1. Why Cable Tension Control Matters: The Physics and Safety Imperative 为什么电缆张力控制很重要：物理学与安全命令

To understand the importance of properly setting motor torque on a Cavotec cable reel, we must first understand what happens to a cable when it is wound under tension. When electrical power is transmitted through a cable, the cable must be pulled tightly onto the reel to ensure good contact between successive layers, to prevent slippage, and to maintain a compact coil geometry that minimizes reel size. However, there is a limit to how much tension a cable can withstand before the material itself begins to fail. This limit, expressed in units of stress (force per unit area, typically in newtons per square millimeter), is fundamental to the cable’s design and safety.

For NSHTÖU cables, this limit is 15 newtons per square millimeter. This specification is not arbitrary—it is determined through extensive materials testing and represents the maximum sustained tensile stress that the copper conductors and the surrounding insulation can endure without permanent plastic deformation or rupture. When a cable is subjected to tension exceeding this limit, the copper conductors begin to yield, permanently elongating and losing mechanical strength. The insulation, which is bonded to the conductors, separates from them as the conductors stretch. The result is a cable that may appear to function electrically but is mechanically compromised and unsafe for continued operation.

The challenge for the electrical engineer is to set the motor torque correctly so that the cable reaches the desired tension for reliable winding without exceeding the safe limit. This requires understanding the mathematical relationship between motor torque (measured in newton-meters), cable tension (measured in newtons), and the physical dimensions of the winding process.

1.1 The Economics of Proper Tension Setting 正确张力设置的经济性

Beyond safety, there is an economic dimension to tension control. If tension is set too low, the cable does not wind compactly, leading to inefficient reel geometry and wasted space. The reel becomes larger and heavier than necessary, increasing equipment cost and operational burden. Multiple reels may be needed where a single well-designed reel would suffice. Conversely, if tension is too high, cable life is shortened due to accelerated degradation of the insulation under sustained stress. Replacement costs and associated downtime add up. The engineer’s goal is to find the optimal balance—high enough tension to achieve efficient, reliable winding, but low enough to protect the cable’s long-term integrity. The formula and methodology in this article enable that optimization.

2. Understanding the Relationship Between Motor Torque and Cable Tension 理解电机扭矩与电缆张力的关系

Before diving into formulas, it is important to understand the mechanical relationship between torque and tension. Torque is the rotational force applied by the motor, measured in newton-meters. It represents the motor’s ability to rotate the reel against resistance. Cable tension is the linear pulling force on the cable, measured in newtons. It represents the stress the cable experiences.

The connection between these two quantities is the radius at which the force is applied. If the motor applies a torque to the reel through a gearbox, that torque is transmitted to the reel shaft. The reel shaft then transmits force to the cable at a distance equal to the reel’s radius. By the principle of moments (or torque), the force exerted on the cable is equal to the torque divided by the radius. Mathematically, this is the foundation of our calculation.

2.1 The Lever Principle in Reel Systems 卷筒系统中的杠杆原理

Think of a Cavotec reel as a giant lever. The motor is the force source. The reel drum is the lever arm, with its radius being the lever length. The cable being wound is where the force is applied and felt. If you have a motor producing 1000 newton-meters of torque, and the reel drum has a radius of 1 meter, the tension on the cable will be approximately 1000 newtons (assuming ideal conditions). If the reel radius is half a meter, the same motor torque produces twice the cable tension (2000 newtons). This inverse relationship between radius and tension is critical to understand, because as a cable is wound onto a reel, the effective radius increases with each layer added. A motor set to a fixed torque will produce increasingly high cable tension as the reel fills up. This is why advanced reel systems like Cavotec employ active tension control rather than simple constant-torque operation.

3. Core Cable Tension Formula and Its Components 核心电缆张力公式及其组件

Now we arrive at the mathematical foundation of tension control. The formulas are derived from basic mechanical principles, but their application requires careful attention to the physical parameters involved.

