Explain why an unbalanced rotating mass on a shaft cannot be balanced completely by using a single balancing mass in a different transverse plane.What is the minimum number of balancing masses required if they are to be attached in different transverse planes.so that the system is completely balanced?

Mumbai University > Mechanical Engineering > Sem 6 > Finite Element Analysis

Marks: 5M

Year: may 2016

Though Finite Element Analysis is a powerful tool for analysis of a problem, some errors are bound to happen in the final solution. This is due to the fact that ultimately F.E.M. is an approximate method of analysis. It should be noted that if a plate is to be analyzed we first make a mathematical model of the plate and perform analysis of the model. Hence accuracy of analysis will depend on the extent to which the model is accurately prepared.

Normally, three main sources of errors in a typical F.E.M. solution are

• Discretization errors
• Fromulation errors
• Numerical errors.

Discretization errors result from transforming the physical problem into a finite element model and can be related to modelling the boundary shape.These errors are more prominent in 2-D and 3-D problems and can be reduced by increasing the number of element to a sufficient extent.

* Formulation errors* result from the use of elements that do not describe the behaviour of the physical problem. For example, if we choose to formulate a particular finite element on the assumption that displacements vary linearly over the domain, the solution will show errors in case the displacements do not vary linearly.

Numerical errors include truncation errors or roundoff errors. A slight error due to roundoff in one element is likely to result in an appreciable error due to cumulative effect of these errors throughout the domain.Such error can be minimised by feeding the data accurately enough to as many decimal places as feasible.