Discussion on the principle of rapid torque of integrated gear motor and practice analysis

The ordinary gear motor has the advantages of simple structure, strong anti-pollution ability and convenient processing, but its structural form makes it inevitably have defects such as radial force imbalance and large output torque pulsation.
The compound gear motor is a new type of actuator that combines the internal and external gear motor principle with the wheel train theory. It has the advantages of large displacement, good torque uniformity, low noise, and balanced radial pressure. The transient output torque of the composite gear motor is studied by taking the three idler compound gear motor as an example. The analysis method of the multi-inert wheel compound gear motor is similar.
1The working principle of the compound gear motor The fixed-shaft wheel three-in-wheel composite gear motor is mainly composed of a center wheel, an idler gear, an internal gear, a sealing block, front and rear side plates, front and rear end covers (not shown), etc. Three external gear motors are formed with three idlers, and the three idlers simultaneously form three internal gear motors with the internal gears. The sealing block acts as both the outer gear motor housing and the inner and outer gear motors. The oil chamber is separated from the oil discharge chamber, and at the same time plays a role in auxiliary distribution. The compound gear motor adopts an end face distribution structure, and the front and rear plates are the flow distribution plates. The high-pressure oil enters the three external meshing and three internal meshing chambers through the oil hole on the side plate, and the internal gear, the three idler wheels and the central wheel generate a torque under the action of the oil pressure, and the driving gear rotates.
2Combined gear motor output torque 2.1 Geometry displacement and flow The composite gear motor consists of three internal gear motors and three external gear motors. The geometric displacement is qM=12m2Bz1 (1) where: z1 is the number of teeth of the center wheel ; B is the width of the gear; m is the modulus of the gear.
2.2 Theoretical average output torque The theoretical average output torque of the compound gear motor is TMt=pMqM2=pM×12m2z1B2=6pMm2z1B(2) where: pM is the motor inlet and outlet pressure difference, p=pH-pT is the inlet pressure, pT For the outlet pressure, it is usually assumed that pT=0; qM is the motor geometry displacement, qM=12m2Bz1.
3 Transient Output Torque of a Composite Gear Motor 3.1 Overview The transient torque of a compound gear motor fluctuates around the theoretical output torque TMt (or the actual average output torque TM = TMtMm). Assuming that the hydraulic motor supply pressure is pH=const and the supply flow rate Qs=const, there is pMQsMvMm=TM(t)M(t)=const(3) where: pH is the supply (inlet) pressure; Qs is the supply (inlet) flow; Mv is volumetric efficiency; Mm is mechanical efficiency; TM(t) is transient output torque; M(t) is transient output angular velocity.
It is known from equation (3) that when TM(t) changes, M(t) necessarily changes, so the transient torque of the motor is studied to be consistent with the transient angular velocity or rotational speed of the research motor. There are two methods to study the transient torque of hydraulic motor. One is to study the transient force of hydraulic pressure to obtain transient torque. The other is to study the transient discharge volume. VM(t)=qM(t)2qM(t) is called Transient geometry displacement, qM(t) is the transient drain volume of the non-flow concept, and the transient output torque is analyzed according to the formula TM(t)=pMVM(t).
In this paper, the transient torque of the composite gear motor is studied by visual analysis. For convenience, it is assumed that the mechanical efficiency of the motor is Mm=100.
3.2 Transient Torque of External Geared Motor The composite gear motor is composed of internal and external gear motors. The torque characteristics are determined by the torque characteristics of the internal and external gear motors. Therefore, the internal and external gear motor torque theory is the basis of the compound gear motor torque theory.
When the external gear motor is working, the hydraulic pressure in the circumferential direction on the center wheel is 260F1=pMB(Ra1-Rc1)=pHB(Ra1-Rc1)(4) where: pM is the motor inlet and outlet pressure difference; B is the gear width; Ra1 is The center tooth tip circle radius; Rc1 is the meshing point C to O1 transient radius.
Then the hydraulic torque T1 generated on the center wheel is T1=F1? =pHB(R2a1-R2c1)/2(5) is similar to the hydraulic pressure F2 and hydraulic torque T2 on the driven wheel is F2=pHB(Ra2-Rc2)(6)T2=pHB(R2a2-R2c2)/2(7) Where: Ra2 is the crankshaft radius of the driven wheel (idler wheel); Rc2 is the transient radius of the meshing point C to O2.
If the angular velocity is M, the torque TM1 superimposed on the motor output shaft is TM1M=T11 T22(8) where: 1 is the driving wheel (center wheel) angular velocity; 2 is the driven wheel (idle wheel) angular velocity.
Take M=1, the torque TM1 converted to the center wheel is TM1=T1 21T2=T1 R'1R'2T2(9) where: R'1 is the center wheel circle radius; R'2 is the idle wheel outer mesh joint The radius of the circle.
Substituting equations (5) and (7) into equation (9), there are two variables in TM=pHB2[(R2a1-R2c1)R'1R'2(R2a2-R2c2)](10) equation (10) Rc1 and Rc2 can simplify equation (10) to TM=pH2B[2R'1(h'1 h'2) h'21 h'22R'1R'2-(1 R'1R'2 according to the geometrical relationship of gear meshing. ) f2]=pH(a1-a2f2)(11) where: h'1 is the center tooth height; h'2 is the tooth tip height when the idler is externally engaged; f is the external displacement point-to-node transient displacement ;a1=B2[2R'1(h'1 h'2) h'21 h'22R'1R'2] (constant); a2=B2(1 R'1R'2) (constant).
