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In order to compensate for gear manufacturing and installation errors, the thermal expansion deformation is compensated for and the tooth-side minimum clearance is left for the gear to facilitate lubrication.
It can be determined according to the lower deviation Esti of the tooth thickness, and the maximum value of the backlash caused by the pair of gears is: jt2=Esi1 Esi2 Firstly calculate a small amount of backlash caused by gear manufacturing and installation error JnJn=f2rb1 f2rb2 2.104F2 =102 102 2.104×92=19.2 In the equation, the deviation of the frb gear base section can be obtained by looking up the table; the F tooth direction error can be obtained by looking up the table. Recalculate the tooth thickness deviation EssEss1=-(fatan jtmin Jn2cos)=-(20×tan20° 25 19.22cos20°=-30.8 where the fa center distance deviation value, look up the table to obtain the value; Jtmin minimum backlash value, check the table Available values.
Finally, calculate the deviation value under tooth thickness EsiEsi1=Ess1-Ts=Ess1-f2r1 b2r×2tan=-30.8-222 622×2×tan20°=-78.7 Ts tooth thickness tolerance validity period; Fr ring gear radial runout error, check The table can obtain the value; br cut the radial feed tolerance value, check the table to get the value. Similarly, Esi2=-80.4 is obtained, then jt2=Esi1 Esi2=78.7 80.4=159.1 base circle eccentricity, tooth shape error.
The base circle eccentricity and tooth profile error can be roughly measured by the radial integrated error F′′i1, and the backlash generated for the gear is: jt3=F′′i1 F′′i2=34 36=70 F′′i1 gear diameter To the comprehensive error, the table can obtain the value.
The matching clearance between the gear and the shaft causes the gear to be eccentric to generate a backlash due to the presence of a clearance between the gear and the shaft. According to the drawing design requirements, the two gear eccentricity e1=e2=24, then the maximum backlash is: jt4=2×(e1 e2)×tan=2×(24 24)×tan20°=34.92.3 Bearing error The radial runout of the rolling bearing ED will cause the offset of the center of the gear, the offset is ED/2. In this transmission, E25 bearing is selected, and E'D1 and E'D2 are set as the radial runout of the fixed race, E′′D1 E′′D2 is the radial runout of the rotating race, and the resulting backlash is: jt5=[(E′D1 E′D2) (E′′D1 E′′D2)]tan=[(8 8) (12 12)]tan20°=14.6 The clearance between the rolling bearing and the housing is set to 1,2, and the resulting backlash is: jt6=(1 2)tan=(34 34)tan20°=24.82.4 dial There is a matching clearance in the error dial drive. If the gap is x1, x2, the resulting backlash is: jt7=(x1 x2)tan=(20 20) tan20°=29.1 The total backlash of a pair of meshing gears can be obtained by the above calculation: jt1=jt1 jt2 Jt3 jt4 jt5 jt6 jt7=14.6 159.1 70 34.9 14.6 24.8 29.1=347.1 The lag angle of the driven wheel due to the backlash (ie, the empty back error angle) '12 is '12=2jt1d2=2×347.150000=0.0139 where d2 output shaft Degree circle diameter; d2=50mm=50000m.
Reducing or eliminating backlash can be achieved by controlling or eliminating the effects of backlash. The method frequently used is to appropriately improve the manufacturing precision of the gear, increase the rigidity of the shaft, and adjust the center distance by adding a wheel between the two transmission gears to achieve the purpose of reducing the backlash. In addition, a contact spring can be used, and the counter-torque generated by the contact spring is used to force the gears of all stages to always mesh with the fixed tooth surface during the transmission, thereby eliminating the influence of the backlash on the empty return. Through the production practice, our company uses the plane scroll spring on the output shaft to eliminate the empty return error angle in the transmission chain. The following mainly introduces the calculation of the deformation angle of the plane scroll spring.
The calculation of the spring deformation angle is obtained by the actual measurement, and the maximum output torque on the output shaft is obtained as T=3.9N.
Mm, effective working revolutions n=1. According to the hardness requirements of the selected materials, the tensile strength of the material is b=1275MPa, the outer end of the spring is fixed by pin, the coefficient of the table is K3=0.75, and d1/h=80 is selected (d1 is the diameter of the spring mandrel, h is the spring Material section thickness), the coefficient K4=0.95 can be found from the graph.
The ultimate torque of the spring Tj=TK3=3.90.75=5.4Nmm The cross-sectional dimension of the spring material is selected as the material width b=5mm, then the thickness of the spring material is h=6Tjbb=6×5.45×1275=0.07mm. Take h=0.08mm.
Effective working length of spring material l=EhnK3K4b=×196000×0.08×10.75×0.95×1275=54.2mm Elastic modulus of E spring material, look up E=196000MPa. Deformation angle of spring=TlEI=3.9× 54.2196000×5×0.083/12=5.05° The moment of inertia of the I material section, for the rectangular section I=bh3/12. From the previous calculation, the error angle of the transmission chain is 2.18°, then > empty. Therefore, the use of the planar scroll spring can eliminate the empty return error angle and meet the transmission accuracy requirements. The design of the spring mandrel and the spring box is not exhaustive here. Specific structure.
Conclusion Through theoretical calculation and practice, the application of planar scroll springs and other methods such as adding a wheel to eliminate the empty return error angle on the output shaft of the small modulus gear train (since the drive chain is short, only the spring is used to eliminate Empty back), the effect is better, the structure is simple, the transmission is stable and reliable and can meet the required transmission accuracy requirements.