CN109403950B - Simulation modeling method for star soil drilling driving and control system - Google Patents

Abstract

A simulation modeling method of a star soil drilling driving and control system comprises the steps of sequentially establishing a drill bit and star soil force load model, a rotary motor model, a rotary transmission path model, a loading motor model, a footage transmission path model and a drilling coring model; simulation modeling is carried out on the star soil drilling equipment according to the product composition and the working principle, the adaptive range and the stability of the product work are confirmed through simulation, and when abnormal conditions are simulated, the optimization of the product can be promoted by improving the hardware performance or the control strategy of the product.

Description

Simulation modeling method for star soil drilling driving and control system

Technical Field

The invention relates to a simulation modeling method for a satellite soil drilling driving and control system, and belongs to the technical field of deep space exploration.

Background

The drilling subsystem belongs to a lunar exploration three-phase sampling and packaging subsystem and is used for obtaining a subsurface lunar sample, has the capacity of obtaining lunar soil sampling length not less than 2m and the sample shaping capacity, and can keep certain sample layer information.

In the process of development and test, the drilling subsystem needs effective ground simulation modeling means to carry out simulation analysis on the product driving and control system. According to the functions and working state requirements realized by each mechanism of the drilling sampling device, in the simulation of a control system, the whole large system is required to be divided into a drilling coring closed loop and a shaping expansion closed loop for research, wherein the drilling coring closed loop comprises a rotary closed loop, an impact open loop and a feeding closed loop, the control simulation of the system is required to research the motion process and response characteristics of each single loop and the whole drilling sampling system through the analytic calculation of a mathematical equation, and a formulation basis and a verification means are provided for the research of the drilling rule and the strategy rationality of the system.

At present, no simulation modeling method for a drive control system aiming at sampling operation in a space complex environment exists in China, and a technical blank in the field needs to be filled urgently.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, and provides a simulation modeling method for the star soil drilling driving and control system, wherein simulation modeling is carried out on the star soil drilling equipment according to product composition and a working principle, the adaptive range and the stability of product work are confirmed through simulation, and when abnormal conditions occur through simulation, the optimization of the product can be promoted by improving the hardware performance or the control strategy of the product.

The invention comprises the following technical scheme: a simulation modeling method for a satellite soil drilling driving and control system comprises the following steps:

(1) establishing a drill bit and star soil force-load model: establishing a low-gravity drill bit and star soil force load model in a vacuum environment, and separating the rotation torque and the drill pressure into force loads in two directions with a specific relation in a decoupling mode:

(2) establishing a rotary motor model: according to the characteristics of the direct current brushless motor, expression formulas of output torque and output rotating speed are obtained through the electric and magnetic conversion principle and the derivation of internal acting force, a mathematical model of the rotary motor is established, and the relation between the rotating speed and voltage and the relation between the torque and current are obtained;

(3) establishing a rotary transmission path model: according to the mechanical design of a rotation function, the relationship between the current of the rotation motor and the rotation torque after transmission is further obtained by deducing the transmission ratio and the transmission resistance of a transmission part and substituting the transmission ratio and the transmission resistance into a rotation motor model;

(4) establishing a loading motor model: according to the characteristics of the stepping motor, expression formulas of output torque and output rotating speed are obtained through the electric and magnetic conversion principle and the derivation of internal acting force, a mathematical model of a loading motor is established, and the relation between the rotating speed and the output torque is obtained;

(5) establishing a footage transmission path model: according to the mechanical design of the footage function, the relationship between the rotating speed of the tail end of the footage and the output torque is further obtained by deducing the transmission ratio and the transmission resistance of transmission parts and substituting the transmission ratio and the transmission resistance into a loading motor model;

(6) establishing a drilling coring model: and (5) obtaining a model of the system during drilling coring according to the models established in the step (3) and the step (5), thereby completing simulation modeling of the whole system.

And (2) establishing a force load model of the drill bit with low gravity and the star soil in the vacuum environment in the step (1), and separating the rotation torque and the drill pressure into force loads in two directions with a specific relation in a decoupling mode.

