直齿圆柱齿轮齿廓图形的构建

介绍了用三次样条插值确定直齿圆柱齿轮齿廓的样条插值点和用Mastercam构建直齿圆柱齿轮齿廓的方法。     

Study of a spur gear dynamic behavior in transient regime

In this paper the dynamic behavior of a single stage spur gear reducer in transient regime is studied. Dynamic response of the single stage spur gear reducer is investigated at different rotating velocities.First, gear excitation is induced by the motor torque and load variation in addition to the fluctuation of meshing stiffness due to the variation of input rotational speed. Then, the dynamic response is computed using the Newmark method. After that, a parameter study is made on spur gear powered in the first place by an electric motor and in the second place by four strokes four cylinders diesel engine. Dynamic responses come to confirm a significant influence of the transient regime on the dynamic behavior of a gear set, particularly in the case of engine acyclism condition.     

A study of spur gear pitting formation and life prediction

In this study, a numerical prediction on pitting formation is carried out in spur gear made from austempered ductile iron. General two-dimensional rolling sliding contact situations are considered for the development of the analytical model. The problem is assumed under linear elastic fracture mechanics and the finite element method is used for numerical solutions. Mixed mode stress intensity factors K_I and K_II for cyclic loading are evaluated and related to crack extension by a Paris-type equation. The maximum tangential stress criterion is used to determine the crack-turn-angle during crack propagation under cyclic loading.A series of experimental study is also carried out to determine the pitting formation life. Test specimens were first austenitized in salt bath at 900 °C for 90 min after which they were quenched in salt bath at 325 and 425 °C, for 60 min. A comparison is carried out between numerical and experimental results.     

The influence of operating condition on acoustic emission (AE) generation during meshing of helical and spur gear

The application of high-frequency acoustic emission (AE) technology to condition monitoring of gears is still in its infancy. Understanding the influence of gear operating parameters on the generation of AE is essential in applying the AE technology to gear condition monitoring. This paper presents experimental findings on the influence of speed and load in generating AE for operating helical and spur gears. The experimental findings suggest that any percentage reduction in specific film thickness (λ), a direct consequence of a change in load condition, results in a nine- and four-fold percentage change in AE rms for the spur and helical gear sets, respectively. A numerical model representing changes in AE rms with variation in load and speed under near isothermal conditions for spur and helical gears was also established. In conclusion, it is postulated that the AE technology could offer a means of measuring in situ the effectiveness of a lubricant for operational spur and helical gears thereby establishing if the correct lubricating conditions are present to ensure optimal life usage.     

A study on precision forging of spur gear forms and spline by the upper bound method

Precision forging is an important manufacturing procedure of spline and spur gear forms. It has advantages of improved strength, good tolerance, saving billet material, dispensing with the cutting, etc. In this paper, a mathematical model using an upper bound method is proposed for forging of spur gear forms and spline to investigate the plastic deformation behavior of billet within the die cavity. The material of solid billet was assumed as rigid–plastic and the shape of the tooth profile was accounted for the mathematical modeling of the kinematically admissible velocity field assumed for the plastic zone. The non-uniform velocity was employed for simulating the inhomogeneous deformation and the effect of barreling during the forging. Using the present model, various effects of forming parameter such as the friction factor, reduction, number of teeth, etc. upon the non-dimensional forging pressure, forging force and barreling of the spur gear forms and spline were analyzed systematically and the results compared with those of other researcher's analytical and experimental work. It is shown that the present modeling of the process improves knowledge of the process design performance for the precision forging of spur gear form and spline.     

