An Elementary Theory of the Bourdon Gage

1946 ◽  
Vol 13 (3) ◽  
pp. A207-A210
Author(s):  
Alfred Wolf
Keyword(s):  
Wall Thickness ◽  
Maximum Stress ◽  
Transverse Section ◽  
Elementary Theory ◽  
Thin Walled ◽  
Longitudinal Extension

Abstract A theory of the Bourdon gage is presented based upon two elements of strain, namely, the bending of the walls in a transverse section through the gage tubing, and a longitudinal extension parallel to the axis of the tubing. Practical formulas are derived for the calculation of the sensitivity and the torque of the Bourdon gage. An estimate is made of the maximum stress. The sensitivity of a very thin-walled gage is shown to be proportional to the inverse first power of the wall thickness. Results of a few measurements show agreement with the theory.

Minimum Weight of Tapered Round Thin-Walled Columns

1952 ◽  
Vol 19 (3) ◽  
pp. 375-380
Author(s):  
Morris Feigen
Keyword(s):  
Wall Thickness ◽  
Minimum Weight ◽  
Weight Ratio ◽  
Optimum Shape ◽  
Bending Stress ◽  
Round Tube ◽  
Cylindrical Column ◽  
Truncated Cone ◽  
Thin Walled ◽  
Tapered Column

Abstract It is shown that the optimum wall thickness of a cylindrical round tube column is a function of load only and is independent of diameter. The optimum wall thickness of a tapered round thin-walled column is found to be constant along its length. The optimum shape of a tapered round thin-walled column is derived, being that column whose bending stress in the buckled state is constant along its length. The weight ratio of the optimum tapered column to an equal-strength optimum cylindrical column is found to be 0.8924. It is shown that a double truncated cone whose diameter ratio is in the range 0.35 ⩽ D1/D2 ⩽ 0.50 closely approaches the optimum column. If it is specified that no portion of the double truncated cone shall yield, then the weight advantage of the cone over the cylindrical column is rapidly lost as the stress in the cylindrical column approaches the yield stress. In the inelastic range the weight advantage of the tapered column will be less than in the elastic range.

The linear elastic in-plane bending of curved hollow profiles having a thin-walled rectangular section

1992 ◽  
Vol 27 (3) ◽  
pp. 145-149 ◽  
Author(s):  
F J M Q De Melo ◽  
M A P Vaz
Keyword(s):  
Cross Section ◽  
Thin Shell ◽  
Transverse Section ◽  
Accurate Solution ◽  
Rectangular Section ◽  
Element Analysis ◽  
Linear Elastic ◽  
Graphical Result ◽  
Thin Walled ◽  
Shell Finite Element

This paper presents a simple solution for the flexibility calculation of curved profiles having a rectangular thin-walled cross-section. Some assumptions related to geometric details about the shape of the deformed structure are included in the present analysis, aiming at an economic and accurate solution. Results concerning the distortion of the transverse section are compared with the corresponding data from the solution with a thin shell finite element analysis. A flexibility factor for the structure analysed here is presented as a graphical result.

Optimal Design of an Elastic Column of Thin-Walled Cross Section

1968 ◽  
Vol 35 (2) ◽  
pp. 285-288 ◽  
Author(s):  
N. C. Huang ◽  
C. Y. Sheu
Keyword(s):  
Optimal Design ◽  
Cross Section ◽  
Wall Thickness ◽  
Cross Sections ◽  
Unit Length ◽  
Compressive Load ◽  
Median Line ◽  
Vertical Column ◽  
Thin Walled ◽  
Allowable Compressive Stress

This paper treats the optimal design of a vertical column that is built-in at the lower end. In addition to its own weight, the column is to carry an axial compressive load at its unsupported upper end. The column is to be designed as a thin-walled tube. The median line is to be the same for all cross sections; the wall thickness, though constant along the median line of any cross section, is allowed to vary along the length of the tube. Accordingly, the weight per unit length of the tube is proportional to the bending stiffness. For given length and total weight, the variation of the wall thickness along the column is to be determined to maximize the critical value of the compressive load at the upper end. The influence of a maximum allowable compressive stress on the design is also investigated.

scholarly journals Investigation of an inverse thermal injection mould design methodology in dependence of the part geometry

2021 ◽  
Author(s):  
C. Hopmann ◽  
J. Gerads ◽  
T. Hohlweck
Keyword(s):  
Wall Thickness ◽  
Injection Moulding ◽  
Thermal Design ◽  
Internal Stresses ◽  
Cooling Channel ◽  
Injection Mould ◽  
Compression Moulding ◽  
Compression Pressure ◽  
Injection Moulding Process ◽  
Thin Walled

