In our investigation of mobile space launch pads, we have focused on the heavy-duty screw gears that enable mode transformation between launch and transport configurations. These screw gears are critical components in the supporting arms and conversion devices, and their reliable operation directly affects the success of launch missions. When resistance increases or seizure occurs, the entire launch pad may fail to perform its required functions. Therefore, I analyzed the factors that cause increased transmission resistance in these screw gears and designed a series of experiments to quantify the influence of lubrication, positioning and guidance, bearing corrosion, rotational speed, and transmission cycles. The screw gears in question are not ordinary power screws; they are large-scale, heavily loaded mechanisms that must operate under extreme conditions, including high axial loads, seawater spray, long storage periods, and repeated launch cycles. Our goal was to establish a systematic understanding of how each factor contributes to resistance and to provide design and maintenance guidance for future heavy-lift launch platforms.
The functional principle of the screw gears used in the supporting arm and conversion device is as follows. A hydraulic motor provides input torque, which is amplified by a reducer with a fixed transmission ratio. The reducer output drives the screw shaft. The thread pair converts the rotational motion of the screw into the linear motion of the nut. The nut is integrated with an inner sleeve, so the inner sleeve moves up and down as the screw rotates. The screw gears thus act as the primary motion conversion element. The overall transmission ratio from the motor to the screw shaft is 604:1, meaning that the screw rotates very slowly while producing a large axial force. The relationship between the motor torque and the screw torque can be expressed as:
$$T_{screw} = i \, \eta_{reducer} \, T_{motor}$$
where \(T_{screw}\) is the torque on the screw shaft, \(i = 604\) is the reduction ratio, \(\eta_{reducer}\) is the efficiency of the reducer, and \(T_{motor}\) is the hydraulic motor output torque. The axial force \(F\) generated by the screw gears is related to the screw torque by the thread geometry:
$$T_{screw} = F \frac{d_2}{2} \tan(\lambda + \rho)$$
where \(d_2\) is the pitch diameter of the thread, \(\lambda\) is the lead angle, and \(\rho\) is the friction angle. The friction angle depends on the coefficient of friction \(\mu\) between the screw and nut materials: \(\rho = \arctan \mu\). Therefore, any increase in friction coefficient directly increases the required torque for a given axial load, which manifests as increased transmission resistance. The screw gears are designed with a material combination of 38CrMoAl or 40Cr for the screw and ZCuAl10Fe3 for the nut. The nut is the sacrificial component and is expected to wear over time.
We constructed a fault mode analysis model for increased resistance in the screw gears. The model identified eight primary influencing factors: bearing corrosion, lack of lubrication in the thread pair, thread wear, corrosion of the circular nut, failure of the circular nut limit, over-constraint, lack of lubrication in the reducer, and foreign objects. Each factor affects the resistance through different mechanisms. I will describe each mechanism in detail and then present the experimental studies that we conducted to quantify their effects.
Bearing corrosion is a major contributor to increased resistance. The bearings in the screw gears are designed with a safety factor of 3 to 4, so roller fracture is unlikely under normal design loads. However, during long-term storage or operation in humid and salty environments, the bearing rollers and races can corrode. Corrosion increases the rolling friction coefficient and may even transform rolling contact into rolling-sliding contact. The friction torque of a corroded bearing can be modeled as:
$$M_{bearing} = f_1 F d + f_0 \nu n d^3$$
where \(f_1\) is a coefficient related to the bearing type and load, \(F\) is the equivalent dynamic load, \(d\) is the bearing bore diameter, \(f_0\) is a coefficient related to lubrication and bearing type, \(\nu\) is the kinematic viscosity of the lubricant, and \(n\) is the rotational speed. When corrosion occurs, \(f_1\) and \(f_0\) both increase, leading to higher friction torque. Because the screw gears are difficult to disassemble for inspection, internal corrosion can remain undetected until resistance becomes severe.
