WO2022135612A1 - 一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法 - Google Patents

一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法 Download PDF

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WO2022135612A1
WO2022135612A1 PCT/CN2022/072663 CN2022072663W WO2022135612A1 WO 2022135612 A1 WO2022135612 A1 WO 2022135612A1 CN 2022072663 W CN2022072663 W CN 2022072663W WO 2022135612 A1 WO2022135612 A1 WO 2022135612A1
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gear
axis
measured
tooth profile
involute
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PCT/CN2022/072663
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English (en)
French (fr)
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石照耀
孙衍强
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北京工业大学
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Publication of WO2022135612A1 publication Critical patent/WO2022135612A1/zh
Priority to US18/202,953 priority Critical patent/US11971324B2/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B5/00—Measuring arrangements characterised by the use of mechanical techniques
    • G01B5/20—Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures
    • G01B5/202—Measuring arrangements characterised by the use of mechanical techniques for measuring contours or curvatures of gears
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G01M13/021—Gearings

Definitions

  • the invention relates to a gear measurement method, in particular to a normal meshing tooth profile measurement method of an involute helical cylindrical gear.
  • gear As an important basic transmission component, gear has the advantages of large bearing capacity, high transmission precision, and constant transmission power. It has become a key component for transmitting motion and power in various mechanical equipment. Therefore, ensuring the quality of gears is an important part of promoting gear manufacturing and wide application.
  • the tooth surface of an involute cylindrical gear is an involute helical surface, and there are four common characteristic lines: involute, helical, normal meshing tooth profile and contact line, as shown in Figure 1.
  • involute involute
  • helical normal meshing tooth profile
  • contact line as shown in Figure 1.
  • the evaluation of gear tooth surface quality is achieved by measuring involutes and spirals.
  • the cross shaft involute helical cylindrical gear transmission belongs to the point contact transmission, and the track left by the contact point on the tooth surface is the normal meshing tooth shape. Therefore, the cross-axis involute helical cylindrical gear is driven by the normal meshing tooth profile, and the measurement of the normal meshing tooth profile can reflect the actual motion condition of the gear. In generative processing such as hobbing, shaving, and worm grinding, the movement of the tool and the gear is based on the normal meshing tooth profile. Therefore, in the generation method machining, controlling the normal meshing tooth profile has a unique advantage in controlling the machining quality of the gear.
  • the measurement of the gear tooth surface adopts the involute and helical measurement methods, which sometimes cannot effectively reflect the real information of the gear transmission quality and processing quality.
  • the existing measuring instruments do not have the function of measuring the normal meshing tooth profile.
  • the purpose of the invention is to make up for the deficiency of the existing measuring instrument without the normal meshing tooth profile measurement function, effectively obtain the real information that can reflect the gear transmission quality and processing quality, and provide a normal meshing tooth profile of the involute helical cylindrical gear. Measurement methods.
  • ⁇ is the name of the coordinate system
  • O is the center of symmetry of the tested gear
  • X, Y, Z are the three coordinate axes under the coordinate system ⁇ , respectively
  • the Z axis coincides with the axis of the measured gear
  • r b is the base cylinder radius of the measured gear.
  • the plane S is the tangent plane of the base cylinder of the tested gear, which is tangent to the base cylinder of the tested gear on the straight line EF, and intersects with the involute helical tooth surface of the tested gear on the straight line MN.
  • the straight line MN is the generation generatrix of the involute helical tooth surface of the measured gear.
  • the straight line ad' 0 is the meshing line of the measured gear, which is a line of action that transmits displacement and force; the meshing line ad' 0 is located in the tangent plane S, and is connected to the involute helical tooth surface. It occurs that the busbars MN are perpendicular to each other.
  • the locus of the intersection of the meshing line ad' 0 and the involute helical tooth surface of the measured gear on the tooth surface is the normal meshing tooth profile ad 0 .
  • the normal meshing tooth profile has the advantage of conforming to the principle of action line based on the meshing principle. It is the only curve involved in meshing on the tooth surface of the involute helical cylindrical gear.
  • the cross-axis involute helical cylindrical gear is driven by the normal meshing tooth profile. , and its measurement error reflects the actual motion conditions such as gear transmission quality and work stability. And when measuring the normal meshing tooth profile, the measurement direction is perpendicular to the tooth surface of the gear to be measured, so that higher measurement accuracy can be obtained.
  • gear hobbing, tooth shaving, worm grinding and other generative processing the movement of tools and gears is realized in the form of machining normal meshing tooth profile; unique advantage.
  • the normal meshing tooth profile shows irreplaceable advantages in the field of involute helical cylindrical gear transmission and processing, but the current measuring instruments do not have the normal meshing tooth profile measurement function.
  • the present invention relates to a method for measuring the normal meshing tooth profile of an involute helical cylindrical gear, which can be measured through the gear measuring center.
  • the tooth surface of the involute helical cylindrical gear is the involute helical surface, which is a space curved surface formed by a straight line tangent to the base cylinder and having a fixed angle with the axis rolling along the base cylinder, as shown in Figure 3. Show.
  • the equation of the involute helical surface of the gear under test is:
  • x, y, z are the three-dimensional coordinates in the coordinate system O-xyz respectively
  • r b is the radius of the base cylinder
  • ⁇ is the sum of the involute expansion angle and the pressure angle
  • ⁇ ztan ⁇ b /r b
  • ⁇ b is the base circle helix angle
  • the involute helical surface of the tested gear rotates around the z-axis together with the coordinate system S(O-x, y, z), the corresponding rotation angle is ⁇ , and there is an instantaneous contact point on the involute helical surface.
