Tooth Trace Research Articles

Hot Finish Rolling of Injection-Molded Plastic Helical Gears. Properties of Finished Tooth Form.

Hot finish rolling has been developed as a simple finishing method for injection-molded plastic gears. In the present paper, properties of the hot-finish-rolled tooth form are discussed so as to obtain general information for improving the quality of the injection-molded plastic helical gears. The plastic helical gear generally has a positive pressure angle error on the tooth profile and a helix angle error on the tooth trace. After the hot finish rolling process, the finished gear has a negative pressure angle error on the driven tooth flank and a positive pressure angle error on the followed tooth flank. Sliding of tooth flanks along the profile contributes to inducing these errors. Hence, hot finish rolling including the process of reversing the rotation of gears is very useful for improving the quality of the tooth profiles of plastic gears. However, the hot finish rolling process exhibits no sliding along the face width, and thus it cannot improve the quality of a tooth trace which has a helix angle error. It can be expected that sliding along the face width will be useful for improving this error. For example, the axial feed of the work gear might induce such sliding.

A Method for Evaluating the Friction Coefficient of Spur Gear Tooth Flanks. Examinations with a Rack Model.

The friction coefficient of gear tooth flanks is an important factor in clarifying the mechanism of surface failures such as pitting and scoring and in improving the performance of power transmission gears. This is a basic study to establish a method for evaluating the friction coefficient of a spur gear pair under uniformly distributed load along the tooth trace using the fillet strains measured by strain gauges. Experiments with a rack model were carried out with static loads. The frictional and normal forces acting on the working flank were derived by solving the system of equations concerning the fillet strains on the working and nonworking flank sides. The accuracy of the ratio of the friction force to the normal force was examined. The results demonstrate that in order to obtain a meaningful friction coefficient of spur gears it is very important to consider the independence of the relation between the fillet strain and the forces on the working flank.

Effect of Tooth Bearing on Fillet Stress of Straight Bevel Gear.

In order to investigate the effect of a tooth bearing on static and dynamic fillet stress, the fillet strain is measured under various transmitted tooth load in a power-circulating-type gear testing machine for a straight bevel gear, and the measured results are discussed. The results are as follows. The state of the tooth bearing influenced by increase in transmitted tooth load differs in the toe bearing and the heel bearing. At the toe bearing, the dynamic load has a marked effect on the distribution of fillet strain in the tooth trace direction, but it does not at the heel bearing. While the bevel gear runs, there is a change in the position of maximum fillet strain in the tooth trace direction at the toe bearing under various transmitted tooth load.

Measurement of Three-Dimensional Curved Surface of Machine Part Using Holographic Interferometry. 1st Report. Correspondence between Coordinate System of Measured Surface and That of its Image.

In interferometry measurement using laser holography, it is not easy to find a definite relation between the measured image pattern and the topography of the actual surface. The main reason is that each of the measuring object, measurig apparatus, electronic data processor and CRT display has its own coordinate system, and the transformig or mapping relation between them is obscure. In this report, measured image of some test pieces with plane and cylindrical surfaces were compared with their simulated figure. Subsequently, tooth flank of a gear, which is a three-dimensional curved suface in which high accuracy in form is required, was chosen as the object of measurement. To obtain the relation between each coordinate system of a measuring object, of optical parts in the measuring appartus and of the image on a CRT, a method is proposed which requires the simulated contour of the diffracted figure of the objective curved surface to be measured corresponding to and fitting the actually measured and observed image pattern on the CRT. The experimental and simulated results indicate that the pixel position of the image on the CRT can correspond to the coordinate value of the tooth flank, and that the transformation of the measured image on the CRT to the error surface of tooth flank defined on the plane of action of the gear, i. e., to the tooth form chart and to the tooth trace form chart, is possible.

A Study on a Gear-Cutting Method for Parallel-Depth Hypoid Gears. 1st Report; Gear-Cutting Theory.

The purpose of this study is to develop a geat-cutting method for hypoid gears to obtain good tooth bearing and to attain good performance for practical use. In this report, the authors propose a new cutting method of the parallel-depth hypoid gears which mesh with each other at one point at a constant angular velocity ratio. The most important point that the authors want to claim is that not only is the conjugate contacting granted, but also the designer can control the trace of the point contact mark on the tooth surface as he desires. Finally, the authors show an example of the design in which the trace of the point contact mark coincides with the tooth trace.

