CN111553026B - Locomotive axle load cushioning adjustment method - Google Patents

Locomotive axle load cushioning adjustment method Download PDF

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CN111553026B
CN111553026B CN202010431770.7A CN202010431770A CN111553026B CN 111553026 B CN111553026 B CN 111553026B CN 202010431770 A CN202010431770 A CN 202010431770A CN 111553026 B CN111553026 B CN 111553026B
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padding
locomotive
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CN111553026A (en
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崔潇
赵刚
李传龙
王建
曲松
王晓雷
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CRRC Dalian Co Ltd
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Abstract

The invention discloses a locomotive axle load cushioning adjustment method, which comprises the steps of establishing locomotive axle load adjustment mechanical modeling; according to the locomotive axle weight, adjusting mechanical modeling, selecting an objective function and a constraint equation, and optimizing numerical solution; to obtain one series of padding amounts and/or two series of padding amounts. Aiming at the condition that the locomotive axle weight adjustment cushioning scheme in the prior art is not easy to solve, the invention expands the range of providing the cushioning scheme. In addition, when the primary padding axle load is adjusted, the weighing index of the whole car is ensured, and meanwhile, the weighing index of the bogie is ensured.

Description

Locomotive axle load cushioning adjustment method
Technical Field
The invention relates to the technical field of locomotive production, in particular to a locomotive axle weight cushioning adjustment method.
Background
In locomotive production, after assembly, the vertical force generated by each wheel on the track is often different due to factors such as center of gravity offset, manufacturing errors and the like. The locomotive is required to be weighed before leaving the factory, the weight of each wheel of the locomotive can be obtained by weighing, and the wheel weight difference and the axle weight difference are calculated. The wheel weight difference is required to be kept at +/-4%, and the axle weight difference is required to be kept at +/-2%, so that the effective exertion of traction adhesive force is ensured.
At present, for a locomotive with unqualified weighing, a main means for adjusting the wheel weight difference and the axle weight difference of the locomotive is to add a steel metal pad under a primary spring or a secondary spring (primary padding or secondary padding for short), and the calculation of a locomotive axle weight adjustment padding scheme is to calculate the padding thickness of the primary padding or the secondary padding at each position through locomotive design parameters and wheel weight measurement values obtained by locomotive weighing, so that the locomotive is ensured to meet the specified axle weight difference and wheel weight difference requirements when weighing is performed again after the padding adjustment. The whole structure of the locomotive is shown in fig. 1 and 2. Wherein, global coordinate system X axis is vertical, and the Y axis is vertical, and the Z axis is horizontal. The positions 1 to 4 in fig. 1 represent the positions of the secondary springs.
The locomotive axle weight adjustment cushioning scheme calculation mainly comprises: and (5) establishing a mechanical model and optimally solving. In the aspect of mechanical modeling, a three-degree-of-freedom mechanical model is adopted, and in the optimization solution, an objective function adopts the root mean square of the wheel weight difference, as shown in a formula (1)
Figure BDA0002500841960000011
Wherein j is the number of wheels, n is the total number of wheels, F j For the measurement of the wheel weight value,
Figure BDA0002500841960000012
is the average value of the wheel weight measurement value.
In the method, the requirement of an objective function is too high in optimization solution, and although the requirement of the formula (1) is basically met, the locomotive axle weight adjustment and padding scheme can meet the wheel weight difference and axle weight difference indexes, the adjustment scheme which does not meet the formula (1) is eliminated in many cases, so that the range of the scheme can be reduced. Therefore, for the situation that the locomotive axle weight adjustment cushioning scheme is not easy to solve, a solution scheme cannot be given.
In summary, in the existing calculation method for the locomotive axle weight adjustment and padding scheme, the adopted objective function is too strong in optimization solution, so that the padding scheme cannot be given for the situation that part of the solution is not easy to adjust. In addition, for the one-train shimming case, the shimming scheme provided cannot guarantee that the truck weighing requirements are met.
Based on this, the prior art still remains to be improved.
Disclosure of Invention
In order to solve the technical problems, the embodiment of the invention provides a locomotive axle load shimming adjustment method to solve the technical problems that the shimming scheme in the prior art has strong objective function requirement, is not easy to adjust, and can not meet the bogie weighing requirement in some cases.
The embodiment of the invention discloses a locomotive axle load cushioning adjustment method, which comprises the following steps:
establishing locomotive axle weight adjustment mechanical modeling;
according to the locomotive axle weight, adjusting mechanical modeling, selecting an objective function and a constraint equation, and optimizing numerical solution;
to obtain one series of padding amounts and/or two series of padding amounts.
