+1" = 6.083' and the 4' dimension becomes 4'-1" = 3.917'. The path length in the shifted position is

A'B'C'D' = (6.0832+52)1/2+ 8 + (3.9172+52)1/2 = 7.874 + 8 + 6.352 = 22.226 ft.

The path is 22.226 - 22.213 = 0.013 ft = 0.16" longer in the shifted position, so the chain must stretch in order for the crate to shift forward 1 inch. This increases the tension and makes the crate stable against forward shifts.

Now suppose the crate attempts to shift backward 1 inch due to the truck accelerating quickly. In the shifted position, the 6' dimension becomes 6'-1" = 5.917' and the 4' dimension becomes 4'+1" = 4.083'. The length of the chain now needs to be

A'B'C'D' = (5.9172+52)1/2+ 8 + (4.0832+52)1/2 = 7.747 + 8 + 6.455 = 22.202 ft.

3.17

The path is now 22.213 - 22.202 = 0.011 ft = 0.13" shorter, so the chain loosens up. Accelerations combined with vibration will eventually cause the chain to go slack, leaving the crate unsecured.

This problem can be corrected by chaining the crate midway between the anchor points A and D, so the 6' and 4' dimensions become 5' and 5'. Then chain would have to stretch in both forward and backward shifts, making the crate stable.

The crate can also shift in the width direction (into and out of the paper in the figure) when the truck makes turns. A chain over load from the left side of bed to right is also needed, with the crate centered between anchor points.

Example 2 The left figure below shows a stack of tires chained to the trailer floor. The tires are midway between the anchor points, so the stack should not shift forward or backward from braking and accelerating. But it can shift sideways when the truck turns because the chain moves off center, making the path over the tires shorter.

The right photo shows textiles wrapped in coils and banded to pallets this way. Unless these pallet loads are sized to block and brace each other in the trailer, they will likely come apart.

Example 3 The figure below shows a door leaning against the wall of a trailer. It is strapped across its midsection (EB = BF) to the floor at anchor points A and D. Strap ABCD forms a rectangle. Triangle ABE is isoceles (AB=BE) no matter what position the door is in. If the door were to slide down the wall, AB would not change because BE doesn't. So the strap length wouldn’t change. Nevertheless, the door is likely to end up flat on the floor because it gravitates toward the lowest position.

3.18

Example 4 The figure below shows top views of 3 drums banded together in two different ways. Which arrangement is likely to loosen up during transportation? Hint: look at the photo on the right.

This can be answered by comparing the distance around the drums in both positions. For the in-line arrangement, the band can be viewed as two straight segments joined to two half circles on the left and right. The two half circles together have a length of 2πR and the two straight segments together have a length of 8R. The distance around the drums is therefore (8+2π)R. In the triangular arrangement, there are three 120O arcs, which together form a complete circle. They are joined with 3 straight segments, each 2R long, so the distance around the drums is (6+2π)R. This is 2R shorter. The band would have to stretch to go from the triangular to the in-line position. The in-line arrangement is likely to loosen up.

Example 5 The photo below shows an attempt to keep a pallet load centered between the walls of a trailer using 2 pallets as wedges. Will this work? Ideally, the 2 pallets should be shorter so they lie flat on the floor. Then the load cannot move sideways. As used in the photo, they will work only if there is enough friction between the pallets and the load to prevent sliding.

3.19

Natural Frequency

When something flexible is bumped, it vibrates for a short time. An example is a circuit board inside a computer. The rate at which it vibrates is its "natural frequency". Anything that has mass and is flexible has a natural frequency. This definition covers just about everything. Other examples are the sheet metal cabinet of an appliance, the sheet of glass in a window, the filament in a light bulb, a product on a cushion, and a loaded truck trailer on its suspension.

Frequency is measured in cycles per second (cps) or "Hertz" (Hz). 1 Hz = 1 cps. A cycle is defined to be one complete up and down motion. In the figure below, if one cycle takes 40 ms to complete, the natural frequency is fn = 1/0.04 = 25 cps or 25 Hz.

The "spring-mass system" shown above is used as a model. Its natural frequency depends on both the mass and the stiffness of the spring. An increase in mass without changing the spring slows the system down and lowers the natural frequency. An increase in the stiffness of the spring without changing the mass speeds it up and raises the natural frequency.