  • the trajectory of the contact point on the involute helical surface in the coordinate system S(O-x,y,z) is the normal meshing tooth profile.
  • the traditional measurement scheme is to measure the involute on the involute helical tooth surface of the measured gear, that is, the two-axis control method: when the measured gear rotates at a constant speed, the sensing probe of the measuring instrument is on the tangent plane of the measured gear base cylinder. It only moves along the tangential direction synchronously to realize the information data collection of the involute.
  • This traditional method is simple in principle, easy to implement, and the measurement accuracy is easily affected by the size of the gear to be measured; and when measuring the involute of the tooth surface of the involute helical cylindrical gear, the measurement direction is not perpendicular to the tooth surface of the measured gear, which will lead to To measure the error, the larger the helix angle of the measured involute helical cylindrical gear, the greater the measurement error and the worse the measurement accuracy.
  • the measurement scheme involved in the present invention is to measure the normal meshing tooth profile of the involute helical tooth surface of the measured gear, that is, a four-axis control strategy: when the measured gear rotates at a constant speed, the sensing probe of the measuring instrument is on the measured gear.
  • the tangential plane of the base cylinder not only moves along the tangential direction, but also superimposes the radial and axial movements simultaneously.
  • the sensing probe moves along the gear meshing line in the tangent plane of the base cylinder of the tested gear, and the collected tooth surface information data is the normal meshing tooth profile on the involute helical tooth surface of the measured gear.
  • the four-axis control strategy of the normal meshing tooth profile measurement on the gear tooth surface can also have the following extended applications:
  • the meshing line ad' 0 is a straight line in the tangent plane S perpendicular to the Y axis, and the trajectory of the intersection with the measured gear involute helical tooth surface on the tooth surface is Normal meshing tooth profile ad 0 .
  • the four-axis control strategy can be simplified to three-axis control: when the measured gear rotates at a constant speed, the sensing probe of the measuring instrument not only synchronizes along the tangential direction (X-axis direction) in the tangential plane S of the measured gear base cylinder ) movement, and also superimpose the movement in the axial direction (Z-axis direction) synchronously.
  • control axis Z-axis direction
  • the sensing probe of the measuring instrument is in the tangent plane S of the base cylinder of the measured gear. Movements in the tangential (X-axis direction) and radial (Y-axis direction) are synchronized.
  • the sensing probe of the measuring instrument will move and measure along the straight line ad' 1 in the tangent plane S of the base cylinder of the measured gear, so as to realize the measurement of the involute ad 1 on the tooth surface of the measured involute helical cylindrical gear. measurement, as shown in Figure 2.
  • the method effectively avoids the influence of the measured gear size on the measurement accuracy, and also reduces the requirements for the accuracy of the guide rail of the measuring instrument, and is an efficient and high-precision involute measurement method.
  • This method measures the normal meshing tooth profile on the tooth surface of the tested gear.
  • the cross-axis involute helical cylindrical gear is driven by the normal meshing tooth profile.
  • the measurement of the normal meshing tooth profile can reflect the transmission quality and Work stability and other actual motion conditions;
  • This method measures the normal meshing tooth profile on the tooth surface of the measured gear.
  • the generation method processing such as gear hobbing, shaving, and worm grinding
  • the movement of the tool and the gear is based on the normal meshing tooth profile. It is realized that controlling the normal meshing tooth profile has a unique advantage in controlling the machining quality of the gear.
  • This method can realize the measurement through the gear measurement center, which breaks the traditional two-axis linkage measurement method, and adopts four-axis linkage measurement, which makes up for the lack of the existing measuring instrument without the normal meshing tooth profile measurement function, and effectively improves its measurement accuracy. Influenced by the measured gear size;
  • the measurement direction of this method is perpendicular to the measured gear tooth surface, which can obtain high measurement accuracy and effectively obtain real information that can reflect the gear transmission quality and processing quality;
  • Figure 1 is a schematic diagram of four characteristic lines on an involute helical surface.
  • Figure 2 is a schematic diagram of the normal meshing tooth profile on the tooth surface of the measured gear.
  • Figure 3 is a schematic diagram of an involute helical model.
  • Figure 5 is a simplified schematic diagram of the three-dimensional height of the measuring instrument.
  • FIG. 6 is a simplified schematic diagram of the top view height of the measuring instrument.
  • Figure 7 is a schematic diagram of the position of the sensing probe when measuring the normal meshing tooth profile.
  • ⁇ is the name of the coordinate system
  • O is the center of symmetry of the tested gear
  • X, Y, Z are the three coordinate axes under the coordinate system ⁇ , respectively
  • the Z axis coincides with the axis of the measured gear
  • r b is the base cylinder radius of the measured gear.
  • the plane S is the tangent plane of the base cylinder of the tested gear, which is tangent to the base cylinder of the tested gear on the straight line EF, and intersects with the involute helical tooth surface of the tested gear on the straight line MN.
  • the straight line MN is the generation generatrix of the involute helical tooth surface of the measured gear.
  • the straight line ad' 0 is the meshing line of the measured gear, which is a line of action that transmits displacement and force; the meshing line ad' 0 is located in the tangent plane S, and is connected to the involute helical tooth surface. It occurs that the busbars MN are perpendicular to each other.
