An optimization method for target velocity curve of hydraulic cylinder of zero-impact engineering machinery boom based on trigonometric function

Abstract

A method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions relates to a method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom. The present invention aims to solve the technical problem that during the movement of the hydraulic cylinder of the existing engineering machinery boom, the speed of the hydraulic cylinder fluctuates greatly due to the influence of the nonlinear force at the boom joint, which causes the boom to vibrate. The present invention proposes a hydraulic cylinder speed planning optimization method based on an S-shaped trigonometric function curve, which suppresses the speed fluctuation of the hydraulic cylinder during the movement of the engineering machinery boom, improves the operation efficiency and accuracy, and protects the safety of the operation. The present invention improves the target speed curve of the boom hydraulic cylinder and is based on the original hydraulic system of the concrete pump truck boom. It does not require additional hardware and can therefore be easily implemented on existing pump trucks.

Description

Technical Field

[0001] The invention relates to a method for optimizing a target speed curve of a hydraulic cylinder of a zero-impact engineering machinery boom. Background Art

[0002] For construction machinery boom systems, each arm segment is connected by articulated joints. Therefore, appropriate clearances are designed into the joints. Since clearances at these joints are inevitable, during boom segment rotation, the presence of clearances can cause a loss of contact between the arm segment and the joints of the connecting mechanism. If contact is restored, severe impacts can occur at the boom joints, leading to boom vibration. This is particularly pronounced during boom startup, when the direction of the applied force rapidly changes, causing impacts at the hinge gaps. Before the boom is operational, grease is applied to each joint. Therefore, the movement and force transfer between the components within the joints actually occur at the grease-gap interface. The boom's operational performance is constrained by the behavior of these interfaces. Sudden changes in contact forces between components at these gap interfaces can cause vibration, wear, and noise in the arm segments, impacting the boom system's operational accuracy, stability, and service life.

[0003] At construction sites, engineering machinery booms must frequently start and stop while performing operations, while also placing high demands on end-of-line precision during these starts and stops. The dynamics analysis of joints with clearance reveals that the motion of the boom section is closely related to the forces acting on the boom joints. Friction at the boom joints is affected by factors such as grease status and wear, exhibiting nonlinear variations and making it difficult to accurately model and predict. The boom hydraulic cylinder controls boom movement. Fluctuations in the hydraulic cylinder's speed can cause boom vibration, impacting operational efficiency and reducing the boom's service life. Therefore, the boom hydraulic cylinder's target speed curve needs to be optimized to mitigate the impact of nonlinear forces acting on the boom joints, including friction and other difficult-to-model forces. Summary of the Invention

[0004] The present invention aims to solve the technical problem that during the movement of the hydraulic cylinder of the existing engineering machinery arm, the hydraulic cylinder movement speed fluctuates greatly due to the influence of the nonlinear force at the arm joint, causing the arm to vibrate, and provides an optimization method for the target speed curve of the hydraulic cylinder of the zero-impact engineering machinery arm based on trigonometric functions.

[0005] The method for optimizing the target speed curve of the zero-impact engineering machinery boom hydraulic cylinder based on trigonometric functions of the present invention is carried out according to the following steps:

[0006] Using trapezoidal function and cosine function as basis functions, the advantages of both are combined to construct the S-shaped target velocity curve function of the hydraulic cylinder (such as Figure 2As shown), the hypotenuse of the trapezoidal function is replaced by a cosine function of 1 / 4 period, and the expression is:

[0007]

[0008] Where y is the displacement of the hydraulic cylinder piston rod, represents the derivative of y, which is the speed of the hydraulic cylinder piston rod. t1, t2, and t3 respectively represent the duration of the start-up acceleration interval, the uniform motion interval, and the deceleration and stop interval in the S-shaped target speed curve of the hydraulic cylinder. v represents the target speed of the hydraulic cylinder piston rod (known quantity). a=v / 2, ω1=π / t1, ω2=π / t3, t'=t-t1-t2; t1=t3;

[0009] ω n is the natural frequency of the boom structure system (known quantity).

