CN111581721A - Gear clearance-considered transient vibration impact numerical modeling method for transmission system - Google Patents

Gear clearance-considered transient vibration impact numerical modeling method for transmission system Download PDF

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CN111581721A
CN111581721A CN202010363554.3A CN202010363554A CN111581721A CN 111581721 A CN111581721 A CN 111581721A CN 202010363554 A CN202010363554 A CN 202010363554A CN 111581721 A CN111581721 A CN 111581721A
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夏元烽
庞剑
杨亮
周翠
苏家杰
昌诗力
王兰军
李文娟
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Chongqing Changan Automobile Co Ltd
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Abstract

The invention discloses a method for modeling transient vibration impact numerical values of a transmission system by considering gear clearances, which comprises the following steps: s1, measuring the equivalent inertia, rigidity and damping of each part of the transmission system according to experiments; s2, establishing a nonlinear lumped parameter model of the transmission system comprising the gear clearance: s3, establishing a system dynamics control equation:
Figure DDA0002475927170000011
j is an equivalent inertia matrix, C is a damping matrix, K is a stiffness matrix, T is a system excitation matrix, theta is an angular displacement,
Figure DDA0002475927170000012
in order to be the angular velocity of the object,
Figure DDA0002475927170000013
is the angular acceleration; and S4, substituting the system excitation matrix during transient vibration impact of the transmission system into a system dynamics control equation, and solving to obtain the transient vibration impact response of the transmission system. The transient vibration impact phenomenon of the transmission system can be simulated and analyzed, a foundation is provided for controlling transient vibration impact and noise generated by the automobile transmission system, and the NVH performance is improved.

Description

Gear clearance-considered transient vibration impact numerical modeling method for transmission system
Technical Field
The invention belongs to the technical field of mechanical transmission and vibration noise, and particularly relates to a transient vibration impact numerical modeling method of a transmission system considering gear clearance.
Background
With the continuous development of the automobile industry, people have higher and higher requirements on the driving comfort in the automobile, and the noise vibration in the automobile is an important index of the comfort. When the automobile transmission system is in an operating state, transient operations such as rapid accelerator stepping, accelerator retracting, clutch stepping and the like easily cause transient vibration impact and noise of a transmission chain. For example, in the process of a vehicle stepping on an accelerator in a transient state, because a transmission system has gear gaps, spline gaps and assembly gaps, when the torque of an engine suddenly changes or is reversed, transient impact noise is easily generated by the automobile transmission system. The suppression of transient vibration impact noise of a transmission system is a difficult point in the debugging and matching process of the whole vehicle, reduces the sound quality in the vehicle, and is easy to cause consumer complaints.
At present, consumers and automobile manufacturers pay more and more attention to noise and vibration problems generated by a transmission system, however, an effective numerical modeling method for predicting the magnitude of transient vibration impact of the transmission system of an automobile is lacked. Therefore, it is highly desirable to establish a numerical modeling method capable of predicting transient vibration shocks of the drive train.
Disclosure of Invention
The invention aims to provide a numerical modeling method for transient vibration impact of a transmission system considering gear clearances, which can simulate and analyze the transient vibration impact phenomenon of the transmission system, provide a basis for controlling transient impact vibration and noise generated by an automobile transmission system and improve NVH (noise vibration harshness) performance.
The invention relates to a method for modeling transient vibration impact numerical values of a transmission system considering gear clearances, which comprises the following steps:
s1, measuring the equivalent inertia, rigidity and damping of each part of the transmission system according to experiments;
s2, establishing a nonlinear lumped parameter model of the transmission system comprising the gear clearance:
s3, establishing a system dynamics control equation:
Figure BDA0002475927150000011
j is an equivalent inertia matrix, C is a damping matrix, K is a stiffness matrix, T is a system excitation matrix, theta is an angular displacement,
Figure BDA0002475927150000012
in order to be the angular velocity of the object,
Figure BDA0002475927150000013
is the angular acceleration;
and S4, substituting the system excitation matrix during transient vibration impact of the transmission system into a system dynamics control equation, and solving to obtain the transient vibration impact response of the transmission system.
