A kinematics modeling method of an electric fork truck

Abstract

The application discloses a kind of kinematics modeling methods of electric fork truck, including fork truck itself kinematics model, motor acceleration and fork truck body acceleration conversion model, motor rotation angle and fork truck front wheel rotation angle conversion model.The application is first by respectively establishing fork truck itself kinematics model, motor acceleration and fork truck body acceleration conversion model, motor rotation angle and fork truck front wheel rotation angle conversion model, then the kinematics accurate model of electric fork truck is obtained by combining fork truck itself kinematics model, motor acceleration and fork truck body acceleration conversion model, motor rotation angle and fork truck front wheel rotation angle conversion model, the model considers the real working condition of fork truck, describes the connection between the rotation angle, speed of motor and ground coordinate system;So as to solve the accurate motion control of fork truck desired position.

Description

Technical Field

[0001] This invention belongs to the field of electric pallet forklift technology, specifically relating to a kinematic modeling method for electric forklifts. Background Technology

[0002] Forklifts are engineering vehicles widely used in ports, railway stations, airports, freight yards, factory workshops, warehouses, distribution centers, and logistics centers. They are essential and highly efficient equipment for loading, unloading, and handling palletized goods within ship holds, truck beds, and containers, as well as for pallet and container transportation. Forklifts can generally be divided into two main categories: internal combustion forklifts and electric forklifts. Benefiting from factors such as manual labor substitution, environmental upgrades, and electrification, electric forklifts are becoming the mainstream transportation vehicles in the material handling industry, replacing internal combustion forklifts. However, electric forklifts struggle to achieve precise motion control of the desired forklift position. Describing the relationship between the target motion of the controlled object and the motion of each drive unit through electric forklift dynamics modeling can effectively solve these problems.

[0003] A hybrid electric pallet forklift and its motion method (patent application number 201910530060.7) proposes a hybrid electric pallet forklift and its motion method using mechanical coupling. However, this structure relies on mechanical hard synchronization, which has the problem of twisting the mechanical structure when the motion is not synchronized. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of precise motion control of a forklift at a desired position, and to provide a kinematic modeling method for an electric forklift.

[0005] The technical solution provided by this invention is: a kinematic modeling method for an electric forklift, including a kinematic model of the forklift itself, a conversion model of motor acceleration and forklift body acceleration, and a conversion model of motor rotation angle and forklift front wheel rotation angle; Step 1: Establish the kinematic model of the forklift itself First, establish a fixed ground coordinate system with X and Y as markers. Then, establish a vehicle body coordinate system with the forklift's center of mass P as the mass point, the x-axis as the longitudinal direction of the forklift's movement, and the y-axis as the lateral direction of the forklift's movement. Indicates the turning angle of the forklift's front wheels. Indicates the slip angle of the front wheel. , This represents the slip angle of the rear wheel. The slip angle generates a lateral force on the tire. , , The lateral force of the tires controls the steering motion of the forklift. The longitudinal characteristics of a forklift system are affected by the longitudinal forces of the tires. Under the influence of tire slip ratio, ground friction, and vehicle weight, the forklift tires will experience... , , The longitudinal force of the tires controls the longitudinal movement of the forklift. The forces exerted by each tire of the forklift on the forklift's center of gravity are described above. dot, use This indicates the forklift's sideslip angle. The heading angle represents the forklift's center of gravity. , They represent the center of mass respectively. In the vehicle body coordinate system, the lateral and longitudinal velocities, Indicates the center of mass The vector velocity of motion, This represents the yaw rate of the forklift's center of mass. This represents the distance from the center of gravity to the center axis of the front wheel. This represents the distance from the center of gravity to the rear wheel's center axis. This indicates the wheelbase of the two rear wheels of the forklift; The following assumptions are made regarding the forklift tires. 1) For a forklift moving at high speed, the lateral force of the tires can be considered to increase linearly when the sideslip angle β is less than 4°; 2) The tire slip angle β is extremely small during the movement of the forklift; Based on the above assumptions, the mathematical model of the forklift is as follows:

[0006] The lateral force of the tire is composed of Let m represent the mass of the forklift, and let m represent the lateral acceleration. express,

[0007] The yaw moment of inertia of the forklift body is caused by This indicates that the yaw acceleration of the forklift body is caused by This indicates that the torque of the front and rear wheels of the forklift is expressed in terms of... express, Rewriting equation (1) above, we get

[0008] Rewriting equation (2) above, we get

[0009] The linear relationship between tire lateral force and front wheel steering angle can be obtained.