Further, the establishing locomotive axle readjustment mechanics modeling includes:
establishing a static equilibrium equation of the locomotive;
and (5) establishing a relation equation of the wheel weight and the padding amount.
Further, the establishing a locomotive static equilibrium equation includes:
establishing a three-degree-of-freedom model of the stress of the vehicle body and the framework;
respectively writing balance equations of three degrees of freedom for the vehicle body, the front framework and the rear framework;
a relation equation of the first series spring supporting force, the second series spring supporting force and displacement is written in series;
further, the establishing the wheel weight and padding amount relation equation comprises the following steps:
bringing the balance equation of the three degrees of freedom into the relation equation of the primary spring supporting force, the secondary spring supporting force and the displacement, and finishing to obtain a relation formula among an external force vector, a displacement vector and a rigidity matrix;
and obtaining a wheel weight change vector and a padding amount formula.
Further, the relation formula among the external force vector, the displacement vector and the rigidity matrix is as follows:
AX＝W
wherein A is a rigidity matrix, X is a displacement vector, and W is an external force vector.
Further, the wheel weight change vector and the padding amount formula are as follows:
Q＝ΩΔ
Ω＝k 1 (DA -1 C+E)
wherein Q is the weight change of the locomotive wheel, omega is the load increase coefficient matrix, delta is the padding amount, A is the rigidity matrix, and k 1 The supporting rigidity of each axle box of the primary spring is represented by a matrix of external force generated by unit cushioning quantity, D is represented by a coefficient matrix, and E is represented by a unit matrix.
Further, the selecting an objective function and a constraint equation according to the locomotive axle weight adjustment mechanics modeling, and optimizing the numerical solution includes:
and setting an objective function, a constraint wheel weight difference, a constraint axle weight difference and a constraint unbalanced force based on the two-system padding.
Further, the selecting an objective function and a constraint equation according to the locomotive axle weight adjustment mechanics modeling, and optimizing the numerical solution includes:
and setting an objective function, a constraint wheel weight difference, a constraint axle weight difference, a constraint wheel weight adjustment tolerance, and a constraint front bogie weighing and a constraint rear bogie weighing based on the first padding.
Further, based on the two-system padding, the optimization solving objective function and the constraint formula are as follows:
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R
wherein F is a wheel weight measurement value of the whole vehicle, S is 2 norms of each axle weight difference, and A is the weight of the whole vehicle 3 Constraint matrix for wheel weight difference, A 4 A constraint matrix for the axle weight difference, R is the unbalanced force tolerance, Ω is a matrix sub-block in the load enhancement coefficient matrix Ω,Δis part of the elements in the padding amount delta.
Further, based on the first series of padding, the optimization solving objective function and the constraint formula are as follows:
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R
A 5 Ω 1 Δ 1 +A 5 1 ΩF 1 ≤0
A 6 Ω 2 Δ 2 +A 6 Ω 2 F 2 ≤0
wherein F is a wheel weight measurement value of the whole vehicle, S is 2 norms of each axle weight difference, and A is the weight of the whole vehicle 3 Constraint matrix for wheel weight difference, A 4 A constraint matrix for the axle weight difference, R is the unbalanced force tolerance, Ω is a matrix sub-block in the load enhancement coefficient matrix Ω,Δf is part of the element in the padding quantity delta 1 Wheel weight measurement value for front bogie singly weighing, F 2 For the wheel weight measurement when the rear bogie is individually weighed,Ω 1 is the matrix of the load increase coefficients of the front bogie,Ω 2 and the load increase coefficient matrix of the rear bogie. Delta 1 Delta for front bogie 2 Cushion the rear bogie, A 5 Constraint matrix for front bogie weighing index, A 6 And (5) constraining the matrix for the weighing index of the rear bogie.