  • the locus of the intersection of the meshing line ad' 0 and the involute helical tooth surface of the measured gear on the tooth surface is the normal meshing tooth profile ad 0 .
  • the normal meshing tooth profile has the advantage of conforming to the principle of action line based on the meshing principle. It is the only curve involved in meshing on the tooth surface of the involute helical cylindrical gear.
  • the cross-axis involute helical cylindrical gear is driven by the normal meshing tooth profile. , and its measurement error reflects the actual motion conditions such as gear transmission quality and work stability. And when measuring the normal meshing tooth profile, the measurement direction is perpendicular to the tooth surface of the gear to be measured, so that higher measurement accuracy can be obtained.
  • gear hobbing, tooth shaving, worm grinding and other generative processing the movement of tools and gears is realized in the form of machining normal meshing tooth profile; unique advantage.
  • the normal meshing tooth profile shows irreplaceable advantages in the field of involute helical cylindrical gear transmission and processing, but the current measuring instruments do not have the normal meshing tooth profile measurement function.
  • the test instrument includes a base 1, an X linear movement axis group 2, a Z linear movement axis group 3, a Y linear movement axis group 4, a rotary axis group 5, a gear adjustment mechanism 6 to be measured, and a
  • the measuring gear is fixed to the top 7, the measured gear is fixed to the mandrel 8, the measured gear 9, the sensing probe 10 and the computer control device CS.
  • the X-axis linear moving axis group 2 includes an X-axis base 21 , an X-axis slider 22 , an X-axis motor 23 and an X-axis grating 24 .
  • the Z-axis linear moving axis group 3 includes a Z-axis base 31 , a Z-axis slider 32 , a Z-axis motor 33 and a Z-axis grating 34 .
  • the Y linear moving axis group 4 includes a Y-axis base 41 , a Y-axis slider 42 , a Y-axis motor 43 and a Y-axis grating 44 .
  • the rotary shaft group 5 includes a rotary shaft motor 51 and a rotary shaft grating 52 .
  • the three linear moving axis groups (2, 3, 4), the rotary axis group 5 and the gear adjustment mechanism 6 under test are installed on the base 1.
  • the measured gear 9 is installed on the rotary shaft group 5 through the measured gear adjustment mechanism 6 , the measured gear fixing center 7 and the measured gear fixing mandrel 8 .
  • the rotary shaft motor 51 is coupled and connected to the gear 9 to be tested, and can drive the gear 9 to be tested to rotate at a constant speed.
  • the rotary shaft motor 51 is precisely controlled by the computer control device CS to realize any angle of rotation of the gear 9 under test, and its rotation angle can be monitored in real time by the rotary shaft grating 52 and fed back to the computer control device CS.
  • the sensing probe 10 is arranged at the opposite position of the measured gear 9, and can realize the movement in three coordinate directions.
  • the sensing probe 10 is installed on the Y-axis slider 42, and the Y-axis slider 42 is coupled to the Y-axis motor 43, so that the Y-axis slider 42 can move linearly along the Y-axis direction;
  • the shaft grating 44 monitors and feeds back in real time.
  • the Y-axis slider 42 is mounted on the Y-axis base 41 through the slide rail, and the Y-axis motor 43 and the Y-axis grating 44 are also mounted on the Y-axis base 21 .
  • the Y linear moving axis group 4 is installed on the Z-axis slider 32, and the Z-axis slider 32 is coupled to the Z-axis motor 33, so that the vertical movement of the Z-axis slider 32 in the Z-axis direction can be realized; Shaft grating 34 monitors and feeds back in real time.
  • the Z-axis slider 32 is mounted on the Z-axis base 31 through the slide rail, and the Z-axis motor 33 and the Z-axis grating 34 are also mounted on the Z-axis base 31 .
  • the Z linear moving axis group 3 is installed on the X-axis slider 22, and the X-axis slider 22 is coupled and connected to the X-axis motor 23, which can realize the linear movement of the X-axis slider 22 in the X-axis direction; Shaft grating 24 monitors and feeds back in real time.
  • the X-axis slider 22 is mounted on the X-axis base 21 through the slide rail, and the X-axis motor 23 and the X-axis grating 24 are also mounted on the X-axis base 21 .
  • the X linear moving axis group 2 is installed on the base 1 of the testing instrument.
  • the computer control device CS can receive the three-way position signals fed back by the X-axis grating 24, the Z-axis grating 34 and the Y-axis grating 44, and then accurately control the X-axis motor 23, the Z-axis motor 33 and the Y-axis motor 43 to realize three coordinate axes. precise linear movement.
  • the measurement scheme involved in the invention is to measure the normal meshing tooth profile ad 0 on the involute helical tooth surface of the measured gear, that is, a four-axis control strategy: when the measured gear rotates at a uniform speed, the sensing The probe 10 starts from point a on the involute helical tooth surface of the measured gear, and not only moves along the X-axis direction in the tangent plane S of the base cylinder of the measured gear, but also synchronously superimposes the movement in the Y-axis direction and the Z-axis direction.
  • the sensing probe 10 of the measuring instrument ends by moving to point d' 0 .
  • the tooth surface information data collected by the sensing probe 10 is the normal meshing tooth profile ad 0 on the involute helical tooth surface of the gear under test.