The force-load model of the drill bit and the star soil in the step (1) is specifically as follows:

F_z＝nsinε(V₁+V₂)；

wherein M is_hAs bit resistance, F_zFor the driving force of footage, D is the drill diameter, D₀As a central failure zone, H₁Is the horizontal component of the force in the central region, H₂For the horizontal component of the shear failure force, V₁Acting on the vertical component of the force, V, for the central region₂For the vertical component of the shearing failure force, α is the angle between the cutting face and the cutting edge, h_tFor the failure zone height, n is the number of cutters of the drill bit.

The concrete form of establishing the rotary motor model in the step (2) is as follows:

wherein, c_mIs a torque coefficient, I_dIs the armature current of the motor, B is the damping coefficient, omega is the angular velocity of the mechanical rotation of the motor, J is the integral moment of inertia, T_sThe torque is loaded to the dc motor.

The concrete form of establishing the rotation transmission path model in the step (3) is as follows:

wherein, T_pTo output torque, F_fIs rolling friction force, f is rolling friction coefficient, i_HsFor the gear ratio of the reducer, T_hzD is the nominal diameter of the spline shaft for the drilling mechanism turning moment.

The specific form of the loading motor model established in the step (4) is as follows:

T_e＝-k_mi_asin(N_rθ)+k_mi_bcos(N_rθ)

wherein i_a、i_bCurrent of A, B two phases, k_mIs a back electromotive force coefficient, k_mω₀sin(N_rTheta) is the rotation voltage, N_rNumber of rotor teeth, ω₀Is the motor speed, T_eRepresenting an electromagnetic torque.

The specific form of establishing the footage transmission path model in the step (5) is as follows:

wherein, J_jtIs the moment of inertia of the drum, F_sgsFor upward loading of the tension of the wire rope, r_jtIs the radius of the winding drum, N is the number of turns of the steel wire rope around the winding drum, alpha is the angular acceleration of the winding drum, B_spTo obtain the coefficient of friction of engagement, θ₀Is the harmonic rotational position.

The concrete form of the drilling coring model established in the step (6) is as follows:

wherein, F_fTo rolling friction force, i_HsF is the rolling friction coefficient, d is the nominal diameter of the spline shaft, T is the transmission ratio of the reducer_hzFor rotary force of drilling mechanismMoment, J_jtIs the moment of inertia of the drum, F_sgsFor upward loading of the tension of the wire rope, r_jtIs the radius of the winding drum, N is the number of turns of the steel wire rope around the winding drum, alpha is the angular acceleration of the winding drum, B_spTo obtain the coefficient of friction of engagement, θ₀Is the harmonic rotational position.

Compared with the prior art, the invention has the following advantages: aiming at the extraterrestrial earth and extraterrestrial earth star soil state, a model of the action relationship between lunar soil and a drill bit is constructed, the similarity with the real working condition is higher, and the action result is close to under the influence of environmental factors such as microgravity, vacuum and the like. Decoupling of horizontal dimension and vertical dimension is adopted, and a load formed by the acting force of a complex working condition forms a rotation and bit pressure force load mode through a certain relation. And a mechanical-electrical integration modeling is adopted, and a power source head and control parameters are combined with the output force load and the speed of a final end effector to establish a mathematical model of the whole set of drilling and coring system. And a control method combining inner ring control and outer ring control is adopted to realize a drilling strategy and complete stable work of the system under the condition of uncertain load.

The application object of the invention is the first extraterrestrial celestial body drilling and sampling device in China, and the system is a motion control system aiming at uncertain loads, and adopts a control strategy based on force load identification and assisted by other parameter boundary domains, so that no precedent is made in China.

The effect achieved by the invention is high in approximation degree with the actual effect, and the simulation waveform of the control system basically reflects the waveform under the real working state by inputting the simulation loads under different conditions; the invention combines the correction after the actual operation, and the application ensures that the system achieves the maximum uncertain factor adaptability in the limited resources, can execute the work under the severe working conditions, and is actually verified.