By adopting the technical scheme, the invention has at least the following beneficial effects:
aiming at the condition that the locomotive axle weight adjustment cushioning scheme in the prior art is not easy to solve, the invention expands the range of providing the cushioning scheme. In addition, when the primary padding axle load is adjusted, the weighing index of the whole car is ensured, and meanwhile, the weighing index of the bogie is ensured.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a diagram of a whole locomotive;
FIG. 3 is a flow chart of an embodiment of the present invention;
FIG. 4 is a schematic view of a stress space of a vehicle body according to an embodiment of the present invention;
FIG. 5 is a schematic view of a front frame force-bearing space according to an embodiment of the present invention;
FIG. 6 is a schematic view of a rear frame force-bearing space according to an embodiment of the present invention;
FIG. 7 is a schematic view of a vehicle body XOY plane force according to an embodiment of the present invention;
FIG. 8 is a schematic view of a vehicle body XOZ plane force according to an embodiment of the present invention;
FIG. 9 is a schematic view illustrating the force applied to the front frame XOY plane in accordance with one embodiment of the present invention;
FIG. 10 is a schematic view of a front frame XOZ plane force according to one embodiment of the present invention;
FIG. 11 is a schematic view of a rear frame XOY plane force according to an embodiment of the present invention;
FIG. 12 is a schematic view of the stress on the XOZ plane of the rear frame in accordance with one embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
It should be noted that, in the embodiments of the present invention, all the expressions "first" and "second" are used to distinguish two entities with the same name but different entities or different parameters, and it is noted that the "first" and "second" are only used for convenience of expression, and should not be construed as limiting the embodiments of the present invention, and the following embodiments are not described one by one.
As shown in fig. 3, some embodiments of the present invention disclose a method for adjusting a locomotive axle load, comprising:
establishing locomotive axle weight adjustment mechanical modeling;
according to the locomotive axle weight, adjusting mechanical modeling, selecting an objective function and a constraint equation, and optimizing numerical solution;
to obtain one series of padding amounts and/or two series of padding amounts.
In the embodiment, the main purpose of the establishment of the mechanical modeling is to establish an equation of the relation between the padding amount and the wheel weight change according to the mechanical property; and the optimization solution is to sum up equations into an optimization problem, select reasonable objective functions and constraints and solve the objective functions and constraints. The invention establishes a locomotive whole-vehicle weighing model, and provides a new objective function, a wheel weight difference, a shaft weight difference and a bogie weighing index constraint equation in the aspect of optimizing and solving. As shown in FIG. 3, when the axle weight of the locomotive is subjected to the cushioning adjustment, locomotive design parameters, locomotive whole-locomotive weighing results and bogie weighing results are input first, then a locomotive axle weight adjustment mechanical model is established, a locomotive axle weight adjustment cushioning scheme is solved, and finally a primary cushioning amount and/or a secondary cushioning amount are obtained.
According to some preferred embodiments of the present invention, a method for adjusting a locomotive axle load is disclosed, and on the basis of the above embodiments, the establishing a locomotive axle load adjustment mechanical model includes: establishing a static equilibrium equation of the locomotive; and (5) establishing a relation equation of the wheel weight and the padding amount.
Wherein said establishing a locomotive static equilibrium equation comprises:
establishing a three-degree-of-freedom model of the stress of the vehicle body and the framework;
respectively writing balance equations of three degrees of freedom to the vehicle body, the front framework and the rear framework column to obtain 9 equations;
and writing relation equations of the first series of spring supporting force, the second series of spring supporting force and displacement.
The building of the relation equation of the wheel weight and the padding amount comprises the following steps:
bringing the balance equation of the three degrees of freedom into the relation equation of the primary spring supporting force, the secondary spring supporting force and the displacement, and finishing to obtain a relation formula among an external force vector, a displacement vector and a rigidity matrix; and further obtaining a wheel weight change vector and a padding amount formula.
Specifically, in some embodiments, the relationship formula among the external force vector, the displacement vector and the stiffness matrix is:
AX＝W
wherein A is a rigidity matrix, X is a displacement vector, and W is an external force vector.
The wheel weight change vector and the padding amount formula are as follows:
Q＝ΩΔ
Ω＝k 1 (DA -1 C+E)
wherein Q is the weight change of the locomotive wheel, omega is the load increase coefficient matrix, delta is the padding amount, A is the rigidity matrix, and k 1 The supporting rigidity of each axle box of the primary spring is represented by a matrix of external force generated by unit cushioning quantity, D is represented by a coefficient matrix, and E is represented by a unit matrix.
In some embodiments of the present invention, the selecting an objective function and a constraint equation according to the locomotive axle weight adjustment mechanics modeling, and optimizing a numerical solution includes:
and setting an objective function, a constraint wheel weight difference, a constraint axle weight difference and a constraint unbalanced force based on the two-system padding.
And setting an objective function, a constraint wheel weight difference, a constraint axle weight difference, a constraint wheel weight adjustment tolerance, and a constraint front bogie weighing and a constraint rear bogie weighing based on the first padding.
