Engineering Analysis

Principia provides a multidisciplinary approach to the study of mechanical systems. The field of mechanical engineering encompasses a broad range of disciplines from electro-mechanical engineering to combustion. In order to provide the highest level of mechanical engineering consulting to our clients, Principia’s engineers have technical backgrounds and over 40 years of experience that spans the entire breadth of the mechanical engineering field. We have provided consulting services for products ranging from aircraft, ships and automobiles, to medical devices, industrial equipment and consumer products.

Principia’s engineers also have the hardware and software tools necessary to inspect, analyze and test almost any mechanical system. We have a wide range of measurement and testing tools for mechanical systems and materials including an Instron tensile tester, microscopes, accelerometers, strain gages, and load cells. In addition, Principia has state of the art software for data analysis, finite element modeling, dynamics, computer aided drawing and drafting, vehicle accident reconstruction, and occupant motion in vehicle accidents.

Our experience allows us to tackle large-scale, complex mechanical issues. The following case study involves the analysis of a large cement plant ball mill and combines several mechanical engineering disciplines including fatigue and fracture mechanics, continuum mechanics, dynamics and statics.

The examples below illustrate some of our capabilities in mechanical engineering:

+ Finite Element Analysis of a Ball Mill

Cement plants utilize large ball mills to crush the raw materials used in cement production, called clinker, into powder. The mill consists of a large cylindrical tube 54 feet long and 16 feet in diameter that is partially filled with four-inch diameter steel balls. The ends of the steel cylinder are attached to trunnions that are supported on journal bearings. The photograph below shows the incident trunnion.

Ball Mill
Assembly

As the ball mill rotates, the steel balls in the cylinder rise up one end of the inside surface of the mill and eventually tumble down to the bottom. The raw material is fed into the ball mill at the ends, and the steel balls impacting together eventually grind the material into a powder which is collected through slots at the center of the mill. The figure below shows a computer-generated model of a ball mill containing the cylinder, the two trunnions on the ends and the drive gear.

When cracks began to appear in the trunnions of a ball mill, Principia was hired to analyze the stresses created in the trunnions during operation to determine if they were being overloaded and to help define the specifications for new trunnions. In order to complete this work, Principia needed to understand the loads created on the trunnions during operation. The loads imparted on the supporting trunnions resulted from three main components:

  • Static load or weight of the ball mill
  • Dynamic loads imparted during rotation of the ball mill
  • Gear interaction loads

Although the first task seems straightforward, it is difficult to weigh a piece of equipment that is several hundred tons. In order to determine the weight of the ball mill, Principia used the original mechanical drawings of the ball mill (figure at the right) to create a full three-dimensional model of the entire ball mill.

drawing
assembly_exploded

The figure to the left below is the exploded view of the solid model created from the old drawings. This computer-generated model was given appropriate material properties to determine the weight of the ball mill. This was then added to an estimate of the weight of the steel balls and the clinker. The end result was a total weight of over 800 tons supported by the two trunnions.

In order to determine the additional forces generated during ball mill operation, Principia used a discrete element modeling package (DEM) that calculates the forces created by the interaction of many individual particles, which in this case are steel balls moving inside the rotating cylinder. This type of computational model is relatively new and requires significant computing resources. The computer program simulated the ball mill with 11,600 steel balls to determine the forces generated at the trunnions. The figure below shows a screen shot of the computer model after five seconds of rotation.

mill5sec
Front

The gear interaction loads were calculated using the geometry of the gears and the torque applied to the drive gear. In this case, the resulting gear force actually lowered the load on the drive side trunnion.

After determining all the loading conditions Principia completed a finite element model (FEM) of the trunnion using this, loading as boundary conditions to determine the stresses imparted during operation. It was determined that the stresses during normal operation were not sufficient to create the observed cracks in the trunnion. A sample result of the FEM is shown to the left (normal stresses in the z-direction) for the trunnion.

+ Automobile Lanekeeping Assistance

Automotive engineering and technology is a core area of Principia’s mechanical engineering expertise. Our engineers have experience working in the automotive industry, and we have over 20 years of experience in vehicle design, handling, crashworthiness and electronic control systems. A perfect example that highlights our automotive background and expertise is an electronic control system that helps prevent unintended lane departures developed by one of our engineers during his doctoral work at Stanford University.