The easiest way to change the natural frequency of a real component is to change the way it is connected to the product. A circuit board for example is usually supported by four corner posts. Its natural frequency can be increased by adding another support in the middle, which increases the stiffness.

Consumer Products Most electronic products like TV’s, CD players, and computers have multiple natural frequencies. Each one is for a particular component inside, like a circuit board. These components usually have natural frequencies between 5 and 100 cps. The natural frequency of a component can depend on its orientation during shipment because the "mode" of vibration can change. The spring-mass system shown above has two principle modes of vibration: up-and-down and side-to-side (like a tree swaying in the wind). Each mode has its own natural frequency.

3.20

If this spring-mass system is placed on the floor of a truck trailer with the coil spring vertical, the up-and-down motion of the trailer will excite the up-and-down mode. If the same spring- mass system is attached to the wall of the trailer with the coil spring horizontal, the up-and- down motion of the trailer will excite the side-to-side or "rocking" mode. The rocking mode usually has a lower natural frequency than the up-and-down mode.

Package Natural Frequency When you put a product on a cushion and place it in a box, you create another spring-mass system, the product as a whole (the mass) on its cushion (the spring). The natural frequency of a product on a cushion is usually in the tens of cps. This new spring-mass system doesn't change the natural frequencies of any of the components inside the product.

Stack Natural Frequency A stack of packages has a natural frequency that is lower than the natural frequency of an individual package. The figure below shows why. In the stack of 4 packages on the left, each package consists of a product (the mass) on a cushion (the spring). This stack has approximately the same natural frequency as the stack on the right, where all 4 masses have been combined into one larger mass and all 4 cushions have been combined into one softer cushion. Compared to a single package, the stack on the right has 4 times the mass and 1/4 the stiffness, so its natural frequency is much lower. If the natural frequency of a package is 25 Hz, the natural frequency of a stack of these packages could be 5 Hz.

Truck Trailers and Railcars A truck trailer or railcar is essentially a large spring-mass system. The trailer is an aluminum box built on a framework of steel beams. This is the mass. It sits on a set of springs attached to the axles. You change the mass of the trailer every time you load or unload the trailer. The stiffness of the springs however remains constant. Truck trailers and railcars tend to have frequencies in the 2 - 8 Hz range.

Importance of Natural Frequency Natural frequency is important because it determines how products with flexible components react to vibration during transportation. A product that has natural frequencies in the 2-8 Hz range may resonate during transportation. This can cause flex cracking, abrasion, settling and other problems. The best way to prevent resonance is to redesign the product to get its natural frequencies out of the 2-8 Hz range. Packaging will not do this.

3.21

Finding Natural Frequency Three different ways to find natural frequency are described below.

! Visual Method Bumpithe spring-mass system and observe how fast it vibrates. Pick a reference position during its motion and measure how long it takes to complete a certain number of cycles. If it takes 10 sec to complete 20 cycles, the natural frequency is 20/10 = 2 cps. This technique is difficult to apply because the human eye cannot follow motion that takes place this fast.

! Accelerometer Method Mount an accelerometer on the spring-mass system and set it vibrating by bumping it. The signal from the accelerometer will be a sine wave with gradually decreasing peaks. The number of cycles in a given time can be counted and the natural frequency calculated from this. In the example below, the circuit board completes 5 cycles in 200 ms, so its natural frequency is fn = 5 cycles/0.200 seconds = 25 cps or 25 Hz. It doesn't matter how many cycles you choose to do the calculation. The number you get for 1 cycle will be the same as for 100 cycles.

One problem with this method is that the accelerometer adds mass to the object whose natural frequency is to be measured. This lowers the frequency at which it vibrates. In the example above, if the circuit board vibrates at 25 Hz with the accelerometer on it, it might vibrate at 28 Hz when the accelerometer is removed. The error is less than 5% if the object outweighs the accelerometer by a factor of 10 or more.

