Finite elemental analysis question set 3
Question
Polymer composite materials have been recently considered in
bearing lightweight design application. Figure Q1 shows a rolling
bearing system for a gear transmission application. It is known that
the contact between the steel rollers and the polymer composite
races (inner and outer) is highly non-linear and so the quality of
results from FE simulations accounting for the rollers/races
interaction are likely to have a major impact on designing the
bearing system.
Part a
For the bearing system as shown in Figure Q1 and as the FE analyst, briefly summarise the
modelling requirements and technical data required to develop bearing contact model
under real operational conditions. (6 marks)
Part b
The use of contact elements has been widely accepted for accurate bearing system contact
simulations, though gap elements are still used. Explain the main reasons and the limitations
of using gap elements in bearing contact analysis. (8 marks)
Part c
Why do linear stress-strain relationships simplify the bearing contact simulation? State the
main possible sources of non-linearity in the bearing system (use sketches to present them)
and compare them in term of their convergence. (10 marks)
Part d
It has been found that the FE simulation CPU time required to complete the analysis is still
very high although all the bearing materials (steel and polymer composite) are assumed to
be elastic. Explain the main reasons of that. Sometimes, the steel rollers can be assumed as
rigid body, discuss the assumption on the quality of the output. (10 marks)
Part e
Using annotated illustrations to explain Newton’s method to solve f(x) = 0 (f(x) is a nonlinear
equation for a single degree of freedom x). The polymer composite outrace used in the
bearing system has a stiffness, x, defined by the function x 29 + x 7 + 1 = 0. Given that the
initial estimated stiffness is x0 = -1, use Newton's Method to show that with n = 4, the race’s
stiffness is -0.956, to an accuracy of 10-3, i.e., the convergence criterion is 0.001 xn1 xn
, where n is the number of iterations. (16 marks)
Question
Polymer composite materials have been recently considered in
bearing lightweight design application. Figure Q1 shows a rolling
bearing system for a gear transmission application. It is known that
the contact between the steel rollers and the polymer composite
races (inner and outer) is highly non-linear and so the quality of
results from FE simulations accounting for the rollers/races
interaction are likely to have a major impact on designing the
bearing system.
Part a
For the bearing system as shown in Figure Q1 and as the FE analyst, briefly summarise the
modelling requirements and technical data required to develop bearing contact model
under real operational conditions. (6 marks)
Part b
The use of contact elements has been widely accepted for accurate bearing system contact
simulations, though gap elements are still used. Explain the main reasons and the limitations
of using gap elements in bearing contact analysis. (8 marks)
Part c
Why do linear stress-strain relationships simplify the bearing contact simulation? State the
main possible sources of non-linearity in the bearing system (use sketches to present them)
and compare them in term of their convergence. (10 marks)
Part d
It has been found that the FE simulation CPU time required to complete the analysis is still
very high although all the bearing materials (steel and polymer composite) are assumed to
be elastic. Explain the main reasons of that. Sometimes, the steel rollers can be assumed as
rigid body, discuss the assumption on the quality of the output. (10 marks)
Part e
Using annotated illustrations to explain Newton’s method to solve f(x) = 0 (f(x) is a nonlinear
equation for a single degree of freedom x). The polymer composite outrace used in the
bearing system has a stiffness, x, defined by the function x 29 + x 7 + 1 = 0. Given that the
initial estimated stiffness is x0 = -1, use Newton's Method to show that with n = 4, the race’s
stiffness is -0.956, to an accuracy of 10-3, i.e., the convergence criterion is 0.001 xn1 xn
, where n is the number of iterations. (16 marks)
