2.1.1 The finite element method
4.6Static performance characteristics of a measurement system
4.7Dynamic performance characteristics of a measurement system
Figure 0‑1 Part in ansys software…………………………………..
While working on placement at Tecomet in midleton, they were contracted to produce a medical implant that required the press fit of a stainless-steel pin into a polymer body. The design of the part required that the mating surfaces of the parts were flush. This was regarded as a critical to quality component.
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The problem arises when the mating surfaces of the press fit are situated in a hole in part. This meant that the press fit couldn’t be controlled by sight as the press would be carried out using a manual press and it would be unable to be inspected on site afterwards for quality purposes.
This created the requirement for a process to be developed that would allow the control and verification of the fit
The overall aim of this project is to measure and control the press fit assembly of a medical device.
To achieve this aim there are several objectives to be met.
- Conduct a literature review of FEA, relevant Metrology systems, control systems and the forces exerted in a press fit.
- Establish a suitable mesh design to allow for an accurate FEA of the parts.
- Compare different methods of measuring force and displacement to help choose a suitable control system.
- Verify FEA results through application of relevant mechanics theory.
- Establish a project management plan for semester 2
1. Literature review
To be able to conduct a FEA analysis of the parts, it is necessary to understand how FEA works. This is important as to produce accurate and verifiable results it is necessary to apply a suitable mesh with appropriate loadings and boundary conditions.
2.1 Finite element analysis
2.1.1 The finite element method
The finite element method is where an object is broken up into several “elements” which form a mesh. This allows for complex mathematical equations to be carried out at discrete points (nodes), achieving an approximation of the distribution of stress in a part.
2.1.2 1D, 2D or 3D?
Best practice in finite element modelling is to reduce the problem to its simplest form. If a 3D part can be reduced to 1D or 2D this greatly simplifies the application of a mesh and boundary conditions.
2..1.3 Element type
As there are many element types available in FEA, it is important to understand the effectiveness of each one. The element type depending on the boundary and loading conditions. Generally, as the complexity of design increases, the number of elements suitable for that analysis decreases.
The size of the chosen element is important, because as the area decreases, the accuracy of the overall calculation increases. The downside to this, is that more elements require more computational power. To balance this out, it is not necessary to place small elements in positions of low interest in relation to determining stress variations.
Aside from preserving available computational power, there is a limit in element size where smaller elements will not produce any significant improvement in the accuracy of the analysis. This is called the mesh convergence and means that an optimal mesh can be produced for any model.
As FEA approximates physical equations, when creating a mesh, the more elements created i.e. the finer a mesh, the more accurate the results. Unfortunately, as the number of elements increases so does the number of equations, leading to the need for increased computational power and in the case of complex model’s significant time requirements.
The component of FEA that has the largest impact on the accuracy of the result is the mesh. Factors that must be considered when constructing a quality mesh are:
- Extreme interior angles
- Free edges
- Coincident elements
- Poor positioning of mid-side nodes
Warping occurs when the face of a plane is forced out of position
Distortion of an element refers to when it is forced to deviate from its original shape.
Extreme interior angles are when element angles are too small or needlessly large. Occurrence of these angles in the mesh will contribute to distortion. Ideal angles depend on the type of element used, with triangular elements requiring 60°, and quadrilateral 90°. Angles greater than 180° will cause a failure of the model as there is then no solution to the inverse of the Jacobian matrix and hence a determinant. In FEA the Jacobian matrix is used to determine the deviation of an element from its ideal shape.
Free edges are unconstrained edges, these should only occur at the model boundaries.
Coincident elements are when multiple elements are overlaid with shared nodes.
Poorly positioned mid nodes will cause distortion and can lead, in extreme cases, to significantly reduced performance of the mesh elements.
2.3 FEA errors
When trying to determine the possible errors in a FEA, it is important to consider the factors that can influence the accuracy of the analysis. Are the material properties used in the analysis accurate? Are the selected boundary conditions and loads an accurate interpretation of real-world working conditions? Several sources of error must be considered before accepting the results of an analysis.
2.3.1 Meshing errors:
Meshing errors occur when element distribution is not adequate to represent the stress distribution in the model. i.e. large elements or rough mesh in areas of high stress concentrations. Geometric errors occur in the mesh when the chosen elements in the model are not an accurate representation of the geometry of the model. This can occur when linear elements are used to model a curved surface. As with using the wrong element type, mismatching different types of elements can create errors.
2.3.2 Material properties
The material properties given to the software must be correct. Giving wrong values for properties e.g. young modulus will render any analysis results invalid.
Due to the difficulty of establishing boundary conditions from real world conditions, this is one of the biggest sources of errors in FEA.
Establishing accurate boundary conditions can be difficult
As with boundary conditions it can be difficult to establish and quantify loads and pressures and their positions of influence on the model. Also, as these are positioned at the nodes of the elements, by the software itself, which would not necessarily be an accurate placement, this also adds a degree of error in the result.