Tooth-Trace Crowning in Form Grinding of Helical Gears.

A method for modifying tooth traces (crowning) of helical gears finished in form grinding is described. Three kinds of additional motion in grinding process, (a) the approaching motion between the grinding wheel and work axes, (b) the additional Screw motion of the work gear, and (c) the shifting motion of the grinding wheel. are introduced for crowning of helical gears. Equations for calculating the tooth profiles of the crowned helical gears ground with these additional motions are derived. The shapes of the tooth surfaces of the crowned helical gears are illustrated using the contour lines which indicate the distance from the theoretical involute tooth surface. From the results of numerical calculation, it is shown that use of the approaching motion between the grinding wheel and work axes is the most practical method of crowning because it produces both tooth surfaces at the same time, accomplishing suitable profile modification at the tooth ends where the contact between the meshing teeth starts.

Design of Angular Hypoid Gears. 1st Report. Pitch Cone and Basic Dimensions.

This paper discusses about how to design and get the angular hypoid gears, when their pinion offsets are given above or below center. It is unable to apply the calculating methods of design and gear cutting to be used in the hypoid gears with a 90-degree shaft angle to the angular hypoid gears as they are. Then the present report describes on several conditions required to expand the design method of hypoid gears heretofore into the angular hypoid gears. Consequently the design elements of the offset, the spiral angle, the cutter radius, the curvature of the tooth trace, and so on have been treated as a positive value usually, but it becomes clear that they have to mark the plus or minus sign for the method of common design.

Cold rolling of zigzag-toothed gears. Improvement of material flow by arranging the teeth in zigzags.

A new type of cylindrical gear which is called a zigzag-toothed gear is proposed.This type of gear has the same cross-sectional profile as a conventional spur gear, and a tooth trace which is arranged in zigzags on a cylindrical surface. A specigl configuration, such as a zigzag-toothed gear, improves the material flow in gear rolling so that there is a more precise form of tooth. In rolling this type of gear, the axial flow of material, which seems to be indispensable to complete the gear rolling but never appears in the rolling of conventional gears, is induced. Additionally, this type of gear has the advantage of maintaining good conditions for the lubricant and the ability to support some thrust load.

Three-dimensional photoelastic analysis of hourglass worm gear. 2nd Report, Case of modified hindley worm gear.

While many geometrical studies on the hourglass worm gear have been reported, there are few studies on its intensity. In this study, the stress distribution in the direction of the tooth trace of the modified Hindley-type worm gear used now was analyzed by the three-dimensional photoelastic method. As a result, it was shown that the root stress distribution in the direction of the tooth trace in normal setting becomes higher on both the tension side and compression side at the part of throat. However by setting the worm shaft to the ending side or starting side, the stress distribution becomes lower than that in the normal setting state.

Fundamental research on the hobbing of austempered spheroidal graphite cast iron. On the most suitable clearance angle of the hob.

This paper discusses the hobbing of gears made of austempered spheroidal graphite cast iron, which has become an object of attention recently as a new material for gears. This iron has many advantages, such as the properties of a cast material and a high strength equivalent to that of steels, and is also an economical material. However, this cast iron is hobbed before heat treatment at present, for the hobbing of teeth of a hardened gear blank is considered to be very difficult. Yet, if the cutting of a hardened gear blank is possible, the cost will be lower because the gear can be used without performing a finishing operation on the tooth surface removing the distortion from heat treatment. In this study, a basic test was conducted using a TiN - coated fly-tool having the same form as one blade of a hob. Next, a hobbing test was conducted using a TiN-toated hob with a large clearance angle of 15°. As a result, the following conclusions were obtdined : ( 1 ) A groove length of only 3.75 meters can be achieved for the work by a (TiN- coated) fly-tool with a clearance angle of 12°. ( 2 )A (TiN- coated) hob with a clearance angle of 15°can apply to ADI. ( 3 ) The accuracy of the tooth profile and the tooth trace of a hobbed ADI gear correspond to the JIS 1 st and 4 th grades. respectively.