3.1 Maximum Allowable Tension 最大允许张力

The first step in any tension calculation is to determine the maximum tension that the cable can safely withstand. This is calculated by multiplying the maximum allowable stress (in newtons per square millimeter) by the total cross-sectional area of all the load-bearing conductors in the cable. For a cable with multiple cores, this means summing the cross-sectional areas of each core.

For example, if an NSHTÖU cable has three power conductors each with a cross-section of 50 square millimeters, the total conductor area is 150 square millimeters. The maximum allowable tension is therefore 15 × 150 = 2,250 newtons. This represents the absolute limit—the tension at which the cable will begin to be damaged. In practice, engineers design systems to operate well below this limit, typically at 60 to 80 percent of the maximum, to provide a safety margin.

3.2 Motor Torque Required to Achieve a Target Tension 实现目标张力所需的电机扭矩

The second formula relates the desired cable tension to the motor torque that must be applied. This formula accounts for the mechanical efficiency of the drive system—the gearbox and bearings are not perfect, and some energy is lost to friction.

This formula is the heart of the engineering calculation. The numerator (F times R) represents the mechanical torque required at the reel drum to produce the desired cable tension. The denominator divides by the efficiency to account for losses in the drive train. If the efficiency is 90 percent (η = 0.90), then the motor must produce about 11 percent more torque than the mechanical requirement to compensate for losses.

3.3 The Challenge of Variable Radius 变量半径的挑战

Here lies a subtle but critical complication. As cable is wound onto the reel, the effective radius (the distance from the reel’s center to the outer surface of the wound cable) increases. With the first layer of cable, the radius might be 0.5 meters. With the second layer added, it might be 0.6 meters. With the third and fourth layers, it might be 0.7 and 0.8 meters respectively. If the motor is set to a constant torque, the cable tension will increase proportionally to the radius. This means that as the reel fills up, the cable experiences increasing tension, and near the end of winding, the tension may exceed the safe limit even though the motor torque is unchanged.

This is why modern Cavotec reel systems do not use simple constant-torque control. Instead, they use constant-tension control, where the motor torque is continuously adjusted to maintain a constant cable tension as the radius changes. However, to set up such a system, the engineer must first understand the radius dynamics and calculate what constant torque (if any) would be appropriate for single-layer winding or other specific scenarios.

4. NSHTÖU Cable Specifications and Tensile Strength Limits NSHTÖU 电缆规格与拉力极限

NSHTÖU cables are designed for low-voltage reeling applications in industrial, mining, and port environments. The “NSHTÖU” designation indicates a cable conforming to standards including VDE 0250-814 and similar international equivalents. These cables are characterized by flexible Class 5 stranded copper conductors, EPR (ethylene propylene rubber) insulation, and a resilient outer sheath designed to withstand mechanical abuse.

Table 1 presents the complete specifications for commonly deployed NSHTÖU cables. The “Maximum Tension” column is calculated by multiplying 15 N/mm² by the total cross-sectional area of the load-bearing conductors. For example, a 4 G 25 cable has four conductors of 25 square millimeters each, totaling 100 square millimeters. The maximum tension is therefore 15 × 100 = 1,500 newtons.

Notice that the “G” designation indicates cables with ground/earth conductors included. These earth conductors contribute to the total cross-sectional area for purposes of calculating maximum tension, but in real-world installations, only the power conductors typically carry the main load. Some engineers choose to calculate maximum tension using only the power conductor area, providing an additional safety margin. This conservative approach is particularly appropriate in applications where the earth conductors might be sized smaller than the power conductors.

5. Cavotec Motorized Reel Systems: Configuration and Control Principles Cavotec 电机化卷筒系统：配置与控制原理

Cavotec is a leading supplier of cable reel systems for industrial applications. Their motorized reels are distinguished by sophisticated control systems that manage cable tension, motor speed, and safety interlocks. Understanding how a Cavotec system is configured is essential to properly calculating and setting motor torque.