[0010]

[0011]

[0012] Among them, the lateral force of the front tire, the lateral force of rear tire 1, and the lateral force of rear tire 2 are respectively composed of... , , It is stated that the lateral stiffness of the front wheel, the lateral stiffness of rear wheel 1, and the lateral stiffness of rear wheel 2 are respectively determined by... , , This indicates that the front wheel slip angle, rear wheel 1 slip angle, and rear wheel 2 slip angle are determined by... , , express, Due to the side slip angle during the actual driving of the forklift It is very small, and can be approximated as , ,at the same time Neglecting the comparison with the forklift travel length, let have to The sideslip angles of the front wheel, rear wheel 1, and rear wheel 2 can be obtained.

[0013]

[0014]

[0015] Substituting equations (6) to (8) into equations (5-1), (5-2), and (5-3) above, we can obtain...

[0016] Rear wheel 1 side stiffness and rear wheel lateral stiffness The same, therefore, In addition, let , , Rewriting equation (3) above, we get

[0017] Rewriting equation (4) above, we get

[0018] Because when the forklift is moving Very small, making , The above equation (12) can be rewritten as (11) to obtain

[0019] Substituting equations (9), (10), and (11) into equations (13) and (14) above, we can obtain...

[0020]

[0021] Forklift heading angle yaw rate of the forklift's center of gravity Relationship

[0022] By forklift speed With acceleration Get Relationship

[0023] From the relationship between the vehicle coordinate system and the ground coordinate system

[0024] Select the center of gravity sideslip angle yaw rate lateral angle Velocity of the center of mass As the system's state variable; front wheel steering angle is selected. Vehicle acceleration As input to the system; select the forklift's X-direction velocity in the fixed coordinate system. Y-direction velocity The state-space equations are established as the output of the system.

[0025] Step 2: Establish the conversion model between motor acceleration and forklift body acceleration Design a converter to translate motor acceleration into forklift body acceleration to simulate the acceleration and deceleration of a forklift under real-world operating conditions. The output of the linear motor affects the longitudinal force of the vehicle, and the longitudinal force of the tires generates the vehicle's acceleration. Describe the relationship between tire lateral forces under braking and driving conditions; Scenario 1: Braking Condition Under braking conditions, the conversion model between motor acceleration and forklift body acceleration can be obtained.

[0026] The coefficient of friction between the tire and the road surface is expressed as: The vertical pressure of the forklift's front tires is expressed as... Tire slip ratio is expressed as The longitudinal velocity component of the tires along the vehicle body is expressed as: The radius of the front tire is expressed as The rotational speed of the front tires is expressed as Let the mass of the forklift be m, and the acceleration due to gravity be g. Represented as

[0027] The longitudinal stiffness of the tire is expressed as: The unit lateral stiffness of a tire is expressed as The front tire slip angle is expressed as ; Based on equations (22) to (26), we can obtain

[0028] Scenario 2: Drive Condition Under driving conditions, slip ratio With intermediate parameters Change to

[0029] Based on equations (22), (23), (24), (28), and (29), we can obtain equation (29).

[0030] The input to the motor acceleration to forklift body acceleration conversion model is the state variables of the forklift model: center of gravity sideslip angle β, yaw rate r, yaw angle ψ, body speed v, acceleration of the straight motor, and rolling friction between the ground and the wheels. The output is the body acceleration. Step 3: Establish the conversion model between motor rotation angle and forklift front wheel rotation angle The conversion model between motor rotation angle and forklift front wheel rotation angle can be obtained.

[0031] The reduction ratio of the planetary gear reducer is expressed as: The reduction ratio between the sun gear and the planetary gears is expressed as: The steering motor rotation angle is expressed as The backlash error is expressed as ; The input to the conversion model between motor rotation angle and forklift front wheel rotation angle is the error between the motor rotation angle and the simulated backlash. The actual rotation angle of the forklift front wheel is output through equation (32) and equation (31). By combining the kinematic model of the forklift itself, the conversion model of motor acceleration and forklift body acceleration, and the conversion model of motor rotation angle and forklift front wheel rotation angle, an accurate kinematic model of the electric forklift is obtained.