Increased automobile safety is one of the primary goals of new vehicle technology. Over the past few decades, passive safety features such as crumple zones, seat belts and airbags have become standard features in vehicles and have saved countless lives. More recently, active electronic control systems are being utilized in vehicles to assist the driver in avoiding accidents by preventing unstable vehicle behavior. Anti-lock brake systems (ABS) that prevent wheel lockup are now common, and electronic stability control systems designed to prevent skidding are seeing increased popularity. The goal of this new system is to take these active safety systems one step further and electronically assist the drive in preventing unintended lane departures. Although drivers are generally good at this task, they are far from infallible; in 2005 for instance, 58% of all fatalities involved only one vehicle and in addition, the first harmful event for 32% of fatal accidents was a collision with a fixed obstacle (NHTSA Traffic Safety Facts 2005).

The design of an electronic lanekeeping assistance system required development in three distinct areas: mechanical design of a new steering system, sensing technology to determine lane position, and a control algorithm that would seamlessly work with the driver to maintain the lane boundaries. The test bed for this new system is a 1997 Chevrolet Corvette C5 shown to the right at the testing grounds at Moffett Airfield.

Test Corvette
Sensors for Lane Position

In order to determine lane position, this system integrated the global positioning system (GPS) with inertial sensors that measure rotation rate and acceleration. With corrections from a nearby base station this sensing system can pinpoint the vehicle position with accuracies measured in inches. Combining this sensing technology with accurate road maps provides all the information needed to determine the vehicle’s lane position.

Control Algorithm

The control algorithm used to help the driver prevent unintended lane departures is unique in that it seamlessly integrates with the driver’s steering command, but does not alter the underlying vehicle dynamics. The control theory treats the roadway environment as a series of hills and valleys. The valleys represent safe regions of the road while the hills represent more dangerous regions. It is helpful to think of the vehicle as a ball rolling down the road. As it approaches a hill it will be pushed down towards the valley; in essence this is how the control system works to help the driver remain in the lane. The following figure gives a graphical representation of this control approach for a single lane.

If the driver is doing a good job and staying towards the safe regions of the road, he or she will not notice the influence of the system. However, if the driver begins to drift towards the outside of a turn, for example, the control system will begin to add additional steering inputs to assist the driver in keeping the vehicle inside the lane boundaries.

lane keeping
Lateral Error

The final working system performed extremely well. It was unobtrusive to the driver under normal conditions, and even with no steering input from the driver the system prevented the vehicle from departing the lane. The figures to the left shows the road map of the lane centerline and the resulting vehicle path with no driver input. The performance predictions and the actual vehicle motion show excellent correlation. As predicted, without steering input the vehicle drifts to the outside of every turn until the system (or hill) adds enough extra steering input to keep the vehicle in the lane.

+ Occupational Injuries from Vibration

Occupational hazards exist in practically every work environment. The hazards that exist, however, vary significantly depending on the work environment. The occupational hazards that exist in an office environment are very different than those that exist in a construction site or railroad environment. Operators of heavy industrial machinery (cranes, bull dozers, forklifts, jack hammers, etc.) are exposed to relatively high levels of vibration and harshness. When chronic injuries occur to people in these work environments, a big question that arises is the contribution of the work environment to the injury.

Tamper

The following example illustrates the tools and techniques that Principia utilizes to assist our clients in understanding and quantifying the harshness of a particular work environment and how it relates to a particular injury. The case involves an operator of a railway tamper who was suffering from tarsal tunnel syndrome, a repetitive stress injury that is the ankle equivalent of the common wrist injury carpal tunnel. The figure to the left shows the tamper, a large machine that rides on the railway and compacts the gravel ballast below the railway ties. This process of compacting the gravel ballast creates a good deal of vibration. Is this vibration high enough to cause a repetitive stress injury such as tarsal tunnel?

To answer this question, Principia measured the vibration transmitted to the operator’s feet during the most extreme operations of the railway tamper. The photograph to the right shows a tri-axial accelerometer, a device used to measure acceleration, mounted on the footrest used by the operator. The accelerations in three perpendicular directions were recorded during all phases of the tamper’s operation.

Triax

The charts to the left show an example of the measured accelerations. In order to produce meaningful results, a frequency analysis was done on the acceleration signals to compare the magnitudes of the signal with published standards on vibration exposure from the International Organization for Standardization (ISO). The figure below is an example of the frequency-domain acceleration levels during the harshest operation of the tamper compared to the standards for impaired working efficiency. It turns out that the harshest conditions experienced by the tamper operator can be endured for between four and eight hours with no impairment of working efficiency. In fact, the standard gives an exposure limit for safety that is twice as high as the limit for working efficiency, making the most extreme tamper vibrations safe for an entire 8-hour working day.