A Study on the Design of Thin-Shaped Straight Bevel Gears : 2nd Report, Numerical Analyses of the Effects of Rim-Web Configuration upon the Root Stress Distribution along the Tooth Trace

Various configurations of thin-shaped bevel gears are widely used such as in the main reduction gear of helicopters and hovercraft. But a reasonable and concise design guide for these bevel gears has to be obtained, since the tooth of the bevel gear has a complex from. The purpose of this study is to establish a design guide and to propose the desirable configuration for thin-shaped straight bevel gears. In this report, the desirable configuration is examined numerically using the finite element method. The results are summarized as follows : (1) As a desirable configuration of a thin shaped bevel gear, it is recommended from the viewpoint of root stress that the rim is supported by a web at the center of its width. (2) When the rim is supported at the center of its width, a flat web, a cone-shaped web, a web composed of cone-shaped and and flat plates and a web composed of root stress. (3) For practical use, it is recommended that the bevel gear has a flat web at the center of rim width and a rim whose thickness varies in direct proportion to the change of tooth height.

Cold rolling of zigzag toothed gears. (Improvement of material flow by arranging the teeth in zigzags).

A new type of cylindrical gear which is called da zigzag toothed gear is proposed. This type of gear has the same cross-sectional profile as a conventional spur gear, and a tooth trace which is arranged in zigzags on a cylindrical surface. A special configuration, such as a zigzag toothed gear, improves the material flow in gear rolling so that there is a more precise form of the tooth. In rolling this type of gear, the axial flow of material, which seems to be indispensable to complete the gear rolling but never appears in the rolling of conventional gears, is induced. Additionally, this type of gear has the advantage of maintaining good condition for the lubricant, and the ability to support some thrust load.

Roll-finishing of a quenched gear. 1st report. Fundamental investigation.

In the present report, the possibility of the roll-finishing of a quenched gear was discussed. In order to reveal the effects of the quenching of a gear on a roll-finished tooth form, computer simulations were carried out. In the simulation, an increase of flank hardness by quenching was regarded as an increase of contact compliance of the tooth flank, i. e. an increase in resistance to contact deformation. The simulation result showed that an increase in contact compliance reduced the amount of rounding down at both tooth edges on a roll-finished tooth trace. Then, experiments of the roll-finishing of a quenched work-gear were carried out. In these experiments, the roll finishing of work-gears with flank hardness HRC = 40 induced a fairly good tooth form, as in the simulation results. However, when the flank hardness of the work gear was HRC = 55, a strong interference between the tooth tip of the die-wheel and the tooth root of the work-gear was induced and roll-finishing did not proceed.

Fundamental research on the hobbing of austempered spheroidal graphite cast iron. (2nd Report: On the most suitable clearance angle of the hob).

This paper discusses the hobbing of gears made of austempered spheroidal graphite cast iron, which has become an object of attention recently as a new material for gears. This iron has many advantages, such as the properties of a cast material and a high strength equivalent to that of steel, and is also an economical material. However, this cast iron is hobbed before heat treatment at present, for the hobbing of teeth of a hardened gear blank is considered very difficult. Yet, if the cutting of a hardened gear blank is possible, the cost will be lower because the gear can be used without performing a finishing operation on the tooth surface removing the distortion from heat treatment. In this paper, a basic test is conducted by using a TiN-coated fly-tool having the same form as one blade of a hob. Next, a hobbing test is conducted using a TiN-coated hob with a large clearance angle of 15°. As a result, the following conclusions are obtained: (1) A groove length of only 3.75 m can be achieved for the work by a (TiN-coated) fly-tool with a clearance angle of 12°. (2) A (TiN-coated) hob with a clearance angle of 15° can apply to ADI. (3) The accuracy of the tooth profile and the tooth trace of a hobbed ADI gear correspond to the JIS 1st and 4th grades, respectively.

Effects of load distribution on the antiseizure capacity of lubricating oil. Experimental results with crowned cylinders.