  • the above process requires the computer control device CS to simultaneously precisely control the synchronous movement of the X-axis motor 23 , the Z-axis motor 33 and the rotary axis motor 51 to realize the entire measurement process.
  • the four-axis control strategy of the normal meshing tooth profile measurement on the gear tooth surface can also have the following extended applications:
  • the four-axis control strategy can be simplified to three-axis control: when the measured gear rotates at a constant speed, the sensing probe of the measuring instrument not only synchronizes along the tangential direction (X-axis direction) in the tangential plane S of the measured gear base cylinder ) movement, and also superimpose the movement in the axial direction (Z-axis direction) synchronously.
  • control axis Z-axis direction
  • the sensing probe of the measuring instrument is in the tangent plane S of the base cylinder of the measured gear. Movements in the tangential (X-axis direction) and radial (Y-axis direction) are synchronized.
  • the sensing probe of the measuring instrument will move and measure along the straight line ad' 1 in the tangent plane S of the base cylinder of the measured gear, so as to realize the measurement of the involute ad 1 on the tooth surface of the measured involute helical cylindrical gear. measurement, as shown in Figure 2.
  • the method effectively avoids the influence of the measured gear size on the measurement accuracy, and also reduces the requirements for the accuracy of the guide rail of the measuring instrument, and is an efficient and high-precision involute measurement method.
  • the normal meshing tooth profile is unique.
  • the cross-axis involute helical cylindrical gear is driven by the normal meshing tooth profile, and the measurement of the normal meshing tooth profile can reflect the actual motion conditions such as the transmission quality and working stability of the gear.
  • gear hobbing, shaving, worm grinding and other generating methods the movement of the tool and the gear is realized based on the normal meshing tooth profile, and controlling the normal meshing tooth profile has a unique advantage in controlling the processing quality of the gear .
  • the gear measuring center is used to measure the normal meshing tooth profile on the tooth surface of the tested gear, which makes up for the deficiency that the existing measuring equipment cannot measure the normal meshing tooth profile; it breaks the traditional two-axis linkage measurement method and adopts four-axis linkage measurement, which effectively improves the limitation that its measurement accuracy is easily affected by the size of the measured gear.