AbstractThe production of injection moulded components with low shrinkage and warpage is a constant challenge for manufacturers. The thermal design of the injection mould plays an important role for the achievable quality, especially the placement of the cooling channels. This design is usually based on empirical knowledge of the mould designers. The construction is supported iteratively by injection moulding simulations. In the case of thick-walled plastic optics with big wall thickness jumps, the shrinkage is compensated by injection compression moulding. In this process, the thin-walled areas freeze earlier and the necessary compression pressure introduces stresses into these areas which reduces the optical performance. An adapted cooling channel design can reduce these problems. At the IKV, Institute for Plastics Processing in Industry and Crafts at the RWTH Aachen University, a methodology was developed which inversely calculates the cooling requirement of the moulded part A demand-oriented cooling channel system is derived based on the computed results. The aim of the research projects is to minimise displacement and internal stresses by temperature control of the moulded parts according to the demand. In this paper, the methodology is applied to three different geometries, representing three classical parts for the injection moulding process. Three different quality areas in the mould for the inverse optimisation are defined and investigated. For each geometry the cooling channel designs are then validated in injection moulding simulations based on the results from the thermal optimisation. It can be shown that for different component geometries and thicknesses, different quality areas are advantageous and decrease the maximum warpage of the parts. For thin-walled ribbed components, a 2D approach leads to a 15% smaller displacement, for components with wall thickness jumps, all investigated quality ranges show no differences in displacement, but a surface in the middle of the part is preferred due to a 3 °C lower standard deviation of the temperature distribution.

The Effect of Hoop Stress on the Burnthrough Susceptibility During In-Service Welding of Thin-Walled Pipelines

2008 ◽  
Author(s):  
Matthew A. Boring ◽  
William A. Bruce
Keyword(s):  
Failure Mechanism ◽  
Wall Thickness ◽  
Hoop Stress ◽  
Pipe Diameter ◽  
Welding Parameters ◽  
Minor Effect ◽  
Circumferential Welds ◽  
Welding Arc ◽  
Thin Walled ◽  
Longitudinal Welds

Most companies control the risk of burnthrough by prohibiting welding on pipelines with wall thicknesses below a specified thickness. This is a safe approach but the risk of burnthrough depends not only on the wall thickness, but also on the welding parameters and the operating parameters of the pipeline which include pressure. It is generally acknowledged that the hoop stress caused by pressurizing the pipeline has a relatively minor effect on the risk of burnthrough since the size of the area heated by the welding arc is small. While this has certainly been shown to be true for thicker materials, previous research has shown that the pressure can have a dramatic effect on burnthrough risk for thinner materials. The objective of this project was to further investigate the effects pressure and hoop stress has on the burnthrough risk of welding onto thin-walled pipelines in service. For circumferential welds, pressure and wall thickness determine the burnthrough risk and pipe diameter appears to have no effect. The failure mechanism for circumferential welds is consistently a burnthrough. For longitudinal welds, pipe diameter does appear to affect burnthrough risk even though the effect appears to be secondary to pressure and wall thickness. The pipe diameter is believed to be more influential for longitudinal welds because of the larger area of heated material that is exposed to the hoop stress. Also, the results indicate that the magnitude of the hoop stress has a direct effect on the failure mechanism for longitudinal welds (i.e., burnthrough or weld centerline cracks). For longitudinal welds, the failure mechanism is commonly burnthrough for welds made onto pipes with a hoop stress below 30% specified minimum yield stress (SMYS) which indicates that the internal pressure of the pipe is the main driving force for failure. Longitudinal welds made on pipes which are experiencing hoop stress above 30% SMYS commonly fail by weld cracking. It is important to note that even though pressure does have an effect on the burnthrough susceptibility of welds made on thin-walled pipelines, pressure only becomes a factor for welds made at heat input levels in excess of what is predicted safe by thermal analysis modeling.

scholarly journals Evidence for Stacking Faults in Multiaxial Strained Alpha-Brass

1983 ◽  
Vol 27 ◽  
pp. 363-368
Author(s):  
R. B. Roof
Keyword(s):  
Wall Thickness ◽  
External Surface ◽  
Large Strain ◽  
Stacking Faults ◽  
Multiaxial Loading ◽  
Tube Surface ◽  
Line Broadening ◽  
X Ray ◽  
Thin Walled Tube ◽  
Thin Walled

As part of a program studying the effects of large strain deformations resulting from multiaxial loading to a variety of materials, a thin walled tube (0.46” O.D. x 0.02” wall thickness) of 70-30 Brass was subjected to strain deformation in the following directions 1) along the tube axis, εz = 0.3393; 2) circumferential around the tube surface, εθ = -0.0121; 3) perpendicular to the wall thickness, εR = 0.3514. This report describes the results of an x-ray examination of the external surface of the tube by the line broadening technique.

