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12th IFToMM World Congress Besan on France June18 21 2007 Test Research on Two Motors Driven Double Crank Ring Plate Type Pin Cycloid Gear Planetary Drive Weidong He Lixing Li Xin Li Dalian Jiaotong University Dalian Jiaotong University University of Maryland Dalian China Dalian China Maryland U S A Abstract This paper describes the kinematic principle and1 the structural characteristics of the two motors driven double crank ring plate type pin cycloid gear planetary drive we originally presented The results of the tooth profile optimization and parameter optimization design are presented Experimental test results of the load carrying capacity transmission efficiency vibration and noise intensity of the new drive are mainly described According to theoretical calculation and testing results with the same diameter of the pin center circle and with similar transmission ratio the load carrying capacity of the optimized double crank four ring plate type pin cycloid gear planetary drive is three times more than that of a traditional cycloid reducer The outstanding advantages of the new drive have been proved both by theoretical calculation and by testing results Keywords double crank ring plate type pin cycloid gear planetary drive optimization load carrying capacity test I Introduction It is known that traditional cycloid drives have several advantages compared with traditional involute planetary drives such as the smaller volume the wider range of transmission ratio the usage of hardened gear tooth the multi tooth engagement the larger load carrying capacity the higher transmission efficiency and the smoother operating But it has a weak point that the arm bearing supporting the cycloid gear is placed inside the cycloid gear For this reason the size of the arm bearing is restricted by the geometry of the cycloid gear Thus the overall load carrying capacity of the drive is limited The three ring plate type involute gear planetary reducer developed in the recent years also has more advantages than the conventional less tooth difference planetary drive for example the wider range of transmission ratio the elimination of the output unit and the higher rigidity of the output shaft Further more the arm bearing is placed outside the planet gear and therefore its size is no longer restricted by the geometry factor Hence the load carrying capacity can be greatly increased However this type of E mail hwdong E mail llx1933 E mail mike xin li 1 hello reducer also has some shortcomings such as the small contact ratio the large pressure angle the usage of soft gear tooth of the internal involute gear and the difficulty to achieve dynamic balance The double crank ring plate type pin cycloid gear planetary drive Chinese patent ZL02231994 8 we developed can creatively overcome the shortcomings of the two kinds of reducers previously mentioned Its load carrying capacity is greatly increased Especially the drive can achieve dynamic balance with four ring plates so that the operation of the reducer is extremely smooth The appearance of the new development would surely provide the reducer industry a brand new cycloid planetary drive which has small volume light weight wide range of transmission ratio high transmission efficiency simple construction high rigidity of the output shaft much higher load carrying capacity 1 2 3 and high valuation in practice During the optimization design of the new drive with the given parameter and overall size the load carrying capacity of the whole drive can be greatly increased by the tooth profile optimization 4 and the parameter optimiza tion 5 Meanwhile under the condition of the strength the shape of the ring plate is optimally designed to reduce its weight and its vibration during operating In order to validate the theory of the optimization design 6 three prototypes with different structural designs have been developed and manufactured and the load carry capacity transmission efficiency vibration and noise intensity of the prototypes has been tested The results show that the design theory is right II Kinematics principle and structural characteristics A Kinematics principle The kinematics diagram of the double crank ring plate type cycloid drive is shown in figure 1 The pin gear is mounted on the coupler ring plate BC of a parallel linkageABCD The center P O of the pin gear is at the middle point of the coupler The center C O of the cycloid gear 5 which meshes with the pin gear 2 is at the middle point of the fixed linkAD The length l of the crank is equal to the eccentricity CPO O between the pin gear and cycloid gear CHANGSHU INSTITUTE OF TECHNOLOGY 61 155 18 17 2014 1 10 Download 12th IFToMM World Congress Besan on France June18 21 2007 As a motor drives crank 1 to rotate the coupler with the pin gear mounted does a pure translation The whole pin gear moves along a circle with its radius equal tol The center point P Oof the pin gear moves along the circle of radiuslabout the center point c O When the pin gear engages the cycloidal gear the former drives the latter to rotate about the fixed axis c O The torque is then outputted through an output shaft Let p r be the pin gear pitch radius and c r be the cycloid gear pitch radius We havelrr cp Supposing the angular velocity of the driving crank is 1 and then the velocity B at the jointBbetween the link BC and the driving crank AB can be obtained asl 1B Because of the nature of the translation motion the velocity of any point on the coupler is identical Thus we can see that the velocity of the pin gear at the point B is equal to the velocity of the cycloid gear at the pitch pointP that is BP We then obtain lrc 12 1 where 2 is the angular velocity of the cycloidal gear and the output shaft Substituting cp rrl into equation 1 yields 12cpc rrr Thus cp c cp c 2 1 zz z lzlz lz rr r cp c Where c z is the number of teeth of the cycloid gear and p z is the number of teeth of the pin gear Figure 1 