This method can sometimes be modified by placing the accelerometer near the spring- mass system. When bumped, vibrations are transmitted to the surroundings and picked up by the accelerometer. "Pickups" on electric guitars work on this principle. This method is difficult to execute if there are several spring-mass systems with similar natural frequencies nearby. The accelerometer will pick up a mix of natural frequencies.

3.22

! Vibration Table Method Subject the spring-mass system to a "frequency sweep" on a "vibration table" (below) and look for resonance. This is the method used most often.

This machine (also called a "shaker") consists of a rigid aluminum table connected to a piston that sits in a cylinder. An external pump supplies high pressure hydraulic fluid to the cylinder. A valve controlled by an electric signal alternately diverts the flow from the bottom of the piston to the top, forcing the table to move up and down. The frequency and amplitude of vibration can be adjusted by varying the control signal. An accelerometer attached to the underside of the table records the motion so that frequency and amplitude can be displayed.

The standard procedure for finding the natural frequencies of a product using a vibration table is ASTM D999. The test is normally done on the product by itself and then on the package.

1. To find the natural frequencies of all the components of a product, fix the product to the table so that it doesn't bounce around during the test. Remove its cover so that these components can be observed.

Set the table to move up and down at a rate that is very slowly increased from 2 cps to 100 cps (sometimes to 200 cps). This frequency sweep usually takes about 2 minutes. During the sweep, observe components for resonance. When you see a component vibrating wildly, it is resonating. It resonates whenever the table frequency matches the component’s natural frequency. As soon as resonance is observed, record the table frequency that causes this. This is displayed on a computer screen.

3.23

At the end of the sweep, a product like a TV may have exhibited as many as 10 or more resonant frequencies in the 2 -100 Hz range. Each one corresponds to the natural frequency of a particular component. The cover itself may also have a natural frequency in the 2 -100 Hz range, so it must be replaced and the sweep repeated. If the TV is turned on its side, these frequencies may change because the modes of vibration may change. So it must be tested in other orientations.

The frequency sweep described above is done on the product by itself. Placing the product on a cushion in a box creates another spring-mass system. So the package can also have a natural frequency.

! Package Natural Frequency The natural frequency of the package is found by setting it on the table without strapping it down so that it can bounce around. It is subjected to the same 2 -100 Hz frequency sweep. The package bounces up and down when the table frequency matches its natural frequency.

3.24

Random Vibration

Accelerometers have been attached to trailers at various locations to record motion in the longitudinal, lateral and vertical directions (below). This information is used to drive vibration tables to simulate transportation.

Regardless where they are placed, accelerometers record a continuous signal like the one shown below. This is called "random vibration" because no two segments of this signal will match when overlaid on top of each other.

The acceleration builds up and dies out in a random fashion because the truck encounters bumps in the road, makes turns, and brakes or accelerates in an unpredictable way. There will occasionally be "transient shocks" from the truck going over bumps and railroad tracks. These show up as tall spikes in the signal. Even though the vibration is random, the same characteristic frequencies are present in all parts of the recorded signal. The amplitudes also follow a somewhat predictable pattern.

A summary of the vibration environments found on trucks, trains, ships and planes is given below.

Truck Trailers When a truck goes over a raised bump in the road, the tires flatten out a little, the trailer’s suspension springs compress a little, and the floor of the trailer bends a little, all at the same time. This sets the tires vibrating (spring-mass system #1), the trailer as a whole moving up and down on its springs (system #2), and the floor flexing (system #3). Their frequencies are normally found to be in the following ranges:

suspension 2 Hz (fully loaded) to 8 Hz (empty trailer) tires 15 Hz (low pressure) to 20 Hz (high pressure) floor 50 Hz (fully loaded) to 100 Hz (empty trailer)

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The frequency at which the trailer vibrates up and down on its suspension depends on how much weight is in the trailer. Adding more weight to the trailer lowers the frequency. An empty trailer vibrates up and down at about 8 cps and a fully loaded one at about 2 cps.

A tire is a spring-mass system. The mass is the rubber tire and the spring is the compressed air inside it. The frequency at which a tire vibrates depends on the inflation pressure. Since the mass of the tire does not change, pumping more air into it increases its stiffness and raises the frequency. Tires with low pressure vibrate at about 15 cps and tires with high air pressure about 20 cps.