Effect of Including the Bauschinger Phenomenon in the Formula for Collapse Pressure of Thin-Walled Pipes

2020 ◽  
Author(s):  
Alastair Walker ◽  
Ruud Selker ◽  
Ping Liu ◽  
Erich Jurdik
Keyword(s):  
Hydrostatic Pressure ◽  
Wall Thickness ◽  
Bauschinger Effect ◽  
Pipe Wall ◽  
Large Diameter ◽  
Pipe Material ◽  
Pipe Wall Thickness ◽  
Collapse Pressure ◽  
Compressive Stresses ◽  
Thin Walled

Abstract The method presented by DNVGL in DNVGL-ST-F101 [1], “Submarine pipeline systems”, 2017, for calculating the collapse pressure of submerged pipelines is well-known for design of pipes intended to operate in very deep water. Such pipes are regarded as quite thick-walled with diameter to wall thickness ratio in the range of 15 to 30. There is now substantial experience in the practical manufacture, installation and operation of such pipes. Recently there has been a growing use of large diameter pipelines to transport high volumes of gas over great lengths at moderate water depths. The pipes are considered to be thin-walled with ratios of diameter to wall thickness in the range of 30 to 45. This paper assesses the validity of the DNVGL design method when applied to the design of such thin-walled pipes. A particular aspect of the buckling pressure of large diameter pipes is the effect of the Bauschinger phenomenon. The phenomenon occurs when pipes made using the UOE method are subjected to internal pressure, to provide expansion of the pipe during manufacture, thus reducing the out-of-roundness of the pipe wall, and subsequently subjected to external hydrostatic pressure during pipeline operation. To date the Bauschinger phenomenon has been recognised as resulting in a reduction of the circumferential compressive yield of the pipe material. This reduction is accommodated in the DNVGL design formula. Recent research into material properties has shown that the Bauschinger effect also has the effect of reducing the modulus of steel materials over a range of values of applied circumferential compressive stresses. The paper reviews the basis of the Bauschinger phenomenon and presents results from very detailed accurate testing of UOE pipe material. The tests determine the levels of modulus for pipes subject to circumferential compressive stresses. Although results for compressive stress-strain values have previously been available for pipes subject to high levels of hydrostatic pressure it has been considered that the Bauschinger effect is not generally significant for thick-walled pipes. The tests reported here consider the calculation of material modulus levels for low levels of stress that correspond to the buckling stress of thin-walled pipes. The calculated collapse pressure for such pipes is examined in this paper and compared to corresponding results from the DNVGL design formula to provide guidance on the effect of design levels of pipe wall thickness due to inclusion of the Bauschinger effect. The comparisons are for example pipe wall thickness and material conditions. Conclusions are drawn that including the Bauschinger effect in the calculated pipe wall thickness can have a beneficial effect with regard to pipe manufacturing and installation costs for pipe subjected to mild heat treatment.

Multiple performance characteristics optimization in end milling of thin-walled parts using desirability function

2020 ◽  
Vol 44 (1) ◽  
pp. 84-94 ◽  
Author(s):  
Djordje Cica ◽  
Stevo Borojevic ◽  
Goran Jotic ◽  
Branislav Sredanovic ◽  
Sasa Tesic
Keyword(s):  
Surface Roughness ◽  
Wall Thickness ◽  
End Milling ◽  
Influential Factor ◽  
Machining Process ◽  
Cnc Machine Tools ◽  
Reference Plane ◽  
Machining Parameters ◽  
Machining Strategy ◽  
Thin Walled

With the development of high-performance CNC machine tools, milling has been established as one of the main means of machining thin-walled parts. Thus, the selection of process parameters for milling operations is an important issue in end milling of thin-walled parts to assure product quality and increase productivity. The current study explores three machining parameters, namely wall thickness, feed, and machining strategies, that influence dimensional and form errors, surface roughness, and machining time milling of 7075-T6 aluminum alloy thin-walled parts. The effects of machining parameters on each of the response variables were analyzed using graphs of the main effects and three-dimensional surface plots. Analysis of the results show that the most influential factor for wall thickness deviation, dimensions deviation, perpendicularity deviation, flatness deviation, surface roughness of inner walls, surface roughness of outer walls, and surface roughness of reference plane was machining strategy, while feed is the most influential parameter affecting the machined time, followed by the machining strategy. The desirability concept has been used for simultaneous optimization in terms of machining parameters of the thin-walled parts machining process. Finally, a confirmation test with the optimal parameter settings was carried out to validate the results.

Technological sample for evaluation of filling capacity of thin-walled body aluminum castings

2021 ◽  
pp. 387-391
Author(s):  
R.M. Kharchev ◽  
A.N. Grachev
Keyword(s):  
Production Process ◽  
Wall Thickness ◽  
Aluminium Alloys ◽  
Complex Configuration ◽  
Body Parts ◽  
Sample Design ◽  
Aluminum Castings ◽  
Thin Walled ◽  
Technological Sample ◽  
Filling Capacity

Prerequisites for development of technological sample design for assessment of filling capacity of thin-walled body parts of complex configuration with wall thickness of 3 mm are considered. The production process of the obtained sample, as well as the results of its application for aluminium alloys are presented.

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