5.1 Typical Cavotec Reel Architecture 典型的 Cavotec 卷筒结构

A Cavotec motorized reel system typically consists of several key components: an electric motor (usually AC induction, ranging from 1 kW to 30+ kW depending on application), a gearbox (reducing high-speed motor shaft rotation to slower reel drum rotation), a reel drum (the actual cylinder onto which cable is wound), and a control unit (the electronics that manage acceleration, deceleration, tension monitoring, and safety functions). The control unit is crucial—it not only sets the motor torque but also continuously monitors cable tension through a load cell or hydraulic pressure sensor, adjusting the torque to maintain the desired setpoint as the reel radius changes.

5.2 Constant-Tension vs. Constant-Torque Operation 恒张力 vs 恒扭矩运行

Modern Cavotec systems typically operate in constant-tension mode for cable winding, where the control electronics continuously adjust motor current (and therefore torque) to maintain a user-set tension target. However, the engineer setting up the system must first determine what the appropriate tension target should be. This is where our formula comes in. The engineer calculates the maximum allowable tension based on the cable type, then sets the constant-tension target to 60–80 percent of that maximum, providing a safety margin. The Cavotec control unit then manages the detailed implementation, adjusting torque moment-by-moment to maintain that tension as the reel fills.

6. Step-by-Step Torque Calculation Methodology 逐步扭矩计算方法

Now that we understand the components, we can work through the calculation process systematically. This methodology applies to any scenario where you need to determine motor torque for NSHTÖU cable on a Cavotec or similar motorized reel.

6.1 Gather Required Information 收集所需信息

Before any calculation, you must identify and record several key parameters. These include the cable type and conductor configuration (which determines the cross-sectional area and therefore maximum tension), the reel drum diameter (which determines the radius), the mechanical efficiency of the drive system (which you should obtain from Cavotec specifications or the gearbox manufacturer), and the desired operating tension (which should be 60–80 percent of the calculated maximum).

6.2 Calculate Maximum Allowable Tension 计算最大允许张力

Use the formula F_max = σ × A, where σ is 15 N/mm² for NSHTÖU, and A is the total conductor cross-section. Look up A in Table 1 or in the cable manufacturer’s documentation.

6.3 Determine Working Tension 确定工作张力

Multiply F_max by 0.70 to obtain a conservative working tension at 70 percent of maximum. Some aggressive operations use 0.80 (80 percent), but 0.70 is recommended for long cable life and reliability. If you are uncertain, consult the cable manufacturer or use the more conservative figure.

6.4 Identify Effective Reel Radius 识别有效卷筒半径

The effective radius is the distance from the reel’s center to the outer surface of the wound cable. For initial winding calculations, use the bare drum radius (the radius of the empty reel). For later-stage winding (when layers are already accumulating), account for the added radius contributed by previously wound layers. Typically, each layer of cable adds approximately twice the cable’s outer diameter to the radius.

6.5 Determine Drive System Efficiency 确定驱动系统效率

The mechanical efficiency accounts for energy losses in the gearbox and bearings. For Cavotec systems, typical efficiency ranges from 0.85 to 0.95. If you do not have specific data, use 0.90 as a conservative estimate. Higher efficiency numbers (closer to 0.95) apply to newer, well-maintained systems; lower numbers apply to older or heavily loaded systems.

6.6 Calculate Required Motor Torque 计算所需电机扭矩

Apply the formula M = (F × R) / η, substituting the working tension, current reel radius, and efficiency. The result is the motor torque (in newton-meters) that should be set in the Cavotec control unit.

7. Practical Calculation Examples with Real-World Dimensions 使用实际尺寸的实际计算示例

7.1 Example 1: Port Crane with 4 G 35 Cable on Empty Reel 例子 1：港口吊机在空卷筒上使用 4 G 35 电缆

Scenario: A port crane operator is commissioning a new cable reeling system using Cavotec equipment. The cable is NSHTÖU 4 G 35 (four conductors of 35 mm² each, plus earth conductors). The reel drum has a bare radius of 0.45 meters. The drive system (motor and gearbox) has a rated efficiency of 0.92.

Step 1 — Calculate maximum allowable tension. From Table 1, NSHTÖU 4 G 35 has a total conductor area of 4 × 35 = 140 mm² (counting only the power conductors; ignoring earth conductors for this calculation). F_max = 15 × 140 = 2,100 newtons.

