Actual Gear Research Articles

Optimized tooth profile based on identified gear dynamic model

A new method to determine the dynamic model of a practical gear system is proposed by the identification of the relation between the rotational movement of gears and the acoustical noise signal measured on the gear tester. The rotational movement alone the line of action of gears is treated as the input of the dynamic gear system and the acoustical noise signal as the output. The parameters of the model are estimated by the LSM (least square method). By an example that the gear pair works under a certain design load and rotational speed, the identified model is verified and the optimized gear tooth profile modification is derived based on the identified model. The tested results show that the profile modification can greatly reduce gear noise.

103 長寿命域におけるオーステンパ処理球状黒鉛鋳鉄(ADI)の面圧強さに関する基礎研究 : き裂の発生から損傷に到るまでの進展過程の観察および疲労限予測(OS02-1 歯車の強度I)

Austempered Ductile Iron (ADI), which has much the same strength and toughness as usual steels, has been developed. ADI has many advantages in mechanical properties and manufacturing, for example, weight reduction due to smaller density than that of steel, good properties of vibration and noise, low cost in machining and heat treatment of blanks due to near-net-shape casting. It has been reported that ADI can be sufficiently applied as a medium hardness gear material. Recently, two steps bending phenomenon of S-N curve for the bending fatigue strength of ADI is reported, and the fatigue phenomenon in long life region over 10,000,000 time number of cycles is discussed. However, the surface durability in long life region has not been clarified until now. In this paper, surface durability of ADI rollers in long life region is investigated using a disk machine which simulates the rolling and sliding action of gears. Furthermore, fatigue limit for surface durability of ADI is estimated by observations with crack initiation and propagation.

Estimation of gear tooth transverse crack size from vibration by fusing selected gear condition indices

Gears are common power transmission elements and are frequently responsible for transmission failures. Since a tooth crack is not directly measurable while a gear is in operation, one has to develop an indirect method to estimate its size from some measurables. This study developed such a method to estimate the size of a tooth transverse crack for a spur gear in operation. Using gear vibrations measured from an actual gear accelerated test, this study examined existing gear condition indices to identify those correlated well to crack size and established their utility for crack size estimation through index fusion using a neural network. When tested with vibrations measured from another accelerated test, the method had an averaged estimation error of about 5%.

Prediction of Power Losses Due to Tooth Friction in Gears

Sliding friction between gear teeth is recognized as one of the main sources of power loss in geared transmissions as well as a potential source of vibration and noise. Its accurate modeling is therefore of primary importance in efficiency and vibration analyses of mechanical transmissions. For lubricated contacts, various empirical friction laws based on results from simulators can be found in the literature. One of their limitations comes from the specimen surface texture, which is often different to that of actual gears. Moreover, most of these models were established for high slide-to-roll ratios and cannot be used for low slide-to-roll ratios as encountered near the pitch point in gears. In this article, friction measurements were derived from an EHL simulator with contact conditions and surface finish close to those in gears and which covers a wide range of sliding/rolling conditions. A new traction law is proposed and integrated in a three-dimensional dynamic model of gears with consideration of tooth friction. The numerical results are then compared with the experimental evidence from a gear test rig. It is observed that tooth friction can strongly affect dynamic transmissibility through bearing mounts. Finally, the need of an accurate friction model for reliable power loss predictions is stressed. Presented at the STLE Annual Meeting in Toronto, Ontario, Canada May 17-20, 2004 Reviewed led by Liming Chang

Tooth Action and Tooth Bearing of a Pair of Nonintersecting-nonparallel Axis Conical Involute Gear

Conical involute gears used for marine transmission are mostly helical conical involute gears. Besides these gears are not intersecting axis gears but also nonintersecting-nonparallel axis gears. In this case the contact between tooth surfaces of a pair of gears is point contact. Hence the tooth surface durability is generally small. This research aims at the establishment of the design and production system of the Concave conical gears for marine transmissions. First the gear tooth action of a pair of nonintersecting-noparallel axis gears is analyzed. Secondly, test gears are made and tooth bearing test are proves. Tooth bearing marks are in good agreement with the theoretical ones.