shows the velocity direction of the cycloid gear and the pin gear at the pitch point p is identical to B so the rotation direction of the cycloid gear about c O is opposite to that of the driving crank about centerA Thus we put a negative sign in the formula of the transmission ratio of the cycloid drive as follows cp c 2 1 12 zz z i 2 B Structural characteristics The double crank ring plate type pin cycloid planetary drive we creatively presented not only keeps the advantages of the ring plate type drive such as the elimination of the output unit and the higher rigidity of the output shaft but also the arm bearing is placed outside of cycloid gear the radial size of the bearing is no longer restricted any more and to obtain high load carrying capacity In addition it has also some advantages as follows 1 The new drive with our presented optimum tooth profile has the more number of teeth in meshing simultaneously so that the transmission is smooth and the load carrying capacity is high 2 The pressure angle of the meshing teeth at different positions is different The pressure angle is smaller at the position where the acting force is greater vice versa In the procedure of optimization design of the tooth profile the tooth at the position of large pressure angle would not enter in meshing so that the angle between the total normal force and its peripheral component at the pitch point is less than 20 Thus the transmission efficiency is high and the service life of the bearing is long 3 The range of transmission ratio of the drive is wide For the single stage i 6 120 at least i 12 88 for power transmission 4 The cycloid gear the pin and pin roll in the new reducer are made of bearing steel grad GCr15 or GCr15iMn to be hardened In addition with the factor of multi tooth engagement the load carrying capacity greatly increases 5 For the two motors driven double crank four ring plate type pin cycloid planetary reducer shown in figure 2 the two cranks are now both active so that there is no dead point problem of the mechanism Based on the mechanical nature of an electrical motor if one motor s load is increased then its speed will be reduced accordingly vise versa Thus the two motors can always be balanced with the equal load and the equal rotation speed Fig 1 The kinematic diagram of the double crank ring plate type pin cycloid gear planetary drive Fig 2 Two motors driven double crank four ring plate type planetary reducer 5 CHANGSHU INSTITUTE OF TECHNOLOGY 61 155 18 17 2014 1 10 Download 12th IFToMM World Congress Besan on France June18 21 2007 III The results of tooth profile optimization and parameter optimization design A Mathematic model for tooth profile optimization With a set of given parameters such as the radius of the pin center circle p r the radius of pin roller rp r eccentricitya and the number of teeth of the pin gear p z in order to compensate the manufacture errors and to achieve better lubrication condition the suitable values of mesh backlash c and radial clearance j need to be determined Let jrr prp where the value of the equidistance modification rp r 0 and the value of the displacement modification p r 0 Determine the equivalent angle modification value c for the conjugate curve so that the working segment of the actually modified profile is going to coincide with the conjugate curve In accordance with the requirement that the number of teeth in transmitting force simultaneously should be greater than four determine the two end points B and C of the working segment of the tooth profile and the position angles B and C Divide BC into m 1 interval Then the objective function and constraint conditions can be described as follows jrr r r rrFrrF prp p rp prpprp 0 0 min 3 where m i ciciprp xx m rrF 1 1 ci x is x coordinate value of the cycloidal gear modified by angle modification at the point ci y and ci x is x coordinate value of the cycloidal gear modified by positive equidistance and positive displacement modification at the point cici yy Both the value of ci x and ci x are calculated by general analytical equation of modified tooth profile As a result of this procedure the combination of positive equidistance and positive displacement modifications with the optimum values of rp r and p r makes the working segment of the tooth profile approximate to the angle modification curve to the greatest extent shown in figure 3 B Mathematic model for parameter optimization Because the value of the diameter of the pin centers circle p dand the mounting dimensions are standardized in series the design variables which affect the load carrying capacity of the new drive are the eccentricity a radius of the pin roller rp r and radius of the pin sp r The optimiza tion objective is to maximize the load carrying capacity rated torque of the reducer with the given p dand the corresponding overall dimensions based on the tooth profile optimization and the accurate force analysis 4 The design variable vector is X 1 x 2 x 3 x T a rp r sp r T Objective function xT max xT The constraint conditions are established for the contact strength the bending strength the elastic deflection angle and the working life of the bearing The model of parameter optimization is built with total eleven constraint conditions Based on the models of the tooth profile optimization and the parameter optimization a computer program has been developed Its flow chart is shown in figure 4 C Results of optimization design By using the program of the tooth profile optimization and the parameter optimization a two motors driven double crank four ring plate type reducer has been designed Given parameters diameter of the pin center circle p d 218mm transmission ratio i 34 motor s speed n 1000 r min The results of the tooth profile optimization of the cycloid gear are equidistance modification rp r Origin O is at the center of the cycloidal gear Fig 3 Tooth profile optimization of cycloid gear Fig 4 Flow chart of the optimization design Origin O is at the