Further, the S2 specifically includes: equivalently establishing each part of a transmission system into a model comprising a plurality of degrees of freedom, connecting adjacent degrees of freedom by adopting a rigidity and damping unit, and considering gear gaps among a plurality of groups of degrees of freedom;
the modeling method considering the degree of freedom of the gear clearance is as follows: two gears which are meshed with each other are respectively i and j; gear i is the driving gear and its inertia and reference circle radius are JiAnd Ri(ii) a Gear j is a driven gear, its inertia andthe reference circle radius is JjAnd RjThe backlash between gear i and gear j isij；
The nonlinear meshing stiffness of the gear i and the gear j is as follows:
Figure BDA0002475927150000021
wherein xi is a unit step function, kIIIs a second order stiffness, xij＝Riθi-RjθjFor relative meshing displacement, θiFor angular displacement of gear i, thetajIs the angular displacement of gear j;
let sgn be a sign function, the interaction torque between the driving and driven gears is:
Figure BDA0002475927150000022
Figure BDA0002475927150000023
order:
Figure BDA0002475927150000024
then T,i(xij) Is the offset torque, T, to the driving gear i,j(xij) Is the biasing torque to the driven gear j.
Further, the transmission system in S1 includes an engine, a transmission, a propeller shaft, a transaxle, a drive shaft, tires, and a suspension.
Further, the equivalent inertia matrix J ═ diag (J) in S31,J2,J3,J4,J5,J6,J7)，
Figure BDA0002475927150000025
Figure BDA0002475927150000031
Wherein, J1Is the inertia of the engine, J2Is transmission input shaft inertia, J3Is the inertia of the output shaft of the transmission, J4For inertia of the input shaft of the drive axle, J5Is inertia of output shaft of drive axle, J6Is the equivalent inertia of the tire, J7Equivalent inertia of the whole vehicle;
c1for clutch damping, c2For transmission gear contact damping, c3For drive shaft damping, c4For drive axle gear contact damping, c5For drive shaft damping, c6Tire and suspension equivalent damping;
k1to torsional rigidity of the clutch, k2For transmission gear contact stiffness, k3For torsional stiffness of the drive shaft, k4For drive axle gear contact stiffness, k5Is the torsional stiffness of the half-shaft, k6For the equivalent stiffness of the tire and suspension,
R2for the transmission input shaft gear pitch radius, R3For the gear pitch radius, R, of the output shaft of the transmission4For the input shaft gear pitch radius of the drive axle, R5The radius of a pitch circle of a gear of an output shaft of the drive axle;
system excitation matrix T ═ TE(t) T,2T,3T,4T,50 TV(t)}T；TE(T) is engine excitation torque, TV(T) is the vehicle load torque, T,2Is the offset torque, T, to the transmission input shaft,3Is the offset torque, T, to the output shaft of the transmission,4Is the offset torque, T, to the input shaft of the drive axle,5Is the biasing torque to the transaxle output shaft.
Further, the load torque of the whole vehicle
Figure BDA0002475927150000032
Wherein m is the mass of the whole automobile, g is the gravity acceleration, r is the rolling radius of the tire, v is the speed of the automobile, C is the wind resistance coefficient, and A is the windward area of the automobile.
According to the method, the nonlinear lumped parameter model of the transmission system containing the gear clearance is established, the system excitation matrix during transient vibration impact of the transmission system is substituted into the system dynamics control equation, the angular displacement, the acceleration and the angular acceleration are obtained through solving, the transient vibration impact response of the transmission system is represented through the angular displacement, the acceleration and the angular acceleration, the transient vibration impact phenomenon generated by the transmission system during transient loading or unloading of the engine torque can be predicted, a foundation is provided for controlling the transient impact vibration and noise generated by the automobile transmission system, and the NVH performance is improved.