1212 大局的形状パラメータを用いた三次元歯面修整の新しい評価法(OS1-3 振動(1))

The purpose of this research is to derive the meaningful parameters and the new procedure of measurement of tooth flank topography to evaluate the individual gear accuracy objectively. For this purpose, the tooth flank topography is characterized as the curved surface and the parameters for tooth flank topography are derived from the 3-dimensional measured deviations of tooth flanks. After derivation of a new definition of the pitch deviation, the parameters for the 1st and 2nd order form deviations are derived. Using those parameters, three-dimensional modification of a tooth flank is characterized according to the order of the surface. They can be calculated from the measured conventional deviations and separation process of measured deviations into 1st and 2nd order form deviations are automatically performed and the parameters are calculated at the same process. Actual gear flanks of a bevel gear are measured and the newly proposed parameters are calculated and evaluated.

コニカルギヤの相対歯面形状解析(O.S.08-1 コニカルギヤ・その他)

Conical involute gears are used with intersecting or skew axes for controlling backlash. However the contact between tooth surfaces of a pair of conical involute gears is point contact, so the load carrying capacity is generally small. To overcome this week point of the conical involute gear, it is necessary for the tooth surface to be modified. In this paper, first, ease off of conical involute gears is calculated by means of a tooth contact analysis. We get it in the whole tooth surface and called it "relative tooth surface". Secondly the gear tooth action of a pair of intersecting or skew axes is analyzed. Finally, test gears are made and tooth bearing tests are performed. Experiment results prove that theoretical analysis holds true.

微少油量潤滑(MQL)条件下におけるオーステンパ処理球状黒鉛鋳鉄(ADI)歯車の性能に関する研究(O.S.02-2 歯車の強度(2))

Austempered Ductile Iron (ADI), which has much the same strength and toughness as usual steels, has been developed. ADI has many advantages in mechanical properties and manufacturing, such as weight reduction, good properties of vibration and noise, low cost in machining and heat treatment of blanks due to near-net-shape casting. Using these advantages, it has been reported that ADI can be sufficiently applied as a medium hardness gear material. In addition, it is important to reduce the amount of the lubricant when many problems, i.e. global environment, resource conservation and cost reduction, etc., are considered. So it is necessary to examine the performance of ADI under oil-free condition or Minimal Quantity Lubrication (MQL) condition. In this paper, MQL condition is investigated using a disk machine which simulates the rolling and sliding action of gears. Then the surface failure strength of ADI gears under spray MQL condition is examined using a power-circulating type gear testing machine in comparison with steel gears which have almost the same hardness of ADI. As the results of experiments, the surface failure strength of ADI gears under MQL condition is larger than that of SCM435 gears.

A Fundamental Study on the Surface Failure Strength of Austempered Ductile Iron (ADI) Gears [Performance of ADI Rollers under Minimal Quantity Lubrication (MQL) Conditions

Austempered Ductile Iron (ADI), which has much the same strength and toughness as usual steels, has been developed. ADI has many advantages in physical properties and manufacturing, such as weight reduction, good properties of vibration and noise, low cost in machining and heat treatment of blanks due to near-net-shape casting. Using these advantages, it has been reported that ADI can be sufficiently applied as a medium hardness gear material. In addition, it is important to reduce the amount of the lubricant when many problems, i.e. global environment, resource conservation and cost reduction, etc., are considered. So it is necessary to examine the perfarmance of ADI under oil-free condition or Minimal Quantity Lubrication (MQL) condition. In this paper, the surface failure strength of ADI rollers is investigated using a disk machine which simulates the rolling and sliding action of gears. In particular, the surface failure strength under the MQL conditions is examined in comparison with the steel which has almost the same hardness of ADI. As the results of experiments, the surface failure strength of ADI rollers under MQL conditions is as same as that of SCM 435 rollers under usual lubricated condition.