[0032] This invention first establishes a kinematic model of the forklift itself, a conversion model of motor acceleration and forklift body acceleration, and a conversion model of motor rotation angle and forklift front wheel rotation angle, respectively. Then, it combines these models to obtain a precise kinematic model of the electric forklift. This model considers the actual working conditions of the forklift and describes the relationship between the motor's rotation angle, speed, and the ground coordinate system, thereby solving the problem of precise motion control of the forklift at the desired position. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of an electric pallet forklift system according to the present invention; Figure 2 This is a force analysis diagram of forklift dynamics according to the present invention; Figure 3 This is a block diagram of a model for converting motor acceleration into forklift body acceleration according to the present invention; Figure 4 This is a block diagram of a model for converting motor rotation angle to forklift front wheel rotation angle according to the present invention; Figure 5 This is a block diagram of the kinematic model of an electric forklift according to the present invention; In the diagram, 1-planetary gear; 2-planetary reducer; 3-steering servo motor; 4-forklift front wheel; 5-straight servo motor; 6-sun gear; 7-forklift rear wheel; 8-forks; 9-cab. Detailed Implementation

[0034] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0035] A kinematic modeling method for an electric forklift includes a kinematic model of the forklift itself, a conversion model of motor acceleration and forklift body acceleration, and a conversion model of motor rotation angle and forklift front wheel rotation angle.

[0036] The specific process of kinematic modeling for electric forklifts is as follows: Step 1: Establish the kinematic model of the forklift itself A schematic diagram of an electric pallet forklift system according to the present invention is shown below. Figure 1 As shown.

[0037] Reference Figure 1The diagram illustrates the structure of an electric pallet forklift system, including a cab 9, forks 8, front wheels 4, rear wheels 7, a steering servo motor 3, a planetary reducer 2, planetary gears 1, a sun gear 6, and a straight-line servo motor 5. The steering servo motor 3, after being reduced in speed by the planetary reducer 2, rotates on the sun gear 6 via the planetary gears 1, thus enabling the lateral rotation of the front wheels 4. The straight-line servo motor 5, with its main shaft connected to the central axle of the front wheels 4, is the power unit that enables the forklift's forward and backward movements.

[0038] A force analysis diagram of forklift dynamics is shown below. Figure 2 As shown, first, a fixed ground coordinate system with X and Y as markers is established. Then, a vehicle body coordinate system is established with the forklift's center of mass P as the mass point, the x-axis as the longitudinal direction of the forklift's movement, and the y-axis as the lateral direction of the forklift's movement.

[0039] The steering characteristics of a forklift system are affected by the lateral forces exerted on the tires, among which... This indicates the turning angle of the forklift's front wheels. At the same time, the tires will undergo certain deformations during the forklift's movement, resulting in the tire slip angle. Indicates the slip angle of the front wheel. , This represents the slip angle of the rear wheel. The slip angle generates a lateral force on the tire. , , The lateral force of the tires controls the steering movement of the forklift.

[0040] The longitudinal characteristics of a forklift system are affected by the longitudinal forces of the tires. Under the influence of tire slip ratio, ground friction, and vehicle weight, the forklift tires will experience... , , The longitudinal force of the tires controls the longitudinal movement of the forklift.

[0041] The forces exerted by each tire of the forklift on the forklift's center of gravity are described above. Dot. Use This indicates the forklift's sideslip angle. The heading angle represents the forklift's center of gravity. , They represent the center of mass respectively. In the vehicle body coordinate system, the lateral and longitudinal velocities, Indicates the center of mass The vector velocity of motion, This represents the yaw rate of the forklift's center of mass. This represents the distance from the center of gravity to the center axis of the front wheel. This represents the distance from the center of gravity to the rear wheel's center axis. This indicates the wheelbase of the two rear wheels of the forklift.

[0042] Without affecting the accuracy of the model, and taking into account the actual situation, the following assumptions are made about the forklift tires.

[0043] 1) For a forklift moving at high speed, the lateral force of the tires can be considered to increase linearly when the slip angle β is less than 4°.