center of the cycloidal gear CHANGSHU INSTITUTE OF TECHNOLOGY 61 155 18 17 2014 1 10 Download 12th IFToMM World Congress Besan on France June18 21 2007 Fig 6 The testing device of the reducer 60 70 80 90 100 012345 Fig 7 The efficiency vs output torque of the prototype 0 7317mm displacement modification p r 0 5817 mm The results of the parameter optimization are a 2mm rp r 7mm sp r 5mm The maximum torque is max T 4480 Nm The structure of the new reducer is shown in figure 5 As the result shows the load carrying capacity of the newly designed two motors driven double crank four ring plate type planetary reducer is 3 times more than that of the traditional cycloid planetary reducer BX5 35 with the same radius of the pin center circle and with similar optimized parameters a 2 5mm rp r 7mm sp r 5mm As described in the previous section the arm bearing is the weakest part of the traditional cycloid planetary reducer and it can not be enlarged because of the geometry of the cycloid gear Therefore in order to reduce the bearing s stress it often needs to increase the eccentricity and consequently the pitch circles of both the cycloid gear and the pin gear In the design of the new drive the arm bearing is placed outside the cycloid gear Therefore its size is no longer restricted This design change could greatly increase the overall load carrying capacity Another critical factor is the contact strength In order to increase the load carrying capacity to the greatest extent we can optimally increase the eccentricity to enlarge the equivalent curvature radius of the cycloid tooth profile and the pin gears so that we can have higher contact strength Meanwhile both the tooth profile optimization and the parameter optimization can improve the contact strength as well Due to all these factors the load carrying capacity of the reducer is greatly increased In addition the supporting span of the pin in the four ring plate type pin cycloid drive is about only the half size of that in a traditional cycloid drive therefore its bending strength and rigidity is much stronger which consequently results in higher load carrying capacity IV Performance test of the prototype A Load carrying capacity test Three prototypes with three different structural designs have been developed and manufactured Here we use the two motors driven double crank four ring plate type pin cycloid gear planetary drive as an example The testing device is shown in figure 6 The input and the output shafts of the reducer are connected to torque and speed sensors respectively The two shafts are also connected to an efficiency meter The input shaft is connected to an electrical motor with adjustable speeds The output shaft is connected to a magnetic particle brake machine Different load conditions were tested during the experiment Each load condition lasted for one hour Parameters such as speed torque efficiency noise temperature and vibration were recorded every 30 minutes The testing results compared to a traditional cycloid planetary reducer BX5 35 are shown in table I Design parameter p d i n P max T Unit mm r min kW N m BX5 35 218 35 1500 5 5 1126 Prototype 218 34 1000 15 4480 TABLE I Test results of the prototype The testing results show that the rated power and the rated torque of the new reducer with the same radius of the pin roller center circle is three times more than that of the traditional reducer In the mean time its transmission Fig 5 Structure of two motors driven double crank four ring plate type pin cycloid planetary reducer Efficiency Torque T kN m CHANGSHU INSTITUTE OF TECHNOLOGY 61 155 18 17 2014 1 10 Download 12th IFToMM World Congress Besan on France June18 21 2007 efficiency is as high as 92 as shown in figure 7 B Noise intensity and vibration test The experiment system used in the test is equipped with the PCB acceleration sensor and other measure hardwares which are all the products of NI Company of USA The acceleration sensors were mounted on rigid places of the circumference and end surface of the bearing seat so that the tested result would be accurate 7 The location of the test point is shown in figure 8 Point 1 is near the front end of the output shaft bearing Point 2 right above the output shaft Point 3 right above the input shaft bearing Points 4 and 5 symmetrically at the case cover The test data of the signal of the sensor show that the acceleration amplitude of the frequency and power spectra density respectively increases with the increasing of the rotate speed under the constant load The distribution in frequency domain has no obvious changes along with the increasing rotate speed At the constant rotate speed the changes of the load almost have no influence on the amplitude and spectrograms of the amplitude and power The acceleration vibration spectrograms of the test point 1 at speeds 500 r min 1000 r min and under the full load are respectively shown in figure 9 and figure 10 The signal of the sensor at test point shows the axial vibration which is transmitted through the bearing seat and the case from the source i e the running mechanism The scale value of the acceleration is 10 09 m s2 From the spectrogram of point 1 it is shown that the spectral region is wide and has two different zones One is from 0 to 300 Hz where the maximum peak occurs between 150 and 200 Hz The other is from 300 Hz to 1500 Hz and peaks occur around 450 Hz 625 Hz 720 Hz and 800 Hz The acceleration vibration spectrograms of the test point 2 at speeds 500 r min 1000 r min and under the full load are respectively shown in figure 11 and figure 12 The signal of the sensor at test point 2 shows the vertical vibration which is transmitted through the bearing seat and the case from the source i e the running mechanism The scale value of the acceleration is 53 04 m s2 Fig 11 Acceleration frequency spectrogram of test point 2 at rotate speed 500 r min and under full load Fig 8 Location of the test point 0500100015002000 0 00 0 05 0 10 0 15 0 20 Frequency H