The floor of a trailer is a spring-mass system because the floor is flexible. Its natural frequency also depends on how much weight is in the trailer. Since the stiffness of the floor is fixed, adding more weight to the trailer lowers the frequency. The normal range is 50 to 100 cps.

The floor accelerations of a trailer with leaf spring suspension are usually less than ½ g most of the time, and for air-ride trailers, ¼ g.

Railcars Railcars (boxcars, flatcars, tankcars) have coil spring suspension systems. The suspension and floor frequencies are similar to those for truck trailers. There is no tire frequency because railcars have solid steel wheels. But there is a rocking frequency due to the wheels trying to follow a non-straight track. The frequencies found on railcars are normally in the following ranges:

rocking about 1 Hz suspension 2 Hz (fully loaded) to 8 Hz (empty boxcar) floor 50 Hz (fully loaded) to 100 Hz (empty boxcar)

The floor accelerations for railcars are less than ¼ g most of the time.

Ships Ships have floor frequencies similar to those for trucks and railcars, but vary widely in low frequency content. Low frequency motion is due to waves making the ship rise and fall. Frequencies are normally found to be in the following ranges:

rise and fall 1 Hz or less floor 50 Hz to 100 Hz

Planes Planes also have floor frequencies similar to those of trucks and railcars and vary widely in low frequency content. Low frequency motion is due to air turbulence, which causes the plane to rise and fall. Frequencies are normally found to be in the following ranges:

rise and fall 1 to 10 Hz floor 50 Hz to 100 Hz

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Simulating Random Vibration The figure below shows how a truck ride is simulated on a vibration table. First, vibration recorders are mounted on the floor of the trailer and the truck is taken for a ride on whatever route is to be simulated. Back in the lab the recorded signal is used to create a "power spectral density (PSD) plot". This plot contains frequency and amplitude information. Finally, the PSD plot is used to drive a vibration table. The table in theory simulates the up-and-down motion of the trailer floor. The standard test for this is ASTM D4728.

Measuring Random Vibration Vibration recorders sample accelerations at regular time intervals (below), typically every millisecond. This goes on for hours. At the end of a trip, it will have recorded millions of samples.

The software that operates the recorder finds the average and standard deviation of the sampled data. The average acceleration will be zero because there will be as many positive G’s as negative ones. Positive g's come from the trailer floor moving up and negative g's from it moving down. The standard deviation, which is a measure of the variation in g- values around the mean, is not zero. If N is the number of recorded samples and G1, G2, etc are the sampled accelerations,

average = (G1 + G2 + G3 ... + GN) / N = 0

std.dev. = [ {(G1 - mean) 2 + (G2 - mean)

2 + (G3 - mean) 2 ... + (GN - mean)

2}}/(N-1) ]1/2

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Since the number of samples is large and the mean is zero, the standard deviation is

std.dev. = [ (G1 2 + G2

2 + G3 2 ... + GN

2) / N ]1/2 = rms G

The standard deviation is also called the "rms G" (root mean square G) because of the way it is calculated: square root of the mean value of the squares of the sampled g’s. The rms G is a measure of the overall severity of the ride. The rms G for a truck ride is typically about ½ g if the truck has leaf spring suspension and ¼ g if it has air ride suspension. For a train ride it is about ¼ g.

The recorded accelerations have a normal (bell-shaped) distribution with a mean of zero. The standard deviation therefore has the same meaning that it does for any normal distribution. Specifically, ! 68.3% of the sampled G’s should be less than 1 standard deviation in magnitude ! 95.4% should be less than 2 standard deviations ! 99.7% should be less than 3 standard deviations

Almost all of the sampled accelerations should lie within ± 3 standard deviations. Only about 0.3% or 3 out of every 1000 should exceed this. The 20 g shocks that can occur when the trailer goes over railroad tracks and in potholes are examples of these outliers. When calculating the standard deviation, they are weighted the same as all of the other sampled accelerations. Because they are so few in number, these high G shocks have no effect on the rms G.

For illustration purposes, suppose the vibration recorder samples only 10 accelerations. They are shown in the table below.