  • the radial (Y-axis direction) and axial (Z-axis direction) movements respectively, simplified measurement of the normal meshing tooth profile and meshing method measurement of the involute can be achieved.
  • the method is also suitable for involute measurement of spur gears.

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  • General Physics & Mathematics (AREA)
  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
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Abstract

本发明公开了一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，该方法测量被测齿轮齿面上的法向啮合齿形，交叉轴渐开螺旋圆柱齿轮是通过法向啮合齿形来传动运动的，测量法向啮合齿形反映齿轮的传动质量和工作平稳性实际运动工况；在滚齿加工、剃齿加工、蜗杆砂轮磨展成法加工中，工具与齿轮的运动基于法向啮合齿形来实现，控制法向啮合齿形对控制齿轮加工质量具有独特的优势；通过齿轮测量中心实现测量，采用四轴联动测量，有效改善其测量精度易受被测齿轮尺寸的影响；分别限制径向和轴向的运动实现法向啮合齿形的简化测量和啮合法测量渐开线；该方法适用于直齿圆柱齿轮的渐开线测量，齿轮齿面上的法向啮合齿形与渐开线重合，因此该方法同样适用。

Description

一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法 技术领域
本发明涉及一种齿轮测量方法，特别涉及一种渐开线螺旋圆柱齿轮的法向啮合齿形测量方法。
背景技术
齿轮作为一种重要的基础传动件，其传动具有承载能力大、传动精度高、传动功率恒定等优点，已成为各类机械设备中用于传递运动和动力的关键部件。因此，保障齿轮质量是促进齿轮加工制造、广泛应用的重要一环。
渐开线圆柱齿轮的齿面是渐开螺旋面，常见特征线共有四条：渐开线、螺旋线、法向啮合齿形和接触线，如图1所示。在现行的国际标准、国家标准中，评价齿轮的齿面质量均是采用测量渐开线和螺旋线来实现的。
交叉轴渐开螺旋圆柱齿轮传动，属于点接触传动，接触点在齿面上留下的轨迹即为法向啮合齿形。因此，交叉轴渐开螺旋圆柱齿轮是通过法向啮合齿形来传动运动的，测量法向啮合齿形可以反映齿轮的实际运动工况。在滚齿加工、剃齿加工、蜗杆砂轮磨等展成法加工中，工具与齿轮的运动是基于法向啮合齿形来实现的。因此，在展成法加工中，控制法向啮合齿形对控制齿轮加工质量具有独特的优势。
但目前，不论是三坐标测量机还是齿轮测量中心，对于齿轮齿面的测量均是采用渐开线和螺旋线测量的方式，该测量方式有时无法有效反映齿轮传动质量和加工质量的真实信息，并且现有的测量仪器没有法向啮合齿形的测量功能。
基于上述齿轮齿面测量的现状和问题，提出了一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，并可以通过齿轮测量中心来实现测量。
发明内容
本发明的目的在于弥补现有测量仪器没有法向啮合齿形测量功能的不足，有效获取可以反映齿轮传动质量和加工质量的真实信息，提供了一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法。
如图2所示，建立坐标系δ(O-X,Y,Z)，其中δ为坐标系名称，O为被测齿 轮的对称中心，X,Y,Z分别为坐标系δ下的三个坐标轴，Z轴与被测齿轮的轴线重合，r b为被测齿轮的基圆柱半径。平面S是被测齿轮基圆柱的切平面，与被测齿轮基圆柱相切于直线EF，并且与被测齿轮渐开螺旋齿面相交于直线MN。直线MN即为被测齿轮渐开螺旋齿面的发生母线。在渐开线齿轮传动过程中，直线ad’ 0为被测齿轮的啮合线，是一条传递位移和力的作用线；啮合线ad’ 0位于切平面S内，并且与渐开螺旋齿面的发生母线MN相垂直。啮合线ad’ 0和被测齿轮渐开螺旋齿面的交点在齿面上的轨迹就是法向啮合齿形ad 0。
法向啮合齿形基于啮合原理具有符合作用线原则的优势，是渐开螺旋圆柱齿轮齿面上唯一一条参与啮合的曲线，交叉轴渐开螺旋圆柱齿轮是通过法向啮合齿形来传动运动的，其测量误差反映齿轮的传动质量和工作平稳性等实际运动工况。并且在测量法向啮合齿形时，测量方向与被测齿轮齿面垂直，可以获得较高的测量精度。在滚齿加工、剃齿加工、蜗杆砂轮磨等展成法加工中，工具与齿轮的运动均是采用加工法向啮合齿形的形式来实现；控制法向啮合齿形对控制齿轮加工质量具有独特的优势。法向啮合齿形在渐开螺旋圆柱齿轮传动和加工领域，均表现出不可替代的优越性，但目前的测量仪器都没有法向啮合齿形的测量功能。
因此，本发明涉及一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，并可以通过齿轮测量中心实现测量。
渐开螺旋圆柱齿轮的齿面都是渐开螺旋面，它是由一根与基圆柱相切，并且与轴线有固定夹角的直线沿着基圆柱滚动而形成的空间曲面，如图3所示。被测齿轮的渐开螺旋面方程为：