Lack of lubrication in the thread pair is another critical factor. The original design uses a 7403 wide-temperature grease, which has high load-carrying capacity, a wide operating temperature range, and low loss. However, its high viscosity makes it impossible to replenish through a grease gun. The screw gears must be fully disassembled, cleaned, and re-greased. During launch, water spray, and natural storage, the grease can gradually be lost, washed away, or degraded. Once the grease is depleted, the friction coefficient between the screw and nut increases, and the thread friction torque rises. The thread friction torque is given by:
$$T_{thread} = \frac{F d_2}{2} \tan \rho$$
where \(\rho = \arctan \mu\). For a well-lubricated thread, \(\mu\) may be as low as 0.05 to 0.10; for a dry or poorly lubricated thread, \(\mu\) can exceed 0.15 to 0.20. This difference can double the thread friction torque.
Thread wear is inevitable with repeated use. The nut material ZCuAl10Fe3 is softer than the screw material, so the nut threads wear first. As wear progresses, the surface roughness increases, the contact area becomes uneven, and the friction torque rises. The wear rate can be approximated by Archard’s law:
$$V = k \frac{F_n s}{H}$$
where \(V\) is the wear volume, \(k\) is the wear coefficient, \(F_n\) is the normal load, \(s\) is the sliding distance, and \(H\) is the hardness of the softer material. For the screw gears, the sliding distance per cycle is \(s = \pi d_2 N\), where \(N\) is the number of revolutions per cycle. Over many cycles, the accumulated wear changes the thread profile and increases resistance.
The circular nut is installed at the bottom of the screw shaft. It is used for axial positioning of the screw, adjustment of the bearing axial clearance, and bearing the tensile load from the supporting arm. It contacts the upper seat bushing through a stop washer or stop block. If the circular nut or stop washer corrodes, the friction coefficient between the contact surfaces increases. When the circular nut rotates with the screw, the friction resistance at the contact surface rises, contributing to the overall resistance. The friction torque at this interface is:
$$T_{nut} = \mu_{nut} F_{axial} r_{contact}$$
where \(\mu_{nut}\) is the friction coefficient of the corroded interface, \(F_{axial}\) is the axial load, and \(r_{contact}\) is the effective contact radius. Corrosion can increase \(\mu_{nut}\) from 0.1 to 0.3 or higher.
Failure of the circular nut limit can cause self-locking. If the limit fails, the circular nut may rotate relative to the screw due to friction, and the end face friction resistance gradually increases. This self-locking action also imposes additional axial loads on the thread pair and bearings, further increasing resistance. The self-locking condition occurs when the friction angle exceeds the lead angle:
$$\rho > \lambda$$
Under self-locking, the screw gears may become impossible to back-drive, and the resistance can increase dramatically.
Over-constraint is a subtle but important factor. In the screw gears, the inner sleeve moves up and down with the nut. The inner sleeve is radially positioned by the thread pair and also by guide parts such as the copper sleeve and upper seat bushing. Ideally, the guide parts should not bear radial forces. However, due to manufacturing errors, the axis of the inner sleeve may not coincide with the axis of the screw. The load application point may not lie exactly on the axis. The thread load distribution is not uniform due to elastic deformation. As the inner sleeve moves, the screw pair has some play due to manufacturing errors. These effects cause the inner sleeve to experience a radial tilting force. The inner sleeve then presses against the guide parts, creating over-constraint and additional friction. The additional friction torque due to over-constraint can be expressed as:
$$T_{over} = \mu_{guide} N_{radial} r_{guide}$$
where \(\mu_{guide}\) is the friction coefficient between the inner sleeve and guide parts, \(N_{radial}\) is the radial contact force caused by tilting, and \(r_{guide}\) is the effective radius of the guide surface. Reducing over-constraint by optimizing the clearance or removing unnecessary guide surfaces can significantly lower resistance.