0.2 g’s 0.4 - 0.1 - 0.6 0.1 0.9 - 0.3 - 0.5 0.7 - 0.8

The average and standard deviation are

average = (0.2 + 0.4 - 0.1 ... - 0.8)/10 = 0 std.dev. = [(0.22 + 0.42 + 0.12 ... + 0.82)/10]1/2 = 0.54 g’s

The rms G is 0.54 g’s. This is typical for a truck trailer with leaf spring suspension. If sampling were continued for a much longer time, about 68.3% of the samples will be between -0.54 and +0.54 g’s, about 95.4% will be between -1.08 and +1.08 g’s, and almost all will be between -1.62 and +1.62 g’s.

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PSD Plot The same software also finds the frequencies present and their "power densities". This is done using the same sampled accelerations.

To find the frequencies present, the software views the random vibration as an infinite collection of sine waves whose frequencies are 1 Hz, 2Hz, 3 Hz, etc. The amplitudes of these sine waves are adjusted so that when added together, they reproduce the recorded signal. When this technique is applied to the random vibration coming from the floor of a truck trailer, three dominant (large amplitude) frequencies emerge: the suspension, tire and floor frequencies.

The power density associated with each frequency is related to the amplitude of the sine wave with that frequency. The power density is half the amplitude squared divided by the frequency spacing, which is 1 Hz. A large power density means that the associated frequency contributes a lot to the motion of the trailer floor.

A PSD plot for a truck trailer with leaf spring suspension carrying a medium load and traveling over interstate expressways is shown below. It shows frequency on the horizontal axis and power density on the vertical axis. PSD plots are done on log-log scales because variations in power density can be enormous.

There are three peaks on this PSD plot. They occur at frequencies 3.5 Hz, 17 Hz and 50 Hz. These frequencies correspond to the suspension, tires and floor flexing respectively. The power density associated with the suspension is about 0.01 G2/Hz. The other two peaks have power densities on the order of 0.001 and 0.0005 G2/Hz, which is ten to twenty times less. The roughness of the ride is therefore due mainly to the trailer moving up and down on its suspension.

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Vibration Table vs Actual Truck Ride The simulation method just described was designed to make the table move like the trailer floor during an actual road trip. Due to equipment limitations and other factors, it usually doesn't. In some ways the table ride is less severe than the road trip and in some ways, more severe. The main problems are:

1. Limited Range of Motion Trucks (railcars, ships and planes too) move in 6 ways: surge, heave, sway, roll, pitch, yaw). Rolling (rocking) back and forth) is especially important. Boxcars rock from side to side because the tracks are not perfectly straight. Trailers also do this when the wheels on one side hit a pothole. This can cause stacks of boxes to hit the walls of the trailer. This doesn't happen on a vibration table that only moves up and down. In addition, most tables cannot produce large amplitude, low frequency motion or small amplitude, high frequency motion very well.

2. Exclusion of "Jolts" The power density levels shown on the PSD plot are calculated using millions of sampled accelerations. Large shocks caused by the truck going over railroad tracks and in potholes are too few in number to affect the power density. But these shocks are often the ones that cause damage. Some vibration controllers have been designed to superimpose large shocks separately from the PSD information.

3. Exclusion of "White Noise" White noise is the low level background vibration that is always present because there is no such thing as a perfectly smooth road. When using the vibration recorder, a "trigger level" is specified to conserve memory. This tells the recorder to save a measurement only if it is above a certain g-level. This eliminates a large number of very low g-levels (the white noise). When these are taken out of the calculation of power density, the result is higher than actual power density levels.

4. Enveloping PSD plots must be manually entered into the vibration table controller. Actual plots contain hundreds of peaks and valleys. For simplicity, they are often replaced with a simpler "envelope" (below) that is drawn just above the actual plot. Since PSD plots are done on log-log scales, large errors in power densities can result if the envelope is drawn too high.

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5. Which Plot to Use A PSD plot is valid only for the particular trailer, floor location (where the recorder was placed), weight of load, road condition, and truck speed at the time the recording is made. Heavy loads tend to lower the suspension frequency and reduce power density levels. Higher speeds tend to raise power density levels. Road conditions affect them the most. So a PSD plot for a particular trip cannot represent all situations. Based on various studies, ASTM has created the representative plots shown below for the different modes of transportation.