Specifically, based on the two-system padding, the optimization solving objective function and the constraint formula can be:
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R
wherein F is a wheel weight measurement value of the whole vehicle, S is 2 norms of each axle weight difference, and A is the weight of the whole vehicle 3 Constraint matrix for wheel weight difference, A 4 A constraint matrix for the axle weight difference, R is the unbalanced force tolerance,Ωfor matrix sub-blocks in the load enhancement coefficient matrix omega,Δis part of the elements in the padding amount delta.
Wherein the first formula is an objective function, the second formula is used for constraining the wheel weight difference, the third formula is used for constraining the axle weight difference, and the fourth formula is used for constraining the unbalanced force. Effectively expanding the range of cushioning schemes that can be provided.
Based on the first series of padding, the optimization solving objective function and the constraint formula are as follows:
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R
A 5 Ω 1 Δ 1 +A 5 1 ΩF 1 ≤0
A 6 Ω 2 Δ 2 +A 6 Ω 2 F 2 ≤0
wherein F is a wheel weight measurement value of the whole vehicle, S is 2 norms of each axle weight difference, and A is the weight of the whole vehicle 3 Constraint matrix for wheel weight difference, A 4 A constraint matrix for the axle weight difference, R is the unbalanced force tolerance,Ωfor matrix sub-blocks in the load enhancement coefficient matrix omega,Δf is part of the element in the padding quantity delta 1 Wheel weight measurement value for front bogie singly weighing, F 2 Wheel weight measurement value omega for independent weighing of rear bogie 1 Is the matrix of the load increase coefficients of the front bogie,Ω 2 and the load increase coefficient matrix of the rear bogie. Delta 1 Delta for front bogie 2 Cushion the rear bogie, A 5 Constraint matrix for front bogie weighing index, A 6 And (5) constraining the matrix for the weighing index of the rear bogie.
The first formula is an objective function, the second formula is used for restraining the wheel weight difference, the third formula is used for restraining the axle weight difference, the fourth formula is used for restraining the wheel weight adjustment tolerance, the fifth formula is used for restraining the front bogie weighing index, and the sixth formula is used for restraining the rear bogie weighing index.
The following description will be made taking a 6-axis C0-C0 locomotive as an example.
(1) Mechanical model establishment
The space schematic diagram of the stress of the vehicle body and the framework is shown in fig. 4-6. A three-degree-of-freedom model (vertical displacement, nodding and rolling) is adopted, wherein the supporting force of a secondary spring is represented by F, and the supporting force of a primary spring is represented by F. For example F 1A 、F 1B Is the vertical force generated by the secondary spring at the side A, B of the 1 position. f (f) 1A 、f 1B Is the vertical force generated by the primary spring at the side of position A, B.
The detailed diagram of the vehicle body is shown in fig. 7 and 8, wherein alpha 3 Is the turning angle of the vehicle body point head beta 3 Is the rolling angle of the vehicle body. Writing three degrees of freedom balance equations to the train body train as shown in formulas (2) to (4)
F 1A +F 1B +F 2A +F 2B +F 3A +F 3B ＝0 (2)
(F 1B +F 2B +F 3B +F 4B )l 6 -(F 1A +F 2A +F 3A +F 4A )l 6 ＝0 (3)
-(F 1A +F 1B )(l 3 +l 7 )-(F 2A +F 2B )(l 7 -l 4 )+(F 3A +F 3B )(l 7 -l 4 )+(F 4A +F 4B )(l 7 +l 3 )＝0 (4)
Wherein l 3 The longitudinal distance from the 1-position secondary spring to the 2-axis and the 4-position secondary spring to the 5-axis; l (L) 4 The longitudinal distance from the 2-position secondary spring to the 2-axis and the 3-position secondary spring to the 5-axis; l (L) 6 Is half the lateral distance of A, B side two-way spring, l 7 Is the longitudinal distance from the gravity center of the vehicle body to the 2-axis.
Drawing detailed force diagram of front frame as shown in fig. 9 and 10, α 1 For the front frame nodding corner, beta 1 Is the front frame side roll angle. Writing three degrees of freedom equilibrium equations to the front skeleton column as shown in equations (5) - (7)
(f 1B +f 1A +f 2B +f 2A +f 3B +f 3A )-(F 1B +F 1A +F 2B +F 2A )＝0 (5)
(f 1B +f 2B +f 3B )l 5 -(f 1A +f 2A +f 3A )l 5 +(F 1A +F 2A )l 6 -(F 1B +F 2B )l 6 ＝0 (6)
(f 3A +f 3B )l 2 -(f 1A +f 1B )l 1 +(F 1A +F 1B )l 3 -(F 2A +F 2B )l 4 ＝0 (7)
Wherein l 1 For a wheelbase of 1 to 2, 5 to 6. l (L) 2 For a wheelbase of 2-axis to 3-axis, 3-axis to 4-axis. l (L) 5 The side A, B is half the lateral distance of the spring.
