Ming-de ZHANG，Jia-1in WANG（Mechanical Engineering Institute，Chongqing University of Technology，Chongqing 400054，China）

Measurement and analysis method of radial comprehensive deviation of cylindrical gear

Ming-de ZHANG*，Jia-1in WANG
（Mechanical Engineering Institute，Chongqing University of Technology，Chongqing 400054，China）

For some problems of vibration，noise and radial comprehensive deviation which are difficult to quickly detect in the process of cylindrical gear transmission，it applied classic gear measurement principle of double-flank to design a integrated roll tester of rapid detection for cylindrical gear manufacturing precision error which adapted to the production site.100 cylindrical gears with the same specifications were done the related experiments by the above analysis.And the graph about vibration noise and transmission error in the transmission process was output by Matlab.Finally，the tooth surface manufacturing errors and defects were detected accurately and it achieves the gear fast sorting operation，this paper provided an effective measurement method of assessing the pros and cons about the quality of gear in the factory quickly.

Cylindrical gear，Radial comprehensive deviation，F(xiàn)ast sorting，Double-flank

Hydromechatronics Engineering

http：//jdy.qks.cqut.edu.cn

E-mail：jdygcyw@126.com

1 Introduction

Gear is one of the core components in aerospace，transportation，metallurgy，shipbuilding，automobile，etc，and its accuracy level plays a crucial role to the overall performance of machine.With the rapid development of Chinese economy，automation and production chain which service to production field has made the fast development.Gear transmission mechanism has been involved in the structure of the plant among the various machines，so its importance can be imagined.Especially in large machines and some large gear transmission system，the accuracy of single gear tooth profile error and tooth shape will directly affect the quality of the mechanical equipment and the smooth transmission.If the tooth fracture and other accidents occurs，it would be a great threat to the safety of the workers.Therefore，how to quickly improve the quality and productivity of the gear is the urgent problem for industry to need to solve.An efficient method for assessing levels of precision tooth has become the most direct means in actual production process to improve the efficiency of the gear.There are many factors to affect the accuracy，such as：profile error，tooth surface roughness，deputy backlash gear requirements and so on.Factors that the impact of the gear transmission accuracy can be attributed to the hob and the gear to be cut relative position and relative movement is changed，the changes in the relative position and the movement will cause a radial and tangential error in hobbing process.Shi［1］has induction and analysis the existing frontier small module gear measurement techniques，and presented new insights on the current situation and development trend of small module gear measurements.Wan［2］analyzed the development status of Gear Measuring Center and direct drive technology at home and abroad，and one scheme based on the direct drive technology equipment CNC system has been proposed to enhance the overall performance of the existing model of the instrument.Zhou［3］studied the error assessment technology of straight bevel gear deeply，and designed the measurement program of straight bevel gears.

Gear measurement problems in the field of cuttingedge technology can be summarized as follows：the rapid gear measurement techniques in production site，measurement technology about extremely max and small gear，gear parallel measurement based visual measurement and network gear for closed loop measurement technology［4-9］.Generally gear measurements can divide into：analysis measurement based on the tooth profile，gear radial and tangentialand tooth distance measurements，function-based measurement based on integrated measurement（double-flank，single-flank measurement）and the individual and the overall error of measurement gear include single and complex measurement［10-13］.Development of gear measuring instruments from the view of gear measurement of the degree of automation in the present stage，it has developed from the old manual methods to measure the vibration signal by the two-sided action meshing gears，following this，the sensor sends the signal to computer.After it，the computer uses its algorithm and analyzes the internal gear transmission error directly.The measuring method of gear can be divided into single-flankand，double-flank.Because the form of double-flank measurements had the superiority of high work efficiency and low operating disturbance environment compared with the other measurement methods.And it included the information about eccentric thickness，surface roughness，the transmission quality and the other aspects of gear can be obtained by this way accurately.Therefore，the prototype machine of gear error measuring instrument which this paper researched and prior consided the method of doubleflank gear error measurement.