Figure PCTCN2022072663-appb-000001
其中，x,y,z分别为坐标系O-xyz下的三维坐标，r b是基圆柱半径，θ是渐开线展开角与压力角之和，μ＝ztanβ b/r b，其中β b是基圆螺旋角。
当被测齿轮的渐开螺旋面连同坐标系S(O-x,y,z)绕z轴旋转时，对应转角为ψ，并且在渐开螺旋面有一个瞬时接触点。渐开螺旋面上接触点在坐标系S(O-x,y,z)内的轨迹就是法向啮合齿形。
在齿轮啮合传动过程中，如下等式成立：
Figure PCTCN2022072663-appb-000002
其中，ψ是转角，α t＝μ+θ+ψ。
将方程组的解(2)式代入与被测齿轮坐标系S(O-x,y,z)下是渐开螺旋面方程(1)中，得被测齿轮渐开螺旋面上的法向啮合齿形方程为：
Figure PCTCN2022072663-appb-000003
传统的测量方案是测量被测齿轮渐开螺旋齿面上的渐开线，即两轴控制方法：在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面内仅同步沿着切向移动，实现渐开线的信息数据采集。这种传统方法原理简单，便于实现，测量精度易受被测齿轮尺寸的影响；并且测量渐开螺旋圆柱齿轮齿面渐开线时，测量方向与被测齿轮齿面并不垂直，将会带来测量误差，被测渐开螺旋圆柱齿轮的螺旋角越大，测量误差就越大，测量精度也就越差。
而本发明涉及的测量方案是测量被测齿轮渐开螺旋齿面上的法向啮合齿形，即四轴控制策略：在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面内不仅同步沿着切向移动，还同步叠加径向和轴向的移动。此时，传感测头在被测齿轮基圆柱的切平面内沿着齿轮啮合线移动，采集到的齿面信息数据即为被测齿轮渐开螺旋齿面上的法向啮合齿形。
齿轮齿面上法向啮合齿形测量的四轴控制策略，还可有如下扩展应用：
(1)法向啮合齿形的简化测量
倘若，令y＝r b，即被测齿轮基圆柱的切平面S与坐标系δ(O-X,Y,Z)的Y轴垂直，如图4所示，则有
sin(α t+ψ 0)-(α t-ψ+tanα ttan 2β b)cos 2β bcos(α t+ψ 0)＝1  (4)
被测渐开螺旋圆柱齿轮的啮合线方程为：
z＝x tanβ b-r b(1+tan 2β b)tanα tcosβ bsinβ b   (5)
在被测渐开螺旋圆柱齿轮啮合传动过程中，啮合线ad’ 0为垂直于Y轴的切平面S内的一条直线，与被测齿轮渐开螺旋齿面的交点在齿面上的轨迹就是法向啮合齿形ad 0。此时，四轴控制策略可简化为三轴控制：在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面S内不仅同步沿着切向(X轴方向)移动，还同步叠加轴向(Z轴方向)的移动即可。
(2)啮合法测量渐开线
倘若，四轴控制策略测量过程中控制轴向(Z轴方向)固定在某一位置，即在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面S内同步沿着切向(X轴方向)和径向(Y轴方向)的移动。
此时，测量仪器的传感测头将会在被测齿轮基圆柱的切平面S内，沿直线ad’ 1移动测量，实现对被测渐开螺旋圆柱齿轮齿面上渐开线ad 1的测量，如图2所示。该方法有效避免了因被测齿轮尺寸对测量精度的影响，也降低了对测量仪器导轨精度的要求，是一种高效高精度的渐开线测量方法。
本发明的渐开线螺旋圆柱齿轮的法向啮合齿形测量方法有以下显著特点：
1.该方法测量被测齿轮齿面上的法向啮合齿形，交叉轴渐开螺旋圆柱齿轮是通过法向啮合齿形来传动运动的，测量法向啮合齿形可以反映齿轮的传动质量和工作平稳性等实际运动工况；
2.该方法测量被测齿轮齿面上的法向啮合齿形，在滚齿加工、剃齿加工、蜗杆砂轮磨等展成法加工中，工具与齿轮的运动是基于法向啮合齿形来实现的，控制法向啮合齿形对控制齿轮加工质量具有独特的优势。
3.该方法可以通过齿轮测量中心实现测量，打破了传统两轴联动的测量方式，采用四轴联动测量，弥补现有测量仪器没有法向啮合齿形测量功能的不足，有效改善其测量精度易受被测齿轮尺寸的影响；
4.该方法的测量方向与被测齿轮齿面垂直，可以获得较高的测量精度，有效获取可以反映齿轮传动质量和加工质量的真实信息；
5.该方法控制y＝r b可将法向啮合齿形测量简化三轴联动，可保障测量的高精度和高效率；控制轴向固定可为渐开线测量提供新的测量思路，有效避免了因被测齿轮尺寸对渐开线测量精度的影响；
6.该方法同样适用于直齿圆柱齿轮的测量，此时齿轮齿面上的法向啮合齿 形与渐开线重合，因此该方法同样适用。
附图说明
图1为渐开螺旋面上四条特征线示意图。
图2为被测齿轮齿面上的法向啮合齿形示意图。
图3为渐开螺旋面模型示意图。
图4为y＝r b时被测齿轮齿面上的法向啮合齿形示意图。
图5为测量仪器三维高度简化示意图。
图6为测量仪器俯视高度简化示意图。
图7为测量法向啮合齿形时传感测头位置示意图。
附图中，1、基座，2、X直线移动轴组，3、Z直线移动轴组，4、Y直线移动轴组，5、回转轴组，6、被测齿轮调整机构，7、被测齿轮固定顶尖，8、被测齿轮固定芯轴，9、被测齿轮，10、传感测头，21、X轴基座，22、X轴滑块，23、X轴电机，24、X轴光栅24，31、Z轴基座，32、Z轴滑块，33、Z轴电机3，34、Z轴光栅，41、Y轴基座，42、Y轴滑块，43、Y轴电机，44、Y轴光栅，51、回转轴电机，52、回转轴光栅。
具体实施方式
下面结合附图及具体实施方式对本发明作进一步的详细描述。但不应将此理解为本发明上述主题的范围仅限于以下的实施方式，凡基于本发明内容所实现的技术均属于本发明的范围。