Drawings

FIG. 1 illustrates a cutting tool model;

FIG. 2 illustrates a cutting tool cutting lunar soil model;

FIG. 3 illustrates outside shear failure of the central failure zone;

FIG. 4 illustrates the effect of the cutting tool twist angle on the bit drag torque;

FIG. 5 shows the effect of the driving force of advancing the ruler on the moment of resistance of the drill;

FIG. 6 illustrates the operating principle of the planetary gear mechanism;

FIG. 7 is a mathematical model of a planetary gear mechanism;

FIG. 8 is a schematic block diagram of the operation of a rolling spline pair;

FIG. 9 shows the force applied to the rolling spline pair;

FIG. 10 harmonic gear model;

FIG. 11 force analysis of the sizing drum;

FIG. 12 is a DC motor control block diagram;

FIG. 13 is a block diagram of a stepper motor control;

FIG. 14 is an exploded view of the system operating control;

FIG. 15 is a block diagram of the system control.

Detailed Description

Modeling the mechanical soil effect:

the interaction between the drill and the lunar soil mainly relates to the cutting action of the vertical teeth of the drill and the soil body, so the theoretical modeling analysis focuses on the mechanical interaction between the cutting tool of the drill body and the soil body, and the cutting tool model and the cutting tool cutting lunar soil model are shown in figures 1a-c and figure 2.

Wherein q is_ε-the cutting tool mounting surface is exposed to a distributed load of lunar soil, q_ε＝q/sinε

γ_ε-lunar soil volume weight gamma_gComponent normal to the cutting plane, gamma_ε＝γ_gsinε

dR₁-the resultant of pressure and friction on the bottom failure boundary surface;

dP₁-the force of the cutting tool on the central failure zone;

beta is the failure angle of the cutting tool, and the included angle between the failure boundary surface at the bottom end and the cutting plane;

d_rdistance to failure, d_r＝h_t(cotα+cotβ)；

Gamma-cutting tool twist angle.

From the ultimate balance of the infinitesimal central failure region, the method can be obtained

Elimination of dR₁Integration along the cutting edge of the cutting tool to obtain P₁And its horizontal component H₁And a vertical component V₁As follows

H₁＝P₁sin(α+δ)+c_alh_tcotα (9)

V₁＝P₁cos(α+δ)-c_alh_t (10)

Outside the central failure region, the cutting tool shears and cuts lunar soilForce P₂Resisting shear stress tau at the shear plane as shown in figure 3.

Wherein alpha is_B-the actual cutting angle of the cutting tool at point B of the cutting edge;

τ — shear stress on the outside of the central failure zone,

sigma is the pressure stress of lunar soil acting on the shear fracture surface;

P₂-the cutting means are adapted to shear the force of destruction;

β_Bthe cutting tool has a failure angle at point B of the cutting edge.

From the ultimate balance of the shear plane outside the central failure region, P can be obtained₂And its horizontal component H₂And a vertical component V₂As follows

H₂＝P₂cosβ_B (12)

V₂＝P₂sinβ_B (13)

In summary, the total cutting force P of the cutting tool, its horizontal component H and vertical component V can be obtained. The failure angle beta in P is still unknown under the condition that the cutting tool parameters, the lunar soil parameters and the load parameters are determined. Since the end-of-life boundary always presents the location at which the cutting tool cutting force is minimal, i.e., the weakest fracture surface, this location can be obtained by numerical iterative search or derivation. Since the relation of P with respect to β is complex, this document will solve by numerical iterative search.

By integrating the resistance moment of the cutting tool at infinitesimal level and superimposing the resistance moment M produced by shearing the fracture surface₂The resistance moment M of the core drill bit can be obtained_hAs follows

M_h＝n(M₁+M₂) (17)

F_z＝nsinε(V₁+V₂) (18)

Wherein: n-number of cutters of core bit

Analysis of drill bit and lunar soil effects

Influence of the cutting tool twist angle

Under the condition that other parameters are not changed, the torsion angle gamma of the cutting tool is selected as a variable, and the resistance moment M of gamma to the drill bit can be obtained by the compiled matlab program_hThe effect of (c) is shown in the figure.