In a crowned gear pair, which is employed to prevent end-tooth bbearing, the load distribution in the tooth trace direction is elliptical. This paper describes the effects of crowning on the antiseizure capacity of a gear base oil. The experiments were carried out by two-cylinder tests at high specific slidings comparing the results under uniform bearing. The antiseizure capacity of the gear base oil in the tests with crowned cylinders was higher than that in the tests with uncrowned cylinders. Though the contact width in the axial direction at seizure became small and the Hertzian stress at seizure became high as the radius of crowning was decreased, the radius of crowning hardly affected the antiseizure capacity. Finishing the surface roughness finely is an effective means to decrease the friction coefficient and to increase the antiseizure capacity of the gear base oil in the higher range of sliding velocity.

Effects of load distribution on the anti-seizure capacity of lubricating oil. 2nd report. Experimental results with crowned cylinders. Part 1.

In a crowned gear pair, which is employed to prevent end tooth bearing. the load distribution in the tooth trace direction is elliptical. In this report. the effects of crowning on the anti-seizure capacity of a gear base oil have been examined by two-cylinder tests at high specific slidings comparing with the results under uniform bearing. The anti-seizure capacity of the gear base oil in the test with crowned cylinders is higher than that in the test with uncrowned cylinders. Though the contact width in the axial direction at seizure becomes small and the Hertzian stress at seizure becomes high as the radius of crowning is decreased, the radius of crowning hardly affects the seizure load. The outer surface bulk temperature just before seizure, which becomes high as the radius of crowing is increased, is hardly affected by the radius of crowning at high sliding velocities.

Acceptance Condition for Toothform- and Toothtrace Accuracy of Cylindrical Involute Gears and its Effect On Power Transmitting Characteristics : 1st Report, Acceptance of Gears with Bad Tooth Flank Form

To express the quality of the form of a gear tooth flank, the error surface defined as the difference between an ideal involute helicoid and an actual tooth flank of cylindricai involute gears expressed on the plane of action, is useful. Here, a method to illustrate the error surface for the form of a gear tooth flank from some tooth form- and tooth trace checking curves measured along some definite positions on a tooth flank is introduced. This method vas used in a simulation of power transmitting characteristics of cylindrical involute gears, and the problem of gear acceptance was discussed. It was found to be a problem to receive gears whose quality was actually out of tolerance and showed poor performances. The results of the state of tooth flank loading in the simulation suggested that this mistake occured due to the insufficiency of the test method of gear quality at acceptance.

Stress analysis of hourglass worm gear. 1st report Case of classical hindley worm gear.

While many geometrical studies on the hourglass worm gear have been reported, there are few studies on its intensity. In this paper the root stress distribution in the direction of the tooth trace and the stress distribution in the direction of the tooth depth are measured by the three-dimensional photoelastic method, when a pair of classical hindley worm gear are loaded statically. The results indicate that maximum tensile stress is generated on the root of the tooth which is located at 60 degrees to 70 degrees from the contact markings along the worm tooth trace.

Effects of load distribution on the anti-seizure capacity of lubricating oil. (1st report Effects of contact width under uniform bearing)

As a basic study for making clear the effects of load distribution in the tooth trace direction on the anti-seizure capacity of lubricating oil, the effects of contact width on asperity interaction and the anti-seizure capacity under uniform bearing have been studied for a gear base oil with a two-cylinder test rig at a high specific sliding. The seizure took place from the mixed lubrication state. Though the asperity interaction is high at a small contact width, the effects of contact width on the asperity interaction diminishes as the contact width is enlarged. At a small surface roughness, the seizure load and the outer surface bulk temperature just before seizure increase as the contact width is enlarged. On the other hand, at a large surface roughness, in the higher sliding velocity range, the seizure load diminishes as the contact width is enlarged over a certain value, and the outer surface bulk temperature just before seizure is lower than that at the small one.

A simple method of bevel gear cutting (2nd report, Crowning method)

In the previous report the authors proposed a new simple method of bevel gear cutting. In the method, the cutter and the gear work are set and driven in a basic simple manner. The tooth surface of the gear is eased off on its tip and root and has the narrow bearing zone along the tooth trace on it. This paper investigates two methods that give some crowning along the tooth trace. In the first method, the cutter blade traverses along the bottom of the tapered tooth space and cuts simultaneously the both side surface of the tooth space. In the second method, the cutter axis is set with an angle to the crown gear axis and the cutter blade is fed a little deeper at both inside and outside of the bevel gear teeth. The investigation shows that the latter method gives a simple estimation of the magunitude of the tooth crowning and an easy setting of the cutter.