Huijuan Su

Al as solid solution hardener in steels

Abstract Aluminium in solution in the ferrite in ferrite/pearlite steels has been found to have little influence on strength of the ferrite probably because up-till recently it has been added in very small amounts (0˙02–0˙08 wt-%Al) as a grain refining addition. There is indeed some doubt in the literature as to whether Al can solid solution harden. This lack of knowledge has not been important while Al additions are small but recently Al has been added in much greater amounts 0˙5–2% in some new grades of transformation induced plasticity (TRIP) steels. These steels have often an essentially ferritic structure with retained austenite and bainitic ferrite. The main thrust of the paper has therefore been to determine the solid solution hardening effect of Al in ferritic structures. Steels with varying Al levels from 0˙02 to ∼2% at two C levels, 0˙02 and 0˙1% were tensile tested after hot rolling so as to determine the solid solution hardening effect of Al. It was found in the 0˙1%C steel that some of the pearlite transformed to martensite on raising the Al level to 1% and this resulted in preyielding and lower strength levels than would have been obtained from a ferrite/pearlite structure. However, when the Al level was kept to the maximum allowable before martensite formed a marked solid solution hardening by Al was observed. Hall-Petch plots were also obtained from steels in which martensite was not present and it was found that a 1%Al addition increased the yield strength by 70–80 MPa and this increase was not dependent on the grain size as has been found for Si. It can be concluded that Al is a substantial solid solution hardener of steel but the strengthening effect of Al is often obscured at low additions by its ability to remove nitrogen from solution and at high additions by its tendency to favour martensite formation and cause preyielding of the ferrite.

Use of computer algebra in Hamiltonian calculations

The use of Hamiltons Principle in determining the governing partial differential equations of motion for such problems as the free vibration of complex elastodynamic systems has been known for many years, but the implementation of the integration procedure using symbolic computation does not appear to have been solved. In this paper we present the application of a computer algebra package called REDUCE that takes away the human cost. We show the use of this package in a simple example, and for a twisted beam such as an idealised helicopter blade.

AN EXACT DYNAMIC STIFFNESS MATRIX FOR A TWO-PART BEAM-MASS SYSTEM AND ITS APPLICATIONS

Using two different, but related approaches, an exact dynamic stiffness matrix for a two-part beam-mass system is developed from the free vibration theory of a Bernoulli-Euler beam. The first approach is based on matrix transformation while the second one is a direct approach in which the kinematical conditions at the interfaces of the two-part beam-mass system are satisfied. Both procedures allow an exact free vibration analysis of structures such as a plane or a space frame, consisting of one or more two-part beam-mass systems. The two-part beam-mass system described in this paper is essentially a structural member consisting of two different beam segments between which there is a rigid mass element that may have rotary inertia. Numerical checks to show that the two methods generate identical dynamic stiffness matrices were performed for a wide range of frequency values. Once the dynamic stiffness matrix is obtained using any of the two methods, the Wittrick-Williams algorithm is applied to compute the natural frequencies of some frameworks consisting of two-part beam-mass systems. Numerical results are discussed and the paper concludes with some remarks.

Influence of the Load Occupancy Ratio on the Dynamic Response of an Elevator Car System

In predictions of the dynamic behaviour of an elevator car system, it is important to take into account the influence of passengers’ behaviour in the car. In this paper a simulation model to analyse the influence of various loading car conditions on the dynamic response of the elevator system is developed. This involves the investigation of the dynamic response of the car with different loads. An experimental rig with a rectangular elevator platform fixed on the top of four silent blocks attached to a shaker is designed to conduct experimental tests. The car is excited over a range of frequencies and amplitudes. A number of passengers wearing different type of shoes in the car are investigated. The transmissibility measurements are carried out with a harmonic excitation applied first to an empty car and then to the car with a number of passengers. An excellent agreement from experimental tests with the model predictions is achieved. The passenger’s role to act as a dynamic absorber is assessed and recommendations to achieve the best ride quality under load conditions are provided and summarised.

Influence of Al on strength and impact behaviour of hot rolled plain C–Mn steels

Abstract The influence of Al on the strength and impact properties of hot rolled plain C–Mn low S steels has been examined at two C levels, 0˙02 and 0˙1% and two N levels, 0˙001 and 0˙004–0˙005% (where percentage is to be taken as wt-%). It has been found that Al is an excellent element to add to hot rolled steels, an addition of 0˙2% to a plain 0˙1C–1˙4Mn steel with 0˙004–0˙005%N resulting in an impact transition temperature of −95°C at a strength level of ∼300 MPa. At this Al level, Al removes the N from solution but also importantly refines the grain boundary carbides and to a lesser degree the grain size resulting in a 40°C lowering of the impact transition temperature in a coarse grained steel (15–20 μm; d− 1/2, 7–8 mm−1/2). Strength is not affected by this Al addition. The decrease in strength due to the removal of nitrogen from solution as AlN is balanced by the solid solution hardening from the Al in solution in the iron lattice, (a 1%Al addition increasing the strength by ∼70 MPa), and the small grain refinement that occurs from AlN precipitation. Increasing the Al level to 1% in the 0˙1%C steels, results in the formation of martensite with consequent deterioration in impact behaviour. When the N level is reduced to very low levels, 0˙001%N, no grain refinement in the γ occurs in the 0˙02% and 0˙1%C steels at the 0˙2%Al level. The solid solution hardening effect of Al now dominates the properties with the impact transition temperature remaining constant due to Al refining the grain boundary carbides.

The coupled nonlinear dynamics of a lift system

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.

Investigation into the damping and stiffness characteristics of an elevator car system

Modelling the dynamic performance of an elevator car system represents a complex task and forms an important step in the elevator system design procedure. The need to consider the behaviour of passengers travelling in the car complicates the procedure further. This paper presents an original approach to identify the stiffness and damping characteristics of an elevator car system. A simplified model is developed and the experimental rig with a rectangular elevator platform fixed on the top of four silent blocks attached to a shaker is setup. The transmissibility measurements are carried out with a harmonic excitation applied first to a platform with no passenger load and then to the platform with one passenger within the frequency range of 1 – 20 Hz. A single person standing on the platform is employed in order to assess the passenger’s contribution to the dynamic behaviour of the elevator car system. The curve fitting technique implemented in MATLAB is used to determine the damping and stiffness coefficients both for the empty car system and the car-passenger system. Investigation on the tolerances for both parameters is carried out. An approach to simplify the experimental procedure and to reduce the number of individual tests is proposed.

Dynamic Stiffness Formulation and Free Vibration Analysis of a Moving Timoshenko Beam

A moving Timoshenko beam is analyzed for its free vibration characteristics using the dynamic stiffness method. First the governing differential equations of motion in free vibration of a moving Timoshenko beam are derived using Hamilton’s principle. The derivation gives the expressions for shear force and bending moment from the natural boundary conditions which are consequential of the Hamiltonian formulation. Next the dynamic stiffness matrix is developed by solving the governing differential equations of motion and then eliminating the arbitrary constants from the general solution so as to form the force-displacement relationship of the harmonically vibrating moving Timoshenko beam. The resulting dynamic stiffness matrix, which turns out to be a Hermitian matrix, is used in conjunction with the Wittrick-Williams algorithm to determine the natural frequencies and mode shapes of some examples. In the analysis, simply supported, fixed-simply supported and fixed-fixed end conditions are considered. Results using the Timoshemko theory are compared and contrasted with the corresponding results obtained from the Bernoulli-Euler theory. The critical speeds for all three end conditions are illustrated. Representative mode shapes are presented for different moving speeds. Finally, some conclusions are drawn.