Lack of lubrication in the reducer also affects the overall resistance. The reducer transmits torque from the motor to the screw gears. If the lubricating oil in the reducer becomes viscous, leaks, or oxidizes, the gears, shafts, and bearings inside the reducer are not properly lubricated or cooled. This accelerates wear and reduces transmission efficiency. The reducer efficiency \(\eta_{reducer}\) decreases, and the motor must provide higher pressure to overcome the internal losses. The relationship between motor pressure and resistance can be written as:
$$\Delta p = \frac{2\pi T_{total}}{V_m \eta_m \eta_{reducer}}$$
where \(\Delta p\) is the motor pressure difference, \(T_{total}\) is the total resistance torque of the screw gears, \(V_m\) is the motor displacement, and \(\eta_m\) is the motor efficiency. An increase in \(T_{total}\) or a decrease in \(\eta_{reducer}\) both raise the required pressure.
Foreign objects in the thread pair can cause severe damage. The nut material is softer than the screw material, so hard particles trapped between the threads will indent and scratch the nut threads. This increases surface roughness and friction. In extreme cases, foreign objects can cause thread fracture, leading to seizure. The contact pressure in the thread pair is high, so even small particles can cause significant damage. The contact pressure can be estimated by:
$$p = \frac{F}{A_{contact}}$$
where \(A_{contact}\) is the actual contact area between the threads. For heavy loads, \(p\) can exceed the yield strength of the nut material, causing plastic deformation and accelerated wear.
To quantify the influence of these factors, we designed a series of experiments. The experiments included lubrication grease tests, positioning and guidance tests, bearing corrosion tests, rotational speed tests, and transmission cycle tests. For the comparison tests, we performed three lifting and lowering cycles. For the transmission cycle test, we performed 60 cycles. All tests used a load that was gradually increased to 180 t, a lifting stroke of 24 mm, and a screw rotational speed of 80 rpm unless otherwise specified. The measured variable was the torque at the reducer output, which is directly related to the resistance of the screw gears.
The lubrication grease test compared two greases: a calcium-based grease according to GB/T491-2008 and the 7403 wide-temperature grease. The screw and nut were cleaned and coated with each grease separately. The load was increased stepwise to 180 t. The results are summarized in Table 1.
| Test Item | Load | Lifting Stroke (mm) | Screw Speed (rpm) |
|---|---|---|---|
| Clean screw and nut, coat with 7403 grease | Stepwise to 180 t | 24 | 80 |
| Clean screw and nut, coat with calcium-based grease | Stepwise to 180 t | 24 | 80 |
Table 1. Lubrication grease influence test conditions.
The resistance torque data showed that the calcium-based grease produced lower resistance than the 7403 grease at all load levels. After disassembly, the screw and nut surfaces coated with calcium-based grease had a more uniform oil film. The percentage increase in resistance torque with 7403 grease relative to calcium-based grease was calculated as:
$$\Delta T = \frac{T_{7403} – T_{Ca}}{T_{Ca}} \times 100\%$$
The results were 18% at 50 t, 21% at 100 t, 12% at 150 t, and 8% at 180 t. These data indicate that the calcium-based grease reduces resistance more effectively at low and medium loads. At 180 t, the two greases converged in performance because the load-carrying capacity of the calcium-based grease is lower than that of the 7403 grease. As the thread contact pressure increases, the calcium-based grease may be squeezed out, reducing its lubrication effect. Therefore, for heavy-duty screw gears, the grease selection must balance low viscosity for efficiency and high pressure capacity for load carrying.
The positioning and guidance test investigated the effect of over-constraint. We tested three configurations: increasing the inner diameter of the upper bushing and copper sleeve by 0.3 to 0.5 mm, removing the copper sleeve, and removing the upper bushing. The test conditions are shown in Table 2.
| Test Item | Load | Lifting Stroke (mm) | Screw Speed (rpm) |
|---|---|---|---|
| Increase inner diameter of upper bushing and copper sleeve by 0.3–0.5 mm | Stepwise to 180 t | 24 | 80 |
| Remove copper sleeve | Stepwise to 180 t | 24 | 80 |
| Remove upper bushing | Stepwise to 180 t | 24 | 80 |
Table 2. Positioning and guidance influence test conditions.