St Venants principle
St Venant principle states that if a load acting on a small area of a body, is replaced with a distributed load over the same area, that this change affects the stresses locally but not at a distance away.
2.4 Numerical errors
As the software only allocates a certain amount of memory to each value and calculation, it will eventually have to round off numbers. These round offs are usually insignificant as they are usually minute values, but when large numbers of calculations occur, can lead to an accumulation of the round of error.
2.4.2 Ill- conditioning
This refers to when a set of equations from the FEA have a solution vector that is sensitive to changes in the coefficient matrix. In the model this can occur where an area of high stiffness matrix is supported by an area of lower stiffness, where deformation in the stiff region distorts the results in the area of lower stiffness.
The magnitude of the ill conditioning in the model can be measured by
Metrology is the science of measurement. To be able to produce verifiable measurements, the components of a measurement system must be traceable back to international standards. All measurements have a a level of uncertainty as it impossible to achieve a perfectly true value due to inaccuracies that are impossble to remove in any measurement system.
Figure 2‑1 Standard traceability pyramid
4.2Standards of measurement
Standards within metrology can be broken into several distinct categories.
Primary: This is the highest-level definition of a measurement. These are the basis from which all other lower standards are calibrated. They are defined with incredibly high levels of precision and accuracy. Taking the metre for example, it is defined as the distance travelled by light in a vacuum in 1/299 792 458 of a second (Physics.nist.gov, 2018)
Secondary: These are the national standards from which the calibration standards in labs are based on. In Ireland these are at the National standards authority of Ireland.
Tertiary and below: These are the standards used in workshops and labs e.g. gauge blocks. These come in different grades depending on their use – Calibration, Inspection or workshop use.
The purpose of standards is to ensure traceability of measurements back to national standards. As you move from the primary standards down the chain, the level of uncertainty increases.
4.3 Measurement systems
4.3.1Methods of measurement
There are two different methods that can be used to determine the correct value of a measurement.
Direct – The value of the measurement taken is compared directly to the appropriate standard.
Indirect – this method is used when the desired characteristic cannot be measured directly or would be difficult to obtain. For example, stress isn’t calculated directly it is obtained from taking a length measurement.
These can further be broken down into:
Absolute – This is where the scale starts at zero and only moves in one direction.
Comparative- Where an unknown value is recorded and compared to another know value.
Null measurement – this is the opposite of the deflection method.
Substitution – this method involves measuring the unknown quantity, the replacing it with a known quantity to get the same read out or value.
Contact – the sensor or instrument, comes into contact with the measurand
Contactless – the sensor or instrument used, does not come into contact with the measurand
When developing a measurement system, it is important to limit the variation within the system. Variation occurs as controlled where there is a consistent pattern over time and uncontrolled, where the variation over time is unpredictable. A stable process can only have controlled variation. (Itl.nist.gov, 2018).
The variation can be broken into process, system and results.
While accuracy and precision can be used interchangeably outside metrology, within metrology they have very distinct and important differences. The main objective of a measurement system is to provide both accurate and precise values.
Accuracy – This is a measure of how close the value measured is to its true value.
Precision- This is a measure of how close, repeated measurements of a value are to each other.
Bias – this is the deviation of the average value from multiple measurements of a part, from its true value.
Stability – this is the change in total variation over time.
Linearity -when the output is linearly proportional to the input
Uncertainty – put simply this is the amount of doubt about a measurement value. It affects calibration and testing.
4.4 Gauge R&R
Average and range
4.6Static performance characteristics of a measurement system
When developing a measurement system there are several characteristics that must be understood and controlled to allow for accurate and precise results
4.7 Dynamic performance characteristics of a measurement system
Speed of response
4.8 Sources of error
When designing a measurement system there are two types of error that need to be accounted for. Controllable errors are errors where their source can be determined, and an allowance made for. Random errors are where their source can not be determined and hence can’t be accounted for.
These are errors which occur in the calibration of the calibration equipment. Due to the extremely high tolerances in calibration equipment, slight changes in temperature, heat and humidity during calibration of these instruments can lead to errors.
There are 3 main ambient conditions that must be considered when determining the results of a measurement system. These are
While humidity and pressure are only of concern in high level calibration, temperature changes can have a significant effect on the results obtained in a measurement system. Temperature can affect both the part being measured and the instrument used. Firstly, where a part is machined, it must be allowed cool to an ambient temperature before measurement.
The part and instrument must also be at an ambient temp.
Using a formula for linear thermal expansion (Quantumstudy.com, 2018): The above highlights that when a part and instrument have the same co-efficient of expansion and at the same ambient temperature then they will be accurate. But if they have a different co-efficient then different temperatures will increase error in measurement. Consequently, great care should be taken not to handle parts of instruments excessively or else they are given enough time to come to an ambient temperature.
This error occurs when the stylus or probe of an instrument in forced into a part, causing a deflection of the stylus or indentation of the part.
These are errors where the source is uncontrollable and inconsistent. These generally cannot be accounted for in systems as their effects cannot be predetermined.