Drawing detailed force diagram of the rear frame as shown in fig. 11 and 12, α 2 For the rear frame nodding corner, beta 2 Is the rear frame side roll angle. And writing three-degree-of-freedom balance equations to the rear frame column as shown in formulas (8) - (10)
(f 4B +f 4A +f 5B +f 5A +f 6B +f 6A )-(F 3B +F 3A +F 4B +F 4A )＝0 (8)
(f 4B +f 5B +f 6B )l 5 -(f 4A +f 5A +f 6A )l 5 +(F 3A +F 4A )l 6 -(F 3B +F 4B )l 6 ＝0 (9)
(f 6A +f 6B )l 1 -(f 4A +f 4B )l 2 +(F 3A +F 3B )l 4 -(F 4A +F 4B )l 3 ＝0 (10)
The relationship between the supporting force of the primary spring and the supporting force and displacement of the secondary spring is written, as shown in formulas (11) - (30), wherein the supporting rigidity of each axle box of the primary spring is k 1 The supporting rigidity of each group of springs of the secondary springs is k 2 ，x 1 For vertical displacement of the frame 1, x 2 For vertical displacement of the frame 2, x 3 For vertical displacement of the vehicle body
f 1B ＝k 1 x 1 -k 1 l 1 α 1 +k 1 l 5 β 1 (11)
f 1A ＝k 1 x 1 -k 1 l 1 α 1 -k 1 l 5 β 1 (12)
f 2B ＝k 1 x 1 +k 1 l 5 β 1 (13)
f 2A ＝k 1 x 1 -k 1 l 5 β 1 (14)
f 3B ＝k 1 x 1 +k 1 l 1 α 1 +k 1 l 5 β 1 (15)
f 3A ＝k 1 x 1 +k 1 l 1 α 1 -k 1 l 5 β 1 (16)
f 4B ＝k 1 x 2 -k 1 l 2 α 2 +k 1 l 5 β 2 (17)
f 4A ＝k 1 x 2 -k 1 l 2 α 2 -k 1 l 5 β 2 (18)
f 5B ＝k 1 x 2 +k 1 l 5 β 2 (19)
f 5A ＝k 1 x 2 -k 1 l 5 β 2 (20)
f 6B ＝k 1 x 2 +k 1 l 2 α 2 +k 1 l 5 β 2 (21)
f 6A ＝k 1 x 2 +k 1 l 2 α 2 -k 1 l 5 β 2 (22)
F 1B ＝k 2 (x 3 -x 1 )+k 2 l 3 α 1 -k 2 (l 7 +l 3 )α 3 -k 2 l 6 β 1 +k 2 l 6 β 3 (23)
F 1A ＝k 2 (x 3 -x 1 )+k 2 l 3 α 1 -k 2 (l 7 +l 3 )α 3 +k 2 l 6 β 1 -k 2 l 6 β 3 (24)
F 2B ＝k 2 (x 3 -x 1 )-k 2 l 4 α 1 -k 2 (l 7 -l 4 )α 3 -k 2 l 6 β 1 +k 2 l 6 β 3 (25)
F 2A ＝k 2 (x 3 -x 1 )-k 2 l 4 α 1 -k 2 (l 7 -l 4 )α 3 +k 2 l 6 β 1 -k 2 l 6 β 3 (26)
F 3B ＝k 2 (x 3 -x 2 )+k 2 l 4 α 2 +k 2 (l 7 -l 4 )α 3 -k 2 l 6 β 2 +k 2 l 6 β 3 (27)
F 3A ＝k 2 (x 3 -x 2 )+k 2 l 4 α 2 +k 2 (l 7 -l 4 )α 3 +k 2 l 6 β 2 -k 2 l 6 β 3 (28)
F 4B ＝k 2 (x 3 -x 2 )-k 2 l 3 α 2 +k 2 (l 7 +l 3 )α 3 -k 2 l 6 β 2 +k 2 l 6 β 3 (29)
F 4A ＝k 2 (x 3 -x 2 )-k 2 l 3 α 2 +k 2 (l 7 +l 3 )α 3 +k 2 l 6 β 2 -k 2 l 6 β 3 (30)
Bringing the formulas (2) to (10) into the formulas (11) to (30) to arrange into the formula (31)
AX＝W (31)
Wherein A is a rigidity matrix, X is a displacement vector, W is an external force vector, and W can be calculated by a formula (32)
W＝CΔ (32)