[0010] The value of t2 should be determined according to the actual working conditions and is a known quantity.

[0011] In the above formula The derivation process is as follows:

[0012] Step 1: Calculate the acceleration target curve and displacement target curve function of the hydraulic cylinder piston rod;

[0013] 1.1: Derivative formula (1) to obtain the acceleration target curve expression:

[0014]

[0015] is the acceleration of the hydraulic cylinder piston rod; according to the above formula, the acceleration curve of the S-shaped speed target curve is continuous and there is no mutation point;

[0016] 1.2: Integrate formula (1) to obtain the target displacement curve of the hydraulic cylinder piston rod:

[0017]

[0018] Step 2: Calculate the arm end displacement y in the start-up acceleration interval L and speed

[0019] 2.1: In order to simplify the parameter optimization process of the speed target curve, the boom structure is equivalent to a second-order basic mass-spring system, and its motion equation is:

[0020]

[0021] Among them, ω nis the natural frequency of the boom structure system (known quantity), y L is the displacement of the arm end; y is the displacement of the hydraulic cylinder piston rod;

[0022] 2.2: Substitute formula (3) into (4) to obtain y L and its derivative, velocity The value y in the starting acceleration interval t∈[0, t1) L1 and

[0023]

[0024] The trigonometric coefficients C1 and C2 in the formula are determined by the boundary conditions:

[0025]

[0026] Obtain:

[0027]

[0028] Step 3: Calculate the displacement y of the arm end in the uniform motion range L and speed

[0029] 3.1: Displacement y of the end of the arm segment L and its derivative value y on the uniform motion interval t∈[t1, t1+t2) L2 and for:

[0030]

[0031] The trigonometric coefficients C3 and C4 in the formula are determined by the boundary conditions:

[0032]

[0033] Obtain:

[0034]

[0035] 3.2: Simplify formula (10) and define the transformation matrix R(t):

[0036]

[0037] Then formula (10) can be simplified as:

[0038]

[0039] Step 4: Calculate the arm end displacement y in the stop and deceleration interval L and speed y Land its derivative, velocity The value y in the stop deceleration interval t∈[t1+t2, t1+t2+t3] L3 and for:

[0040]

[0041] The trigonometric coefficients C5 and C6 in the formula can be obtained by the boundary conditions:

[0042]

[0043] Obtain:

[0044]

[0045] Step 5: Solve the target velocity curve parameters according to the boundary conditions:

[0046] In order to suppress the residual vibration of the boom system and achieve a stable state at the end of the movement, it is necessary to achieve:

[0047]

[0048] These conditions can be expressed as:

[0049]

[0050] Combining formulas (13) to (17), we have:

[0051] R -1 (t1+t2+t3){-R(t1+t2)V2+R(t1)V1+V1}-V2=0

[0052]

[0053] Step 6: Simplify the target speed curve parameters:

[0054] In order to further simplify the design of the target speed curve, let t1 = t3 and we can get:

[0055] R -1 (2t1+t2){-R(t1+t2)+R(t1)+I2-R(2t1+t2)}V1=0 (19)

[0056] Where I2 is the 2×2 identity matrix; expand and simplify formula (19), and we have:

[0057]

[0058] Because the value of t2 must be determined according to the actual working conditions (needs to be determined according to the stroke of the hydraulic cylinder and the working requirements), formula 20 can only require The conditions for calculation are:

[0059]

[0060] Among them, since V1 does not exist when k2=1, the value range of k2 is an integer set starting from 2. However, since the faster the acceleration, the faster the boom moves and the higher the working efficiency, k2 takes the minimum value 2, that is, t1 takes the minimum value, so

[0061] Therefore, when the speed target curve parameters satisfy t1=t3 and When the speed fluctuation during the boom movement is controlled, the speed fluctuation during the boom movement can be suppressed.