Intermodal" shipments are even harder to simulate. A trailer on a flatcar (TOFC) is one type of intermodal shipment (left photo below). A sea container (box with no wheels) on a flatcar (COFC) is another (right photo). Sea containers are off-loaded onto a truck chassis and transported to the final destination as an over the road highway trailer.

TOFC shipments contain both flatcar and trailer dynamics. This combination is very different from the dynamics of the trailer or flatcar alone. It is in general not possible to combine the separate PSD plots for these two modes of transportation to simulate this.

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It is not clear how to compare a random vibration test on a vertical vibration table to an actual truck ride. Comparing actual damage on the table to damage on the road has shown that 1 hour on the table is almost always more damaging than 1 hour on the road.

There is no universally accepted relationship between table time and road time. It depends on the situation. This is why ASTM D4728 recommends doing both table and road tests and comparing damage to establish the relationship between the two. The unofficial view is that for most trucks traveling on highways,

1 hour on the table = 500 miles on the road (ASTM)

Since a truck traveling at 70 mph would cover 500 miles in about 7 hours, this represents a “time compression” of about 7 to 1, meaning 1 hr on the table = 7 hrs on the road.

ISTA (Procedure 3E) believes that the table ride is not so severe. For pallet loads of product on cross country hauls, it recommends using

minutes on table = (trip distance in miles) / 5 (ISTA)

According to this, 60 minutes on the table represents 300 miles on the road. A truck would travel this in about 4 hrs, so this represents a time compression of about 4 to 1.

The fact that there are very different versions of the relationship between table time and road time says that driving vertical vibration tables using PSD plots does not simulate the actual transportation environment for all products and packages.

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Review Questions

1. What location in the trailer is the quietest? In a railcar?

2. Where in a stack of packages is the most likely location for product damage during a truck ride? Where is the most likely location for package damage?

3. What is "hunting" (in a packaging sense) and why is it important?

4. Boxes of cereal are palletized on a GMA pallet. Ideally, how long should the forks on the fork truck that handles these pallets be? Why?

5. About how many back-and-forth rubs could a label on a package experience during a 600 mile truck ride?

6. How does vibration adversely affect electronic products packaged in plastic bags? Medical products?

7. A suitcase containing hairspray and clothing exploded on the baggage carousel at an airport (true story). Explain how this could happen.

8. Does the back and forth shaking that occurs during transportation mix up foods like salad dressing?

9. Explain how vibration can cause liquid-filled bottles to leak during transportation.

10. Boxes of cereal are palletized on a GMA pallet. How tall can the pallet load be if you don't want it to tip during accelerations, braking and turns? At this height, can it fit in a standard highway trailer?

11. Approximately what length of 20" wide stretchwrap do you need to wrap a 48"x40"x46" load on a pallet if you follow the recommended procedure and use no prestretch? What length if you use the recommended amount of prestretch? The break point strain is 150%.

12. Two marks are drawn 5" apart on stretchwrap before it enters the rollers of a stretchwrap machine. If you want to apply the recommended amount of prestretch to this film (break point strain = 300%), how far apart should these marks be when the film is on the pallet load?

13. Large thin glass panels are stood upright and strapped to a pallet as shown on the right. Is this arrangement stable?

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14. What is the best way to unitize a pallet load of 12"x12"x12" boxes? Stretchwrap, bands or adhesives?

15. Show that the crate in Example 1 is stable against forward and backward shifts if it is placed midway between anchor points before it is chained to the bed of the trailer. Does this also make it stable against side-to-side shifts?

16. In the stability Example 3, prove that triangle ABE is isoceles.

17. A flat plate supported at its four corners has a low natural frequency. How could you raise its natural frequency?

18. How can turning a product on its side change its natural frequencies? Give an example of a product that has different natural frequencies in different orientations.

19. A stack of 5 identical packages has a natural frequency of 10 Hz. What is the natural frequency of a stack of 2 of these packages?

20. An accelerometer is attached to a rigid part of a product inside its package. The package is raised an inch above the floor and flat dropped to set the product vibrating on its cushion. The accelerometer records the signal shown below. What is the natural frequency of the product on its cushion?