Wherein, the padding quantity delta is a vector formed by the padding quantity of the padding positions, C is a matrix of external force generated by the unit padding quantity, and the padding positions comprise 20 positions of primary springs and secondary springs. The formula (31) is introduced into the formula (32)
X＝A -1 CΔ (33)
The weight change amount of the locomotive wheel can be calculated by formulas (34) to (46)
Q＝[ΔQ 1 ΔQ 2 ΔQ 3 ΔQ 4 ΔQ 5 ΔQ 6 ΔQ 7 ΔQ 8 ΔQ 9 ΔQ 10 ΔQ 11 ΔQ 12 ] (34)
ΔQ 1 ＝f 1B +k 1 δ 1 ＝k 1 (x 1 -l 1 α 1 +l 5 β 1 +δ 1 ) (35)
ΔQ 2 ＝f 1A +k 1 δ 2 ＝k 1 (x 1 -l 1 α 1 -l 5 β 1 +δ 2 ) (36)
ΔQ 3 ＝f 2B +k 1 δ 3 ＝k 1 (x 1 +l 5 β 1 +δ 3 ) (37)
ΔQ 4 ＝f 2A +k 1 δ 4 ＝k 1 (x 1 -l 5 β 1 +δ 4 ) (38)
ΔQ 5 ＝f 3B +k 1 δ 5 ＝k 1 (x 1 +l 2 α 1 +l 5 β 1 +δ 5 ) (39)
ΔQ 6 ＝f 3A +k 1 δ 6 ＝k 1 (x 1 +l 2 α 1 -l 5 β 1 +δ 6 ) (40)
ΔQ 7 ＝f 4B +k 1 δ 7 ＝k 1 (x 2 -l 2 α 2 +l 5 β 2 +δ 7 ) (41)
ΔQ 8 ＝f 4A +k 1 δ 8 ＝k 1 (x 2 -l 2 α 2 -l 5 β 2 +δ 8 ) (42)
ΔQ 9 ＝f 5B +k 1 δ 9 ＝k 1 (x 2 +l 5 β 2 +δ 9 ) (43)
ΔQ 10 ＝f 5A +k 1 δ 10 ＝k 1 (x 2 -l 5 β 2 +δ 10 ) (44)
ΔQ 11 ＝f 6B +k 1 δ 11 ＝k 1 (x 2 +l 1 α 2 +l 5 β 2 +δ 11 ) (45)
ΔQ 12 ＝f 6A +k 1 δ 12 ＝k 1 (x 2 +l 1 α 2 -l 5 β 2 +δ 12 ) (46)
Wherein DeltaQ 1 ～ΔQ 12 Delta as a component of the weight change of the locomotive wheel 1 ～δ 20 Is the padding amount. The vector and the padding amount after the wheel weight transformation can be expressed as a formula (47) and a formula (48)
Q＝ΩΔ (47)
Ω＝k 1 (DA -1 C+E) (48)
The weight change Q of the locomotive wheel in the formula (47) can be calculated according to the weighing result obtained by weighing the whole locomotive, so that the padding quantity delta is calculated according to the formula (47), C is an external force matrix generated by the unit padding quantity, D is a coefficient matrix, and E is a unit matrix. In the actual cushioning process, only one series of springs is often cushioned, or only two series of springs are cushioned. Therefore, matrix subblocks in the load factor matrix Ω need to be takenΩPart of the elements in deltaΔThe solution is performed as shown in equation (49).
Q＝ΩΔ (49)
For equation (49), only an approximate solution can often be found, which generally requires an optimization method.
Optimization solution
The general paradigm of the optimization solution is shown in equation (50):
minf(x)
s.t.A 1 x≤B 1
A 2 x＝B 2
C 1 (x)≤0
C 2 (x)＝0 (50)
wherein minf (x) is an objective function, A 1 x≤B 1 For linear inequality constraint, A 2 x＝B 2 Constraint of linear equality, C 1 (x) =0 is a nonlinear equation constraint, C 2 (x) And less than or equal to 0 is the constraint of nonlinear inequality. x is the variable to be solved.
