Rack Tooth Research Articles

Development of Crawl-type Transfer Mechanism using Driving Disk Attached to Parallel with Wall. Application to Straight Track Transfer System.

The aim of this work is to supply a new, cost effective transfer system for wheelchair users. In this context, a new mechanism, known as "crawl-type", has been developed. This system is composed of three parts, traction guides, drive guides, and a hoist carrier. The former two kind of guides were attached with wall, the latter one was engaged with a pair of traction guides and was moved by propulsion force using crawl-type mechanism. By attaching a driven disk on the hoist carrier to be parallel with wall, drive guides become to fabricate easily using two-dimensional plate. The drive guide resembles to a rack tooth, which is drawn as a part of parallel curve to cycloid one. A width of tooth was analyzed by varying the number of rollers and sliding ratio of disk against virtual line. The analysis show that maximum width of tooth was obtained when the number of rollers is six and at non-sliding condition. By using this kind of rack, reversible transfer by crawl-type mechanism has been become to be available.

Fret retractable neck for stringed musical instruments

A stringed musical instrument (12) that can be played either in a fretted or a fretless mode includes an interconnected fret assembly (38) including frets (24) and a longitudinal fret interconnecting member (40) that is attached to, and movable with, the frets. A movable linear cam structure (46) has two cams at each fret, one positioned on each side of the fret interconnecting member, and includes rack teeth (52) which mesh with a pinion (62) driven by a lever (66) for causing linear movement of the linear cam structure. The interconnecting member is an elongated slat (40) which is positioned in a slot (50) between the cams. The linear-movable cam includes an elongated guide protrusion (56) and an interior cavity (30) of the fingerboard, in which the cam rides, defines an elongated guide slot (58) for receiving the guide protrusion and thereby limiting lateral movement of the linear cam. The linear cam structure and the interior cavity have tapered lateral sides.

A Reconsideration of the Geometry Factor for the Standard and Profile Shifted Teeth

A semi-empirical equation for the determination of the stress concentration factor for spur gears is introduced. The effects of some design parameters such as fillet radii of rack cutters, teeth number, and profile shifting factor, on the stress distribution at the fillets of gear teeth are investigated. Values of the modified geometry factors for the standard and profile shifted teeth are also derived. It is hoped that the present investigation may yield a more accurate prediction of the localized stresses at tooth fillets than the results thus far available.

Strength of Contact Part of Rack Tooth for Leg Fixing Device of Juckup Rigs

The rack teeth of a leg fixing device, which is indispensable for a jackup rig to operate in harsh environment, such as the North Sea, take severe load and the Hertz contact pressure of the contact part exceeds the yield point of the material. In this case, plastic deformation of the contact part gives favorable effect on the distribution of load among mutually contacting several pairs of rack teeth. Accordingly, it is very important to study on the strength of contact part of rack tooth for static and cyclic loading.In this paper, static tests and cyclic contact tests on scale models of rack tooth contact part are performed. Then three kinds of analyses (3-dimensional, plane stress and plane strain analysis) are performed on the static contact model by using the finite element method for elasto-plastic contact problem. Following conclusions are obtained from a comparison between the results obtained from the calculation and the static test as well as from the results of the cyclic contact test.(1) Comparing the calculated results of three kinds of analyses by the finite element method, it is made clear that the effect of the stress in the direction of plate thickness on the stress and strain distributions on the contact area is predominant.(2) From the comparison between calculations and experiment concerning strain, maxi-mum displacement, residual displacement and contact width, it is shown that the results of the 3-dimensional analysis correlates quite well with the experiment ones.(3) From the results of the 3-dimensional calculations on the contact model with various thickness of the plate, it is found that the feature of the transition from plane stress state to plane strain state is made clear.(4) Cyclic contact test up to 2×104 cycles shows the characteristic of the behavior of displacement and strain of the models. It is clarified that there will be no problem as for the strength of the contact part even under such high contact pressure σH equal to Brinell Hardness HB as σH/HB=1.0.