21. How can you tell when a spring-mass system is resonating during a frequency sweep on a vibration table? Why does resonance occur?

22. Identify the spring-mass systems present in the window air conditioner shown below. How you would experimentally find the natural frequency of each?

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23. True or False? A random vibration signal recorded off the floor of a trailer during a road trip contains different frequencies because the truck encounters different size bumps in the road.

24. A product contains a 20 Hz (natural frequency) fan blade, a 5 Hz motor and a 90 Hz circuit board. Which component is likely to vibrate the most during a truck ride?

25. What is the main difference in the motion of the vibration table when testing according to ASTM D999 and ASTM D4728?

26. The PSD plot below is for a truck carrying a medium to heavy load on interstate expressways. How would the plot change if the truck were carrying a light load and traveling over rough city roads? How would it change if you added 10 large shocks from the truck going over bumps and in potholes?

27. A PSD plot is constructed from sampled accelerations. How would it change if a higher trigger level were used on the vibration recorder?

28. How high should you set the trigger level on a vibration recorder if you want to record only large shocks (railroad tracks and potholes)?

29. Where should a vibration recorder be placed on a truck trailer?

30. Are the following statements regarding random vibration true or false?

a. The table reproduces the motion of the truck floor in real time. b. The duration of a random vibration test on a shaker driven by a PSD plot should be

about the same as actual road time. c. The suspension, tire and floor frequencies are present in the motion of the table. d. Railroad tracks, potholes, and other isolated shocks show up as sharp spikes on the

PSD plot.

31. A loaded truck travels from Lansing, MI to Miami, FL on the I-75 expressway. If you want to simulate this on a vibration table driven by a PSD plot for the trip, how long would you run the test according to ASTM? According to ISTA?

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Answers to Review Questions

1. Front and center, meaning as far forward as possible in the trailer and midway between the walls.

2. Top for product because movement is greatest there. Bottom for package because the compression force is greatest there.

3. Railcar wheels moving from side to side trying to follow an uneven track. This causes the railcar to sway and roll. The load can impact the walls.

4. A GMA (Grocery Manufacturers Association) pallet measures 48"x 40". The center of gravity (CG) of a homogenous load like boxes of cereal should be at the geometric center. The forks should be at least ½(48") = 24" long so that the fork tips can extend beyond the CG. Otherwise the load will tip forward. Ideally, they should also be shorter than 40" so that they don't stick out beyond the pallet in front. Otherwise the driver might ram other pallet loads when loading a trailer.

5. Assume an average speed of 60 mph. Rub time = 600 mi/60 mph = 10 hrs = 36,000 sec. A trailer vibrates up and down at about 5 cps. So 36,000 x 5 cps x 1 back & forth rub per cycle = 180,000 rubs.

6. Vibration causes back and forth rubbing. This could generate static electricity and cause a spark, which could damage electronics. For sterile medical devices, static attracts dust and lint. Vibration can also cause flex-cracking.

7. Rough handling caused the cap to come off the can and the nozzle to impact the suitcase, discharging bursts of hairspray along with the flammable propellent. This built up inside the closed space and a spark caused by the clothes rubbing together ignited it.

8. No, unless it is very violent shaking. The constant vibration often accelerates the separation of liquids and solids in suspensions like salad dressing and ketchup.

9. Either 1) the caps loosen up and the liquid leaks out, or 2) impacts to the cap cause the liner to momentarily over-compress and create temporary gaps, or 3) the liquid soaks into the liner, especially if paper, and leaks out.

10. A GMA pallet is 48"x 40". The height should be less than twice the base, so less than 80". A standard trailer is 110" tall on the inside with a useable height of about 106", so yes, there is sufficient room for it.

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11. Start with 2 horizontal wraps on the bottom 2" below the deck and spiral up using 50% overlap. Then 2 wraps on top (2" over), spiral back down, and end with 2 wraps on bottom (2" over). There are 10 wraps total as shown below. The distance around the load is 2(48"+ 40") = 176" = 14.67 ft. With no prestretch, the total length needed is 10 x 14.67 = 146.7 ft. The recommended amount of prestretch is 2/3(150) = 100%, which means that the wrap must be stretched to twice its length. Then only ½(146.7) = 73.3 ft are needed.

