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1、 38 机电设备 2003 年第 5 期 滑动摩擦及轴承间隙必导致齿轮机构的齿轮振动 Sliding Frictions and Bearing Clearances Inevitably Leading to the Gear Vibration of a Gearing 徐辅仁 (上海理工大学 上海 200093) 摘 要 不计齿间及轴颈与轴承间摩擦的经典渐开线齿轮理论认为，若输入扭矩保持恒定，则齿轮机构运行平稳，不会振动。本文的研究充分表明：尽管齿轮机构的输入扭矩保持不变，然而，由于滑动摩擦及轴承间隙的存在，齿轮必产生振动。本文指出，对于具备足够刚性的齿轮机构而言，降低齿间及轴颈与轴承间
2、滑动摩擦系数并减小轴承间隙是抑制齿轮振动的有效措施。 关键词 滑动摩擦 轴承间隙 齿轮振动 齿轮机构 Abstract The classical involute gearing theory, which omits the effect of sliding frictions between teeth and between bearings and journals, thinks that if the input torque of the gearing is kept constant the gears do not vibrate .It has fully been
3、proved by researches of this article that even though the input torque of the gearing is kept unchanged, the gears surely generate vibration because of the existence of sliding frictions and bearing clearances. This article indicates that decreasing sliding friction coefficients between teeth and be
4、tween bearings and journals and reducing clearances between bearings and journals are the effective measures for restraining vibration of gears in the gearing with enough rigidity. Keywords sliding friction, bearing clearance, vibration of gears, gearing 1 The Study Object and Basic Parameters The i
5、nvolute cylindrical standard spur gearing ( is called the gearing for short ) is taken as the study object of this article. Let the numbers of teeth on the driving and driven gears be Z1 and Z2 respectively, the base circle radius of the driving gear be rb1, the pressure angle on the gear pitch circ
6、les and the gear modulus beand m respectively, the input torque of the driving gear be M1, the clearance between the driving gear journal and its bearing be 1. Since the distance between two bearing centers has been adjusted to the standard center distance d (Fig.1) in assembling the gearing bearing
7、s, the bearing center distance OB1OB2 may be expressed by the following equation: OB1OB2=d=21m(Z1+Z2) ( 1) Fig-1 2 Basic Hypotheses Although the bearing center distance has been adjusted to d , the clearances between journals and 机电设备 2003 年第 5 期 39 bearings always exist. Generally gear centers O1 a
8、nd O2 do not coincide with bearing centers OB1 and OB2 during the gearing operating, so the gear center line O1O2 is not strictly parallel to the bearing center line OB1OB2 , and the gear meshing angle also is not strictly equal to the pressure angle . However, it must be indicated here that because
9、 standard center distances of the most of gearings are much greater than bearing clearances, the angles between O1O2 and OB1OB2 caused by bearing clearances are so small that they can completely be omitted. In order to make researches in this article be not too complex, on the basis of above fact an
10、d operating features of conventional gearings, here are introduced following hypotheses : a ) the gear center line O1O2 is parallel to the bearing center line OB1 OB2 throughout the operation. b ) the meshing angle of the gearing is equal to the pressure angle of the gearing throughout the operation
11、. c ) the input torque of the driving gear keeps constant throughout the operation. d ) there is no any inertia and inertia moment interference during the operation. e ) gears, gear journals, bearings, bearing housings and the frame are absolutely rigid, do not create any elastic deformation during
12、the operation. 3 Determining the Position of the Contact Point between the Gear Journal and the Bearing by the Classical Involute Gear Theory It is known from geometrical properties of involute gearings that the tooth profile common normals on all the meshing points coincide with the inner common ta
13、ngent of two gear base circles during the gearing meshing, and the action direction of the normal load between tooth profiles is along the theoretical meshing line N1N2 throughout (Fig.2). It is well known that because the classical involute gear theory omits the frictions between teeth and between
14、gear journals and bearings, it is considered that there only are the normal forces at those places. According to the mechanics balance condition, it is thought that either for two pairs of teeth meshing or for single pair of teeth meshing the magnitude of the reaction RG of the bearing to the drivin
15、g gear journal equals FG , which direction is opposite to FG and always parallel to N1N2 .Let the contact point between the driving gear journal and the bearing be G ,which also is the action point of RG (shown in Fig.2). Because the meshing angle and input torque keep unchanged in the gearing opera
16、ting, the direction and magnitude of FG , and the direction, magnitude and action point position of RG also keep constant . Therefore, the classical involute gearing theory thinks if the input torque keeps constant, the gearing will keep stable and not vibrate (create vibration) throughout the operation. Fig-2 4 The Variat