広範囲の歯車に適用可能なピッチ誤差の新しい定義と評価(O.S.04-2 歯車の検査(2))

The purpose of this research is to derive the meaningful parameters and the new procedure of measurement of tooth flank topography to evaluate the individual gear accuracy objectively. For this purpose, the tooth flank topography is characterized as the curved surface and the parameters for tooth flank topography are derived from the 3-dimensional measured deviations of tooth flanks. For the first step, a new definition of the pitch deviation is proposed. The pitch deviation is calculated with multiple deviations of a tooth flank. According to this new definition, a pitch error should be expressed by the angle, not by the length, and it can be calculated from the measured conventional deviations. Actual gear flanks of a bevel gear are measured with the new measuring procedure and the new pitch deviation is calculated.

2508 ADI 歯車の面圧強さに関する基礎研究(微少油量潤滑 (MQL) 条件下における面圧疲労強度)

Austempered Ductile Iron (ADI), which has much the same strength and toughness as usual steels, have been developed. ADI has many advantages in mechanical properties and manufacturing, such as weight reduction, good properties of vibration and noise, low cost in machining and heat treatment of blanks due to near-net-shape casting. Using these advantages, it has been reported that ADI can be sufficiently applied as a medium hardness gear material. In addition, it is important to reduce the use of the lubricating oil when many problems, i. e. global environment, resource conservation and cost reduction, etc., are considered. So it is necessary to examine the performance of ADI under oil-free condition of Minimal Quantity Lubrication (MQL) condition. In this paper, the surface durability of ADI rollers is investigated using a disk machine which simulates the rolling and sliding action of gears. In particular, the surface durability under the MQL conditions is examined in comparison with the steel which has almost the same hardness of ADI.

Solving the Control Problem for Electrochemical Geartooth-Profile Modification Using an Artificial Neural Network

The paper describes a new method for electrochemical tooth-profile modification based on real-time control, and establishes a mathematical model of the electrochemical tooth-profile modification process. The law is found for processing electric current using the artificial neural network, when the tooth-profile modification requirements are given. The results from an actual gear demonstrate that this technology is feasible, and has potential application in production.

Minimization of transmission error in helical gears

A method of minimizing transmission error in helical gears is presented. Using the concept of optimal modification of the plane of action to generate the new tooth profile, the idea of perfect plane of action of helical gears is introduced. The cubic splines are used to determine the optimal helical tooth profile. The method proposed in this work constitutes a general tooth correction method and makes the design, unlike other modification schemes presented in the literature, less complex and less sensitive to dynamic factors and retains the involute characteristics. Also the proposed method permits easier cutting of the tooth profile because of the simplicity of the process.

Simulation of Deterioration of Hypoid Gear Performance due to Tooth Flank Wear. 1st Report. Data Processing of Measured Tooth Flank Form Deviation for Performance Simulation.

As a base for the prediction of deterioration of hypoid gear performance due to tooth flank wear, a method of data processing of measured tooth flank form deviation is proposed, that is used for the input data of performance simulation of hypoid gears with manufacturing and alignment error. Simulated contact patterns of tooth flanks as function of different kinds of measured and then processed tooth flank form deviation are compared with observed contact patterns of new and worn gears to find a proper data processing method. This method reflects and compensates the weak points of today's measuring method for tooth flank form deviation of hypoid gears, because the region of measurement on tooth flank cannot cover whole the region of contact zone of tooth flank under load transmission. The influence of uncertainty with obscure value of shaft alignment error in actual gear box is also considered for the performance simulation.

Performance of a rotating gear pair coated with an amorphous carbon film under a loss-of-lubrication condition

The ability of gear boxes to complete their missions following loss of lubrication is an important parameter in design criteria for various machines. This paper shows the results of the actual gear performance test conducted using a gear testing machine that was subjected to a loss-of-lubrication condition immediately after a short operating period under fully lubricated conditions. The result showed that a gear pair subjected to an initial shot peening process and a subsequent PVD process to deposit an amorphous carbon film (WC/C film) could endure the conditions for a very long time before it failed or seized even under a very severe loading condition, thus demonstrating the utility of gears coated with an amorphous carbon film.