Shape heading of splines and solid spur gear forms:: an analysis and some experiments

To analyse the process of near-net shape heading of splines and solid spur gear forms with the 15 actual involute teeth, each with a pressure angle of , where in each case these were to be forged integral with the shaft and one end of the initial deforming cylindrical specimen was considered as constrained. Two types of theoretical approaches, i.e. the upper-bound technique (Chitkara and Bhutta. Proceedings of 28 MT DR Conference, 1990. p. 431–42; Chitkara and Bhutta. International Journal of Mechanical Sciences 1995;37(12):1247–68; 1996;38(8–9):891–916) and the slab method of analysis (Chitkara and Bhutta. International Journal of Mechanical Sciences 1996;38(8–9):871–89) employed earlier for simple forging of the product were suitably modified to account for the constraint, were applied. In each case, the estimated theoretical results for the die loads at increasing die movements were compared with those observed experimentally during the quasi-static incremental heading of splines and solid spur gears using tellurium lead as the model material for the specimens. The characteristic deformation modes and some salient observations made on the working pressures during the heading process vis-à-vis simple forging of these products are given and the results are commented upon.     

Pitch deviation measurement of an involute spur gear by a rotary profiling system

This paper presents surface-profiling based gear pitch deviation measurement for an involute spur gear. A rotary profiling system, which consists of an air-bearing spindle and a displacement sensor with a diamond stylus, is employed to measure gear pitch deviation. In measurement of gear pitch deviation, an eccentric error between a gear axis and a motion axis of the rotary stage in the profiling system would affect accuracy of gear profile measurement. In this paper, at first, the influence of the eccentric error on measurement of gear pitch deviation is estimated in computer simulation based on a geometric model of the profiling system. After that, a new scanning method named “opposite-direction dual scanning method” is proposed so that a steep profile of gear flank surface with a local slope of up to 90° can be measured by the developed rotary profiling system. For compensating distortions in the measured gear tooth profile, which are induced not only by the eccentric error but also by a probe offset introduced by the proposed scanning method, a self-calibration and compensation method is applied. To verify the feasibility of the proposed method, measurement of gear pitch deviation of a master involute spur gear with a certificate data is carried out. Measurement uncertainty of the proposed method is also analyzed.     

Identification of bearing load by three section strain gauge method: Theoretical and experimental research

Reasonable bearing load distribution is important for the safe and reliable operation of rotating machinery. However, it is difficult to measure bearing load in field. This paper puts forward a bearing load identification method based on the measured three section strain values. Shaft is divided into several sections at strain gauge locations. The force and moment equilibrium equations are set up and assembled to form bearing load solving equations. This method can reduce the modeling error, especially for the machines with irregular rotating parts. It can also be applied for the entire shaft system bearing load distribution study with high accuracy and fault tolerant. Test was done on a rotor-bearing system rig. Bearing load distribution in different shaft alignment states is identified and analyzed. Test results show that the bearing load distribution varies sensitively and linearity to the change of bearing elevation. Further research shows that the accuracy of the method depends on the strain gauge locations. It would be best to place the strain gauge at location where the bending moment is sensitive to the change of bearing load. Moreover, mounting the strain gauge further from the bearing reduces the relative error due to the exact reaction point location is not known, which influences the accuracy of beading moment arm from the strain gauge location to the reaction point.     

Geometric design of involute spur gear drives with symmetric and asymmetric teeth using the Realized Potential Method

The index gear drive potential is defined for the estimation of the quality of spur gear drives as a maximum contact ratio obtained at the contact of teeth profiles along the full line of action. In this paper, a new method is proposed for the geometric design of symmetric and asymmetric involute meshing in which the contact ratio of the gear drive is equal to its potential. This method is appropriate for the geometric design of spur gears with a small teeth number and is based on the generalized model of involute meshing. The gear drive potential is assigned as an input value, from which, after appropriate calculations, the geometry of rack-cutters, gears and involute meshing can be determined. Using the proposed method, the areas of the realized potential and the areas of the existence of involute gear drives are defined. In addition, many numerical examples are solved. In the cases of symmetric and asymmetric meshing, the minimum teeth number is obtained when the gear drive potential is larger than one.     