[0044] 2) The tire slip angle β is extremely small during the movement of the forklift.

[0045] Based on the above assumptions, the mathematical model of a forklift can be obtained as follows:

[0046] The lateral force of the tire is composed of Let m represent the mass of the forklift, and let m represent the lateral acceleration. express.

[0047]

[0048] The yaw moment of inertia of the forklift body is caused by This indicates that the yaw acceleration of the forklift body is caused by express.

[0049] Rewriting equation (1) above, we get

[0050] Rewriting equation (2) above, we get

[0051] The linear relationship between tire lateral force and front wheel steering angle can be obtained.

[0052]

[0053]

[0054] Among them, the lateral force of the front tire, the lateral force of rear tire 1, and the lateral force of rear tire 2 are respectively composed of... , , It is stated that the lateral stiffness of the front wheel, the lateral stiffness of rear wheel 1, and the lateral stiffness of rear wheel 2 are respectively determined by... , , This indicates that the front wheel slip angle, rear wheel 1 slip angle, and rear wheel 2 slip angle are determined by... , , express, Due to the side slip angle during the actual driving of the forklift It is very small, and can be approximated as , ,at the same time Neglecting the comparison with the forklift travel length, let have to The sideslip angles of the front wheel, rear wheel 1, and rear wheel 2 can be obtained.

[0055]

[0056]

[0057] Substituting equations (6) to (8) into equations (5-1), (5-2), and (5-3) above, we can obtain...

[0058] Rear wheel 1 side stiffness and rear wheel lateral stiffness The same, therefore, In addition, let , , Rewriting equation (3) above, we get

[0059] Rewriting equation (4) above, we get

[0060] Because when the forklift is moving Very small, making , The above equation (12) can be rewritten as (11) to obtain

[0061] Substituting equations (9), (10), and (11) into equations (13) and (14) above, we can obtain...

[0062]

[0063] Forklift heading angle yaw rate of the forklift's center of gravity Relationship

[0064] By forklift speed With acceleration Get Relationship

[0065] From the relationship between the vehicle coordinate system and the ground coordinate system

[0066] Select the center of gravity sideslip angle yaw rate lateral angle Velocity of the center of mass As the system's state variable; front wheel steering angle is selected. Vehicle acceleration As input to the system; select the forklift's X-direction velocity in the fixed coordinate system. Y-direction velocity The state-space equations are established as the output of the system.

[0067] Step 2: Establish the conversion model between motor acceleration and forklift body acceleration The linear servo motor controls the forklift's forward and backward movement. When the linear motor accelerates to a constant speed, the forklift's own speed will eventually reach the desired constant speed state, and the same applies during deceleration. During this process, the forklift's speed is affected by the changing friction of the ground (when the friction between the front wheels and the ground is low, the wheels will spin freely; when the friction is high, the forklift's speed can better follow the motor speed). Therefore, the forklift's speed does not perfectly follow the linear motor's rotation speed. This invention designs a motor acceleration-forklift acceleration converter to simulate the forklift's acceleration and deceleration states under real-world working conditions.

[0068] The output of the straight motor affects the longitudinal force of the vehicle, and the longitudinal force of the tires generates the vehicle's acceleration.

[0069] Furthermore, the relationship between tire lateral forces under braking and driving conditions is described.

[0070] Scenario 1: Braking Condition Under braking conditions, the conversion model between motor acceleration and forklift body acceleration can be obtained.

[0071] The coefficient of friction between the tire and the road surface is expressed as: The vertical pressure of the forklift's front tires is expressed as... Tire slip ratio is expressed as The longitudinal velocity component of the tires along the vehicle body is expressed as: The radius of the front tire is expressed as The rotational speed of the front tires is expressed as Let the mass of the forklift be m, and the acceleration due to gravity be g. The above... Represented as

[0072] The longitudinal stiffness of the tire is expressed as: The unit lateral stiffness of a tire is expressed as The front tire slip angle is expressed as .

[0073] Based on equations (22) to (26), we can obtain

[0074] Scenario 2: Drive Condition Under driving conditions, slip ratio With intermediate parameters Change to

[0075] Based on equations (22), (23), (24), (28), and (29), we can obtain equation (29).