Step 2 — Determine working tension. To operate conservatively at 70 percent of maximum: F_working = 0.70 × 2,100 = 1,470 newtons.

Step 3 — Identify reel radius. The bare drum radius is 0.45 meters. Since this is the initial winding (empty reel), we use this value directly.

Step 4 — Determine efficiency. The Cavotec system specification indicates η = 0.92.

Step 5 — Calculate motor torque. M = (1,470 × 0.45) / 0.92 = 661.5 / 0.92 = 719 Nm. Round to 720 Nm for the control unit setpoint.

Conclusion: The Cavotec control unit should be programmed to maintain a constant cable tension of 1,470 newtons (or approximately 150 kilograms-force, if displayed in those units). When the motor operates at constant tension, it will automatically adjust its torque from 720 Nm initially (at the empty reel) down to lower values as the reel radius increases and cable layers accumulate. This maintains the constant tension target throughout the winding cycle.

7.2 Example 2: Mining Shovel Cable with Three Layers Already Wound 例子 2：已缠绕三层的矿山铲斗电缆

Scenario: A mining operation is retrieving an NSHTÖU 3 × 120 + 3 G 70/3 cable from its Cavotec reel. Three layers of cable have already been wound, and the operator needs to know what motor torque should be set to safely wind the fourth layer. The bare drum radius is 0.55 meters. Each cable layer has an outer diameter of approximately 65 millimeters, contributing 0.065 meters to the radius.

Step 1 — Maximum allowable tension. From Table 1, 3 × 120 + 3 G 70/3 has approximately 360 mm² (3 × 120) of power conductor area. F_max = 15 × 360 = 5,400 newtons.

Step 2 — Working tension. F_working = 0.70 × 5,400 = 3,780 newtons.

Step 3 — Current reel radius. With three layers already wound, the effective radius is approximately 0.55 + (3 × 0.065) = 0.55 + 0.195 = 0.745 meters.

Step 4 — Efficiency. The Cavotec system is specified at η = 0.90.

Step 5 — Calculate torque. M = (3,780 × 0.745) / 0.90 = 2,816 / 0.90 = 3,129 Nm. Round to 3,130 Nm.

Conclusion: With three layers already wound and the reel radius expanded to 0.745 meters, the required motor torque to maintain 3,780 newtons of tension is about 3,130 newton-meters. Notice this is significantly higher than Example 1, not because the tension is much higher, but because the reel radius is larger. This illustrates why constant-tension control is essential—without it, the torque would need to be continuously adjusted by the operator as the reel fills.

8. Dynamic Loading and Acceleration Considerations 动态负载与加速度考虑

The calculations above assume steady-state winding, where the motor is running at constant speed and cable tension is stable. In reality, Cavotec reels frequently undergo acceleration and deceleration cycles. When the motor accelerates to speed up the winding, inertial forces create additional loads on the cable. When the motor decelerates, these inertial forces can actually reduce the net tension. A properly engineered system accounts for these dynamic effects.

8.1 Inertial Load During Acceleration 加速期间的惯性负载

When the motor accelerates the reel from zero speed to operating speed, the inertia of the reel (and any wound cable already on it) resists this acceleration. By Newton’s second law, this resistance manifests as an additional force on the cable beyond the steady-state tension. The magnitude of this additional force depends on the reel’s moment of inertia and the acceleration rate. For conservative design, the total cable stress during acceleration should not exceed 80 percent of the maximum allowable stress, allowing for the additional inertial loading. This means that the steady-state working tension might need to be set somewhat lower than 70 percent of maximum to ensure safety during transient acceleration phases.

8.2 Cavotec Acceleration Ramp Control Cavotec 加速斜坡控制

Cavotec reel control units typically offer programmable acceleration ramp settings. By extending the acceleration period (ramping the motor up slowly rather than applying full torque suddenly), the peak inertial loads are reduced. The control electronics can be configured to limit the rate of torque change, ensuring that both steady-state and transient cable stresses remain within safe limits. When commissioning a system, the acceleration ramp should be set based on careful calculation of inertial loads, or more conservatively, by testing and measurement under actual operating conditions.