12. The recommended prestretch is b(300%) = 200%. The stretch would need to be 200%(5") = 10". The marks should be 5" + 10" = 15" apart on the pallet load.

13. No. An end view is shown below. The only thing holding the glass upright is friction between the glass and pallet at C and between the glass and strap at D. Vibration will likely cause point C to shift to the left or right. If it does, point D will drop down a little, making the strap loosen up. Once the strap is loose, the glass will tip over because the height of the glass is much greater than twice its base.

14. Stretch wrap. Bands would not be economical because too many would be needed to contact every box. Adhesives won't work well because the pallet pattern is column stacked (this is the only way to stack cubical packages). Applying adhesive only to the tops of boxes results in columns that are not connected to each other.

15. With the crate in the middle, ABCD = (52+52)1/2 + 8 + (52+52)1/2 = 22.142 ft, which is shorter than with the crate in any other location. So the chain would have to stretch if it shifted, increasing the tension and returning the crate to its centered position. This has no effect on lateral stability. The crate could still shift sideways (will unless another chain is used).

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16. The strap is across the door’s midsection, so point B bisects EF. A horizontal line through B bisects AE and a vertical line through B bisects AF. Looking at the small upper and lower triangles on the left, c2 = a2 + b2 = x2, so c=x.

17. Make it stiffer. Put another support in the middle. Or increase the thickness of the plate.

18. It changes the mode of vibration, usually from up-and-down to rocking. An example is the filament in a light bulb. The filament acts like a coil spring. It can vibrate along its length ("longitudinal" vibrations) or like a guitar string ("transverse" vibrations).

19. Something more than 10 Hz because a stack of 2 packages is lighter and stiffer than a stack of 5.

20. 3 cycles/0.100 sec = 30 cps.

21. When it vibrates violently. When the table frequency matches the spring-mass system’s natural frequency, the table pushes up and pulls down on the mass at exactly the right times. Up when it wants to move up, and down when it wants to move down. This amplifies its motion. Resonance occurs when the amplitude of motion is greatest.

22. Compressor, tubes, fan, cabinet and whole product on cushion. To get all frequencies except for the product on its cushion, conduct a frequency sweep from 2 -100 Hz on a shaker with the product tied down to the table and look for resonance. A cheaper way would be to mount an accelerometer on each component, bump it, and deduce the frequency from the signal. For the product on its cushion, set the package on the table, do a frequency sweep and look for bouncing. Or measure it as in question #20.

23. False. It does contain different frequencies, but because the trailer is made up of different spring-mass systems (trailer on suspension, tires and floor), not because of bump size. Bump size determines amplitude, not frequency.

24. The motor, because its natural frequency is in the suspension frequency range, 2 -8 Hz.

25. In ASTM D999, the table vibrates up and down in a smooth sine wave fashion with gradually increasing frequency. In ASTM D4728, it moves randomly (erratically).

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26. With a lighter load, the frequencies and accelerations are higher because the trailer moves up and down faster. Rougher roads also increase the g levels. Increased g levels means greater power densities. So the peaks shift to the right a little and the curve moves up a little. Adding 10 large shocks does nothing because power densities are calculated using millions of sampled g values.

27. All of the sampled g’s below the new trigger level will be eliminated. The power density levels will increase and the table ride will be more severe.

28. Set the trigger level at about 3 times the expected rms G. This should eliminate about 99.7% of the recorded g's. For an average truck ride, this would be 1½ g’s.

29. The recorder should be mounted on the floor if possible. This can be difficult to do. You can mount it inside the pallet on a deckboard, close to a stringer. This hides it, protects it, and gives it the same motion as the floor. Do not place it in a package because it will record what the package is doing, not the floor.

30. a) False. This is almost impossible to do. b) False. Table time is much less than road time for the same amount of damage. c) True. This forms the basis for the PSD method. d) False. A few large shocks have no effect on the PSD plot.

31. ASTM: 1 hr on table = 500 expressway miles. The travel distance is about 1200 miles, so 1200/500 = 2½ hrs. ISTA: minutes on table = miles/5, so 1200/5 = 240 minutes = 4 hrs.