Experimental studies on the effects of reduction in gear tooth stiffness and lubricant film thickness in a spur geared system

Gears are one of the most common mechanisms for transmitting power and motion and their usage can be found in numerous applications. Studies on gear teeth contacts have been considered as one of the most complicated applications in tribology. Depending on the application, the speed and load conditions of teeth may change triggering several types of failures on teeth surface such as wear, scuffing, micro-pitting and pitting. The above-mentioned faults influence changes in vibration and acoustic signals, due to changes in operating conditions such as increase in temperature and decrease in lubricant film thickness and specific film thickness. These abnormal changes result in cumulative effects on localised or distributed faults on load bearing surfaces of gears. Such damages cause reduction in tooth stiffness and severity of damage can be assessed by evaluating the same using vibration-based signals.This paper presents the results of experimental investigations carried out to assess wear in spur gears of back-to-back gearbox under accelerated test conditions. The studies considered the estimation of operating conditions such as film thickness and their effects on the fault growth on teeth surface. Modal testing experiments have been carried out on the same gear starting from healthy to worn out conditions to quantify wear damage. The results provide a good understanding of dependent roles of gearbox operating conditions and vibration parameters as measures for effective assessment of wear in spur gears.     

Experimental measurement of strain and stress state at the contacting helical gear pairs

Contact stress evaluation in gears has been a complex area of research, due to its non-linear and non-uniform nature of stress distribution. The high contact stress on gears results in pitting and scuffing, which leads to tooth failure. Furthermore the effects of friction on gear contacts make the problem more complicated. Hence, in this paper, attempt has been made to study contact stress in gears. The experimental testing and analysis of the helical gear was carried out using Gear Dynamic Stress Test Rig (GDSTR). GDSTR is a newly designed test rig to compute the contact stresses on the gear pair contact, under real gear conditions. GDSTR uses the strain gauge and carbon slip rings to measure the surface contact stresses at the contacting points of a meshed gears. The experimental analysis showed promising results which have been verified by the finite element frictional contact analysis. The experimental testing was carried out on 5° and 25° helical gear pairs. Helical gear models with the same specifications and for different frictional coefficient conditions were also generated using FE modelling. The frictional contact stress analysis using FEM has been used for comparison with the experimental results.     

Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear

Gear wear is one of the most common gear failures, which changes the mesh relationship of normal gear. A new mesh relationship caused by gear wear affects meshing excitations, such as mesh stiffness and transmission error, and further increases vibration and noise level. This paper aims to establish the model of mesh relationship and reveal the vibration characteristics of external spur gears with gear wear. A geometric model for a new mesh relationship with gear wear is proposed, which is utilized to evaluate the influence of gear wear on mesh stiffness and unloaded static transmission error (USTE). Based on the mesh stiffness and USTE considering gear wear, a gear dynamic model is established, and the vibration characteristics of gear wear are numerically studied. Comparison with the experimental results verifies the proposed dynamic model based on the new mesh relationship. The numerical and experimental results indicate that gear wear does not change the structure of the spectrum, but it alters the amplitude of the meshing frequencies and their sidebands. Several condition indicators, such as root-mean-square, kurtosis, and first-order meshing frequency amplitude, can be regarded as important bases for judging gear wear state.     

用积分法计算直齿轮轮齿的弹性变形

用积分法推导确定了由直齿轮轮齿在单位力作用下的弯曲变形、剪切变形和压缩变形所引起的于载荷作用点处沿载荷方向变形的计算公式,编制通用程序对它们进行了计算,并与用传统的分段方法求得的结果进行了比较。结果表明,只有分段段数足够多时,用分段法求得的结果才与积分法达到一致的结果。     

考虑轮齿修形的变厚齿轮啮合刚度数值计算

针对有限元法求解变厚齿轮时变啮合刚度的求解效率低、计算结果易不收敛等问题,基于切片法建立了一种考虑齿向修形的变厚齿轮时变啮合刚度求解模型,在综合考虑齿轮基圆与齿根圆之间关系的基础上,对现有的Weber能量法进行改进,并采用该方法计算了变厚齿轮的时变啮合刚度。通过建立变厚齿轮有限元分析模型,对其进行加载接触分析,计算其啮合刚度,并与所提方法进行比较,结果表明,所提方法可以有效提高计算精度,提升计算效率。在此基础上,采用集中参数法分析了变厚齿轮不同啮合参数和修形参数对时变啮合刚度的影响规律,为变厚齿轮的结构优化设计和系统动力学分析奠定了基础。     