9. Safety Margins and Conservative Design Practices 安全裕度与保守设计实践

Throughout this article, we have emphasized conservative design—choosing working tensions at 60–70 percent of maximum, rather than pushing toward 80 percent or higher. This is deliberate. In real-world industrial operations, conditions are often more variable and unpredictable than laboratory tests. Environmental temperature fluctuations affect material properties. Cable age and prior history of stress affect remaining capacity. Vibration and dynamic loads introduce uncertainties. The electrical engineer should embrace conservatism, knowing that a system designed with 30-percent margin is more likely to operate reliably over its full service life without premature cable failure.

10. Commissioning Procedures and Verification Testing 调试程序与验证测试

After calculating the appropriate motor torque and entering it into the Cavotec control unit, the system should not be simply turned on at full power. Instead, a structured commissioning process should be followed to verify that the calculated values match real-world behavior.

10.1 No-Load Test 空载测试

First, run the motor without any cable on the reel. This verifies that the motor and control unit are functioning correctly and that mechanical systems (bearings, gearbox) are operating smoothly. Observe motor speed, listen for unusual noises, and check that the control unit displays reasonable values.

10.2 Light-Load Test 轻载测试

Next, install a small amount of cable (perhaps 10–20 meters) and run at low motor speed with the tension control set to a low value (perhaps 30–40 percent of the calculated working tension). Observe the tension readout on the control unit’s display or a load cell mounted on the cable. Verify that the displayed tension matches expectations. If it does not, check for mechanical issues or recalibration needs in the load cell or control electronics.

10.3 Progressive Load Test 渐进负载测试

Gradually increase both the motor speed and the tension setpoint, winding more cable while monitoring the tension readout. As you approach the designed working tension (70 percent of maximum), watch for any signs of cable slippage, unusual motor sounds, or unexpected control behavior. The cable should wind smoothly and compactly without visible slack or excessive tension.

10.4 Full-Load Test 满负载测试

Once several layers are wound, run a final test with the motor at normal operating speed and tension at the design setpoint. Monitor the tension readout to verify that it remains stable as successive layers are wound. If the tension drifts significantly, there may be an issue with the load cell calibration or the control algorithm. Document the results and make any necessary adjustments to the setpoint before returning the reel to normal service.

11. Common Mistakes and How to Avoid Them 常见错误以及如何避免它们

11.1 Setting Constant Torque Instead of Constant Tension 设置恒定扭矩而不是恒定张力

The most common mistake is to program the Cavotec control unit for constant motor torque rather than constant cable tension. With constant torque, as the reel radius increases (as cable layers accumulate), the cable tension increases proportionally. By the time the fourth or fifth layer is being wound, the cable may be under 1.5 times or 2 times the initial tension. This can easily exceed the safe limit and damage the cable. Always use the constant-tension feature of the control unit, if available. If the system does not support constant tension (an older system), then torque must be manually adjusted as the reel fills, which is labor-intensive and error-prone.

11.2 Neglecting Efficiency Losses 忽视效率损失

Some engineers use the formula M = F × R without dividing by efficiency, assuming the mechanical efficiency is negligible. This leads to motor torque settings that are too low. The motor cannot deliver the desired cable tension because the calculated torque does not account for gearbox and bearing friction losses. The result is that the cable winds with less tension than intended, potentially leaving slack or uneven pressure between layers.

11.3 Using Bare Drum Radius for All Layers 对所有层使用裸卷筒半径

Some engineers calculate the required torque once, using the bare drum radius, and assume that same torque applies throughout the entire winding process. This fails to account for the increasing radius as cable layers accumulate. If the torque is held constant while the radius increases, the cable tension increases dramatically. The opposite mistake—using a fully loaded radius for initial winding—results in excessive torque at the start, potentially damaging the first layers. The radius must be updated as layers accumulate, or the system must employ automatic constant-tension control that handles this variation.