[0062] The S-shape in the subject matter of the present invention means that the target speed curve in the acceleration interval t1 and the deceleration interval t3 is shaped like the letter S. The significance of this design is based on trigonometric functions, so that the speed, acceleration and jerk of the boom movement are not abrupt.

[0063] The beneficial effects of the present invention are as follows:

[0064] First, the S-shaped target speed curve in the present invention is designed based on trigonometric functions, and the speed has smooth first-order and second-order derivatives, which avoids the sudden changes in speed, acceleration and jerk during the start-up of the boom movement, reduces the inertial force and impact force exerted on the engineering machinery boom during the movement, suppresses the vibration of the boom during the movement from the source, and enhances the smoothness of the arm section movement.

[0065] Second, the present invention optimizes the parameters of the S-shaped target velocity curve according to the natural frequency of the boom system and the zero acceleration boundary condition during the boom movement, further reducing the excitation effect of the boom's own movement on the boom end vibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a flow chart of a method for optimizing a target curve of a zero-impact engineering machinery boom hydraulic cylinder speed based on trigonometric functions according to the present invention;

[0067] Figure 2 It is a schematic diagram of the S-shaped target speed curve of the hydraulic cylinder of the present invention;

[0068] Figure 3 This is the speed response curve of the hydraulic cylinder piston rod in the large-scale expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 0° to 180° based on the trapezoidal target speed curve in the comparative test;

[0069] Figure 4 This is the deployment speed error curve of the hydraulic cylinder piston rod in the large-scale deployment and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 0° to 180° based on the trapezoidal target speed curve in the comparative test;

[0070] Figure 5 This is the retraction speed error curve of the hydraulic cylinder piston rod in the large-scale expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 0° to 180° based on the trapezoidal target speed curve in the comparative test;

[0071] Figure 6 This is the speed response curve of the hydraulic cylinder piston rod in the small-amplitude expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 60° to 120° based on the trapezoidal target speed curve in the comparative test;

[0072] Figure 7 This is the deployment speed error curve of the hydraulic cylinder piston rod in the small-amplitude deployment and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 60° to 120° based on the trapezoidal target speed curve in the comparative test;

[0073] Figure 8 This is the retraction speed error curve of the hydraulic cylinder piston rod in the small-amplitude expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 60° to 120° based on the trapezoidal target speed curve in the comparative test;

[0074] Figure 9 This is the velocity response curve of the hydraulic cylinder piston rod in the large-scale expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 0° to 180° based on the S-shaped target velocity curve in Test 1;

[0075] Figure 10 This is the deployment speed error curve of the hydraulic cylinder piston rod in the large-scale deployment and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 0° to 180° based on the S-shaped target speed curve in Test 1;

[0076] Figure 11 This is the retraction speed error curve of the hydraulic cylinder piston rod in the large-scale expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 0° to 180° based on the S-shaped target speed curve in Test 1;

[0077] Figure 12 This is the velocity response curve of the hydraulic cylinder piston rod in the small-amplitude expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 60° to 120° based on the S-shaped target velocity curve in Test 1.

[0078] Figure 13 This is the deployment speed error curve of the hydraulic cylinder piston rod in the small-amplitude deployment and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 60° to 120° based on the S-shaped target speed curve in Test 1;

[0079] Figure 14 This is the retraction speed error curve of the hydraulic cylinder piston rod in the small-amplitude expansion and retraction motion control experiment of the last boom section of the concrete pump truck boom in the range of 60° to 120° based on the S-shaped target speed curve in Test 1. DETAILED DESCRIPTION

[0080] Specific embodiment 1: This embodiment is a method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions, which is specifically carried out in the following steps:

[0081] Taking trapezoidal function and cosine function as basis functions, the advantages of both are combined to construct the S-shaped target velocity curve function of the hydraulic cylinder, and the hypotenuse of the trapezoidal function is replaced by the cosine function of 1 / 4 period.