The results showed that increasing the inner diameter of the upper bushing by 0.3 to 0.5 mm had almost no effect on the transmission resistance. However, removing the copper sleeve or the upper bushing significantly reduced the resistance torque compared with the original assembly. The resistance data were more stable when the upper bushing was removed. The reduction was more pronounced as the load increased. This confirms that the guide surfaces impose an over-constraint on the inner sleeve, and the resulting radial forces contribute to the resistance. The additional resistance torque due to over-constraint can be estimated from the difference between the original configuration and the configuration without the guide parts. The results suggest that optimizing the guide surface design, such as increasing clearance or using self-aligning bearings, can effectively reduce the resistance of the screw gears.
The bearing corrosion test compared new bearings with corroded bearings. The corroded bearings had visible rust on the rollers and races. The test used the same loading and speed conditions as the previous tests. The results are shown in Table 3.
| Test Item | Load | Lifting Stroke (mm) | Screw Speed (rpm) | Resistance Increase at 180 t |
|---|---|---|---|---|
| New bearings | Stepwise to 180 t | 24 | 80 | Reference |
| Corroded bearings | Stepwise to 180 t | 24 | 80 | Approximately 50% |
Table 3. Bearing corrosion influence test results.
The data showed that corroded bearings had a dramatic effect on the resistance torque of the screw gears. At 180 t, the resistance increased by about 50% compared with new bearings. The effect became more pronounced as the load increased. This is because the corroded bearing surfaces increase the rolling friction coefficient, and the friction torque is proportional to the load. Therefore, controlling bearing corrosion through proper sealing, lubrication, and periodic inspection is essential for maintaining the normal resistance range of the screw gears. In coastal humid and salt-spray environments, corrosion protection measures such as stainless steel bearings, protective coatings, and sealed housings should be considered.
The rotational speed test examined the effect of screw speed on resistance. The screw speed was set by the motor speed through the 604:1 reducer. We tested motor speeds of 40 rpm, 60 rpm, and 80 rpm, corresponding to screw speeds of 0.067 rpm, 0.099 rpm, and 0.13 rpm. The test conditions are listed in Table 4.
| Test Item | Load | Lifting Stroke (mm) | Motor Speed (rpm) |
|---|---|---|---|
| Low speed | Stepwise to 180 t | 24 | 40 |
| Medium speed | Stepwise to 180 t | 24 | 60 |
| High speed | Stepwise to 180 t | 24 | 80 |
Table 4. Rotational speed influence test conditions.
The results showed that the efficiency from the motor to the reducer output did not change significantly with speed. However, the transmission resistance of the screw gears increased with speed. At 80 rpm, the resistance torque was higher than at 40 rpm by approximately 8% at 180 t, 11% at 150 t, 16% at 100 t, and 10% at 50 t. This indicates that the screw gears themselves are sensitive to speed, likely due to viscoelastic effects in the lubricant and increased hydrodynamic drag in the thread contacts. At low speeds and heavy loads, the load distribution in the screw gears becomes uneven, causing fluctuations in the motor and reducer, which can lead to jerky motion. Our tests confirmed that low-speed operation under heavy load can reduce stability. Therefore, for smooth operation, a moderate speed should be selected, but the speed should not be so high that resistance increases excessively.
The transmission cycle test investigated the effect of repeated lifting and lowering on resistance. We performed 60 cycles under a load of 180 t, a stroke of 24 mm, and a screw speed of 80 rpm. The resistance torque was recorded at each cycle. The results showed that the resistance gradually increased over the 60 cycles. The increase was approximately 16% compared with the initial cycle. After the test, the screw gears were disassembled and inspected. No parts were damaged. The nut surface showed more pronounced grooves than before the test, and accumulated copper chips were visible on the first thread of the nut. This indicates that the thread surfaces gradually wore, increasing surface roughness and friction. The wear rate was relatively slow, and the resistance increase remained within the system’s driving capability. Therefore, the screw gears could continue to be used after 60 cycles, but the wear trend should be monitored in service. The relationship between transmission cycles and resistance torque can be approximated by a linear or power-law model:
$$T_{total}(N) = T_0 + k N^m$$
where \(T_0\) is the initial resistance torque, \(N\) is the number of cycles, and \(k\) and \(m\) are empirical constants. For the tested screw gears, \(m\) was close to 1, indicating a nearly linear wear progression.