如图2所示，建立坐标系δ(O-X,Y,Z)，其中δ为坐标系名称，O为被测齿轮的对称中心，X,Y,Z分别为坐标系δ下的三个坐标轴，Z轴与被测齿轮的轴线重合，r b为被测齿轮的基圆柱半径。平面S是被测齿轮基圆柱的切平面，与被测齿轮基圆柱相切于直线EF，并且与被测齿轮渐开螺旋齿面相交于直线MN。直线MN即为被测齿轮渐开螺旋齿面的发生母线。在渐开线齿轮传动过程中，直线ad’ 0为被测齿轮的啮合线，是一条传递位移和力的作用线；啮合线ad’ 0位于切平面S内，并且与渐开螺旋齿面的发生母线MN相垂直。啮合线ad’ 0和被测齿轮渐开螺旋齿面的交点在齿面上的轨迹就是法向啮合齿形ad 0。
法向啮合齿形基于啮合原理具有符合作用线原则的优势，是渐开螺旋圆柱齿轮齿面上唯一一条参与啮合的曲线，交叉轴渐开螺旋圆柱齿轮是通过法向啮合齿形来传动运动的，其测量误差反映齿轮的传动质量和工作平稳性等实际运动工况。并且在测量法向啮合齿形时，测量方向与被测齿轮齿面垂直，可以获得较高的测量精度。在滚齿加工、剃齿加工、蜗杆砂轮磨等展成法加工中，工具与齿轮的运动均是采用加工法向啮合齿形的形式来实现；控制法向啮合齿形对控制齿轮加工质量具有独特的优势。法向啮合齿形在渐开螺旋圆柱齿轮传动和加工领域，均表现出不可替代的优越性，但目前的测量仪器都没有法向啮合齿形的测量功能。
根据图5和图6所示，测试仪器包括基座1，X直线移动轴组2，Z直线移动轴组3，Y直线移动轴组4，回转轴组5，被测齿轮调整机构6，被测齿轮固定顶尖7，被测齿轮固定芯轴8，被测齿轮9，传感测头10和计算机控制装置CS。
X直线移动轴组2包括X轴基座21，X轴滑块22，X轴电机23和X轴光栅24。Z直线移动轴组3包括Z轴基座31，Z轴滑块32，Z轴电机33和Z轴光栅34。Y直线移动轴组4包括Y轴基座41，Y轴滑块42，Y轴电机43和Y轴光栅44。回转轴组5包括回转轴电机51和回转轴光栅52。
三个直线移动轴组(2,3,4)，回转轴组5和被测齿轮调整机构6安装在基座1上。
被测齿轮9通过被测齿轮调整机构6，被测齿轮固定顶尖7和被测齿轮固定芯轴8安装在回转轴组5上。回转轴电机51与被测齿轮9耦合相连，可带动被测齿轮9实现匀速转动。回转轴电机51由计算机控制装置CS精确控制，实现被测齿轮9的任意角度旋转，其旋转角度可由回转轴光栅52实时监测并反馈给计算机控制装置CS。
传感测头10布置在被测齿轮9的对面位置，可实现三个坐标方向上的移动。
传感测头10安装在Y轴滑块42上，Y轴滑块42与Y轴电机43耦合相连，可实现Y轴滑块42沿着Y轴方向的直线移动；同时其直线移动量可由Y轴光栅44实时监测并反馈。Y轴滑块42通过滑轨安装在Y轴基座41上，Y轴电机43和Y轴光栅44也安装在Y轴基座21上。Y直线移动轴组4安装在Z轴滑块32上，Z轴滑块32与Z轴电机33耦合相连，可实现Z轴滑块32的Z轴方向的 垂直移动；同时其直线移动量可由Z轴光栅34实时监测并反馈。Z轴滑块32通过滑轨安装在Z轴基座31上，Z轴电机33和Z轴光栅34也安装在Z轴基座31上。Z直线移动轴组3安装在X轴滑块22上，X轴滑块22与X轴电机23耦合相连，可实现X轴滑块22的X轴方向的直线移动；同时其直线移动量可由X轴光栅24实时监测并反馈。X轴滑块22通过滑轨安装在X轴基座21上，X轴电机23和X轴光栅24也安装在X轴基座21上。X直线移动轴组2安装在测试仪器的基座1上。
计算机控制装置CS可接收X轴光栅24、Z轴光栅34和Y轴光栅44反馈的三路位置信号，进而精确控制X轴电机23，Z轴电机33和Y轴电机43，实现三个坐标轴的精确直线移动。
如图7所示，发明涉及的测量方案为测量被测齿轮渐开螺旋齿面上的法向啮合齿形ad 0，即四轴控制策略：在被测齿轮匀速旋转时，测量仪器的传感测头10由被测齿轮渐开螺旋齿面上a点开始，在被测齿轮基圆柱的切平面S内不仅同步沿着X轴方向移动，还同步叠加Y轴方向和Z轴方向的移动，测量仪器的传感测头10移动到d’ 0点结束。此时，传感测头10采集到的齿面信息数据即为被测齿轮渐开螺旋齿面上的法向啮合齿形ad 0。上述过程，需要计算机控制装置CS同时精确控制X轴电机23、Z轴电机33和回转轴电机51同步运动才可以实现整个测量过程。
齿轮齿面上法向啮合齿形测量的四轴控制策略，还可有如下扩展应用：
(1)法向啮合齿形的简化测量
倘若，令y＝r b，即被测齿轮基圆柱的切平面S与坐标系δ(O-X,Y,Z)的Y轴垂直，则在被测渐开螺旋圆柱齿轮啮合传动过程中，啮合线ad’ 0为垂直于Y轴的切平面S内的一条直线，与被测齿轮渐开螺旋齿面的交点在齿面上的轨迹就是法向啮合齿形ad 0。
此时，四轴控制策略可简化为三轴控制：在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面S内不仅同步沿着切向(X轴方向)移动，还同步叠加轴向(Z轴方向)的移动即可。
(2)啮合法测量渐开线
倘若，四轴控制策略测量过程中控制轴向(Z轴方向)固定在某一位置，即 在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面S内同步沿着切向(X轴方向)和径向(Y轴方向)的移动。
此时，测量仪器的传感测头将会在被测齿轮基圆柱的切平面S内，沿直线ad’ 1移动测量，实现对被测渐开螺旋圆柱齿轮齿面上渐开线ad 1的测量，如图2所示。该方法有效避免了因被测齿轮尺寸对测量精度的影响，也降低了对测量仪器导轨精度的要求，是一种高效高精度的渐开线测量方法。
法向啮合齿形作为被测齿轮渐开螺旋齿面一种典型的特征线，具有唯一性。交叉轴渐开螺旋圆柱齿轮是通过法向啮合齿形来传动运动的，测量法向啮合齿形可以反映齿轮的传动质量和工作平稳性等实际运动工况。在滚齿加工、剃齿加工、蜗杆砂轮磨等展成法加工中，工具与齿轮的运动是基于法向啮合齿形来实现的，控制法向啮合齿形对控制齿轮加工质量具有独特的优势。采用齿轮测量中心实现对被测齿轮齿面上法向啮合齿形的测量，弥补了现有测量设备无法测量法向啮合齿形的不足；打破了传统两轴联动的测量方式，采用四轴联动测量，有效改善了其测量精度易受被测齿轮尺寸影响的限制。此外，分别限制径向(Y轴方向)和轴向(Z轴方向)的运动，可以实现法向啮合齿形的简化测量和啮合法测量渐开线。同时，该方法同样适用于直齿圆柱齿轮的渐开线测量。
