Tension control method and system for producing an ultra-thin strip on a cold tandem rolling mill

Abstract

The application provides a tension control method and system for producing an extremely thin strip steel by a cold continuous rolling unit, sets total tension, basic tension and additional tension, calculates the unit additional tension setting value between racks, and calculates the actual rack tension setting value. The application can effectively reduce the rolling force fluctuation by properly changing the tension setting, and greatly helps the thickness and shape control of the strip steel when the speed changes.

Description

Technical Field

[0001] This invention relates to the field of metallurgical automation, and more specifically, to a method and system for tension control in the production of ultra-thin strip steel in cold continuous rolling mills. Background Technology

[0002] In cold continuous rolling production, the tension between stands is crucial for the high-speed and stable operation of the rolling mill. Tension settings include basic tension settings and additional tension settings. The basic tension setting is the product of the unit tension and the strip cross-sectional area. The unit tension setting is derived from the model process parameter table. The unit tension setting is closely related to the steel grade strength, strip thickness, and the work hardening tendency of the material; generally, the higher the strength, the larger the unit tension setting; and the thinner the material, the larger the unit tension setting. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for tension control in the production of ultra-thin strip steel in a cold continuous rolling mill.

[0004] A tension control method for ultra-thin strip steel production in a cold continuous rolling mill, according to the present invention, includes:

[0005] The steps for setting tension are: setting the total tension, the base tension, and the additional tension;

[0006] Steps for setting additional tension: Unit additional tension setting value between computer racks;

[0007] The steps for calculating the actual inter-rack tension setpoint based on the actual situation are as follows: Calculate the actual inter-rack tension setpoint;

[0008] Ultra-thin strip steel refers to strip steel with a target thickness of less than or equal to 0.5 mm.

[0009] Preferably, the step of setting the tension includes:

[0010] FT total =FT base +FTA

[0011] FT base =stf×b×h

[0012] FT total Indicates total tension; FT base The base tension is represented by FTA; the additional tension is represented by stf; the strip unit tension is represented by b; the strip width is represented by h; and the strip thickness is represented by h.

[0013] Preferably, the step of setting the additional tension includes:

[0014] Steps to determine the velocity breakpoint:

[0015] Calculate the velocity v at each velocity segment point. act_i [pn][sp]:

[0016]

[0017] Among them, v act_i [pn][sp] represents the velocity of the nth rack at the (i+1)th velocity segment point sp;

[0018] v max [pn] represents the maximum speed of the rack;

[0019] pow represents the pow function;

[0020] v thread [pn] indicates the threading speed of the frame;

[0021] i = 0, 1, 2, 3, 4, 5, 6, M-1;

[0022] pn represents the nth stand of the cold continuous rolling mill;

[0023] M represents the number of velocity segmentation points;

[0024] The steps for calculating the influence coefficient of tension on rolling force at each speed segment point of each stand are as follows:

[0025] Calculate the additional inlet tension l_fta_0[pn][sp]:

[0026]

[0027] Among them, FTO base [pn] indicates the foundation tension at the rack inlet;

[0028] Calculate the additional outlet tension l_fta_1[pn][sp]:

[0029]

[0030] Among them, FT1 base [pn] indicates the rack outlet foundation tension;

[0031] Calculate the rolling force parameter l_fr_vr[pn][sp]:

[0032] l_fr_vr[pn][sp]=f(v act_i [pn][sp],FT0 base [pn]+l_fta_0[pn][sp],FT1 base [pn]+l_fta_1[pn][sp])

[0033] Calculate the rolling force parameter l_fr_ft0[pn][sp]:

[0034] l_fr_ft0[pn][sp]=f(v act_i [pn][sp],FT0 base [pn]+0.1×FT0 base [pn],FT1 base [pn])

[0035] Calculate the rolling force parameter l_fr_ft1[pn][sp]:

[0036] l_fr_ft1[pn][sp]=f(v act_i [pn][sp],FT0 base [pn],FT1 base [pn]+0.1×FT1 base [pn])

[0037] Calculate the inlet tension efficiency factor l_ft0_eff[pn][sp]:

[0038]

[0039] Calculate the outlet tension efficiency factor l_ft1_eff[pn][sp]:

[0040]

[0041] The steps for calculating the additional inlet and outlet tension for each rack based on the inlet tension efficiency factor and the outlet tension efficiency factor are as follows:

[0042] Calculate the rolling force parameter l_fr[pn][sp] without additional tension:

[0043] l_fr[pn][sp]=f(v act_i [pn][sp],FT0 base [pn],FT1 base [pn])

[0044] For frame #1, i.e., the first frame, only the additional tension at the outlet is calculated:

[0045]

[0046] For other racks, calculate the additional inlet and outlet tensions:

[0047]

[0048] The steps for calculating the additional tension setpoints at each speed segment point between each frame are as follows:

[0049]

[0050] The steps for setting the unit additional tension value sfta[pn][sp] between computer racks are as follows:

[0051] sfta[pn][sp]=l_fta[pn][sp]×gain[pn][sp]÷b÷h

[0052] gain[pn][sp] represents the correction factor.

[0053] Preferably, the step of calculating the actual inter-rack tension setting value based on the actual situation includes:

[0054] Based on the actual speed, the unit additional tension sfta[pn] at the current actual speed state is calculated using interpolation:

[0055]

[0056] Where v represents the actual speed;

[0057] sfta[pn][sp+1] represents the additional tension at the speed breakpoint sp+1 of the frame;

[0058] sfta[pn][sp] represents the additional tension at the speed breakpoint sp of the rack;

[0059] v act [pn][sp+1] represents the velocity at the frame velocity breakpoint sp+1;

[0060] v act [pn][sp] represents the velocity at the frame velocity breakpoint sp;

[0061] The velocity segment point sp+1 is the next velocity segment point after the velocity segment point sp;

[0062] Calculate the actual inter-frame tension setpoint fta[pn]:

[0063] fta[pn]=FT base +sfta[pn]×b×h.

[0064] Preferably, the fluctuation of rolling force during acceleration and deceleration is reduced by changing the additional tension setting.

[0065] According to the present invention, a tension control system for ultra-thin strip steel production in a cold continuous rolling mill includes:

[0066] The module for setting tension includes: setting total tension, basic tension, and additional tension;

[0067] Module for setting additional tension: Unit additional tension setting value between computer racks;

[0068] Module for calculating actual inter-rack tension settings based on actual conditions: Calculates actual inter-rack tension settings;

[0069] Ultra-thin strip steel refers to strip steel with a target thickness of less than or equal to 0.5 mm.

[0070] Preferably, the module for setting the tension includes:

[0071] FT total =FT base +FTA

[0072] FT base =stf×b×h

[0073] FT total Indicates total tension; FT base The base tension is represented by FTA; the additional tension is represented by stf; the strip unit tension is represented by b; the strip width is represented by h; and the strip thickness is represented by h.

[0074] Preferably, the module for setting the additional tension includes:

[0075] Module for determining velocity breakpoints:

[0076] Calculate the velocity v at each velocity segment point. act_i [pn][sp]:

[0077]

[0078] Among them, v act_i [pn][sp] represents the velocity of the nth rack at the (i+1)th velocity segment point sp;

[0079] v max [pn] represents the maximum speed of the rack;

[0080] pow represents the pow function;

[0081] v thread [pn] indicates the threading speed of the frame;

[0082] i = 0, 1, 2, 3, 4, 5, 6, M-1;

[0083] pn represents the nth stand of the cold continuous rolling mill;

[0084] M represents the number of velocity segmentation points;

[0085] A module for calculating the influence coefficient of tension on rolling force at each speed segment point of each stand:

[0086] Calculate the additional inlet tension l_fta_0[pn][sp]:

[0087]

[0088] Among them, FTO base [pn] indicates the foundation tension at the rack inlet;

[0089] Calculate the additional outlet tension l_fta_1[pn][sp]:

[0090]

[0091] Among them, FT1 base [pn] indicates the rack outlet foundation tension;

[0092] Calculate the rolling force parameter l_fr_vr[pn][sp]:

[0093] l_fr_vr[pn][sp]=f(v act_i [pn][sp],FT0 base [pn]+l_fta_0[pn][sp],FT1 base [pn]+l_fta_1[pn][sp])

[0094] Calculate the rolling force parameter l_fr_ft0[pn][sp]:

[0095] l_fr_ft0[pn][sp]=f(v act_i [pn][sp],FT0 base [pn]+0.1×FT0 base [pn],FT1 base [pn])

[0096] Calculate the rolling force parameter l_fr_ft1[pn][sp]:

[0097] l_fr_ft1[pn][sp]=f(v act_i [pn][sp],FT0 base [pn],FT1 base [pn]+0.1×FT1 base [pn])

[0098] Calculate the inlet tension efficiency factor l_ft0_eff[pn][sp]:

[0099]

[0100] Calculate the outlet tension efficiency factor l_ft1_eff[pn][sp]:

[0101]

[0102] The module that calculates the additional inlet tension and additional outlet tension for each rack based on the inlet tension efficiency factor and the outlet tension efficiency factor:

[0103] Calculate the rolling force parameter l_fr[pn][sp] without additional tension:

[0104] l_fr[pn][sp]=f(v act_i [pn][sp],FT0 base [pn],FT1 base [pn])

[0105] For frame #1, i.e., the first frame, only the additional tension at the outlet is calculated:

[0106]

[0107] For other racks, calculate the additional inlet and outlet tensions:

[0108]

[0109] Module for calculating the additional tension setpoints at each speed segment point between each frame:

[0110]

[0111] The module for the unit additional tension setting value sfta[pn][sp] between computer racks:

[0112] sfta[pn][sp]=l_fta[pn][sp]×gain[pn][sp]÷b÷h

[0113] gain[pn][sp] represents the correction factor.

[0114] Preferably, the module for calculating the actual inter-rack tension setting value based on actual conditions includes:

[0115] Based on the actual speed, the unit additional tension sfta[pn] at the current actual speed state is calculated using interpolation:

[0116]

[0117] Where v represents the actual speed;

[0118] sfta[pn][sp+1] represents the additional tension at the speed breakpoint sp+1 of the frame;

[0119] sfta[pn][sp] represents the additional tension at the speed breakpoint sp of the rack;

[0120] v act [pn][sp+1] represents the velocity at the frame velocity breakpoint sp+1;

[0121] v act [pn][sp] represents the velocity at the frame velocity breakpoint sp;

[0122] The velocity segment point sp+1 is the next velocity segment point after the velocity segment point sp;

[0123] Calculate the actual inter-frame tension setpoint fta[pn]:

[0124] fta[pn]=FT base +sfta[pn]×b×h.

[0125] Preferably, the fluctuation of rolling force during acceleration and deceleration is reduced by changing the additional tension setting.

[0126] Compared with the prior art, the present invention has the following beneficial effects:

[0127] 1. The purpose of this invention is to propose a tension control method and system for the production of ultra-thin strip steel in a cold continuous rolling mill, wherein the purpose of setting additional tension is to reduce the fluctuation of rolling force during acceleration and deceleration.

[0128] 2. This invention addresses the situation where the rolling lubrication state changes drastically during the acceleration and deceleration of ultra-thin strip rolling, leading to drastic changes in rolling force during speed increases and decreases. By appropriately changing the tension setting, the fluctuation of rolling force can be effectively reduced, which greatly helps in controlling the strip thickness and shape when the speed changes. Attached Figure Description

[0129] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0130] Figure 1 This is a schematic diagram of the additional tension calculation process.

[0131] Figure 2 A diagram illustrating the use of additional tension. Detailed Implementation

[0132] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0133] In the production of thin strip steel on a cold rolling mill, tension setting is particularly critical. This invention proposes a tension setting method for the production of ultra-thin strip steel on a cold rolling mill, wherein the purpose of additional tension setting is to reduce the fluctuation of rolling force during acceleration and deceleration. For the rolling of ultra-thin strip steel, the rolling lubrication state changes significantly during acceleration and deceleration, leading to drastic changes in rolling force during speed increases and decreases. Appropriately changing the tension setting can effectively reduce the fluctuation of rolling force, greatly aiding in the control of strip thickness and shape during speed changes. Ultra-thin strip steel refers to strip steel with a target thickness of 0.5 mm or less.