Strain and Fatigue Strength of Rack Tooth Fillet for Leg Fixing Device of Jackup Rigs

The rack teeth of a leg fixing device, which is indispensable for jackup rig to operate in harsh environment, take cyclic load caused by waves and winds. Accordingly, it is very important to know the fatigue strength of rack teeth.In this paper, fatigue tests of rack tooth models and small bar specimens whose material is HT 80 are performed, and the analysis of the rack tooth models by finite element method is performed as elasto-plastic contact problem with friction.Comparing the calculated results with experimental ones, following results are obained.(1) The effect of frictional force on the strain at rack tooth fillet is not negligible.(2) Manson-Coffin type equation proposed by Iida is useful to predict the fatigue crack initiation life for HT 80.

Ultimate Strength Design of Racks for Jack-Up Units

The subject of paper discusses an approach taken in evaluating the load acting on racks for jack-up units (the jack load) together with its computed results. The fracture test of a full-scale rack for a jack-up unit and a finite-element elastic stress analysis for this rack were also conducted. These results led to new design criteria for the ultimate strength design method of racks for jack-up units, when exposed to a combination of loads including stormy conditions. Typically, the ultimate strength of the racks was evaluated on the assumption that the cross section of the rack tooth plastically collapses at its root. During this investigation, it was shown, however, that the ultimate strength of the racks needs to be evaluated also on the premise that the rack tooth is subject to shear fracture caused by its mating pinion tooth.

Fracture behavior of a large scale, torch-cut high tensile strength steel rack

A static loading test is conducted for a torch-cut rack of 80.9 mm in module and 25° in pressure angle with a backplate by using a 10,000 ton press. The tips of the two rack teeth are in mesh with the flank of the two pinion teeth. This paper discusses the plastic deformation and fracture behavior of the rack tooth utilizing the photographs of the rack deformation and the fractographs of its fracture face. The cracks are first initiated on the compressive side of the rack tooth under the shearing displacement, and one of the cracks propagates toward the tensile side under the edge-sliding and tearing displacement modes, resulting in a rack tooth failure.

On the Strength of Racks for Jack-up Units : 4th Report, Estimation of the Static Strength of the Racks, by Using Stnall Scale Specimens, for the Meshings in the Vicinity of Rack Tooth Tip and Fillet

The subject of paper discusses the results of fracture tests for racks of 11.55 mm in module (1/7 of that of the full scale rack) and the finite element elastic stress analysis. These results lead to the conclusion that the differential in the ultimate strength between the full scale and 1/7 scale racks is small and that the ultimate strength of the racks is well expressed, for the varying initial meshing points, in terms of the shear strength of the cross-section with which the pinion tooth tip interferes. The authors also elucidate the difference in the pattern of plastic deformation and fracture of the racks resulting from the difference in the initial meshing point.

On the Strength of Racks for Jack-up Units : 2nd Report: Mainly on Elastic Behavior of a Full Scale Rack with a Back-Plate and Pinions during Static Loading Test

A static loading test is conducted for a rack of 80.9 mm in module with a back-plate for a jack-up unit by using a 10.000 ton press. The tips of two rack teeth are in mesh with the two pinion teeth. 124 strains, 20 displacements, and 4 loads are measured at various locations in the two pinions, the rack, and the apparatus under 32 different static loading conditions. An elastic stress analysis is also conducted by using the FEM under plane stress condition in order to compare strain results. It is shown that the computed strains are higher than those measured by using strain gages for the compressive fillets of the rack and vice versa for the tensile fillets. It is also shown that the tangential strains in the vicinity of the pinion sides are higher than those at the center of the face width for compressive fillets of pinions and vice versa for tensile fillets. Other aspects of strain distribution are also discussed.

On the Strength of Racks for Jack-up Units : 3rd Report: On Plastic Deformation and Fracture Behavior of a Full Scale Rack with a Back-Plate during Static Loading Test

This paper discusses the plastic deformation and fracture behavior of a rack of 80.9mm in module and 25° in pressure angle for a jack-up unit. The fracture testing method for this rack was stated in the 2nd Report of this research. In this report, the author elucidates the mechanisms of the plastic deformation and fracture of the rack teeth. The plastic deformation first occurs in the contact areas of the rack teeth and then expands downward to the fillets. Cracks are initiated on the compressive side of the rack tooth under the shearing displacement mode, and one of the cracks propagates toward the tensile side under the edge-sliding and tearing displacement modes, resulting in a rack tooth failure. The pattern of plastic strain distribution across the face width of the rack teeth and the strain distribution on the chord surface are also discussed.