对所公开的实施例的上述说明，使本领域专业技术人员能够实现或使用本发明。对这些实施例的多种修改对本领域的专业技术人员来说将是显而易见的，本文中所定义的一般原理可以在不脱离本发明的精神或范围的情况下，在其它实施例中实现。因此，本发明将不会被限制于本文所示的这些实施例，而是要符合与本文所公开的原理和新颖特点相一致的最宽的范围。

Claims (7)

  1. 一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，其特征在于：建立坐标系δ(O-X,Y,Z)，其中δ为坐标系名称，O为被测齿轮的对称中心，X,Y,Z分别为坐标系δ下的三个坐标轴，Z轴与被测齿轮的轴线重合，r b为被测齿轮的基圆柱半径；平面S是被测齿轮基圆柱的切平面，与被测齿轮基圆柱相切于直线EF，并且与被测齿轮渐开螺旋齿面相交于直线MN；直线MN即为被测齿轮渐开螺旋齿面的发生母线；在渐开线齿轮传动过程中，直线ad’ 0为被测齿轮的啮合线，是一条传递位移和力的作用线；啮合线ad’ 0位于切平面S内，并且与渐开螺旋齿面的发生母线MN相垂直；啮合线ad’ 0和被测齿轮渐开螺旋齿面的交点在齿面上的轨迹就是法向啮合齿形ad 0。
  2. 根据权利要求1所述的一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，其特征在于：渐开螺旋圆柱齿轮的齿面都是渐开螺旋面，由一根与基圆柱相切，并且与轴线有固定夹角的直线沿着基圆柱滚动而形成的空间曲面；被测齿轮的渐开螺旋面方程为：
    Figure PCTCN2022072663-appb-100001
    其中，x,y,z分别为坐标系O-xyz下的三维坐标，r b是基圆柱半径，θ是渐开线展开角与压力角之和，μ＝ztanβ b/r b，其中β b是基圆螺旋角；
    当被测齿轮的渐开螺旋面连同坐标系S(O-x,y,z)绕z轴旋转时，对应转角为ψ，并且在渐开螺旋面有一个瞬时接触点；渐开螺旋面上接触点在坐标系S(O-x,y,z)内的轨迹就是法向啮合齿形；
    在齿轮啮合传动过程中，如下等式成立：
    Figure PCTCN2022072663-appb-100002
    其中，ψ是转角，a t＝μ+θ+ψ；
    将方程组的解(2)式代入与被测齿轮坐标系S(O-x,y,z)下是渐开螺旋面方程(1)中，得被测齿轮渐开螺旋面上的法向啮合齿形方程为：
    Figure PCTCN2022072663-appb-100003
  3. 根据权利要求1所述的一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，其特征在于：测量被测齿轮渐开螺旋齿面上的法向啮合齿形，即四轴控制策略：在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面内不仅同步沿着切向移动，还同步叠加径向和轴向的移动；此时，传感测头在被测齿轮基圆柱的切平面内沿着齿轮啮合线移动，采集到的齿面信息数据即为被测齿轮渐开螺旋齿面上的法向啮合齿形。
  4. 根据权利要求3所述的一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，其特征在于：齿轮齿面上法向啮合齿形测量的四轴控制策略，还能够有如下扩展应用：
    (1)法向啮合齿形的简化测量；
    (2)啮合法测量渐开线。
  5. 根据权利要求3所述的一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，其特征在于：被测齿轮安装在回转轴组上，通过回转轴电机由计算机控制装置CS精确控制旋转，并由回转轴光栅记录旋转角度；在被测齿轮匀速旋转时，测量仪器的传感测头由被测齿轮渐开螺旋齿面上a点开始，在被测齿轮基圆柱的切平面S内不仅同步沿着X轴方向移动，还同步叠加Y轴方向和Z轴方向的移动，测量仪器的传感测头移动到d’ 0点结束；计算机控制装置CS同时精确控制X轴电机、Z轴电机和Y轴电机同步运动，并同时接收X轴光栅、Z轴光栅和Y轴光栅反馈的位置信号。
  6. 根据权利要求4所述的一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，其特征在于：扩展应用中，法向啮合齿形的简化测量的具体方法为：
    令y＝r b，即被测齿轮基圆柱的切平面S与坐标系δ(O-X,Y,Z)的Y轴垂直，则有
    sin(a t+ψ 0)-(a t-ψ+tana ttan 2β b)cos 2β bcos(a t+ψ 0)＝1  (4)
    被测渐开螺旋圆柱齿轮的啮合线方程为：
    z＝x tanβ b-r b(1+tan 2β b)tana tcosβ bsinβ b  (5)
    在被测渐开螺旋圆柱齿轮啮合传动过程中，啮合线ad’ 0为垂直于Y轴的切平面S内的一条直线，与被测齿轮渐开螺旋齿面的交点在齿面上的轨迹就是法向啮合齿形ad 0；此时，四轴控制策略可简化为三轴控制：在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面S内不仅同步沿着切向(X轴方向)移动，还同步叠加轴向(Z轴方向)的移动即可。
  7. 根据权利要求4所述的一种渐开螺旋圆柱齿轮的法向啮合齿形测量方法，其特征在于：扩展应用中，
    啮合法测量渐开线的具体方法为：
    四轴控制策略测量过程中控制轴向(Z轴方向)固定在某一位置，即在被测齿轮匀速旋转时，测量仪器的传感测头在被测齿轮基圆柱的切平面S内同步沿着切向(X轴方向)和径向(Y轴方向)的移动；
    此时，测量仪器的传感测头将会在被测齿轮基圆柱的切平面S内，沿直线ad’ 1移动测量，实现对被测渐开螺旋圆柱齿轮齿面上渐开线ad 1的测量。
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