Set the gear motor supply pressure to pH, displacement gradient VM=qM2, TM=pHVM, you can determine TM=pHVM=pH(a1-a2f2)(12)When both the driving wheel and the driven wheel are standard gears (R'1) =R1,h1=h2=h=m), then TM=pHB2(4R1h h2 h2R1R2-(1 R1R2)f2)=phBm2(2z1 1 z1z2-(1 z1z2)f2m2) (13) When the number of teeth of the two gears is equal , TM = pHBm2 (z1 1-f2m2) (14) such that TM has a maximum value and a minimum value, and at the supply pressure pH = const condition, torque pulsation is generated. This torque ripple is not caused by an external cause, but by a displacement of the meshing point of the gear motor or its own structural characteristics.
3.3 Transient torque of internal gear motor When the idler angle is d2, the internal gear angle is d3, the required liquid supply volume is dv2 and dv3, and if the liquid supply volume dv=dv2 dv3, the hydraulic energy dE is supplied. =pH(dv2 dv3)=pHdv; if the leakage and mechanical loss are not counted, the output mechanical work dw=T2d2 T3d3, according to the principle of conservation of energy, there is dE=dwpH(dv2 dv3)=T2d2 T3d3(15) where: T2 is Torque on the idler; T3 is the torque on the internal gear; d2 is the idler angle; d3 is the internal gear angle; dv2 is the required supply volume for the idler rotation; dv3 is the required supply volume for the internal gear rotation; pH is for the hydraulic force.
The required liquid supply volume dv2 when the idler rotates through d2 is equal to the product of the area scanned by the tooth profile line between the addendum circle Ra2 and the meshing point diameter Rc2 and the gear thickness, that is, [5] 261dv2 = B2 (R2a2-R2c2) D2 (16) can also get the required liquid volume dv3 of the internal gear.
Dv3=B2(R2c3-R2a3)d3(17) Substituting formula (16) and formula (17) into formula (15), there is (T2 T3d3d2)d2=pHB2[(R2a2-R2c2) (R2c3-R2a2)d3d2] Dv2 (18) Since d3d2 = d3d2 = R" 2R'3 (= z2z3 standard transmission), then equation (18) can be expressed as TM2 = (T2 T3R" 2R'3 = pHB2 [(R2a2-R2c2) (R2c3- R2a3)R′′2R′3](19) where: TM2 is the output torque of the internal gear motor (converted to the output torque on the external gear shaft); R′′2 is the radius of the pitch circle when the idler is engaged; R′3 is inside Gear pitch radius; Ra3 is the inner gear tip radius; R'c2 is the distance from the internal mesh point to the center of the idler; Rc3 is the distance from the internal mesh point to the center of the internal gear.
Finished TM=pHB2[2R"2(h'2 h'3) h'22-R"2R'3h'23-(1-R"2R'3)f'2]=pH(b1-b2f'2 (20) where: R"2 is the pitch circle radius of the idler gear; R'3 is the inner gear pitch circle radius; h'2 is the idler gear tip height; h'3 is the internal gear tooth tip height; ' is the distance from the internal meshing point to its node; b1=B2[2R'2(h'2 h'3) h'22-R'2R'3h'23] (constant); b2=B2(1-R' 2R'3) (constant).
When the internal gear is a standard gear, there are TM=pHB2m2[2z1 (1-R1R2)(1-f'2m2](21)3.4 composite gear motor transient torque and displacement composite gear motor consists of three external gear motors ( The center wheel z1, the idler wheel z2) and the three internal gear motors (idle wheel z2, internal gear z3), the output torque TM can be derived from the theory of the internal and external gear motors.
The output torque of each external gear motor (around the center O or the center axle) TeMi is TeMi(O)=pHB2[2R'1(h'1 h'2) h'21 h'22R'1R'2-(1 R' 2R'1)f2i]=pH(a1-a2f2i)(22) where: fi is the distance from the meshing point of each external gear motor to the corresponding node Pi; i is the external gear motor number, i=1, 2, 3.
Similar to each internal gear motor output torque (relative to the idler geometry center O1, O2, O3) TIMi(Oi) is TIMi(Oi)=pHB2[2R"2(h'2 h'3) h'22-h'23R "2R'3-(1-R"2R'3)f'2i]=pH(b1-b2f'2i)(23) where: f'i is the point of each meshing point of the internal gear motor relative to the node P'i distance.
The torque TMi of an internal gear motor and an external gear motor converted to O is TMi(O)=TeMi(O) R'1R'2TIMi(Oi)=pH(a1-a2f2i c1-c2f'2i)(24) The total output torque TM of the compound gear motor is TM=∑3i=1TeMi(O) ∑3i=1R'1R′′2TIMi(Oi)=pH(A-a2∑3i=1f2i-c2∑3i=1f′2i)(25) Where: A is a constant, A = 2 (a1 c1); c1 is a constant, c1 = b1R'1/R'2; c2 is a constant, c2 = b2R'1/R'2.
3.5 Composite gear motor experimental torque curve and its analysis of the torque curve of the composite gear motor no-load experiment, the torque curve of the loading experiment. The torque ripple of the composite gear motor is relatively small, generally around 0.4, with the increase of torque, although The speed reduction is faster, but the torque ripple variation of the composite gear motor is relatively small.
t/s(a) Torque pulsation curve (T=4.55N?m) t/s(b) Torque pulsation (T=15.4N?m) 4 Conclusions From the above analysis, the output torque of the composite gear motor is determined by three. The displacement of the meshing point of the external gear motor and the displacement of the meshing points of the three internal gear motors and their superposition. Since the displacement movement of the meshing point of the composite gear pump and the compound gear motor is similar, the analysis can be referred to when analyzing the displacement of the meshing point of the composite gear motor.
Through the theoretical analysis of the transient torque of the composite gear motor and the verification of the experimental curve, it can be used as the theoretical basis for the selection and processing of the composite gear motor.