[0082] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the expression of the hydraulic cylinder S-shaped target speed curve function is:

[0083]

[0084] Where y is the displacement of the hydraulic cylinder piston rod, represents the derivative of y, which is the speed of the hydraulic cylinder piston rod. t1, t2, and t3 respectively represent the duration of the start-up acceleration interval, the uniform motion interval, and the deceleration stop interval in the S-shaped target speed curve of the hydraulic cylinder. v represents the target speed of the hydraulic cylinder piston rod. a=v / 2, ω1=π / t1, ω2=π / t3, t'=t-t1-t2; t1=t3;

[0085] ω n is the natural frequency of the boom structure system. Other aspects are the same as those in the first embodiment.

[0086] Specific embodiment 3: This embodiment differs from specific embodiment 1 or 2 in that the horizontal coordinate of the S-shaped target speed curve function of the hydraulic cylinder is the operating time t of the hydraulic cylinder. Other aspects are the same as specific embodiment 1 or 2.

[0087] Specific embodiment 4: This embodiment differs from specific embodiment 3 in that the vertical coordinate of the S-shaped target speed curve function of the hydraulic cylinder is the speed of the hydraulic cylinder piston rod, i.e. The rest is the same as the third specific implementation method.

[0088] Specific embodiment 5: This embodiment differs from specific embodiment 1 in that the S-shaped target speed curve function of the hydraulic cylinder is targeted at each boom section of the engineering machinery boom. Other aspects are the same as specific embodiment 1.

[0089] Specific embodiment 6: This embodiment differs from specific embodiment 5 in that the engineering machinery boom described is a concrete pump truck boom. Other aspects are the same as specific embodiment 5.

[0090] Specific embodiment 7: This embodiment differs from specific embodiment 6 in that the concrete pump truck boom is a six-section boom concrete pump truck. Other aspects are the same as specific embodiment 6.

[0091] Specific embodiment eight: This embodiment differs from specific embodiment seven in that the concrete pump truck boom is a concrete pump truck boom with five sections. Other aspects are the same as specific embodiment seven.

[0092] Specific embodiment 9: This embodiment differs from specific embodiment 8 in that the concrete pump truck boom is a four-section boom concrete pump truck. Other aspects are the same as specific embodiment 8.

[0093] Specific embodiment 10: This embodiment differs from specific embodiment 9 in that the concrete pump truck boom is a three-section boom. Other aspects are the same as specific embodiment 9.

[0094] The present invention is verified by the following test:

[0095] For six-section concrete pump trucks, the last boom section experiences significant speed fluctuations during movement. During construction operations, the last boom section moves frequently, often under harsh working conditions. Operators sometimes need to manipulate the last boom section while the pumping system is operating, making stable movement of the last boom section particularly important. Therefore, the proposed trigonometric function-based zero-impact construction machinery boom hydraulic cylinder speed target curve optimization method was experimentally verified using the last boom section of a concrete pump truck as an example.

[0096] Comparative test: First, based on the trapezoidal target speed curve, a large-scale expansion and retraction motion control experiment of the last arm segment in the range of 0° to 180° was carried out. The experimental results are as follows Figure 3-Figure 5 As shown ( Figure 3 is the speed response curve, Figure 4 To expand the speed error curve, Figure 5 is the retraction speed error curve). At the same time, in order to verify the performance of the trapezoidal target speed curve in the boom small-amplitude motion condition, a small-amplitude deployment and retraction motion control experiment of the last boom section at 60° to 120° was also carried out. The experimental results are shown in the figure below. Figure 6-Figure 8 As shown ( Figure 6 is the speed response curve, Figure 7 To expand the speed error curve, Figure 8 is the retraction speed error curve).