Experimental investigation of fatigue behavior of spur gear in altered tooth-sum gearing

This paper deals with the contact stress, power loss, and pitting of spur gear tooth in altered tooth-sum gearing for a tooth-sum of 100 teeth when altered by±4% tooth-sum. Analytical and experimental methods were performed to investigate and compare the altered tooth-sum gearing against the standard tooth-sum gearing. The experiments were performed using a power recirculating type test rig. The tooth loads for the experimental investigations were determined considering the surface durability of gears. A clear picture of the surface damage was obtained using a scanning electron microphotograph. The negative alteration in the tooth-sum performed better than the positive alteration in a tooth-sum operating between specified center distances.     

温度变化对圆柱齿轮齿形的影响

通过对具有渐开线齿廓的齿轮温度场分析和热应力应变分析,指出标准渐开线齿轮在温度发生变化时,其实际齿廓曲线与理论曲线不相重合,表现为齿形的非渐开线特性,并给出此时的齿形误差。     

Effects of eccentricity defect on the nonlinear dynamic behavior of the mechanism clutch-helical two stage gear

This paper investigates the nonlinear dynamic behavior of an automotive clutch coupled with a helical two stage gear system. The nonlinear dynamic model is simulated by twenty seven degrees of freedom and including three types of nonlinearity: dry friction path, double stage stiffness and spline clearance. The utility of the proposed nonlinear model is illustrated by the industrial need to clearly identify the dynamic behavior of mechanical elements (shafts, bearings, gears, flywheel, pressure plate, hub of the clutch…) and reduce vibration. The governing nonlinear time varying motion equation formulated is resolved by the analytic Runge Kutta method.Then the modeling of the eccentricity defect located on the gear and the flywheel of the clutch is done. The effect of this defect on the nonlinear dynamic behavior of the system is investigated.     

齿面摩擦和啮合刚度对双渐开线齿轮传动动态特性的影响研究

针对双渐开线齿轮传动动态特性问题,通过建立双渐开线齿轮的有限元模型,综合考虑齿面摩擦与齿轮啮合刚度二因素,对双渐开线齿轮传动系统进行了有限元模态分析,运用响应曲面法研究了齿面摩擦与齿轮啮合刚度对双渐开线齿轮振动变形和模态频率的影响;选取不同模态阶数对双渐开线齿轮传动系统进行了动态特性研究,分析了不同模态阶数下双渐开线齿轮的振动变形与模态频率变化状况。研究结果表明,随着齿面摩擦因数与齿轮啮合刚度的增加,不同模态阶数下双渐开线齿轮传动系统各阶振动变形与模态频率均显著增加,齿面摩擦与齿轮啮合刚度对双渐开线齿轮传动动态特性有一定影响,在对齿轮传动系统进行动态特性研究时,必须对齿面摩擦与齿轮啮合刚度进行充分考虑。     

圆锥量规锥度的高精度光学干涉法测量

针对超精密数控机床对圆锥量规锥度高精度测量的需求,研究了一种将“大数”和“小数”相结合,准确测量圆锥量规锥度的方法.介绍了锥度测量系统的基本原理及组成,给出了实验测量结果,分析了测量系统的不确定度.该测量方法利用最大分度间隔误差为0.10〞的多齿分度台构成高准确度分度系统保证测量“大数”部分的准确性,采用激光偏振干涉装...     

Y6DL-3型动态电阻应变仪小信号的测量研究

Y6DL-3型动态电阻应变仪采用交流供桥、载波放大的型式,但在使用中该应变仪中的LCπ型滤波器没有将载波信号完全滤掉,影响了小信号的测量。针对上述实际情况,利用滤波器设计软件Filterlab2.0设计了一个四阶巴特沃斯有源低通滤波器,将其应用在Y6DL-3型动态电阻应变仪中,实验结果表明：所设计的滤波器可以有效抑制载波信号,提高信噪比,得到了理想的滤波效果。为解决同类仪器中的信号干扰问题提供了一种很好的思路和方法。