[0134] In the calculation of setpoints for the mathematical model of the process automation system in a cold-rolled strip steel plant, the tension setting model is an important part. Tension setting includes basic tension and additional tension setting.

[0135] FT total =FT base +FTA

[0136] Among them FT total Indicates total tension; FT base The base tension is indicated by FTA; the additional tension is indicated by FTA.

[0137] The following explains the strategy for setting the basic tension.

[0138] The basic unit tension is categorized according to steel type and specifications, and is based on empirical values ​​derived from material work hardening. The table type is as follows:

[0139]

[0140] Table 1 Tension settings for each frame foundation

[0141] The basic tension is calculated using the following formula:

[0142] FT base =stf×b×h

[0143] Where b represents the strip width; h represents the strip thickness; and stf represents the unit tension of the strip.

[0144] The following explains the strategy for setting additional tension.

[0145] The rolling process in a cold rolling mill involves constantly changing friction systems as the rolling speed varies. When the rolling speed changes, even under relatively stable lubrication conditions, the friction coefficient in the deformation zone varies significantly, ultimately leading to substantial fluctuations in the actual rolling force and severely impacting rolling stability. According to the rolling force calculation model based on rolling principles, tension is a crucial factor affecting rolling force. By appropriately adjusting the tension setting of the stand's forward slide when the speed changes, the fluctuations in rolling force can be effectively reduced; this is known as an additional tension control strategy.

[0146] The following calculations require calculating pn for each stand of the cold rolling mill separately, and iteratively calculating sp for each speed segment point. The additional tension setting calculation strategy is as follows:

[0147] (1) Determine the speed segment point based on the maximum speed calculated from the rolling model. Here, the speed segment point is selected to be equal to 8.

[0148] Calculate the velocity at each velocity segment point:

[0149]

[0150] Among them, v act_i [pn][sp] represents the velocity of the (i+1)th velocity segment point sp in each rack pn;

[0151] v max [pn] represents the maximum speed of each rack;

[0152] v thread [pn] represents the threading speed for each rack;

[0153] i = 0, 1, 2, 3, 4, 5, 6, 7.

[0154] (2) Calculate the influence coefficient of tension on rolling force at each speed segment point of each stand, i.e. tension efficiency factor, including inlet tension efficiency factor l_ft0_eff[pn][sp] and outlet tension efficiency factor l_ft1_eff[pn][sp].

[0155] Tension efficiency is the coefficient of influence of tension change on rolling force. Based on the basic tension setpoint and the speed parameters of the segment speed segment point, the additional inlet tension l_fta_0[pn][sp] and the additional outlet tension l_fta_1[pn][sp] of each speed segment point of each stand are calculated. Using this additional tension, the rolling force parameter l_fr_vr[pn][sp] is calculated according to the rolling force model.

[0156] Additional tension at the inlet:

[0157]

[0158] FT0 base [pn] represents the foundation tension at the inlet of a certain rack;

[0159] Additional tension in export:

[0160]

[0161] FT1 base [pn] represents the foundation tension at the outlet of a certain frame.

[0162] Rolling force parameters:

[0163] l_fr_vr[pn][sp]=f(v act_i [pn][sp],FT0 base [pn]+l_fta_0[pn][sp],FT1 base [pn]+l_fta_1[pn][sp])

[0164] l_fta_0[pn] represents the additional tension at the inlet of a certain rack;

[0165] l_fta_1[pn] represents the additional tension at the outlet of a certain frame.