[0097] Experiment 1: This experiment is an optimization method for the target speed curve of the hydraulic cylinder of the zero-impact engineering machinery boom based on trigonometric functions. The specific steps are as follows:

[0098] The trapezoidal function and cosine function are used as basis functions, and the advantages of both are combined to construct the S-shaped target velocity curve function of the hydraulic cylinder. The hypotenuse of the trapezoidal function is replaced by the cosine function of 1 / 4 period. The expression is:

[0099]

[0100] Where y is the displacement of the hydraulic cylinder piston rod, represents the derivative of y, which is the speed of the hydraulic cylinder piston rod. t1, t2, and t3 respectively represent the duration of the start-up acceleration interval, the uniform motion interval, and the deceleration stop interval in the S-shaped target speed curve of the hydraulic cylinder. v represents the target speed of the hydraulic cylinder piston rod (13 mm / s). a = v / 2, ω1 = π / t1, ω2 = π / t3, t' = t-t1-t2; t1 = t3.

[0101] After calculation, t1 is 2.42s, t3 is also 2.42s, ω n is the natural frequency of the boom structure system (3.9 Hz);

[0102] The value of t2 should be determined according to the actual working conditions and is a known quantity.

[0103] Based on the above S-shaped target speed curve, the last boom segment extension and retraction process was also carried out in the range of 0° to 180°. The experimental results are as follows: Figures 9-11 As shown ( Figure 9 is the speed response curve, Figure 10 To expand the speed error curve, Figure 11 ( ) is the retraction speed error curve. It can be seen that the speed fluctuation amplitude of the last boom segment during the deployment and retraction movement from 0° to 180° is 7.7% and 6.5% respectively, which is consistent with the Figure 3-Figure 5 Compared with the experimental results using the trapezoidal target velocity curve shown in , the vibration amplitude of the boom section during motion is significantly reduced. In order to verify the performance of the S-shaped target velocity curve in small-amplitude boom motion, a small-amplitude expansion and retraction motion control experiment of the last boom section in the range of 60° to 120° was also carried out. The experimental results are shown in the figure. Figure 12-14 As shown ( Figure 12 is the speed response curve, Figure 13 To expand the speed error curve, Figure 14 is the retraction speed error curve).

[0104] In summary, the S-shaped target speed curve has a better effect on suppressing boom speed fluctuations than the trapezoidal target speed curve, regardless of whether the boom is moving at a large or small amplitude. Table 1 summarizes the vibration suppression performance of the S-shaped target speed curve under large and small boom movement conditions for the last boom section of a six-section concrete pump truck. The results show that the proposed S-shaped target speed curve can reduce hydraulic cylinder speed fluctuations by 29.6% to 39.3% compared to the trapezoidal target speed curve.

[0105] Table 1 Summary of experimental results on motion control of hydraulic cylinder of No.6 boom section of concrete pump truck boom

[0106]

Claims

1. A method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions, characterized in that The hydraulic cylinder target speed curve is optimized to the hydraulic cylinder S-shaped target speed curve. The expression of the hydraulic cylinder S-shaped target speed curve function is: Where y is the displacement of the boom hydraulic cylinder piston rod, represents the derivative of y, which is the speed of the boom hydraulic cylinder piston rod. t1, t2, and t3 respectively represent the duration of the start-up acceleration interval, the uniform motion interval, and the deceleration stop interval in the S-shaped target speed curve of the hydraulic cylinder. v represents the target speed of the boom hydraulic cylinder piston rod. a=v / 2, ω1=π / t1, ω2=π / t3, t'=t-t1-t2; t1=t3; ω n is the natural frequency of the boom structure system; The horizontal coordinate of the S-shaped target speed curve function of the hydraulic cylinder is the running time t of the boom hydraulic cylinder, and the vertical coordinate is the speed of the boom hydraulic cylinder piston rod, that is, 2. The method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions according to claim 1 is characterized in that The hydraulic cylinder S-shaped target speed curve function is applied to each boom section in the engineering machinery boom.