[0076] The block diagram of the conversion model between motor acceleration and forklift body acceleration is as follows: Figure 3 As shown.

[0077] Reference Figure 3 As shown, the inputs to the motor acceleration to forklift body acceleration conversion model are the state variables of the forklift model (center of gravity sideslip angle β, yaw rate r, yaw angle ψ, body speed v), the acceleration of the straight motor, and the rolling friction between the ground and the wheels. The output is the body acceleration.

[0078] Step 3: Establish the conversion model between motor rotation angle and forklift front wheel rotation angle The spindle motion of the steering servo motor drives the spindle of the planetary reducer to decelerate. The reducer spindle drives the planetary gears to rotate around the sun gear, controlling the steering motion of the forklift's front wheels. During this process, the number of teeth on the planetary gears and the sun gear are not the same, and in actual working conditions, there may be incomplete meshing of the gears. This will cause the actual steering angle of the forklift to differ from the controller's desired angle, resulting in vibration. Therefore, the forklift electronic synchronization system also requires a motor angle-to-front wheel angle converter to simulate the forklift's steering state under real working conditions.

[0079] The relationship between the motor rotation angle and the front wheel rotation angle can be obtained.

[0080] The reduction ratio of the planetary gear reducer is expressed as: The reduction ratio between the sun gear and the planetary gears is expressed as: The steering motor rotation angle is expressed as The backlash error is expressed as .

[0081] The block diagram of the conversion model between motor rotation angle and forklift front wheel rotation angle is as follows: Figure 4 As shown.

[0082] Reference Figure 4 As shown, the input of the motor rotation angle and forklift front wheel rotation angle conversion model is the motor rotation angle and the error of simulated backlash, and the actual rotation angle of the forklift front wheel is output by equation (31).

[0083] Combining formulas (20) and (21) Figure 3 , Figure 4 achievable Figure 5 Block diagram of the kinematic model of an electric forklift.

[0084] Reference Figure 5 As shown, the accurate kinematic model of the electric forklift is obtained by combining the kinematic model of the forklift itself, the conversion model of motor acceleration and forklift body acceleration, and the conversion model of motor rotation angle and forklift front wheel rotation angle. This model takes into account the actual working conditions of the forklift and describes the relationship between the motor rotation angle, speed and ground coordinate system.