For the secondary padding, the optimization solving objective function and the constraint adopted by the invention are shown as a formula (51):
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R (51)
wherein F is a wheel weight measurement value of the whole vehicle, and S is a 2 norm of each axle weight difference. A is that 3 Constraint matrix for wheel weight difference, A 4 Is a constraint matrix of axle weight differences. R is the unbalanced force tolerance. The 1 st formula is an objective function, the 2 nd formula constrains the wheel weight difference, the 3 rd formula constrains the axle weight difference, and the 4 th formula constrains the unbalanced force.
For the first series of padding, the optimization solving objective function and the constraint adopted by the invention are shown as a formula (52):
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R
A 5 Ω 1 Δ 1 +A 5 1 ΩF 1 ≤0
A 6 Ω 2 Δ 2 +A 6 Ω 2 F 2 ≤0 (52)
wherein F is 1 Single weighing hour wheel for front bogieWeight measurement value, F 2 For the wheel weight measurement when the rear bogie is individually weighed,Ω 1 is the matrix of the load increase coefficients of the front bogie,Ω 2 and the load increase coefficient matrix of the rear bogie. Delta 1 Delta for front bogie 2 The rear bogie is padded. A is that 5 Constraint matrix for front bogie weighing index, A 6 And (5) constraining the matrix for the weighing index of the rear bogie. The 5 th formula is the front bogie weighing index constraint, and the 6 th formula is the about rear bogie weighing index constraint.
The objective functions in the formulas (51) and (52) are more reasonable than the formula (1) in the prior art, so that the requirement of the objective functions is relaxed, and the range of the scheme capable of providing the axle weight adjustment and the padding is widened. The constraint on the bogie weighing index ensures that the axle weight adjustment cushioning scheme can ensure that the bogie weighing and the whole car weighing are qualified at the same time when the primary cushioning is carried out. The formulas (51) and (52) can be solved by adopting a plurality of optimized numerical methods, and numerical calculation is carried out by adopting an interior point method in nonlinear optimization.
In summary, in the locomotive axle weight shimming adjustment method disclosed by the invention, in the optimization solution, the inequality constraint and the unbalanced force constraint of the wheel weight difference and the axle weight difference indexes are provided, and the inequality constraint of the bogie weighing indexes is provided. The application range of the axle weight adjusting and cushioning scheme is enlarged, and the axle weight adjustment of the locomotive can be guided better. For the first-line padding condition, the condition that the whole car is qualified in weighing can be solved, and meanwhile, the bogie is qualified in weighing, so that repeated operations of locomotive weighing and bogie weighing are avoided, the locomotive axle weight adjustment efficiency is improved, and the labor cost is reduced.
It should be noted that, each component or step in each embodiment may be intersected, replaced, added, and deleted, and therefore, the combination formed by these reasonable permutation and combination transformations shall also belong to the protection scope of the present invention, and shall not limit the protection scope of the present invention to the embodiments.
The foregoing is an exemplary embodiment of the present disclosure, and the order in which the embodiments of the present disclosure are disclosed is merely for the purpose of description and does not represent the advantages or disadvantages of the embodiments. It should be noted that the above discussion of any of the embodiments is merely exemplary and is not intended to suggest that the scope of the disclosure of embodiments of the invention (including the claims) is limited to these examples and that various changes and modifications may be made without departing from the scope of the invention as defined in the claims. The functions, steps and/or actions of the method claims in accordance with the disclosed embodiments described herein need not be performed in any particular order. Furthermore, although elements of the disclosed embodiments may be described or claimed in the singular, the plural is contemplated unless limitation to the singular is explicitly stated.
Those of ordinary skill in the art will appreciate that: the above discussion of any embodiment is merely exemplary and is not intended to imply that the scope of the disclosure of embodiments of the invention, including the claims, is limited to such examples; combinations of features of the above embodiments or in different embodiments are also possible within the idea of an embodiment of the invention, and there are many other variations of the different aspects of the embodiments of the invention as described above, which are not provided in detail for the sake of brevity. Therefore, any omissions, modifications, equivalent substitutions, improvements, and the like, which are made within the spirit and principles of the embodiments of the invention, are included within the scope of the embodiments of the invention.