Other factors such as foreign objects and over-constraint due to manufacturing errors were not tested separately because they are best addressed through design and manufacturing quality control. Foreign objects can be prevented by clean assembly, proper sealing, and filtration of lubricants. Over-constraint can be minimized by tolerancing, self-aligning bearings, and flexible couplings. These measures should be implemented in the design phase to avoid resistance increases during operation.
Based on the experimental results, I can draw several conclusions regarding the resistance properties of heavy-duty screw gears in mobile launch pads. First, the lubrication grease should have low viscosity, high load-carrying capacity, and a wide operating temperature range. The calcium-based grease performed better at low and medium loads, but the 7403 grease is more suitable for very high loads because of its higher pressure capacity. A possible solution is to use a grease with a viscosity index improver or a solid lubricant additive to maintain low friction under high pressure. Second, the guide surfaces should be optimized to avoid over-constraint. Increasing clearance or removing unnecessary guide surfaces can reduce resistance. However, removing all guide surfaces may compromise the stability of the inner sleeve, so a balance must be found. Third, bearing corrosion has a major impact on resistance. In coastal and humid environments, corrosion protection is essential. Fourth, the motor pressure difference can reflect the internal resistance of the screw gears. By measuring the motor pressure and speed, the resistance torque can be estimated using the motor displacement and efficiency. This provides a practical condition monitoring method. Fifth, after 60 cycles, the resistance increase was about 16%, which is still within the system’s driving capability. This suggests that the service life of the screw gears can be estimated from wear data, and maintenance intervals can be scheduled accordingly.
In addition to the experimental findings, I developed a mathematical model to predict the total resistance torque of the screw gears as a function of load, speed, lubrication, and wear. The total resistance torque can be decomposed into components:
$$T_{total} = T_{thread} + T_{bearing} + T_{guide} + T_{reducer} + T_{nut}$$
where \(T_{thread}\) is the thread friction torque, \(T_{bearing}\) is the bearing friction torque, \(T_{guide}\) is the guide surface friction torque, \(T_{reducer}\) is the reducer internal loss torque, and \(T_{nut}\) is the circular nut friction torque. Each component can be modeled using the equations presented earlier. For a given load \(F\), screw speed \(n\), and lubrication condition, the model can predict the expected resistance torque. Deviations from the predicted value can indicate abnormal conditions such as corrosion, foreign objects, or excessive wear. This model can be used as a basis for a health monitoring system for the screw gears.
To further illustrate the relative contribution of each factor, I compiled the experimental results into a summary table. Table 5 shows the approximate percentage increase in resistance torque for each factor at a load of 180 t.
| Factor | Approximate Resistance Increase at 180 t | Primary Mechanism |
|---|---|---|
| Bearing corrosion | 50% | Increased rolling friction, rolling-sliding transition |
| Thread wear after 60 cycles | 16% | Surface roughness increase, contact area change |
| Poor lubrication (7403 vs. calcium-based) | 8% | Higher friction coefficient, grease squeeze-out |
| Over-constraint (removing upper bushing) | 20–30% | Radial contact forces, guide friction |
| Speed increase from 40 to 80 rpm | 8–16% | Viscoelastic effects, hydrodynamic drag |
| Circular nut corrosion | Not tested, but potentially 10–40% | Increased end-face friction, self-locking |
| Foreign objects | Variable, can cause seizure | Indentation, scratching, thread fracture |
Table 5. Summary of factors influencing the resistance of heavy-duty screw gears.