[0166] Change the inlet additional tension l_fta_0[pn][sp] and calculate the rolling force parameters:

[0167] l_fr_ft0[pn][sp]=f(v act_i [pn][sp],FT0 base [pn]+0.1×FT0 base [pn],FT1 base [pn])

[0168] Calculate the rolling force parameters by changing the additional outlet tension l_fta_1[pn][sp]:

[0169] l_fr_ft1[pn][sp]=f(v act_i [pn][sp],FT0 base [pn],FT1 base [pn]+0.1×FT1 base [pn])

[0170] Calculate the inlet tension efficiency factor:

[0171]

[0172] Calculate the outlet tension efficiency factor:

[0173]

[0174] (3) Calculate the additional inlet tension and additional outlet tension for each frame based on the tension efficiency factor.

[0175] Calculate the rolling force parameters without using additional tension:

[0176] l_fr[pn][sp]=f(v act_i [pn][sp],FT0 base [pn],FT1 base [pn])

[0177] For frame #1, i.e., the first frame, only the additional tension at the outlet is calculated:

[0178]

[0179] l_fr[pn][sp] represents the rolling force without considering additional tension;

[0180] For other racks, calculate the additional inlet and outlet tensions:

[0181]

[0182] (4) Calculate the additional tension setpoints at each speed segment point between each frame.

[0183]

[0184] l_fta0[pn+1][sp] represents the additional tension at each velocity segment point at the inlet of a certain rack;

[0185] l_fta1[pn][sp] represents the additional tension at each speed segment point at the exit of a certain frame.

[0186] (5) For thin strip rolling in cold continuous rolling mills, in order to ensure the stability of the rolling force of each stand, a correction coefficient gain[pn][sp] needs to be added to the additional tension setting values ​​at each speed segment point between the stands. The purpose is to keep the additional tension setting values ​​within a certain range. Finally, the unit additional tension setting value between stands is:

[0187] sfta[pn][sp]=l_fta[pn][sp]×gain[pn][sp]÷b÷h

[0188] The additional tension control strategy is explained below.

[0189] The additional tension setting values ​​include the tension setting values ​​for eight speed segment points between stands, from low speed to high speed. In the actual rolling process, the specific additional tension setting value for each speed segment point is calculated as follows:

[0190] Based on the actual speed, the unit additional tension sfta[pn] at the current actual speed state is calculated using interpolation:

[0191]

[0192] Where v represents the actual speed;

[0193] sfta[pn][sp+1] represents the additional tension at the speed breakpoint sp+1 of the frame;

[0194] sfta[pn][sp] represents the additional tension at the speed breakpoint sp of the rack;

[0195] v act [pn][sp+1] represents the velocity at the frame velocity breakpoint sp+1;

[0196] v act [pn][sp] represents the velocity at the frame velocity breakpoint sp;

[0197] The velocity segment point sp+1 is the next velocity segment point after the velocity segment point sp;

[0198] Actual inter-rack tension setting:

[0199] fta[pn]=FT base +sfta[pn]×b×h

[0200] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0201] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for tension control in the production of ultra-thin strip steel in a cold continuous rolling mill, characterized in that, include: The steps for setting tension are: setting the total tension, the base tension, and the additional tension; Steps for setting additional tension: Unit additional tension setting value between computer racks; The steps for calculating the actual inter-rack tension setpoint based on the actual situation are as follows: Calculate the actual inter-rack tension setpoint; Ultra-thin strip steel refers to strip steel with a target thickness of less than or equal to 0.5 mm; The step of setting the tension includes: Indicates total tension; Indicates the basic tension; Indicates additional tension; This indicates the unit tension of the strip steel; Indicates the width of the strip; Indicates the thickness of the strip; The step of setting the additional tension includes: Steps to determine the velocity breakpoint: Calculate the velocity at each velocity segment point. : in, This indicates that the nth rack is at the (i+1)th velocity segment point. speed; Indicates the maximum speed of the rack; This represents the pow function; Indicates the belt threading speed of the frame; =0,1,2,3,4,5,6,M-1； This represents the nth stand of the cold continuous rolling mill. M represents the number of velocity segmentation points; The steps for calculating the influence coefficient of tension on rolling force at each speed segment point of each stand are as follows: Calculate the additional tension at the inlet : in, Indicates the tension of the rack inlet foundation; Calculate the additional tension at the outlet : in, Indicates the tension of the rack outlet foundation; Calculate rolling force parameters : Calculate rolling force parameters : Calculate rolling force parameters : Calculate the inlet tension efficiency factor : Calculate the outlet tension efficiency factor : The steps for calculating the additional inlet and outlet tension for each rack based on the inlet tension efficiency factor and the outlet tension efficiency factor are as follows: Calculation of rolling force parameters without additional tension : For frame #1, i.e., the first frame, only the additional tension at the outlet is calculated: For other racks, calculate the additional inlet and outlet tensions: The steps for calculating the additional tension setpoints at each speed segment point between each frame are as follows: Unit additional tension setting value between computer racks Steps: Indicates the correction factor; The step of calculating the actual inter-rack tension setting value based on the actual situation includes: Based on the actual speed, the unit additional tension at the current actual speed state is calculated using interpolation. : in Represents actual speed; This indicates the additional tension at the frame speed breakpoint sp+1; This indicates the additional tension at the frame speed breakpoint sp; This indicates the speed at the frame speed breakpoint sp+1; This indicates the speed at the speed segment point sp of the rack; The velocity segment point sp+1 is the next velocity segment point after the velocity segment point sp; Calculate the actual inter-frame tension setpoint : 。 2. The tension control method for ultra-thin strip production in a cold continuous rolling mill according to claim 1, characterized in that, By changing the additional tension setting, the fluctuation of rolling force during acceleration and deceleration is reduced.