Drawings
FIG. 1 is a schematic structural diagram of the transmission system of the present invention;
FIG. 2 is a schematic view of a nonlinear lumped parameter model of a powertrain system of the present invention;
FIG. 3 is a schematic view of the gear lash of the present invention;
FIG. 4 is a schematic view of a driveline lash unit of the present invention;
FIG. 5 is a schematic illustration of the gear contact stiffness of the present invention;
FIG. 6 is a schematic view of the gear contact damping of the present invention;
FIG. 7 is a schematic illustration of the engine torque transient unloading of the present invention;
FIG. 8 is a schematic representation of the variation of the transmission output shaft angular velocity and the transaxle input shaft angular velocity of the present invention;
FIG. 9 is a graphical illustration of the variation in transmission output shaft angular acceleration and transaxle input shaft angular acceleration of the present invention;
FIG. 10 is a schematic representation of the relative meshing displacement variation between gears of the present invention;
fig. 11 is a schematic representation of the relative angular displacement variation between the rotors of the present invention.
In the figure, 1-engine, 2-speed variator, 3-transmission shaft, 4-driving axle, 5-driving shaft, 6-tyre and 7-suspension.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
Taking a later-driving transmission system as an example, the method for modeling the transient vibration impact value of the transmission system by considering the gear clearance comprises the following steps:
and S1, measuring equivalent inertia, rigidity and damping of each component of the transmission system according to experiments, and referring to FIG. 1, the transmission system comprises an engine 1, a transmission 2, a transmission shaft 3, a drive axle 4, a drive shaft 5, tires 6 and a suspension 7, the structure and the connection mode of the transmission system are conventional technologies, and the invention is not repeated.
The equivalent inertia of the various components of the drive train include:
1) equivalent inertia of main rotating parts such as a crankshaft, a connecting rod, and a flywheel of the engine 1;
2) the input shaft equivalent inertia of the speed changer 2;
3) the output shaft equivalent inertia of the speed changer 2 comprises 1/2 transmission shaft 3 equivalent inertia;
4) the equivalent inertia of the input shaft of the drive axle 4 comprises 1/2 equivalent inertia of the drive shaft 3;
5) the equivalent inertia of the output shaft of the drive axle 4 comprises the equivalent inertia of the drive shaft 5;
6) tire 6 equivalent inertia;
7) and equivalent inertia of the whole vehicle.
Torsional stiffness and damping of the driveline includes:
1) torsional stiffness and damping of a clutch in the engine 1;
2. transmission 2 gear contact stiffness and damping;
3. torsional rigidity and damping of the transmission shaft 3;
4. the gear contact rigidity and damping of the drive axle 4;
5. drive shaft 5 torsional stiffness and damping;
6. the tire 6 and suspension 7 are equivalent in stiffness and damping.
Equivalent inertia, rigidity and damping of each part are obtained according to experimental tests, and specific values are shown in table 1.
TABLE 1 values of equivalent inertia, stiffness and damping for the various components
Parameter(s) Symbol Numerical value Unit of
Inertia of engine J1 0.282 kg.m2
Transmission input shaft inertia J2 0.01420793 kg.m2
Inertia of output shaft of speed variator J3 0.01896806 kg.m2
Rear axle input shaft inertia J4 0.0081547 kg.m2
Rear axle output shaft inertia J5 0.03702 kg.m2
Tyre for vehicle wheelsEquivalent inertia J6 1.55588 kg.m2
Equivalent inertia of whole vehicle J7 284.26 kg.m2
Torsional stiffness of clutch k1 1288.582 Nm/rad
Transmission gear contact stiffness k2 114591559 N/m
Torsional stiffness of drive shaft k3 29220.85 Nm/rad
Drive axle gear contact stiffness k4 114591559 N/m
Torsional stiffness of half shaft k5 30710.54 Nm/rad