Alternative Aircraft Loading Index for Pavement Structural Analysis

The most common practical way to simplify the structural analysis of airfield pavements is the use of equivalent single wheel load models instead of the actual gear of the aircrafts. As the accuracy and reliability of these models strongly affects the design and evaluation of airfield pavements, there is considerable need to investigate both system approaches. The first one, which uses a constant value for the pressure while the radius is variable, is currently under use by the aircraft classification number-pavement classification number method of the International Civil Aviation Organization, but despite this fact it proved to be inadequate to express the aircraft loading in many situations. On the contrary, according to this study, the second model, which has a constant value for the radius while the pressure varies, is more reliable, and it can be an interesting alternative. Thus, based on this model, an aircraft loading index is introduced, which aims to be a simple and reliable factor for expressing the severity of the loading of the aircrafts and a utility for several matters related to the airfield pavement applications.

Vibration Analysis of Multistage Gear System Including Drive Mechanism Elements. 1st Report, Proposal of Three Dimentional Vibration Model and Eigenvalue Analysis of Helical Gear System.

The increasing demand for quiet gears has created an increasing demand for precise analysis of gear drive vibration. There has been a lot of research on gear vibration analysis; most of which was dealt with a single gear pair. This report shows a new method for building a vibration model for an actual gear drive system. Each gear has six degrees of freedom; three translational motions and three swing motions. Stiffness matrixes for each gear shaft and for tooth meshing were made and overlapped into a stiffness matrix for the total system. This enabled easy modelling of the complex gear drive systems; such as multistage gears and branched gears. The results are in good agreement with experimental results with respect to the major resonance frequencies and vibration modes.

Gearing Up With Plastic

This article explains the engineering design concepts behind injection-molded gears that make drives lighter, quieter, and less costly. As the experience base with plastic gears has grown, computer-aided-design (CAD) tools have advanced. The most powerful advantages of plastic gears may be the design opportunities they afford. Gear geometries overlooked by designers used to metal are often easy to mold in plastic, and they can reduce drive size, weight, and cost. The operating speed of plastic gears obviously impacts operating temperature. However, rapid-loading rates can also affect material properties. For some materials, the faster a tooth is loaded, the higher the effective modulus and strength. It is highlighted that designers of plastic gears should also pay special attention to shaft attachment. Bore tolerances naturally impact true center distances, sometimes resulting in loss of proper gear action. Problems with prototypes can also tempt gear designers to change resins—a costly mistake given the different shrinkage characteristics of various plastics. It is better to rework the tooth profile than switch the material, unless it is clear that the wrong material was chosen.

Analysis of Golf Impact Phenomenon and Ball Trajectory.

The effects of the several factors, namely, the friction coefficient between the golf ball and club head, the eccentric hitting, the inclination of the head and the shape of surface, on the release velocity, the spin velocity and the distance and direction of the flying ball after impact, are investigated. A computer program that analyzes the dynamic contact problem with friction is developed and the impact phenomenon between the head and ball is numerically analyzed using this program. The effects of the factors described above are investigated quantitatively. it is shown that back spin is the result of friction between the head and ball, and side spin is the result of eccentric hitting or inclination of the head, which is called the gear action. In addition, it is shown that the shape of surface influences the trajectory of the ball after impact, which is called the round effect.

Analysis of Golf Impact Phenomenon and Ball Trajectory.

The influences of the parameters, i.e., the friction coefficient between the club head and golf ball, the eccentricity and inclination of the head to the target direction and the surface shape of the head, on the release velocity, spin velocity and trajectory of the ball after impact, are investigated. A computer program that analyzes the dynamic contact problem with friction is constructed, and the impact phenomenon between the head and ball is numerically analyzed using this program. The influences of the parameters described above are investigated quantitatively. It is shown that backspin is the result of friction between the head and ball, sidespin is the result of eccentricity or inclination of the head, which is called the gear action, and the surface shape of the head influences the trajectory of the ball after impact, which is called the round effect.