3. A tension control system for ultra-thin strip steel production in a cold continuous rolling mill, characterized in that, include: The module for setting tension includes: setting total tension, basic tension, and additional tension; Module for setting additional tension: Unit additional tension setting value between computer racks; Module for calculating actual inter-rack tension settings based on actual conditions: Calculates actual inter-rack tension settings; Ultra-thin strip steel refers to strip steel with a target thickness of less than or equal to 0.5 mm; The module for setting the tension includes: Indicates total tension; Indicates the basic tension; Indicates additional tension; This indicates the unit tension of the strip steel; Indicates the width of the strip; Indicates the thickness of the strip; The module for setting additional tension includes: Module for determining velocity breakpoints: Calculate the velocity at each velocity segment point. : in, This indicates that the nth rack is at the (i+1)th velocity segment point. speed; Indicates the maximum speed of the rack; This represents the pow function; Indicates the belt threading speed of the frame; =0,1,2,3,4,5,6,M-1； This represents the nth stand of the cold continuous rolling mill. M represents the number of velocity segmentation points; A module for calculating the influence coefficient of tension on rolling force at each speed segment point of each stand: Calculate the additional tension at the inlet : in, Indicates the tension of the rack inlet foundation; Calculate the additional tension at the outlet : in, Indicates the tension of the rack outlet foundation; Calculate rolling force parameters : Calculate rolling force parameters : Calculate rolling force parameters : Calculate the inlet tension efficiency factor : Calculate the outlet tension efficiency factor : The module that calculates the additional inlet tension and additional outlet tension for each rack based on the inlet tension efficiency factor and the outlet tension efficiency factor: Calculation of rolling force parameters without additional tension : For frame #1, i.e., the first frame, only the additional tension at the outlet is calculated: For other racks, calculate the additional inlet and outlet tensions: Module for calculating the additional tension setpoints at each speed segment point between each frame: Unit additional tension setting value between computer racks Modules: Indicates the correction factor; The module that calculates the actual inter-rack tension setting value based on actual conditions includes: Based on the actual speed, the unit additional tension at the current actual speed state is calculated using interpolation. : in Represents actual speed; This indicates the additional tension at the frame speed breakpoint sp+1; This indicates the additional tension at the frame speed breakpoint sp; This indicates the speed at the frame speed breakpoint sp+1; This indicates the speed at the speed segment point sp of the rack; The velocity segment point sp+1 is the next velocity segment point after the velocity segment point sp; Calculate the actual inter-frame tension setpoint : 。 4. The tension control system for ultra-thin strip production in a cold continuous rolling mill according to claim 3, characterized in that, By changing the additional tension setting, the fluctuation of rolling force during acceleration and deceleration is reduced.

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