2 Evaluation method of radial comprehensive deviation of gear

As shown in Fig.1，this paper designed the CNC-sided cylindrical gear meshing roll tester，it is mainly included mechanical module（operative），the software module（control section），CNC module（driver part）and other major modules as shown in Fig.2.This tester has the feature about fast detection speed，comprehensively detecting items and it gives whether the measured gearcouldbereformed.Theworking process of Cylindrical gear rolling inspection machine as follows：firstly，due to the install location affect the final test results so the same level of standard gear and modulus measured gear position calibrated correctly to avoid deviation.Then，the numerical control system is given a drive signal and input the necessary parameters in the detection process，the standard gear and the measured gear do the rotation of forward and reverse according to the given drive signal.For the indirect measurement of radial composite error of gears，so it increases the movable right and left along the X-direction degree of freedom on the mechanical structure. According to the vibration and noise signal，the system can judge whether the gear conform actual processing requirements，and assess whether the gear may have to rebuild according to the size of fluctuation curve and the accuracy level which the user needs.

Fig.1 RoIIing tester of cyIindricaI gear

Fig.2 Component moduIes for CNC roIIing inspection machine of cyIindricaI gear

The motion diagram of Rolling tester of cylindrical gear is shown in Fig.3，and standard gear is placed in a fixed shaft.Due to the additional freedom of movement in the X direction，the driven gear shaft can move along the direction of left and right.The distance of gear rotation center may inheritance of an increase or decrease（equivalent sided gear center distance d），according to the size of single gear tooth surface roughness Ra or defects of tooth surface on the measured gear，then there could be a direct reflection of radial and tooth accuracy on the measured gear.

Fig.3 Movement schematics of cyIindricaI gear roIIing inspection machine

According to the known motion parameters of the primary and driven gear，then it obtained the expression about equivalent change of center distance d：

Among formula：r1，r2were pitch circle radius of measured gear and pinion gear；α，α′，β were helix angle，meshing angle and face’s pressure angle on oblique cylindrical gear.Set up mnis the normal module of gear，the number of teeth of the driving wheel Z1and driven wheel Z2could be respectively obtained by the formula paper：

When the testing gear rotate one circle，it will test the gear tooth surface which reflects all unilateral equivalent center distance d and represented by an array：

Set up：

Order：

Then when the testing gear is even，the bar Moas follows：

When the testing gear is odd number the bar Mjas follows：

Among the formula（4），（5），（6），x1，x2were modification coefficient of initiative gear and driven gear，αtis transvevse pressure angle of gear，dzis the diameter of length bar.

3 Error evaluation project detects of roll tester

Items which Scroll inspection machine to check include radial composite total deviation on Measured gear Fiand single tooth radial composite deviation fi. In the detection process，radial composite total deviation Fiof Spur gears could be interpreted as：when the standard gear meshing with the measured gear for twosided action，standard gear driven by a servo motor and given a rotational movement with a smaller units angle.Driving testing gear for 360°circular motion. In the course of rotation，when the paired gear engagement in the region turned every single tooth occupied angle（360°/Z），a certain amount of fluctuation will occur on the equivalent center distance d，when measured gear turned around，the whole process of maximum rotation fluctuation could be recorded as Fi，as shown in Figure 4，it can be expressed as：

Fig.4 Meshing process error curve

Thereinto，single tooth radial composite deviation fiReflect the maximum amount of individual variation ripple in the process of gear meshing，in the process driving wheel engages with the driven gear，it made changes without interruption throughout the ripple，when the standard gear tooth surface contacted with the measured gear，it will be reflected in the surface shape of the testing gear to the gear shaft end on the sensor，the amount of change in a certain period of corrugation reflected the maximum amount of change on single tooth，as shown in Figure 5，recorded YL［i］is transmission volume fluctuation error on measured single tooth on the left flank，YR［i］is transmission volume fluctuation error on measured single tooth on the right flank，then，single tooth radial composite deviation could be expressed through Mathematical expressions：

Fig.5 Meshing condition of the tested gear on Ieft and right surface

In this paper，detection method of gear transmission error and throughout the analysis process could be expressed as flowchart as shown in Fig.6.