Tire and suspension equivalent stiffness k6 57295.78 Nm/rad
Clutch damping c1 2.1 Nm.s/rad
Transmission gear contact damping c2 5.1 N.s/m
Transmission shaft damping c3 5.5 Nm.s/rad
Drive axle gear contact damping c 4 10 N.s/m
Drive shaft damping c5 200 Nm.s/rad
Tire and suspension equivalent damping c6 250 Nm.s/rad
Transmission input shaft gear pitch radius R2 17.55 mm
Gear pitch radius of output shaft of speed variator R3 86.1 mm
Drive axle input shaft gear pitch radius R4 50 mm
Drive axle output shaft gear pitch radius R5 205 mm
Transmission gear backlash δ23 0.4 mm
Drive axle gear clearance δ45 0.2 mm
S2, establishing a nonlinear lumped parameter model of the transmission system containing the gear clearance, specificallyComprises the following steps: referring to FIG. 2, the drive train components are equivalently established as a model containing seven degrees of freedom, with J in the model1Is the inertia of the engine, J2Is transmission input shaft inertia, J3Is the inertia of the output shaft of the transmission, J4For inertia of the input shaft of the drive axle, J5Is inertia of output shaft of drive axle, J6Is the equivalent inertia of the tire, J7Equivalent inertia of the whole vehicle; c. C1For clutch damping, c2For transmission gear contact damping, c3For drive shaft damping, c4For drive axle gear contact damping, c5For drive shaft damping, c6Tire and suspension equivalent damping; k is a radical of1To torsional rigidity of the clutch, k2For transmission gear contact stiffness, k3For torsional stiffness of the drive shaft, k4For drive axle gear contact stiffness, k5Is the torsional stiffness of the half-shaft, k6For tire and suspension equivalent stiffness, R2For the transmission input shaft gear pitch radius, R3For the gear pitch radius, R, of the output shaft of the transmission4For the input shaft gear pitch radius of the drive axle, R5Is the gear pitch radius theta of the output shaft of the drive axle1For angular displacement of the engine, theta2For angular displacement of transmission input shaft, theta3For angular displacement of the output shaft of the transmission, theta4For drive axle input shaft angular displacement, theta5For angular displacement of the output shaft of the drive axle, theta6For angular displacement of the tyre, theta7The angular displacement of the whole vehicle; t isE(T) is engine excitation torque, TV(t) is the load torque of the whole vehicle,
the two degrees of freedom are connected by adopting a rigidity and damping unit, gear gaps are considered between a transmission input shaft and a transmission output shaft and between a drive axle input shaft and a drive axle output shaft, and the rigidity and the damping between the transmission input shaft and the drive axle output shaft are nonlinear;
referring to fig. 3 and 4, the modeling method considering the degree of freedom of the gear backlash is: two gears which are meshed with each other are respectively i and j; gear i is the driving gear and its inertia and reference circle radius are JiAnd Ri(ii) a Gear J is a driven gear with inertia and pitch circle radius JjAnd RjThe backlash between gear i and gear j isij；
The nonlinear meshing stiffness of the gear i and the gear j is as follows:
Figure BDA0002475927150000061
wherein xi is a unit step function, kIIIs a second order stiffness, xij＝Riθi-RjθjFor relative meshing displacement, θiFor angular displacement of gear i, thetajIs the angular displacement of gear j;
let sgn be a sign function, the interaction torque between the driving and driven gears is:
Figure BDA0002475927150000062
Figure BDA0002475927150000063
order:
Figure BDA0002475927150000064
then T,i(xij) Is the offset torque, T, to the driving gear i,j(xij) Is the biasing torque to the driven gear j.
Referring to fig. 5, the modeling method of the gear contact stiffness considering the gear intermittence is: within the gap range, i.e. | xij|＜ijWith gear teeth not in contact, then the 1 st stage stiffness k Ι0. Outside the gap range, i.e. | xij|≥ijContact of the teeth, then stiffness k of 2 nd orderⅡIs nonlinear Hertz contact stiffness.