Claims

1. A kinematic modeling method for an electric forklift, characterized in that, This includes the establishment of a kinematic model of the forklift itself, a conversion model between motor acceleration and forklift body acceleration, and a conversion model between motor rotation angle and forklift front wheel rotation angle; Step 1: Establish the kinematic model of the forklift itself First, establish a fixed ground coordinate system with X and Y as markers. Then, establish a vehicle body coordinate system with the forklift's center of mass P as the mass point, the x-axis as the longitudinal direction of the forklift's movement, and the y-axis as the lateral direction of the forklift's movement. Indicates the turning angle of the forklift's front wheels. Indicates the slip angle of the front wheel. , This represents the slip angle of the rear wheel. The slip angle generates a lateral force on the tire. , , The lateral force of the tires controls the steering motion of the forklift. The longitudinal characteristics of a forklift system are affected by the longitudinal forces of the tires. Under the influence of tire slip ratio, ground friction, and vehicle weight, the forklift tires will experience... , , The longitudinal force of the tires controls the longitudinal movement of the forklift. The forces exerted by each tire of the forklift on the forklift's center of mass, point P, are described above. This indicates the forklift's sideslip angle. The heading angle represents the forklift's center of mass. , Let represent the lateral and longitudinal velocities of the center of mass P in the vehicle coordinate system, respectively. The vector velocity representing the center of mass P. This represents the yaw rate of the forklift's center of mass. This represents the distance from the center of gravity to the center axis of the front wheel. This represents the distance from the center of gravity to the rear wheel's center axis. This indicates the wheelbase of the two rear wheels of the forklift; The following assumptions are made regarding the forklift tires. 1) For a forklift moving at high speed, the lateral force of the tires is at the slip angle. A value less than 4° is considered a linear increase; 2) Tire slip angle during forklift movement Extremely small; Based on the above assumptions, the mathematical model of the forklift is as follows: The lateral force of the tire is composed of Let m represent the mass of the forklift, and let m represent the lateral acceleration. express, The yaw moment of inertia of the forklift body is caused by This indicates that the yaw acceleration of the forklift body is caused by This indicates that the torque of the front and rear wheels of the forklift is expressed in terms of... express; Rewriting equation (1) above, we get Rewriting equation (2) above, we get The linear relationship between tire lateral force and front wheel steering angle can be obtained. Among them, the lateral force of the front tire, the lateral force of rear tire 1, and the lateral force of rear tire 2 are respectively composed of... , , It is stated that the lateral stiffness of the front wheel, the lateral stiffness of rear wheel 1, and the lateral stiffness of rear wheel 2 are respectively determined by... , , This indicates that the front wheel slip angle, rear wheel 1 slip angle, and rear wheel 2 slip angle are determined by... , , express, Due to the side slip angle during the actual driving of the forklift Very small, approximately considered , ,at the same time Neglecting the comparison with the forklift travel length, let have to The sideslip angles of the front wheel, rear wheel 1, and rear wheel 2 can be obtained. Substituting equations (6) to (8) into equations (5-1), (5-2), and (5-3) above, we can obtain... Rear wheel 1 side stiffness and rear wheel lateral stiffness The same, therefore, In addition, let , , Rewriting equation (3) above, we get Rewriting equation (4) above, we get Because when the forklift is moving Very small, making , The above equation (12) can be rewritten as follows: Substituting equations (9), (10), and (11) into equations (13) and (14) above, we can obtain... Forklift heading angle yaw rate of the forklift's center of gravity Relationship By forklift speed With acceleration Get Relationship From the relationship between the vehicle coordinate system and the ground coordinate system Select the center of gravity sideslip angle yaw rate lateral angle Velocity of the center of mass As the system's state variable; front wheel steering angle is selected. Vehicle acceleration As input to the system; select the forklift's X-direction velocity in the fixed coordinate system. Y-direction velocity The state-space equations are established based on the system output. Step 2: Establish the conversion model between motor acceleration and forklift body acceleration Design a converter to translate motor acceleration into forklift body acceleration to simulate the acceleration and deceleration of a forklift under real-world operating conditions. The output of the linear motor affects the longitudinal force of the vehicle, and the longitudinal force of the tires generates the vehicle's acceleration. Describe the relationship between tire lateral forces under braking and driving conditions; Scenario 1: Braking Condition Under braking conditions, the conversion model between motor acceleration and forklift body acceleration can be obtained. The coefficient of friction between the tire and the road surface is expressed as: The vertical pressure on the front tires of a forklift is expressed as... Tire slip ratio is expressed as The longitudinal velocity component of the tires along the vehicle body is expressed as: The radius of the front tire is expressed as The rotational speed of the front tires is expressed as Let the mass of the forklift be m, and the acceleration due to gravity be g. Represented as The longitudinal stiffness of the tire is expressed as: The unit lateral stiffness of a tire is expressed as The front tire slip angle is expressed as ; Based on equations (22) to (26), we can obtain Scenario 2: Drive Condition Under driving conditions, slip ratio With intermediate parameters Change to Based on equations (22), (23), (24), (28), and (29), we can obtain The input to the motor acceleration to forklift body acceleration conversion model is the forklift model's state variable: center of gravity sideslip angle. yaw rate lateral angle Vehicle speed The acceleration of the linear motor, the rolling friction between the ground and the wheels, and the output is the vehicle body acceleration; Step 3: Establish the conversion model between motor rotation angle and forklift front wheel rotation angle The conversion model between motor rotation angle and forklift front wheel rotation angle can be obtained. The reduction ratio of the planetary gear reducer is expressed as: The reduction ratio between the sun gear and the planetary gears is expressed as: The steering motor rotation angle is expressed as The backlash error is expressed as ; The input to the conversion model between motor rotation angle and forklift front wheel rotation angle is the error between the motor rotation angle and the simulated backlash, and the actual rotation angle of the forklift front wheel is output through equation (32); By combining the kinematic model of the forklift itself, the conversion model of motor acceleration and forklift body acceleration, and the conversion model of motor rotation angle and forklift front wheel rotation angle, an accurate kinematic model of the electric forklift is obtained.

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