3. The method for optimizing the target speed curve of the zero-impact engineering machinery boom hydraulic cylinder based on trigonometric functions according to claim 1 is characterized in that The derivation process is as follows: Step 1: Calculate the acceleration target curve and displacement target curve function of the hydraulic cylinder piston rod; Step 2: Calculate the arm end displacement y in the start-up acceleration interval L and speed Step 3: Calculate the displacement y of the arm end in the uniform motion range L and speed Step 4: Calculate the arm end displacement y in the stop and deceleration interval L and speed Step 5: Solve the target velocity curve parameters according to the boundary conditions; Step 6: Simplify and solve the target speed curve parameters to determine t1.

4. The method for optimizing the target speed curve of the zero-impact engineering machinery boom hydraulic cylinder based on trigonometric functions according to claim 3 is characterized in that The specific process of step 1 in the derivation process is as follows: Step 1.1: S-shaped target velocity curve function for the hydraulic cylinder Taking derivatives, we get the acceleration target curve expression: is the acceleration of the hydraulic cylinder piston rod; Step 1.2: S-shaped target velocity curve function for the hydraulic cylinder Perform integration to obtain the target displacement curve of the hydraulic cylinder piston rod:

5. The method for optimizing the target speed curve of the zero-impact engineering machinery boom hydraulic cylinder based on trigonometric functions according to claim 4 is characterized in that The specific process of step 2 in the derivation process is as follows: Step 2.1: To simplify the parameter optimization process of the speed target curve, the boom structure is equivalent to a second-order basic mass-spring system, and its motion equation is: Among them, y L is the displacement of the arm end; y is the displacement of the hydraulic cylinder piston rod; Step 2.2: Substitute the formula in step 1.2 into the formula in step 2.1 to get y L and its derivative, velocity The value y in the starting acceleration interval t∈[0, t1) L1 and The trigonometric coefficients C1 and C2 in the formula are determined by the boundary conditions: y L1 (t)=0,t=0 Obtain:

6. The method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions according to claim 5 is characterized in that The specific process of step 3 in the derivation process is as follows: 3.1: Displacement y of the end of the arm segment L and its derivative value y on the uniform motion interval t∈[t1, t1+t2) L2 and for: y L2 =C3 cosω n t+C4 sinω n t+2at-at1 The trigonometric coefficients C3 and C4 in the formula are determined by the boundary conditions: yes L2 (t)=y L1 (t),t=t1 Obtain: 3.2: Simplify the last formula in 3.1 and define the transformation matrix R(t): Then the last formula in 3.1 can be shortened to:

7. The method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions according to claim 6 is characterized in that The specific process of step 4 in the derivation process is as follows: Boom end displacement y L and its derivative, velocity The value y in the stop deceleration interval t∈[t1+t2, t1+t2+t3] L3 and for: The trigonometric coefficients C5 and C6 in the formula can be obtained by the boundary conditions: y L3 (t)=y L2 (t),t=t1+t2 Obtain:

8. The method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions according to claim 7 is characterized in that The specific process of step 5 in the derivation process is as follows: In order to suppress the residual vibration of the boom system and achieve a stable state at the end of the movement, it is necessary to achieve: y L (t)=y(t),t=t1+t2+t3 The above conditions can be transformed into: Combining all the formulas in step 4 and the two formulas above, we have:

9. The method for optimizing the target speed curve of the hydraulic cylinder of a zero-impact engineering machinery boom based on trigonometric functions according to claim 8, characterized in that The specific process of step 6 in the derivation process is as follows: In order to further simplify the design of the target speed curve, let t1 = t3 and we can get: R -1 (2t1+t2){-R(t1+t2)+R(t1)+I2-R(2t1+t2)}V1=0 Where I2 is the 2×2 identity matrix; expanding and simplifying the above formula, we have: Because the value of t2 should be determined according to the actual working conditions, we can only require The conditions for calculation are: Among them, since V1 does not exist when k2=1, the value range of k2 is an integer set starting from 2. However, since the faster the acceleration, the faster the boom moves and the higher the working efficiency, k2 takes the minimum value 2, that is, t1 takes the minimum value, so When the speed target curve parameters satisfy t1=t3 and When the boom is moving, the speed fluctuation during the boom movement can be suppressed.

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