Referring to fig. 6, a modeling method of gear contact damping considering gear intermittence is: within the gap range, i.e. | xij|＜ijGear teeth are not contacted, then damping of 1 st level c Ι0. Outside the gap range, i.e. | xij|≥ijGear tooth contact, then damping c of 2 nd orderⅡ。
S3, establishing a system dynamics control equation:
Figure BDA0002475927150000071
j is an equivalent inertia matrix, C is a damping matrix, K is a stiffness matrix, T is a system excitation matrix, theta is an angular displacement,
Figure BDA0002475927150000072
in order to be the angular velocity of the object,
Figure BDA0002475927150000073
is the angular acceleration;
equivalent inertia matrix J ═ diag (J)1,J2,J3,J4,J5,J6,J7)，
Figure BDA0002475927150000074
Figure BDA0002475927150000075
System excitation matrix T ═ TE(t)T,2T,3T,4T,50 TV(t)}T；TE(T) is engine excitation torque, TV(T) is the vehicle load torque, T,2Is the offset torque, T, to the transmission input shaft,3Is the offset torque, T, to the output shaft of the transmission,4Is the offset torque, T, to the input shaft of the drive axle,5Is the biasing torque to the transaxle output shaft.
Load torque of the whole vehicle
Figure BDA0002475927150000076
Wherein m is the mass of the whole automobile, g is the gravity acceleration, r is the rolling radius of the tire, v is the speed of the automobile, C is the wind resistance coefficient, and A is the windward area of the automobile.
S4, substituting the system excitation matrix into the system dynamics control equation during transient vibration impact of the transmission system, and solving to obtain the final product
To the driveline transient vibration impulse response.
Referring to fig. 7, engine torque transient unloading is shown, as an automotive driveline is prone to transient impulsive noise problems during engine torque transient loading, unloading or transient forward and reverse shifts. Therefore, the transient torque variation condition of the engine along with time is obtained according to the experimental working condition and is used as the excitation torque of the engine.
Obtaining angular displacement theta and angular velocity through numerical solution
Figure BDA0002475927150000081
And angular acceleration
Figure BDA0002475927150000082
The obtained angular displacement, angular velocity and angular acceleration can represent transient vibration shock response of the transmission system, and further can predict transient vibration shock phenomenon generated by the transmission system when the engine torque is loaded or unloaded in a transient manner, as shown in fig. 8, 9, 10 and 11.
Referring to FIG. 8, the light line represents the transmission output shaft angular velocity
Figure BDA0002475927150000083
The dark line is the angular speed of the input shaft of the drive axle
Figure BDA0002475927150000084
The angular velocity fluctuation of the two has obvious impact vibration near the peak value and the estimated value.
Referring to FIG. 9, the light line represents the transmission output shaft angular acceleration
Figure BDA0002475927150000085
The deep color line is the angular acceleration of the input shaft of the drive axle
Figure BDA0002475927150000086
There are significant intermittent transient impacts from both angular accelerations.
See alsoFIG. 10, relative meshing displacement x between transmission gears23＝R2θ2-R3θ3Relative meshing displacement x between gears of drive axle45＝R4θ4-R5θ5。x23In the gear clearance of the transmission23Internal reciprocating wave, x45In the gear clearance of the drive axle45The internal reciprocating wave indicates that double-sided impact between the gear teeth has occurred.
See FIG. 11, θ12＝θ1-θ2For relative angular displacement between engine and transmission input shaft, theta56＝θ5-θ6For relative angular displacement between the rear axle output shaft and the tyre, θ67＝θ6-θ7For relative angular displacement between tyre and vehicle, theta34＝θ3-θ4Is the relative angular displacement between the transmission output shaft and the rear axle input shaft. Due to the damping of the system, theta12、θ34、θ56And theta67As time goes on, the vibration is gradually damped.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (5)

1. A method for modeling transient vibration impact values of a transmission system by considering gear backlash is characterized by comprising the following steps:
s1, measuring the equivalent inertia, rigidity and damping of each part of the transmission system according to experiments;
s2, establishing a nonlinear lumped parameter model of the transmission system including the gear clearance;
s3, establishing a system dynamics control equation:
Figure FDA0002475927140000011
j is an equivalent inertia matrix, C is a damping matrix, K is a stiffness matrix, T is a system excitation matrix, theta is an angular displacement,
Figure FDA0002475927140000012
in order to be the angular velocity of the object,
Figure FDA0002475927140000013
is the angular acceleration;
and S4, acquiring a system excitation matrix of the transient vibration impact of the transmission system, and solving to obtain the transient torsional vibration impact response of the transmission system.