Fig.6 AnaIysis fIowchart

4 Experiment

For test the reliability of the actual effect of rolling inspection machine on cylindrical gear，100 of the same type of completed gear on-site processing to online testing，if the precision ratings of measured gear below 7，then it couldn’t be reformed.If the precision ratings higher than 7 and below 6，if the deviation is caused by machining error in this rang，then it couldn’t be reformed.Whereas：if it caused by external factors such as the burr or the dust，then it could be reformed.The test items include noise during gear，gear transmission error and vibration signals during measured gear，taking the error on measurement results about installation position error，amount of applied force during transmission and human operator error and other factors into account.Among them some parameters include measured gear and standard gear shown in Table 1，repeated for each set of gear required installation and take one preferred group，siphon which is more typical of a set of data in MATLAB platform output in Figure 7，F(xiàn)ig.8，F(xiàn)ig.9.A-mong them，the real error and measurement of the 100 measured gears as shown in Fig.10，the result reveals that the tester is stable.

TabIe1 Parameters of standard gear and measured gear

Fig.7 Transmission error on doubIe-fIank gear

Fig.8 Vibration signaI on measured gear

Fig.9 Noise during the process of gear

Fig.10 Comparison between the reaI error and measurement

As shown in Fig.11 is the surface condition of the measured gear，the testing gears about 100 are classified as shown in Table 2，machining accuracy of this batch of gear is 5，software for substandard 6，7 precision gear accordingly categorized and presented in detail the number of repairable and non-repairable gear，as shown in Table 3.

Fig.11 Condition on measured gear tooth surface

TabIe2 Accuracy IeveI of measured 100 gears

TabIe3 Whether gear is repairabIe in substandard gear

It can be seen from Table 3，most of which failed gear in the repairable state，Using this method can be seen to reduce the cost of production plant from the maximum extent.

5 Conclusion

In this paper，it is the existent integrated cylindrical gear rolling inspection machines to the prototype. It made a corresponding improvement in their function and structure，on the gear measurement principle applied more practical principle of double-flank gear detection，solved the facing problem in actual site gear testing process.It proposed the fast sorting gear detection technology site which used in the production site，it provided major initiatives for rapid detection methods of cylindrical gear.And it can be detected include transmission error involving measured gear，transmission gear noise，vibration and other parameters to reflect the performance of gear by this method.It provided new guidance for the rapid detection of cylindrical gears.This method is feasible through a series of testing and analyses of this experiment.

Acknowledgements

This paper is supported by Important National Science&Technology Specific Projects（NO.2011ZX040 02-32）and Innovation Project of Chongqing Graduate（NO.CYS14192）.

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圓柱齒輪徑向綜合偏差測量與分析方法

張明德，王加林
（重慶理工大學(xué)機械工程學(xué)院，重慶 400054）

針對圓柱齒輪傳動過程中的振動、噪聲及徑向綜合偏差難以快速檢測的問題，應(yīng)用了經(jīng)典的雙面嚙合齒輪測量機理，設(shè)計出了一種適應(yīng)于生產(chǎn)現(xiàn)場的圓柱齒輪制造精度誤差快速檢測的綜合滾動檢查機。生產(chǎn)現(xiàn)場的100個同規(guī)格圓柱齒輪經(jīng)由以上分析方法進行了相關(guān)實驗，并將傳動過程中產(chǎn)生的振動、噪聲及徑向綜合偏差在MATLAB平臺下輸出曲線圖。最后，精確檢測出輪齒表面制造誤差及缺陷，實現(xiàn)了出廠齒輪快速分揀動作，為工廠快速評定齒輪傳動質(zhì)量優(yōu)劣提供了一種行之有效的測量方法。

圓柱齒輪；徑向綜合偏差；快速分揀；雙面嚙合

10.3969/j.issn.1001-3881.2015.12.012Document code：A

TH132.413

11 October 2014；revised 20 December 2014；accepted 5 April 2015

*Corresponding author：Ming-de ZHANG，Associate Professor.

E-mail：zmd@cqut.edu.cn