Claims (6)

1. The method for adjusting the axle weight of the locomotive by padding is characterized by comprising the following steps of:
establishing locomotive axle weight adjustment mechanical modeling;
according to the locomotive axle weight, adjusting mechanical modeling, selecting an objective function and a constraint equation, and optimizing numerical solution;
obtaining a first series of padding amounts and/or a second series of padding amounts;
the selecting an objective function and a constraint equation according to the locomotive axle weight adjustment mechanics modeling, and optimizing the numerical solution comprises:
setting an objective function, a constraint wheel weight difference, a constraint shaft weight difference and a constraint unbalanced force based on secondary padding;
the selecting an objective function and a constraint equation according to the locomotive axle weight adjustment mechanics modeling, and optimizing the numerical solution comprises:
setting an objective function, a constraint wheel weight difference, a constraint axle weight difference, a constraint wheel weight adjustment tolerance, a constraint front bogie weighing and a constraint rear bogie weighing based on a first system padding;
based on the two-system padding, the optimization solving objective function and the constraint formula are as follows:
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R
wherein F is a wheel weight measurement value of the whole vehicle, S is 2 norms of each axle weight difference, and A is the weight of the whole vehicle 3 Constraint matrix for wheel weight difference, A 4 A constraint matrix for the axle weight difference, R is the unbalanced force tolerance,Ωfor matrix sub-blocks in the load enhancement coefficient matrix omega,Δis part of the elements in the padding quantity delta;
based on the first series of padding, the optimization solving objective function and the constraint formula are as follows:
min||S||
s.t.A 3 ΩΔ+A 3 ΩF≤0
A 4 ΩΔ+A 4 ΩF≤0
||ΩΔ-Q||≤R
A 5 Ω 1 Δ 1 +A 5 Ω 1 F 1 ≤0
A 6 Ω 2 Δ 2 +A 6 Ω 2 F 2 ≤0
wherein F is a wheel weight measurement value of the whole vehicle, S is 2 norms of each axle weight difference, and A is the weight of the whole vehicle 3 Constraint matrix for wheel weight difference, A 4 A constraint matrix for the axle weight difference, R is the unbalanced force tolerance,Ωfor matrix sub-blocks in the load enhancement coefficient matrix omega,Δf is part of the element in the padding quantity delta 1 Wheel weight measurement value for front bogie singly weighing, F 2 For rear bogie aloneThe wheel weight measurement value during weighing is used for measuring the wheel weight,Ω 1 is the matrix of the load increase coefficients of the front bogie,Ω 2 delta for the matrix of load increase coefficients of the rear bogie 1 Delta for front bogie 2 Cushion the rear bogie, A 5 Constraint matrix for front bogie weighing index, A 6 And (5) constraining the matrix for the weighing index of the rear bogie.
2. The locomotive axle weight shimming method of claim 1, wherein said establishing locomotive axle weight adjustment mechanical modeling comprises:
establishing a static equilibrium equation of the locomotive;
and (5) establishing a relation equation of the wheel weight and the padding amount.
3. The method of claim 2, wherein said establishing a locomotive static equilibrium equation comprises:
establishing a three-degree-of-freedom model of the stress of the vehicle body and the framework;
respectively writing balance equations of three degrees of freedom for the vehicle body, the front framework and the rear framework;
and writing relation equations of the first series of spring supporting force, the second series of spring supporting force and displacement.
4. The method of claim 3, wherein said establishing a wheel weight, cushioning relationship equation comprises:
bringing the balance equation of the three degrees of freedom into the relation equation of the primary spring supporting force, the secondary spring supporting force and the displacement, and finishing to obtain a relation formula among an external force vector, a displacement vector and a rigidity matrix;
and obtaining a wheel weight change vector and a padding amount formula.
5. The method for shimming a locomotive axle load according to claim 4, wherein the relationship formula between the external force vector, the displacement vector and the stiffness matrix is:
AX＝W
wherein A is a rigidity matrix, X is a displacement vector, and W is an external force vector.
6. The method of claim 4, wherein the wheel weight change vector and the padding amount formula are:
Q＝ΩΔ
Ω＝k 1 (DA -1 C+E)
wherein Q is the weight change of the locomotive wheel, omega is the load increase coefficient matrix, delta is the padding amount, A is the rigidity matrix, and k 1 The supporting rigidity of each axle box of the primary spring is represented by a matrix of external force generated by unit cushioning quantity, D is represented by a coefficient matrix, and E is represented by a unit matrix.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4793047A (en) * 1986-12-18 1988-12-27 General Electric Company Method of adjusting the distribution of locomotive axle loads
CN101813566A (en) * 2010-02-08 2010-08-25 吉林大学 Railway vehicle bogie primary-suspension comprehensive parameter measuring device

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4793047A (en) * 1986-12-18 1988-12-27 General Electric Company Method of adjusting the distribution of locomotive axle loads
CN101813566A (en) * 2010-02-08 2010-08-25 吉林大学 Railway vehicle bogie primary-suspension comprehensive parameter measuring device

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