11.4 Exceeding the 15 N/mm² Limit in Safety Calculations 在安全计算中超过 15 N/mm² 的极限

Some operators or engineers, seeing that a cable is rated for 15 N/mm², set the working tension right at 14 or 15 N/mm² to maximize reel capacity. This leaves no safety margin. Any transient overload, any inaccuracy in the load cell, or any unexpected acceleration will push the cable beyond its rated limit. The safe practice is to limit working tension to 60–70 percent of the rated maximum, which is 9–10.5 N/mm² for NSHTÖU. This seems conservative, but it provides essential margin against the unexpected.

12. Cavotec System-Specific Considerations Cavotec 系统特定注意事项

12.1 Cavotec Control Unit Display and Setpoint Entry Cavotec 控制单元显示与设定值输入

Cavotec control units typically display cable tension in units of newtons (N) or kilogram-force (kgf). The control panel has buttons or a touchscreen interface for entering the desired tension setpoint. The electrical technician commissioning the system should verify the unit of display before entering the calculated tension value. Confusing newtons with kilogram-force (where 1 kgf ≈ 9.81 N) would result in setting tension either too high or too low by nearly an order of magnitude.

12.2 Load Cell Calibration 负荷传感器校准

The Cavotec reel’s load cell (the sensor that measures cable tension) requires periodic calibration to ensure accuracy. A load cell that has drifted or become miscalibrated will display incorrect tension readings, leading to incorrect motor torque settings. Before commissioning, request that the installer perform a calibration check. If readings seem inconsistent during testing, suspect load cell calibration and request recalibration.

12.3 Cavotec Hoist Speed and Acceleration Limits Cavotec 提升速度与加速度限制

Cavotec control units offer programmable limits on motor speed and acceleration rate. These should be set conservatively to ensure smooth, predictable cable winding without shock loads. Typical applications use acceleration ramps of 2–5 seconds to bring the motor from zero to full operating speed, rather than instantaneous full-power acceleration. This extended ramp reduces inertial stress on the cable and on the mechanical components.

13. Frequently Asked Questions 常见问题

Q: If I set the tension to 70 percent of maximum and the load cell reads exactly that value, am I safe? 如果我将张力设置为最大值的 70%，并且负荷传感器读数正好是这个值，我是否安全？

Not necessarily. The load cell reading tells you what the steady-state cable tension is at that moment, but it does not account for dynamic effects during acceleration or deceleration, nor does it reveal whether the cable has already been damaged by prior overstress. If the cable has been repeatedly stressed near the limit before this commissioning, it may have weakened. Additionally, if acceleration ramps are set too aggressively, the actual peak stress during acceleration could exceed the static reading. To be truly safe, use a load cell reading of 60–65 percent of maximum as your working setpoint, leaving room for transient effects.

Q: Can I exceed the 15 N/mm² limit temporarily during acceleration, as long as the steady-state tension is within limits? 只要稳态张力在限制内，我能否在加速期间暂时超过 15 N/mm² 的极限？

No. The 15 N/mm² limit applies to all stresses the cable experiences, whether steady-state or transient. Allowing brief excursions beyond this limit will cause cumulative damage to the copper conductors and insulation. Each overstress event reduces the cable’s remaining life. If your acceleration profile causes overstress, extend the acceleration ramp to reduce inertial loads. Better to take an extra few seconds to reach full speed than to shorten cable life by months or years.

Q: What if my reel has an unusually large diameter—say, 2 meters radius instead of the typical 0.5 meters? Does the formula still apply? 如果我的卷筒直径异常大——比如 2 米半径而不是典型的 0.5 米？公式是否仍然适用？

Yes, the formula still applies. A larger reel radius means a larger tension for any given torque, so the motor torque required to achieve a safe cable tension would be correspondingly lower. For example, with a 2-meter radius instead of 0.5 meters, you would need only one-fourth the torque (all else being equal). The advantage of larger reels is that they require less motor power for the same cable tension, but they are heavier and more cumbersome. The formula adapts to any geometry.