Backlash: this is play in the movement of an instrument, before the output is changed. Can be caused by clearance between moving parts of by wear on components.
Friction in the instrument: this is caused by internal parts in an instrument rubbing against each other e.g. a Vernier calipers. Can also be compounded by incorrect use of the instrument.
Vibration in the instrument: This can be caused by the instrument itself or be caused by outside sources. For example, a CMM has moving parts that can cause vibration, but it can also be affected by the vibrations from nearby machines.
These are errors that occur due to poor knowledge in the operation of instruments and how to read their outputs properly e.g. parallax. Can be avoided by proper training and use of SOP’s. Examples of these errors include not understanding GD&T sufficiently to be able to measure dimensions properly, setting up frames that may hold dial indicators in a way that allow angle errors in their readings.
4. Review of standards
There are a large number of standards in relation to metrology and measurement in general the two most important as decided by the author are outlined below.
5.1 ISO 13485
This standard refers to the quality management systems in the manufacture of medical devices. In relation to this project the most relevant section is 7.6 Control and monitoring of measurement equipment. The main points to
- All equipment or instruments used should be calibrated before first use and then at specific intervals
- The calibration standards used must be traceable to national or international standards.
- Equipment and instruments must have unique ID’s to allow monitoring of calibration status.
- All calibrations and adjustments need to be recorded.
- Safeguards must be in place to prevent unauthorised adjustment
- The equipment must be protected against damage in use
- Any computer software used must have documentation of its validation
5.2 ISO 10012
This standard is in relation to measurement management systems. It covers a number of different topics including:
- Measurement uncertainty and traceability
- All measurements need to be traceable back to national standards.
- The uncertainty in a measurement needs to be established before the validation of the measurement process.
- Measurement process
- That suitably trained personal is used
- The equipment and procedures are properly validated.
- Metrological confirmation
- The meter logical characteristics are suitable for the intended use.
- Equipment shall be protected from unauthorized alterations
- The measuring equipment shall be used in a controlled environment. With any changes to these conditions recorded
5. Ansys analysis
To begin the analysis of the part, it was necessary to create the material within the software. The material properties were taken from the manufacturer of the medical grade polymer. (Appendix 1)
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The first problem encountered was the major difference in the reported material properties for the part and pin. Also due to the company that makes the plastic, being American their values are in Imperial. While the ANSYS software changes these to metric on its own, there will be rounding errors in the conversions. There is only a limited number of properties published. This is problematic as ANSYS workbench has the input for a significant number of material properties. Without having a considerable knowledge on how the software works it is unknown how much of an effect these will have on the accuracy of the results.
For the first analysis the part is simplified to only show the contact areas between the body and pin. This analysis is conducted when the surface area contact between the pin and part is at a maximum. Leading to the largest force required to impact the pin into the body. The parts were created in Inventor and imported into the static structural- system analysis in ANSYS workbench.
Due to only needing to control the parts enough to prevent the pin being pressed too far into the body, the analysis will concentrate on the mating surfaces. With the overall part being reduced to the areas of interest. The knurl on the top of the pin was excluded from the model due to the variation in the wear on the knurling tool during manufacture.
Figure 0‑1 Reduced part in ANSYS
The assembly was placed in the software for the first iteration of the analysis. Due to the simplified model, the part was left whole instead of making use of symmetry to reduce it.
A support was placed to the bottom face and sides of the part to simulate being in a fixture when is the manual press. A force was applied over a surface area representing the contact area with the pin.
Figure 0‑3 Force applied to mimic contact area
For the manual press the forces that could be applied were taken as 1kn -25kn. So, analysis began with a 1kn force per total surface area of the pin head being applied. This was then repeated for 2 -5kn
|1kN equivalent||2kN equivalent||3kN equivalent||4kN equivalent||5kN equivalent|
|Maximum shear stress||1.7996e7||3.5993e7||5.3989e7||7.1985e7||8.998e7|
|Maximum shear strain||2.5607m/m||5.12||7.682||10.243||12.8|
|Equivalent stress (von mises)||3.12e7||6.237e7||9.356||1.0245e8||1.5594e8|
|Equivalent strain (Von Mises)||1.55||3.1156||4.634||6.231||7.789|
After conducting the literature review and preliminary analysis there are several more steps that must be taken to achieve the overall aim of the project.
- To keep refining knowledge of and developments in relevant technologies that would be beneficial to this project.
- Due to the variation in the reported material properties for both the propylux and the stainless steel used in to parts, some testing on samples might be required to help improve the results of the ANSYS simulations.
- 3 different systems to measure the placement of the pin are to be designed, constructed of and tested. Due to the space restrictions in the part and between the press and part these will be mechatronics based.
- A purely visual based system to meet the requirements of a visual inspection and would allow for the use of the manual press with not other modifications to it.
- A more complex system based on monitoring the force applied to the pin and its movement. This is envisioned to be used it the process is automated.
- Finally, to test the feasibility of and suitability of an imaging process to allow for high output of pin placement quality control.
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