The data in Table 5 show that bearing corrosion is the most severe single factor, followed by over-constraint and thread wear. Lubrication and speed have moderate effects. These results are consistent with the theoretical models. For example, the bearing friction torque is proportional to the load and the friction coefficient, so a 50% increase in resistance at 180 t implies that the effective friction coefficient of the corroded bearings is about 1.5 times that of new bearings. The thread wear after 60 cycles increased the resistance by 16%, which corresponds to an increase in the friction coefficient of about 16% if the load and geometry are unchanged. The lubrication effect of 8% at 180 t indicates that the 7403 grease has a higher friction coefficient than the calcium-based grease at that load, but the difference is smaller than at lower loads because the calcium-based grease is partially squeezed out.
Our experiments also revealed that the stability of the screw gears is affected by speed. At low speeds, the load distribution among the threads is uneven, and the screw gears may exhibit stick-slip behavior. This can cause vibration and noise, and it may accelerate wear. At high speeds, the resistance increases, but the motion is smoother. Therefore, an optimal speed range exists where the resistance is acceptable and the motion is stable. For the tested screw gears, a motor speed of 60 rpm (screw speed 0.099 rpm) provided a good compromise. However, the optimal speed may depend on the load and lubrication condition.
In terms of design improvements, several recommendations can be made. First, use bearings with better corrosion resistance, such as ceramic or stainless steel bearings, or provide effective sealing and grease renewal. Second, optimize the guide surfaces to allow slight radial compliance, for example by using spherical plain bearings or elastic bushings. Third, select a grease that maintains low friction under high pressure, possibly a grease with a higher base oil viscosity and solid lubricant additives. Fourth, improve the thread surface finish and use a harder nut material or a surface treatment such as nitriding or hard chrome plating on the screw. Fifth, implement a condition monitoring system based on motor pressure and speed to detect early signs of resistance increase. Sixth, establish a maintenance schedule based on the wear trends observed in the transmission cycle test.
The findings of this study have practical implications for the operation and maintenance of mobile launch pads. The screw gears are critical for the safe and reliable operation of the launch pad. Any increase in resistance can lead to delays, increased motor pressure, and potential failure. By understanding the factors that contribute to resistance, we can take proactive measures to prevent them. For example, in coastal environments, the bearings should be inspected and replaced more frequently. The grease should be replenished or replaced at regular intervals, even if the screw gears are not disassembled. The guide surfaces should be checked for wear and proper clearance. The motor pressure should be monitored during each operation, and any abnormal increase should trigger an investigation.
In conclusion, I have analyzed the resistance properties of heavy-duty screw gears in mobile space launch pads. The main factors that increase resistance are bearing corrosion, over-constraint, thread wear, poor lubrication, and speed. Experimental studies quantified the effects of these factors. Bearing corrosion can increase resistance by 50% at 180 t, while thread wear after 60 cycles increases resistance by 16%. Over-constraint can contribute 20–30% of the resistance, and lubrication and speed each contribute 8–16%. The screw gears are designed with a large safety margin, and the observed resistance increases remained within the system’s driving capability. However, to ensure long-term reliability, I recommend using corrosion-resistant bearings, optimizing guide surfaces, selecting appropriate grease, and implementing condition monitoring. The mathematical model and experimental data provided in this study can serve as a foundation for the design, testing, and maintenance of heavy-duty screw gears in launch pad applications.
Future work should focus on long-term field monitoring of the screw gears under real launch conditions. The effects of temperature, humidity, and salt spray on corrosion and lubrication should be studied in more detail. The wear mechanisms of the nut material under high contact pressure should be investigated using tribological testing. The dynamic behavior of the screw gears under varying loads and speeds should be modeled to predict vibration and stability. Finally, the condition monitoring system should be validated with field data to ensure its reliability. By continuing this work, we can enhance the performance and longevity of the screw gears and contribute to the success of future launch missions.