As can be seen from FIG. 4, the cutting tool torsion angle γ and the core drill bit resistance torque M_hAnd presents negative correlation. It can be seen that as the cutter twist angle γ increases, the core bit drag torque M_hIt will be reduced. The design of the torsional angle gamma of the cutting tool is mainly used for chip removal at the bottom of a hole, and the existence of the torsional angle gamma of the cutting tool also enables the cutting tool to generate three-dimensional cutting, so that the actual cutting angle alpha is enabled to be_kIs smaller than the cutting angle of the cutting tool. It is deduced that the actual cutting angle of the cutting tool is reduced as the twisting angle γ of the cutting tool is increased, so that the increase of the twisting angle γ of the cutting tool is beneficial to reducing the resistance moment M of the core bit on the premise of meeting the drilling speed_h。

Influence of footage driving force

Selecting a footage driving force F under the condition that other parameters are not changed_zAs a variable, F is available from the written matlab program_zFor the moment of resistance M of the drill_hThe effect of (c) is shown in fig. 5.

As can be seen from FIG. 5, the footage driving force F_zResistance moment M of core drill bit_hAnd is linearly related. It can also be known from the formula that the driving is along with the footageForce F_zThe larger the cutting force is, the larger the drill resistance moment M_hThe larger. Therefore, the footage driving force F is ensured on the premise of ensuring the drilling speed_zAn appropriate reduction may be selected.

D, simulation modeling of the direct-current brushless motor:

the rotation and impact work of the drilling sampler are controlled by a direct current brushless motor to generate control torque, and the dynamic equation is as follows:

E＝c_en (21)

T_e＝C_mI_d (22)

wherein: u shape_d-applied voltage (V), E-motor induced electromotive force (V), I_d-the motor armature current (A),

r-main circuit equivalent resistance (omega), L-motor armature inductance (H), T_e-an electromagnetic torque (Nm),

T_s-direct current motor load torque (Nm), B-damping coefficient, J-global moment of inertia (Nm)²)，

Omega-angular speed of mechanical rotation of the motor (rad/s), n-rotational speed of mechanical rotation of the motor (rpm),

c_ecoefficient of potential, c_mCoefficient of torque, of

Fig. 12 shows a dc brushless motor controller. Wherein, ASR is outer loop control ware for adjusting motor output rotational speed, and ACR is inner loop control ware for control current, and ordinary ASR and ACR all can adopt PI control. A and B are respectively a current feedback coefficient and a rotating speed feedback coefficient. The motor-driven PWM apparatus can be regarded as a hysteresis loop, and its transfer function is:

ks and Td are its amplification factor and average delay time, respectively.

Gear transmission model (fig. 6, 7):

an equivalent moment of inertia matrix in the equation:

wherein

I_ieMember i is equivalent to a rotational speed ω_s＝i_Hsω_HEquivalent moment of inertia (kg · m) of the system axis of²) I ═ s, d, c, a, H, s denote sun gears, d denote planetary gears, c denotes a crank shaft, a denotes a second-stage external gear, and H denotes a carrier;

r_c-the radius (m) of the circle on which the crankshaft axis lies;

I_ithe moment of inertia of the member i (kg. m)²)；

i_isThe ratio of the rotational speeds of the members i and s; i.e. i_as＝i_Hs；i_cs＝i_ds

a-crankshaft eccentricity (m);

damping matrix

[c]＝[0] (30)

Equivalent stiffness matrix:

wherein

k_sdeEquivalent torsional stiffness of the meshing stiffness of the sun wheel and the planet gears (N.m/rad)

k_sdThe meshing stiffness of the sun and planet wheels (N/m);

r_s-sun gear base radius (m);

k_ceequivalent torsional stiffness of the crankshaft (Nm/rad)

k_c-torsional stiffness of the crankshaft (Nm/rad);

i_csthe speed ratio of the planet and sun;

k_cae-equivalent torsional stiffness (Nm/rad) of the bearing between the external gear and the crankshaft

k_ca-stiffness of the bearing on the outer gear (N/m);

k_areequivalent torsional stiffness to meshing stiffness of the ring gear (Nm/rad)

k_a′_rThe tangential component (N/m) of the mesh stiffness of the ring gear at the mesh point is calculated to be approximately k_a′_r＝k_ar cosβ；

β -equivalent engagement angle (rad);

k_ar-ring gear mesh stiffness (N/m);

i_as-the ratio of the rotational speed of the external gear of the second stage and the sun gear; i.e. i_as＝i_Hs；

k_HceEquivalent stiffness of the bearing on the planet carrier (Nm/rad)

k_Hc-stiffness of the bearings on the planet carrier (N/m);

i_Hs-the reduction gear ratio;

the torsion angle matrix is:

{θ}＝{θ_s θ_de θ_ce θ_ae θ_p}^T (37)

θ_s-input angle (rad);

θ_de-planet relative torsion angle (rad);

θ_p-output shaft relative torsion angle (rad);

θ_ae-second stage external gear relative twist angle (rad);

θ_ce-crankshaft relative torsion angle (rad);

loading:

{T}＝{T_s 0 0 0 -T_p}^T (38)

T_s-direct current motor load torque (Nm);

T_p-output torque (Nm);

T_p＝T_si_Hs (39)

ω_p-output angular velocity (rad/s);

α_poutput angular acceleration (rad/s)²)；

Inputting parameters:

1)ω_sthe sun gear rotation speed;

2)T_sfor loading torque on DC motor

Outputting parameters:

1)ω_pis the output shaft speed;

2)T_pis the output torque;

bearing transfer modeling (fig. 8, fig. 9):

radial:

solving the input torque of rolling spline pair

T_hz＝T_hzclη_hj (42)

Radial dynamic equation of rolling spline pair

ω(t)＝∫α(t)dt (44)

Solving for frictional forces

Axial direction:

axial dynamic equation of rolling spline pair

G+F₁-F₂-F_f＝ma(t) (46)

Inputting parameters:

1) t _ hzcl is gear output torque (unit is N.m)

2)F₁Is the impact force (in N) of the impact spring-weight member on the central shaft

3)F₂For the reaction force of the core-drilling tool to the central shaft (unit is N)

Outputting parameters:

angular acceleration with α (t) as the central axis (in rad/s)²)

T_hzFor drilling mechanism turning moment (unit is N.m)

Intermediate variables:

1)η_hjfor the efficiency (taking eta) of the rotary rolling spline pair bearing_hj＝0.5)

2) J is the equivalent moment of inertia of the rolling spline pair (J is 100kg²)

3) C is damping coefficient (0.5 is C)

4) f is rolling friction coefficient (f is 0.5)

5) d is the nominal diameter of the spline shaft (d is 39mm)

6) mass with m as central axis (taking m as 10kg)

7)F_fIs rolling friction force (unit is N)

Modeling rotation transfer:

by

And T_e＝C_mI_dDerived from the above

And T_p＝T_si_HsAre combined to obtain

And

are subtracted to obtain

Simulation modeling of the stepping motor:

for m₁Representing the number of beats in operation, z_rIndicating the number of rotor teeth, the average value (step angle) theta of the rotor rotation angle per change of the energization state_bComprises the following steps:

stepping motor m we use₁＝4，z_rThe step angle is 1.8 degrees, 50.

The voltage balance equation and the moment balance equation of the stepping motor are as follows:

in the formula u_a，u_bAnd i_a，i_bA, B two-phase voltage and current, R is winding resistance, L is winding inductance, k_mωsin(N_rθ) is the rotation voltage, k_mIs the back emf coefficient, omega is the motor speed, N_rNumber of rotor teeth, T_eIs electromagnetic torque, J is moment of inertia, B is viscous friction coefficient, T_LIn order to load the stepping motor with torque, θ is a rotation angle. The stepper motor controller is shown in fig. 13.

Harmonic gear modeling (fig. 10):

1. dynamic modeling of dynamic errors

In the formula [ theta ]_m、θ_l-rotational position of the motor and the load; n-harmonic gear ratio;

the system kinetic energy is expressed as:

in the formula J_m、J_lThe moment of inertia of the motor and the load;

non-linear spring force for strain wave gear system

The system potential energy is:

k is an equivalent torsional rigidity coefficient between the input end and the output end of the system; elastic force being an arbitrary function of dynamic error

Form (a).