2. The modeling method for the transient vibration impact value of the transmission system considering the gear backlash as claimed in claim 1, wherein said S2 is specifically: equivalently establishing each part of a transmission system into a model comprising a plurality of degrees of freedom, connecting adjacent degrees of freedom by adopting a rigidity and damping unit, and considering gear gaps among a plurality of groups of degrees of freedom;
the modeling method considering the degree of freedom of the gear clearance is as follows: two gears which are meshed with each other are respectively i and j; gear i is the driving gear and its inertia and reference circle radius are JiAnd Ri(ii) a Gear J is a driven gear with inertia and pitch circle radius JjAnd RjThe backlash between gear i and gear j isij；
The nonlinear meshing stiffness of the gear i and the gear j is as follows:
Figure FDA0002475927140000014
wherein xi is a unit step function, kIIIs a second order stiffness, xij＝Riθi-RjθjFor relative meshing displacement, θiFor angular displacement of gear i, thetajIs the angular displacement of gear j;
let sgn be a sign function, the interaction torque between the driving and driven gears is:
Figure FDA0002475927140000015
Figure FDA0002475927140000016
order:
Figure FDA0002475927140000017
then T,i(xij) Is the offset torque, T, to the driving gear i,j(xij) Is the biasing torque to the driven gear j.
3. The modeling method of transient vibration impact value of a transmission system considering gear backlash according to claim 1 or 2, wherein: the transmission system in S1 includes an engine, a transmission, a propeller shaft, a drive axle, a drive shaft, tires, and a suspension.
4. The modeling method for transient vibration impact value of transmission system considering gear backlash as claimed in claim 3, wherein said equivalent inertia matrix J ═ diag (J) in S31,J2,J3,J4,J5,J6,J7)，
Damping matrix
Figure FDA0002475927140000021
Rigidity matrix
Figure FDA0002475927140000022
Wherein, J1Is the inertia of the engine, J2Is transmission input shaft inertia, J3Is the inertia of the output shaft of the transmission, J4For inertia of the input shaft of the drive axle, J5Is inertia of output shaft of drive axle, J6Is the equivalent inertia of the tire, J7Equivalent inertia of the whole vehicle;
c1for clutch damping, c2For transmission gear contact damping, c3For drive shaft damping, c4To driveDamping of contact of the bridge gears, c5For drive shaft damping, c6Tire and suspension equivalent damping;
k1to torsional rigidity of the clutch, k2For transmission gear contact stiffness, k3For torsional stiffness of the drive shaft, k4For drive axle gear contact stiffness, k5Is the torsional stiffness of the half-shaft, k6For the equivalent stiffness of the tire and suspension,
R2for the transmission input shaft gear pitch radius, R3For the gear pitch radius, R, of the output shaft of the transmission4For the input shaft gear pitch radius of the drive axle, R5The radius of a pitch circle of a gear of an output shaft of the drive axle;
system excitation matrix T ═ TE(t) T,2T,3T,4T,50 TV(t)}T；TE(T) is engine excitation torque, TV(T) is the vehicle load torque, T,2Is the offset torque, T, to the transmission input shaft,3Is the offset torque, T, to the output shaft of the transmission,4Is the offset torque, T, to the input shaft of the drive axle,5Is the biasing torque to the transaxle output shaft.
5. The modeling method of transient vibration impact value of transmission system considering gear backlash as claimed in claim 4, wherein said entire vehicle load torque
Figure FDA0002475927140000031
Wherein m is the mass of the whole automobile, g is the gravity acceleration, r is the rolling radius of the tire, v is the speed of the automobile, C is the wind resistance coefficient, and A is the windward area of the automobile.
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US4841685A (en) * 1985-08-16 1989-06-27 University Of Southern California Controllable damper
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