The rayleigh dissipation function is:

in the formula B_sp-harmonic gear mesh friction coefficient;

substituting equations (55), (56), and (57) into the lagrange equation:

obtaining:

T_m＝T_L (63)

inputting parameters:

J₀-moment of inertia of the motor

J₁Wave generator moment of inertia

J_mInput end moment of inertia

J_LLoad moment of inertia

N-reduction ratio

K-nonlinear torsional stiffness

B_sp-coefficient of friction of engagement

E_m-kinetic energy of the electric machine

E_L-load kinetic energy

Description of the intermediate parameters:

1) e-system kinetic energy

3) U-system potential energy

4) D-frictional force of engagement

Reel modeling (fig. 11):

T_l-T_x+T_s＝J_jtα (65)

wherein

T_x＝F_xgsr_jt (66)

T_s＝F_sgsr_jt (67)

F_xgs＝F_sgse^2πNf (68)

Combining the above formula, we can get:

inputting parameters:

1.T_linput torque for the drum

2.F_sgsFor loading the upper tension of the steel wire rope

3.J_jtIs moment of inertia of the drum

Number of turns of N steel wire rope around winding drum

5.r_jtRadius of the drum

Outputting parameters:

alpha is the angular acceleration of the drum

Footage transfer modeling:

J_jtα＝T_l-F_sgse^2πNfr_jt+F_sgsr_jt (70)

combining the above formula, we can get:

drilling coring modeling:

analysis based on drill bit and lunar soil effects

M_hNot only is related to the cutting angle gamma (-K)₁γ + b: i.e., cutting rotational speed), and also with the advance driving force F_zCorrelation (K)₂F_z)。

Analysis according to gyroscopic effects

T_pAnd M_hIs acting force and reacting force, and the control parameters are rotating speed omega and motor current i_HsBy increasing the speed of rotation to let T_pThe rotation speed is reduced as much as possible, and the high rotation speed output is stabilized by adopting the control of a double closed loop.

Analysis according to footage

F_sgsAnd F_zIs acting force and reacting force, and the control parameter is the rotating speed omega₀By reducing the speed of rotation F_zTo reduce M as much as possible, thereby further reducing M_h。

Simultaneous drilling ratio (revolution speed omega and footage speed omega)₀) The amount of samples taken can be controlled. The control strategy and block diagram are shown in fig. 14 and 15.

Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (3)

1. A simulation modeling method for a satellite soil drilling driving and control system is characterized by comprising the following steps:

(1) establishing a drill bit and star soil force-load model: establishing a low-gravity drill bit and star soil force load model in a vacuum environment, and separating the rotation torque and the drill pressure into force loads in two directions with a specific relation in a decoupling mode;

(2) establishing a rotary motor model: according to the characteristics of the direct current brushless motor, expression formulas of output torque and output rotating speed are obtained through the electric and magnetic conversion principle and the derivation of internal acting force, a mathematical model of the rotary motor is established, and the relation between the rotating speed and voltage and the relation between the torque and current are obtained;

(3) establishing a rotary transmission path model: according to the mechanical design of a rotation function, the relationship between the current of the rotation motor and the rotation torque after transmission is further obtained by deducing the transmission ratio and the transmission resistance of a transmission part and substituting the transmission ratio and the transmission resistance into a rotation motor model;

(4) establishing a loading motor model: according to the characteristics of the stepping motor, expression formulas of output torque and output rotating speed are obtained through the electric and magnetic conversion principle and the derivation of internal acting force, a mathematical model of a loading motor is established, and the relation between the rotating speed and the output torque is obtained;

(5) establishing a footage transmission path model: according to the mechanical design of the footage function, the relationship between the rotating speed of the tail end of the footage and the output torque is further obtained by deducing the transmission ratio and the transmission resistance of transmission parts and substituting the transmission ratio and the transmission resistance into a loading motor model;

(6) establishing a drilling coring model: and (5) obtaining a model of the system during drilling coring according to the models established in the step (3) and the step (5), thereby completing simulation modeling of the whole system.

2. The star soil drilling driving and control system simulation modeling method according to claim 1, characterized in that: the concrete form of establishing the rotary motor model in the step (2) is as follows:

wherein, c_mIs a torque coefficient, I_dIs the armature current of the motor, B is the damping coefficient, omega is the angular velocity of the mechanical rotation of the motor, J is the integral moment of inertia, T_sThe torque is loaded to the dc motor.

3. The earth boring driving and control system simulation modeling method according to claim 2, characterized in that: the concrete form of establishing the rotation transmission path model in the step (3) is as follows:

wherein, T_pTo output torque, F_fIs rolling friction force, f is rolling friction coefficient, i_HsFor the gear ratio of the reducer, T_hzD is the nominal diameter of the spline shaft for the drilling mechanism turning moment.

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